Reinforced concrete (khmer).pdf

sikSaKNnamuxkat;ebtugBRgwgedayEdk Reinforced Concrete DESIGN

GñkniBn§³ M. Nadim Hassoun Akthem Al-Manaseer

bkERbeday³ etg qay

viTüasßanCatiBhubec©keTskm<úCa mhaviTüal½ysMNg;sIuvil

qñaM 2010

viTüasßanCatiBhubec©keTskm<úCa Department of Civil Engineering

matika i T.Chhay

matika Contents

I. esckþIepþIm (Introduction)

1>1> rcnasm<½n§BIebtugGarem: ................................................................................................1

1>2> KuNsm,tþi nigKuNvibtþirbs;ebtugGarem: ........................................................................1

1>3> bnÞúk ............................................................................................................................2 1>4> karRbmUlbnÞúk ..............................................................................................................4

1>5> karbMElgbnÞúk ..............................................................................................................8 1>6> eRKOgbgÁúMénrcnasm<½n§§ebtugGarem: ...............................................................................10

1>7> CMhanénkarKNnaeRKOgbgÁúMBIebtugGarem: ....................................................................11

II.lkçN³énebtugGarem: 2>1> ktþaCH\T§iBldl;ersIusþg;ebtug ....................................................................................12 2>2> ersIusþg;rgkarsgát; .....................................................................................................14

2>3> ersIusþg;rgkarTaj ......................................................................................................15

2>4> ersIusþg;rgkarkat; ........................................................................................................15

2>5> m:UDuleGLasÞicrbs;ebtug ............................................................................................16

2>5> m:UDuleGLasÞicrbs;ebtug ............................................................................................16

2>7> m:UDulénPaBrwg b¤m:UDulkmøaMgkat; ..................................................................................16

2>9> bERmbRmYlmaDrbs;ebtug ...........................................................................................17

2>9>1> karrYmmaD ...............................................................................................................17 2>9>2> karrIkmaDedaykarekIneLIgénkemþA ..........................................................................18 2>10> Creep.......................................................................................................................18

2>11> m:UEDlsRmab;TsSn_TaykarrYmmaD nig creep rbs;ebtug ............................................19

2>11>1> m:UEDl ACI 209....................................................................................................19

mhaviTüal½ysMNg;sIuvil NPIC

T.Chhay ii Contents

2>11>2> m:UEDl B3 .............................................................................................................21

2>11>3> m:UEDl GL 2000 ...................................................................................................25

2>11>4> m:UEDl CEB 90......................................................................................................27

2>11>5> m:UEDl CEB 90-99 ................................................................................................30

2>12> m:as;maDebtug ..........................................................................................................41

2>12> RbePTEdkeRbIkñúgebtug .............................................................................................42

III. viPaKFñwmebtugGarem:rgkarBt;begáag Flexural Analysis of Reinforced Concrete Beam

3>1> karsn μt; (Assumption)...............................................................................................44

3>2> RbePTénkar)ak;edaykarBt; nigEdnkMNt;sac;lUteFob ...............................................44 3>2>1> kar)ak;edaykarBt; .................................................................................................44 3>2>2> EdnkMNt;bERmbRmYlrageFobsRmab; tension-controlled section nig compression-

controlled section.................................................................................................45

3>3> emKuNbnÞúk ................................................................................................................47 3>4> emKuNkat;bnßyersIusþg; ..............................................................................................48

3>5> karEbgEckkugRtaMgsgát;smmUl .................................................................................48

3>6> srésEdkrgkmøaMgTajénmuxkat;ctuekaNEkgrgkarBt; ...............................................50

3>6>1> balanced section ....................................................................................................51

3>6>2> PaKryEdkGtibrma ................................................................................................52

3>6>3> PaKryEdkGb,brma ..............................................................................................57

3>7> muxkat;l μm .................................................................................................................57

3>8> bNþúMénEdk .................................................................................................................61

3>9> muxkat;ctuekaNEkgCamYyEdkrgkmøaMgsgát; ...............................................................62

3>9>1> enAeBlEdksgát;eFVIkardl;cMNuc yield .....................................................................63

3>9>2> enAeBlEdksgát;eFVIkarmindl;cMNuc yield ................................................................68

3>10> viPaKmuxkat;GkSret T nigmuxkat;GIu I ........................................................................71

3>10>1> TTwgRbsiT§PaB .....................................................................................................72


matika iii T.Chhay

3>10>2> muxkat;GkSret T RtUv)anKitCaragctuekaNEkg ....................................................73

3>10>3> viPaKmuxkat;ragGkSret T ....................................................................................74

3>11> TMhMénmuxkat;FñwmGkSr T Éeka .................................................................................80 3>11> muxkat;GkSr L páab; ..................................................................................................81

IV. karKNnaFñwmebtugGarem:rgkarkac;begáag 4>1> km<s;RbsiT§PaBsRmab;Fñwm nigkRmalxNÐ ...................................................................82

4>2> muxkat;ctuekaNEkgCamYyEdkrgkarTaj ....................................................................82 4>3> KMlatEdk nigRsTab;karBarEdk ..................................................................................84 4>3>1> KMlatEdk ................................................................................................................84

4>3>2> RsTab;karBarEdk ...................................................................................................85

4>3>2> RsTab;karBarEdk ...................................................................................................86

4>3>4> km<s;Gb,brmarbs;muxkat;ebtug .............................................................................86

4>4>muxkat;ctuekaNEkgCamYyEdkrgkarsgát;......................................................................91

4>5> KNnamuxkat;GkSret T ..............................................................................................98

V. viFIKNnaepSgeTot Alternative Design Methods

5>1> esckþIepþIm (Introduction) .........................................................................................105

5>2> emKuNbnÞúk (Load Factors) ......................................................................................105

5>3> emKuNkat;bnßyersIusþg; (Strength-Reduction Factor φ ) .......................................105

5>4>muxkat;ctuekaNEkgCamYyEdkrgkarTaj (Rectangular Sections with Tension Reinforcement) .........................................................................................................108

5>5> muxkat;ctuekaNCamYynwgEdkrgkarsgát; (Rectangular Sections with Compression Reinforcement) ........................................................................................................111

5>6> karKNnamuxkat;GkSret (Design of T-Section) .....................................................113

5>7> viFI strut and tie (Strut and Tie Method) ................................................................115

5>7>1> esckþIepþIm (Introduction)....................................................................................115

5>7>2> viFIsaRsþKNnatam ACI (ACI Design Procedure) ...............................................118


T.Chhay iv Contents

5>7>3> tRmUvkarsRmab;karKNna (Design Requirement) .................................................120

VI. PaBdab nigsñameRbH 6>1> sñameRbHenAkñúgeRKOgbgÁúMebtug (Deflection of Structural Concrete Members) .........123

6>2> PaBdabxN³ (Instantaneous Deflection) ...............................................................124 6>2>1> m:UDuleGLasÞic (Modulus of Elasticity) .............................................................125

6>2>2> pleFobm:UDuleGLasÞic (Modular Ratio) .............................................................125

6>2>3> m:Um:g;eRbH (Cracking moment) ...........................................................................125

6>2>4> m:Um:g;niclPaB (Moment of inertia) ....................................................................126

6>2>5> lkçN³rbs;muxkat; (Properties of sections) .......................................................130

6>3> PaBdabry³eBlyUr (Long-term Deflection) ............................................................131

6>4> PaBdabGnuBaØat (Allowable Deflection)..................................................................132

6>5> PaBdabEdlbNþalmkBIbnSMbnÞúk (Deflection Due to Combinations of Load) .........132

6>6> PaBdabenAkñúgGgát;rgkarBt; (Cracks in Flexural Members)....................................142

6>7> tRmUvkarrbs;bTdæan ACI Code (ACI Code Requirement) ......................................146

VII. RbEvgEdkbgáb; b¤RbEvgEdkRCYs 7>1> esckþIepþIm .................................................................................................................153

7>2> karbegáItkugRtaMgs¥it..................................................................................................153 7>2>1> PaBs¥itedaykarBt; ..............................................................................................153

7>2>2> karBiesaFsRmab;RbsiT§PaBPaBs¥it........................................................................154 7>3> RbEvgbgáb;sRmab;tMbn;Taj .......................................................................................156

7>3>1> RbEvgbgáb;mUldæan dl ............................................................................................156

7>3>2> emKuN ACI Code sRmab;KNna dl sRmab;srésEdkrgkarTaj..........................158

7>3>3> rUbmnþsRmYlsRmab; dl ..........................................................................................159

7>4> RbEvgbgáb;sRmab;tMbn;sgát; dcl ...............................................................................161

7>5> segçbkarKNna dl kñúgtMbn;Taj.................................................................................162

7>6> muxkat;eRKaHfñak;enAkñúgGgát;rgkarBt;..........................................................................165


matika v T.Chhay

7>7> TMBk;; .........................................................................................................................169

7>6> kartEdk....................................................................................................................172

7>7> karbBaÄb;Edk ............................................................................................................174

VIII. kmøaMgkat;TTwg nigkmøaMgTajGgát;RTUg Shear and Diagonal Tension

8>1> esckþIepþIm .................................................................................................................180

8>2> kugRtaMgkmøaMgkat;enAkñúgFñwmebtugGarem: ....................................................................180

8>3> kareFVIkarrbs;FñwmedayKμanEdkkmøaMgkat;TTwg.............................................................183

8>4> \T§iBlm:Um:g;eTAelIersIusþg;kmøaMgkat; ...........................................................................185

8>5> FñwmmanEdkkmøaMgkat;..................................................................................................188

8>6> tRmUvkarrbs; ACI Code sRmab;karKNnakmøaMgkat;TTwg..........................................191 8>6>1> muxkat;eRKaHfñak;sRmab;karKNnaersIusþg;kmøaMgkat;TTwgmFüm

Critical section for nominal shear strength calculation........................................191

8>6>2> muxkat;EdkGb,brmasRmab;EdkkmøaMgkat;TTwg........................................................191

8>6>3> kmøaMgkat;TTwgGtibrmaEdlTb;edayEdkkmøaMgkat;TTwg sV ....................................193

8>6>4> KMlatEdkkgGtibrma .............................................................................................193

8>6>5> ersIusþg; yield rbs;EdkkmøaMgkat;TTwg.....................................................................194

8>6>6> TMBk;rbs;Edkkg ....................................................................................................194

8>6>7> EdkkgenAEdlenAEk,rTRm .....................................................................................196

8>6>8> RbEvgRbsiT§PaBrbs;EdkdgErk ..............................................................................196

8>7> karKNnaEdkkgbBaÄr...............................................................................................196

8>8> segçbviFIsaRsþKNnaEdkkgbBaÄr..............................................................................198

8>9> kmøaMgkat;TTwgEdlbNþalBIbnÞúkGefr.........................................................................204

8>10> kugRtaMgkmøaMgkat;TTwgenAkñúgGgát;Edlmankm<s;ERbRbYl ..........................................208

8>11> Ggát;rgkarBt;CeRmAeRCA..........................................................................................214


T.Chhay vi Contents

IX. kRmalxNÐmYyTis 9>1> RbePTkRmalxNÐ ......................................................................................................231 9>2> karKNnaénkRmalxNÐtan;mYyTis ............................................................................232

9>3> EdnkMNt;kñúgkarKNnaEdlGnuelameTAtam ACI CODE .........................................235

9>4> EdksItuNðPaB nigEdkrYmmaD.......................................................................................236 9>5> lMGitsrésEdk ..........................................................................................................237

9>8> karEbgEckbnÞúkBIkRmalxNÐmYyTiseTAFñwmTRm..........................................................238

9>9> RbB½n§kRmalxNÐrnUtmYyTis (One-Way joist Floor System) ...................................243

X. ssrrgkmøaMgcMG½kS 10>1> esckþIepþIm ..............................................................................................................248

10>2> RbePTssr.............................................................................................................248

10>3> kareFVIkarrbs;ssrrgbnÞúkcMG½kS .............................................................................250 10>4> lkçxNÐrbs; ACI Code.........................................................................................250

10>5> smIkarsRmab;KNna ...............................................................................................252

10>6> kmøaMgTajcMG½kS.......................................................................................................253

XI. eRKOgbgÁúMrgkarsgát; nigrgkarBt; 11>1> esckþIepþIm .............................................................................................................255

11>2> karsnμt;sRmab;KNnassr .....................................................................................256

11>3> düaRkamGnþrkmμbnÞúk-m:Um:g; (Load-moment interaction diagram) ..........................257

11>4> karpþl;nUvsuvtßiPaB (Safety provisions)..................................................................259

11>5> Balanced condition – muxkat;ctuekaN ..................................................................261

11>6> muxkat;ssreRkamGMeBIbnÞúkcakp©it (Column sections under eccentric loading)......264

11>7> ersIusþg;rbs;ssrsRmab;kar)ak;edaykarTaj (Strength of columns for tension failure) .............................................................265

11>8> ersIusþg;rbs;ssrsRmab;kar)ak;edaykarsgát; (Strength of columns for compression failure) ....................................................268

11>8>1> dMeNaHRsaysakl,g (Trial solution)................................................................269


matika vii T.Chhay

11>8>2> dMeNaHRsayviPaKcMnYn (Numerical Analysis Solution) ......................................271

11>8>3> dMeNaHRsayRbEhl (Approximate Solution) ...................................................273

11>9> ]TahrN_sRmab;düaRkamGnþrkm μ (Interaction Diagram Example) ........................275

11>10> ssrmuxkat;ctuekaNCamYyEdkxag (Rectangular columns with side bars) .......276

11>11> lT§PaBRTbnÞúkrbs;ssrmuxkat;mUl (Load Capacity of Circular Columns) .......278

11>11>1 lkçxNÐ Balanced ...........................................................................................280

11>11>2 ersIusþg;rbs;muxkat;mUlsRmab;kar)ak;edaykarsgát; Strength of circular column for compression failure ...........................................284

11>11>3 ersIusþg;rbs;muxkat;mUlsRmab;kar)ak;edaykarTaj Strength of circular column for tension failure....................................................285

11>12> karviPaK nigkarKNnassredayeRbIdüaRkam Analysis and Design of Column Using Charts ....................................................286

11>13> karKNnassreRkambnÞúkcakp©it (Design of Columns under Eccentric Loading) ...................................................292

11>13>1 KNnassrsRmab;kar)ak;edaykarsgát; (Design of Column for Compression Failure) .....................................................292

11>13>2 KNnassrsRmab;kar)ak;edaykarTaj (Design of Column for tension Failure)...............................................................298

11>14> karBt;tamBIrTis (Biaxial Bending) ..................................................................300

11>15> ssrmUlCamYynwgkarrayEdkes μ IeRkamm:Um:g;Bt;BIrTis Circular Columns with Uniform reinforcement Under Biaxial Bending.............303

11>16> ssrmuxkat;kaer nigctuekaNeRkamm:Um:g;Bt;BIrTis (Square and Rectangular Columns under Biaxial Bending) ................................304

11>16>1> viFI; Bresler Reciprocal Method ......................................................................304

11>16>2> viFIExSvNÐbnÞúk Bresler (Bresler Load Contour Method) .................................305

11>17> viFIExSvNÐbnÞúk Parme (Parme Load Contour Method) ......................................305

11>18> smIkarépÞ)ak; (Equation of failure surface) ........................................................312

XII. ssrEvg 12>1> esckþIepþIm .............................................................................................................315 12>2> RbEvgssrRbsiT§PaB (Effective Column Length) uKl ........................................315


T.Chhay viii Contents

12>3> emKuNRbEvgRbsiT§PaB (Effective Length Factor) K ............................................316

12>4> PaBrwgRkajrbs;Ggát; (Member Stiffness) EI .......................................................321

12>5> EdnkMNt;sRmab;pleFobrlas; (Limitation of The Slenderness Ratio) rKlu / ...321

12>5>1> eRKagGt;eyal (Nonsway Frames) ....................................................................321

12>6> viFIKNnabEnßmm:Umg; (Moment-Magnifier Design Method)....................................323

12>6>1> esckþIepþIm (Introduction)....................................................................................323

12>6>2> m:Um:g;bEnßmenAkñúgeRKagGt;eyal (Magnified Moments in Nonsway Frames) ..324

12>6>3> m:Um:g;bEnßmenAkñúgeRKageyal (Magnified Moments in sway Frames)................325

XIII. eCIgtag FOOTINGS

13>1> esckþIepþIm (Introduction).......................................................................................335

13>2> RbePTeCIgtag (Types of Footings) .......................................................................336

13>3> karBRgaysm<aFdI (Distribution of soil pressure) .................................................339

13>4> karBicarNakñúgkarKNna (Design Consideration) ................................................341

13>4>1> TMhMeCIgtag (size of Footing).............................................................................341 13>4>2> kmøaMgkat;mYyTis ¬kmøaMgkat;Fñwm¦ 1uV One-Way Shear (Beam Shear)............342

13>4>3> kmøaMgkat;BIrTis ¬kmøaMgpug¦ 1uV Two-Way Shear (Punching Shear)..............343

13>4>4> ersIusþg;Bt; nigEdkeCIgtag (Flexural Strength and Footing Reinforcement)....345

13>4>5> lT§PaBRTRTg;rbs;ssrenARtg;)at (Bearing Capacity of Column at Base) .......347

13>4>6> RbEvgEdkRCYs (Development Length of the Reinforcing bars) ......................349

13>4>7> sRmutDIepr:g;Esül ¬karKNnaeCIgtagkñúglkçxNÐlMnwg¦ Differential Settlement (Balanced Footing Design) ........................................349

13>5> eCIgtagebtugsuT§ (Plain Concrete Footings) ........................................................350

13>6> Combined Footings.............................................................................................362

13>7> eCIgtageRkambnÞúkssrcakp©it (Footings under Eccentric Column Loads) .........370

13>8> eCIgtageRkamm:Um:g;BIrTis (Footings under Biaxial Moment) ...............................372

13>9> kRmalxNÐelIdI (Slabs on Ground)........................................................................375


matika ix T.Chhay

13>10> eCIgtagenAelIssrRKwH (Footings on Piles) .........................................................379

XIV. CBa¢aMgTb; Retaining Wall

14>1> esckþIepþIm (Introduction)......................................................................................378

14>2> RbePTCBa¢aMgTb; (Types of Retaining Walls) .........................................................378

14>3> kmøaMgenAelICBa¢aMgTb; (Forces on Retaining Walls) ...............................................380

14>4> sm<aFdIGkmμ nigsm<aFdIskmμ (Active and Passive Soil Pressures) ......................381

14>5> \T§iBlénbnÞúkbEnßm (Effect of Surcharge) ..............................................................386

14>6> kmøaMgkkitenAelI)atCBa¢aMgTb; (Friction on the Retaining Wall Base) ....................387

14>7> sßanPaBlMnwgRbqaMgnwgkarRkLab; (Stability against Overturning) ......................388

14>8> smamaRténCBa¢aMgTb; (Proportions of Retaining Walls).......................................389

14>9> tRmUvkarsRmab;KNna (Design Requirement).......................................................390

14>10> karbgðÚrTwk (Drainage) ........................................................................................391

14>11> CBa¢aMgCan;eRkamdI (Basement Walls) .................................................................406

XV. karKNnasMrab;kmøaMgrmYl Design for Torsion

15>1> esckþIepþIm (Introduction) .....................................................................................411

15>2> m:Um:g;rmYlenAkñúgFñwm (Torsional Moments in Beams)..............................................413

15>3> kugRtaMgrmYl (Torsional Moments in Beams) .......................................................413 15>4> m:Um:g;rmYlenAkñúgmuxkat;ctuekaN (Torsional Moments in Rectangular Sections)....416

15>5> kmøaMgpÁÜbrvagkmøaMgkat; nigkmøaMgrmYl (Combined Shear and Torsion)....................417

15>6> RTwsþIkarrmYlsRmab;Ggát;ebtug (Torsion Theories for Concrete Members) ............418

15>6>1> Skew Bending Theory ......................................................................................418

15>6>2> Space Truss Analogy ........................................................................................419 15>7> ersIusþg;rmYlénGgát;ebtugsuT§ (Torsional Strength of Plain Concrete Members)..422

15>8> karrmYlenAkñúgGgát;ebtugBRgwgedayEdk (Torsion in Reinforced Concrete Memebers (ACI Code Procedure)) .................................................................423


T.Chhay x Contents

15>8>1> sBaØaNTUeTA (General) .....................................................................................423 15>8>2> )a:ra:Em:RtFrNImaRténkarrmYl (Torsional Geometric Parameters) ......................424

15>8>3> m:Um:g;rmYleFVI[eRbH crT (Cracking Torsional Moment crT ) ................................425

15>8>4> m:Um:g;rmYllMnwg nwgm:Um:g;rmYlRtUvKña (Equilibrium Torsion and Compatibility Torsion) ....................................................................................428

15>8>5> karkMNt;énersIusþg;m:Um:g;rmYl (Limitation of Tortional Moment Strength) .........429

15>8>6> muxkat;Rbehag (Hollow Section) .......................................................................431

15>8>7> EdkRTnug (Web Reinforcement).........................................................................431

15>8>8> EdkTb;karrmYlGb,brma (Minimum Torsional Reinforcement) .........................433

15>9> segçbviFIsaRsþKNnaeday ACI Code (Summary of ACI Code Procedures) ........433

XVI. FñwmCab; nigeRKag Continuous Beams and Frames

16>1> esckþIepþIm (Introduction) ......................................................................................445

16>2> m:Um:g;GtibrmaenAkñúgFñwmCab; (Maximum Moment in Continuous Beams)...............446

16>2>1> eKalkarN_viPaK (Basic Analysis) ......................................................................446

16>2>2> karGnuvtþkardak;bnÞúk (Loading Application)......................................................446

16>2>3> m:Um:g;viC¢manGtibrma nigGb,brmaenAkñúgElVg Maximum and Minimum Positive Moments within a Span ...........................447

16>2>4> m:Um:g;GviC¢manGtibrmaenAelITRm (Maximum Negative Moments at Supports) ...448

16>2>5> m:Um:g;enAkñúgFñwmCab; (Moments in Continuous Beams) .......................................449

16>3> eRKagsMNg;GKar (Building Frames) ....................................................................453

16>4> Portal Frames ........................................................................................................455

16>4>1> cugsnøak;BIr (Two Hinged Ends) ........................................................................455

16>4>2> cugbgáb;BIr (Two Fixed Ends) ............................................................................456

16>5> eRKagTUeTA (General Frames) ................................................................................458

16>6> karKNnasnøak;rbs;eRKag (Design of Frame Hinges)...........................................460

16>6>1> Mesnager hinges ...............................................................................................460 16>6>2> Considère hinges ..............................................................................................462


matika xi T.Chhay

16>7> esckþIepþImBIkarKNnasßanPaBkMNt; (Introduction to Limit Design) ....................473

16>7>1> lk μN³TUeTA (General) .....................................................................................473

16>7> 2> KMniténkarKNnasßanPaBkMNt; (Limit Design Concept) ...................................474

16>7> 3> eKalkarN_énsnøak;)aøsÞic (Plastic Hinge Concept)...........................................475 16>8> emkanicénkar)ak; (The Collapse Mechanism) .......................................................477

16>9> eKalkarN_énkarKNnasßanPaBkMNt; (Principles of Limit Design) .......................477

16>10> Ednx<s; nigEdnTabénemKuNbnÞúk (Upper and Lower Bounds of Load Factors) ..479

16>11> karviPaKsßanPaBkMNt; (Limit Analysis)..............................................................479

16>12> mMurgVilrbs;snøak;)aøsÞic (Rotation of Plastic Hinges) ..........................................484

16>12>1> RbEvgsnøak;)aøsÞic (Plastic Hinge Length) ......................................................484

16>12>2> emKuNEbgEckkMeNag (Curvature Distribution Factor ) .................................486

16>12>3> snÞsSn_énPaBsVit (Ductilty Index ) ...............................................................487

16>12>4> mMurgVilEdlRtUvkar (Required Rotation) ..........................................................488

16>12>5> lT§PaBTb;mMurgVil (Rotation Capacity Provided) .............................................488

16>13> segçbviFIsaRsþkñúgkarKNnasßanPaBkMNt; (Summary of Limit Design Procedure) ...........................................................491

16>14> karEbgEckm:Um:g;eLIgvijénm:Um:g;GviC¢manenAkñúgFñwmCab; Moment Distribution of Negative Moments in Continuous Beams................495

XVII. karKNnakRmalxNÐBIrTis Design of Two-Way Slabs

17>1> esckþIepþIm (Introduction) ....................................................................................507

17>2> RbePTkRmalxNÐBIrTis (Types of Two-Way Slabs).............................................507

17>3> kareRCIserIsRbB½n§kRmalxNÐebtugEdlmanlkçN³esdækic© Economical Choice of Concrete Floor Systems..............................................511

17>4> eKalKMnitkñúgkarKNna (Design Concept) ..............................................................512

17>5> ceRmokelIssr nigceRmokkNþal (Column and Middle Strips) ............................514

17>6> kRmas;kRmalGb,brmaedIm,IkMritPaBdab (Minimum Slab Thickness to Control Deflection) ..............................................517


T.Chhay xii Contents

17>7> ersIusþg;kMlaMgkat;TTwgrbs;kRmalxNÐ (Shear Strength of Slabs)...........................524

17>7>1> kRmalxNÐBIrTisEdlRTedayFñwm (Two-Way Slabs Supported on Beams) ........524

17>7>2> kRmalxNÐBIrTisEdlKμanFñwm (Two-Way Slabs without Beams)........................525

17>7>3> EdkkmøaMgkat;TTWgenAkñúgkRmalxNÐBIrTisEdlK μanFñwm Shear Reinforcement in Two-Way Slabs without Beams ...............................525

17>8> karviPaKkRmalxNÐBIrTisedayviFIKNnaedaypÞal; Analysis of Two-Way Slabs by the Direct Design Method ............................530

17>8>1> karkMNt; (Limitations).......................................................................................530

17>8>2> m:Um:g;sþaTicemKuNsrub (Total Factored Static Moment).....................................530

17>8>3> karEbgEckm:Um:g;tambeNþaykñúgkRmalxNÐ (Longitudinal Distribution of Moment in Slabs).............................................532

17>8>4> karEbgEckm:Um:g;tamTTwgkñúgkRmalxNÐ (Transverse Distribution of Moment in Slabs)................................................535

17>8>5> karpþl;rbs; ACI sRmab;\T§iBlrbs;KMrUénkardak;bnÞúk (ACI Provisions for Effects of Pattern Loading).............................................539

17>8>6> karlMGitsrésEdk (Reinforcement Details) ......................................................540

17>8>7> viFIPaBrwgRkajEdlRtUv)anEktRmUvsRmab;ElVgcug (Modified Stiffness Method for End Spans) ...................................................540

17>8>8> segçbviFIKNnaedaypÞal; (Summary of the Direct Design Method (DDM)) ....543

17>9> m:Um:g;KNnaenAkñúgssr (Design Moments in Column)...........................................567

17>10> karbMElgm:Um:g;mines μ IeTAkñúgssr (Transfer of Unbalanced Moments to Columns).............................................569

17>10>1> karbMElgm:Um:g; (Transfer of Moment) ............................................................569

17>10>3> kugRtaMgkmøaMgkat;EdlbNþalBI fM (Shear Stress Due to) fM ...................570

17>11> kRmalxNÐ Waffle (Waffle Slabs) ...................................................................573

17>12> viFIeRKagsmmUl (Equivalent Frame Method)....................................................592

XVIII. CeNþIr Stairs

18>1> esckþIepþIm (Introduction) ......................................................................................606

18>2> RbePTCeNþIr (Types of Stairs)..............................................................................607


matika xiii T.Chhay

XIX. esckþIENnaMBIebtugkugRtaMg Introduction to Prestressed Concrete

19>1> ebtugeRbkugRtaMg (Prestressed Concrete) ...............................................................634

19>1>1> eKalkarN_énkareFVIeRbkugRtaMg (Principles of Prestressing) ...............................634

19>1>2> karGnuvtþeRbkugRtaMgedayEpñk (Partial Prestressing) ..........................................642

19>1>3> karcat;cMNat;fñak;Ggát;rgkarBt;ebtugeRbkugRtaMg (Classification of Prestressed Concrete Flexural Members) ...........................646

19>2> smÖar³ nigtRmUvkarsRmab;beRmIbRmas; (Material and Serviceability Requirement) .....................................................647

19>2>1> ebtug (Concrete) ...............................................................................................647

19>2>2> EdkeRbkugRtaMg (Prestressing Steel) ...................................................................648

19>2>3> EdkBRgwg (Reinforcing Steel) ...........................................................................649

19>3> kMhatbg;eRbkugRtaMg (Loss of Prestress)................................................................649

19>3>1> Lump-sum losses .............................................................................................649

19>3>2> kMhatbg;edaysar (Elastic Shortening of Concrete) ........................................650

19>3>3> kMhatbg;edaysarkarrYmmaD (Loss Due to Shrinkage) .....................................651

19>3>4> kMhatbg;edaysar creep rbs;ebtug ....................................................................652

19>3>5> kMhatbg;edaysar Relaxation rbs;Edk .............................................................653

19>3>6> kMhatbg;edaysarkmøaMgkkit (Loss Due to Friction)..........................................653

19>3>7> kMhatbg;edaysar Anchor set ...........................................................................655

19>4> viPaKGgát;rgkarBt;begáag (Analysis of Flexural Members)....................................660

19>4>1> kugRtaMgEdlbNþalBIlkçxNÐmanbnÞúk niglkçxNÐKμanbnÞúk Stresses Due to Loaded and Unloaded condition...........................................660

19>4>2> EdnkMNt;sñÚl (Kern Limits) ...............................................................................661

19>4>3> karkMNt;témøéncMNakp©it (Limiting Values of Eccentricity) ...........................662

19>4>4> témøkMNt;émkmøaMgeRbkugRtaMgenAeBlepÞr (Limiting Values of the Prestessing Force at Transfer) ..................................664

19>5> KNnaGgát;rgkarBt;begáag (Design of Flexural Members).....................................673


T.Chhay xiv Contents

19>5>1> sBaØaNTUeTA (General)........................................................................................673

19>5>2> muxkat;ctuekaN (Rectangular Sections) ............................................................675

19>5>3> muxkat;Edlmansøab (Flanged Sections) ............................................................677

19>5>4> EdkBRgwgrgeRbkugRtaMg (Nonprestressed Reinforcement) ..................................677

19>6> m:Um:g;eRbH (Cracking Moment) ...............................................................................680

19>7> PaBdab (Deflection) ..............................................................................................683

19>8> KNnasRmab;kmøaMgkat;TTwg (Design for Shear) ....................................................685

19>8>1> viFIcMbg (Basic Approach)..................................................................................686

19>8>2> ersIusþg;kmøaMgkat;Edlpþl;edayebtug (Shear Strength Provided by Concrete) ....686

19>8>3> EdkkmøaMgkat; (Shear Reinforcement).................................................................689

19>8>4> EdnkMNt; (Limitation) ........................................................................................690

19>9> KNnaCMhandMbUgénGgát;ebtugeRbmugRtaMgrgkarBt; Preliminary Design of Prestressed Concrete Flexural Members.....................695

19>9>1> rUbrag nigTMhM (Shapes and Dimensions) .............................................................695

19>9>2> kmøaMgeRbkugRtaMg nigRkLaépÞEdk (Shapes and Dimensions) ...............................695

19>10> kugRtaMgbøúkxagcug (End-Block Stresses) ............................................................698

19>10>1> Ggát;rgkugRtaMgTajmun (Pretensioned Members) .............................................698

19>10>2> Ggát;rgkugRtaMgTajeRkay (Post-tensioned Members) .....................................699

]bsm<½n§ .........................................................................................................................702


esckþIepþIm 1 T.Chhay

I. esckþIepþIm

1>1> rcnasm<½n§BIebtugGarem: ebtug Cafμsib,nimitþEdlekIteLIgedaysarkarpSMKñaénsmÖar³CaeRcIndUcCa f μbMEbk xSac; sIum:gt¾ Twk

nigeBlxøHmanTwkfñaMKImI. smÖar³TaMgenHRtUv)anlaybBa©ÚlKñaedaysmamaRtRtwmRtUv Tuk[kkkøayeTACa ebtug. ebtugCasmÖar³EdleFVIkar)anl¥nwgkarsgát;.

edIm,I[smÖar³eFVIBIebtugGacTb;nwgkarBt;)an luHRtaEtvaRtUv)anBRgwgedaysrésEdk eBlenaH eK[eQ μaHvafa ebtugGarem:. EdkCasmÖar³EdleFVIkar)anl¥nwgkarTaj.

CaTUeTAkñúgkarKNnarcnasm<½n§BIebtugGarem:mYy KWeKRtUvGnuvtþeLIgCaBIrCMhanFM²³ - kMNt;nUvRbePTbnÞúkepSg²EdlGnuvtþmkelIrcnasm<½n§ edayeRbInUvviFIsaRsþRtwmRtUvkñúgkarviPaK

eRKOgbgÁúM. - kMNt;nUvTMhMmuxkat;EdkénRKb;rcnasm<½n§TaMgGs; [manlkçN³esdækic© edayBicarNaelIsuvtißPaB

sßirPaBkareRbIR)as; nigtYnaTIrbs;eRKOgbgÁúM. ebtugGarem: CasmÖar³mYyEdleKeRbIR)as;CaTUeTAenAkñúgkarKNnaGKarRKb;RbePT. vaCasmÖar³Edl

pÁúMeLIgedaysmÖar³BIrRbePTKW ebtug nigEdk. eRKOgbgÁúMEdleFVIBIebtugGarem: RtUv)aneRbIR)as;sRmab;RTnUv bnÞúkeRcInRbePT.

1>2> KuNsm,tþi nigKuNvibtþirbs;ebtugGarem: ebtugGarem: CasmÖar³EdlRtUv)aneKeRbIR)as;y:agTUlMTUlaysRmab;RbePTCaeRcInéneRKOgbgÁúM.

vaRtUv)aneKykmkeRbobeFobCamYynwgEdk sRmab;lkçN³esdækic© nigkarRbtibtþi. KuNsm,tþirbs;ebtugGarem:RtUv)ansegçbdUcxageRkam³ - vamanersIusþg;x<s;kñúgkarsgát; (high compressive strength) - vaTb;Tl;nwgePøIg)anl¥CagEdk - vamanGayukalEvgCamYynwgkarEfTaMTab - sRmab;eRKOgbgÁúMxøHdUcCa TMnb;Twk ssr nigeCIgtag vaCasmÖar³EdlmanlkçN³esdækic©x<s; - vaGacRtUv)aneKeRbIsRmab;kMNt;rUbragtamtRmUvkar nigeFVICaeRKOgbgÁúMcak;eRscCamYynwgPaB

dabGb,brma.


T.Chhay 2 Introduction

KuNvibtþirbs;ebtugGarem:RtUv)ansegçbdUcxageRkam³ - vamanersIusþg;TabkñúgkarTajRbEhlCamYyPaKdb;énersIusþg;rgkarsgát; - vaRtUvkarkarlay karcak; karEfTaM EdlTaMgenHsuT§EtCH\T§iBldl;ersIusþg;rbs;va - Bum<EdleRbIsRmab;cak;ebtugmantémøx<s;. témøBum<esÞIresμ Inwgtémøebtug. - vamanersIusþg;rgkarsgát;TabCagEdkRbEhlCadb;dg EdlCaehtueFVI[muxkat;ssrFMsRmab;

GKareRcInCan;. - vaekItmansñameRbH EdlbNþalmkBIkarrYmmaD nigkarGnuvtþrbs;bnÞúkGefr.

1>3> bnÞúk eRKOgbgÁúMrcnasm<½n§RtUv)anKNnaedIm,IRTnUvbnÞúkCak;lak;.

bnÞúkKWCakmøaMgTaMgLayNaEdlGnuvtþmkelIrcnasm<½n§ Edlpþl;nUvsmamaRtmuxkat;rbs;va. CaTU eTAbnÞúkRtUv)anEckecjCa bnÞúkefr ¬bnÞúkGcl½t¦ nigbnÞúkGefr ¬bnÞúkcl½t¦.

bnÞúkefr (Dead load) EdlrYmmanTm¶n;rbs;rcnasm<½n§ ¬Tm¶n;pÞal;rbs;va¦ nigTm¶n;smÖar³epSg²eTot EdlmanenAelIeRKOgbgÁúM dUcCa \dækar:U )ayGr ek,Óg CBa¢aMg >>>. bnÞúkefrRtUv)anKNnaCamYynwgkRmitRtwm RtUvénTMhMrbs;smÖar³ nigTm¶n;maDrbs;va.

bnÞúkGefr (Live load) CabnÞúkTaMgLayNaEdlminEmnCabnÞúkefr. vaCaRbePTbnÞúkEdlmanlkçN³ minnwg b¤rBa¢Üy b¤cl½t. vaGacGnuvtþmkelIeRKOgbgÁúMyWt² Pøam² bBaÄr b¤edk ehIyGaMgtg;sIuetrbs;vaGac ERbRbYleTAtameBlevla. CaTUeTAbnÞúkGefrrYmman³

- bnÞúkEdlekItBITm¶n;mnusS eRKOgsgðarwm nig]bkrN_smÖar³ - kmøaMgpÁÜbEdl)anBIxül; nig)anBIbERmbRmYlsItuNðPaB - Tm¶n;rbs;RBilRbsinebIman - sm<aFrbs;Twk b¤dImkelICBa¢aMgTb;dI - Tm¶n;rbs;cracrN_mkelIs<an - kmøaMgpÁÜbDINamicEdl)anBIbnÞúkcl½t b¤bnÞúkb:HTgÁic rBa¢ÜyEpndI b¤karpÞúH bnÞúkRBilGacERbRbYlcenøaHBI 22 /2/5.0 mkNmkN → GaRs½yelIGakasFatutamtMbn;. bnÞúkxül;GacERbRbYlcenøaHBI 22 /5.1/75.0 mkNmkN → GaRs½ynwgel,Ónxül;. sm<aFxül;én

eRKOgbgÁúM F RtUv)anKNnatamrUbmnþxageRkam³ 200064.0 VCF s=

Edl F - sm<aFxül; 2/ mkN



V - el,Ónxül; sm / sC - emKuNrUbragrbs;GKar enAcenøaHBI 3.12.1 →

taragTI1³ bnÞúkBRgayesμ I Design live load

Occupancy Content 2/ mkN Assembly hall Fixed seats 2.9 Movable seats 4.8 Hospital Operating rooms 2.9 Private rooms 1.9 Hotel Guest rooms 1.9 Public rooms 4.8 Balconies 4.8 Housing Private house and apartments 1.9 Public rooms 4.8 Institution Classrooms 1.9 Corridors 4.8 Library Reading rooms 2.9 Stack rooms 7.2 Office building Offices 2.4 Lobbies 4.8 Stairs 4.8 Storage warehouses Light 4.8 Heavy 12.0 Yard and terraces 4.8

taragTI2³ dg;sIuet nigdg;sIuetxnic Density

Material Specific gravity 3/ mkg Building material Brick 1.8-2.0 1924 Cement, Portland, loose - 1443 Cement, Portland, set 2.7-3.2 2933 Earth, dry, packed - 1523 Sand or gravel, dry, packed - 1600-1924 Sand or gravel, wet - 1892-1924 Liquids Oils 0.9-0.94 930 Water (at co4 ) 1 1000 Ice 0.88-0.92 898 Metal and mineral Aluminum 2.55-2.75 2645 Copper 9.0 8913 Iron 7.2 7214 Lead 11.38 11380 Steel, rolled 7.85 7855 Limestone or marble 2.5-2.8 2645



Sandstone 2.2-2.5 2356 Shale or slate 2.7-2.9 2805 Normal weight concrete Plain 2.2-2.4 2324 Reinforced or prestressed 2.3-2.5 2405

1>4> karRbmUlbnÞúk edIm,IQaneTAdl;karKNnamuxkat;EdkEdlRtUvkar enAkñúgmuxkat;eRKOgbgÁúM CadMbUgeyIgRtUvRbmUl

bnÞúkTaMgGs;EdlmanGMeBIeTAelIeRKOgbgÁúMenaH. karRbmUlbnÞúkKWeyIgRtUvRbmUlBIelIcuHmkeRkam )ann½yfa dMbUgeyIgRbmUlbnÞúkelIdMbUl b¤elIkRmalxNÐ bnÞab;mkRbmUlbnÞúkmkelIFñwm rYcehIyRbmUlbnÞúkmkelI ssr nigcugeRkayRbmUlbnÞúkmkelIRKwH.

bnÞúkTMnajEckCabIRbePTKW³ - bnÞúkBRgayelIépÞ Edlmanxñat )/( 2mkN bnÞúkenHmanGMeBIelIkRmalxNÐ b¤dMbUl. bnÞúkTaMgenHrYm

man bnÞúkGefr nigbnÞúkefr ¬rYmbBa©ÚlTaMgTm¶n;pÞal;xøÜn¦. - bnÞúkBRgayelIRbEvg Edlmanxñat )/( mkN bnÞúkenHmanGMeBIelIFñwm. bnÞúkTaMgenHrYmmanbnÞúkEdl

)anbBa¢ÚnBIkRmalxNÐmkelIFñwmtamsñameRbH o45 bnÞúkrbs;CBa¢aMg nigbnÞúkpÞal;xøÜn. bnÞúkBRgayelI RbEvgmanragCa ctuekaNEkg ctuekaNBñay nigRtIekaN.

- bnÞúkcMcMNuc Edlmanxñat )(kN bnÞúkenHmanGMeBIelIssr nigRKwH. bnÞúkTaMgenHrYmmanbnÞúkEdl)an bBa¢ÚnBIkRmalxNÐmkelIFñwmehIybnþbBa¢ÚnmkelIssr nigbnÞúkpÞal;xøÜn. eRkABIbnÞúkTMnajTaMgenH enAmanbnÞúkedkeTot. eRkamGMeBIénbnÞúkEdl)anGnuvtþeTAelIrcnasm<½n§

eyIgGackMNt;)an nUvkmøaMgkat;TTwg m:Um:g;Bt; >>>. ]TahrN_³ eKmanpÞHmYyEdlmankMBs;1Can; m4 ehIymanTMhMdUcbgðajkñúgrUb³ k> cUrkMNt;bnÞúkEdlmanGMeBIelIkRmalxNÐ S x> cUrkMNt;bnÞúkEdlmanGMeBIelIFñwm 1B K> cUrkMNt;bnÞúkEdlmanGMeBIelIFñwm 2B X> cUrkMNt;bnÞúkEdlmanGMeBIelIssr C dMeNaHRsay k> kMNt;bnÞúkEdlmanGMeBIelIkRmalxNÐ S bnÞúkEdlmanGMeBIelIkRmalxNÐrYmmanbnÞúkefr nigbnÞúkGefr bnÞúkefrman³



Tile 1cmMortar 4cmConcrete 12cmPlastering 2cm

Plastering 2cmConcrete 12cmMortar 4cm

Tile 1cm

Section A-A

B1

B2

Section B-B

Slab beam column planeB

B

AA

C (20×20)

B2 (20×30)

B1(20×45)

S



- kar:UkRmas; cm1 = 2/22.02201.0 mkN=× - )ayGrkRmas; cm4 = 2/88.02204.0 mkN=× - ebtug ¬Tm¶n;pÞal; self weight¦ kRmas; cm12 = 2/88.22412.0 mkN=× - kMe)arbUkkRmas; cm2 = 2/40.02002.0 mkN=×

bnÞúkGefr EdlmanGMeBIelIkRmalxNÐsRmab;pÞH tamtaragxagelI 2/9.1 mkNL = xageRkamCataragbgðajBIbnÞúkEdlmanGMeBIelIkRmalxNÐ S KitkñúgmYyÉktþaépÞ

RbePTbnÞúk eQ μaHbnÞúk bnÞúk ( )2/ mkN kar:U 0.22

)ayGr 0.88

ebtugkRmalxNÐ 2.88

bnÞúkefr Dead load (D)

kMe)arbUk 0.4

bnÞúkGefr Live Load (L)

bnÞúkGefr 1.9

bnÞúksrub D + L 6.28

x> kMNt;bnÞúkEdlmanGMeBIelIFñwm 1B

Fñwm 1B RTkRmalxNÐ S tamTisEvg + bnÞúkpÞal;xøÜn = mkN /16.2242.045.0 =×× CabnÞúkrayragctuekaN + bnÞúkCBa¢aMg\dæ 10cm= ( ) mkN /1.7201.045.04 =××− CabnÞúkrayragctuekaN + bnÞúkkRmalxNÐ = mkN /32.8)1.02(38.4 =−× CabnÞúkrayragctuekaNBñay + bnÞúkGefr = mkN /61.3)1.02(9.1 =−× CabnÞúkrayragctuekaNBñay xageRkamCataragbgðajBIbnÞúkEdlmanGMeBIelIFñwm 1B KitkñúgmYyÉktþaRbEvg

RbePTbnÞúk eQ μaHbnÞúk bnÞúk ( )mkN / ragBRgaybnÞúk bnÞúkpÞal;xøÜn 2.16 ctuekaN bnÞúkCBa¢aMg 7.1 ctuekaN bnÞúkefr D

bnÞúkkRmalxNÐ 16.64 ctuekaNBñay bnÞúkGefr L bnÞúkcl½t 7.22 ctuekaNBñay



K> kMNt;bnÞúkEdlmanGMeBIelIFñwm 2B

Fñwm 2B RTkRmalxNÐ S tamTisxøI + bnÞúkpÞal;xøÜn = mkN /44.1242.03.0 =×× CabnÞúkrayragctuekaN + bnÞúkCBa¢aMg\dæ 10cm= ( ) mkN /4.7201.03.04 =××− CabnÞúkrayragctuekaN + bnÞúkkRmalxNÐ = ( ) mkN /32.81.0238.4 =−× CabnÞúkrayragRtIekaN + bnÞúkGefr = ( ) mkN /61.31.029.1 =−× CabnÞúkrayragRtIekaN xageRkamCataragbgðajBIbnÞúkEdlmanGMeBIelIFñwm 2B KitkñúgmYyÉktþaRbEvg

RbePTbnÞúk eQ μaHbnÞúk bnÞúk ( )mkN / ragBRgaybnÞúk bnÞúkpÞal;xøÜn 1.44 ctuekaN bnÞúkCBa¢aMg 7.4 ctuekaN bnÞúkefr D

bnÞúkkRmalxNÐ 16.64 RtIekaN bnÞúkGefr L bnÞúkcl½t 7.22 RtIekaN

X> kMNt;bnÞúkEdlmanGMeBIelIssrC

B2 (20×30)S

B1(20×45)



+ bnÞúkssrCan;elI = [(4-0.12)×0.2×0.2]×24=3.72kN

+ bnÞúkkRmalxNÐCan;elI S = 4.38×4×6=105.12kN

+ bnÞúkCBa¢aMgenAelIFñwm 1B = (6-0.2)×(4-0.45)×0.1×20= 41.18kN

+ bnÞúkCBa¢aMgenAelIFñwm 2B = (4-0.2)×(4-0.3)×0.1×20=28.12kN

+ bnÞúkFñwm 1B = (6-0.2)×0.2×(0.45-0.12)×24=9.19kN

+ bnÞúkFñwm 2B = (4-0.2)×0.2×(0.3-0.12)×24=3.28kN

+ bnÞúkGefr = 1.9×(4-0.2)×(6-0.2) = 41.88kN

dUcenHbnÞúksrubEdlmanGMeBIelIssr C = 232.5kN

1>5> karbMElgbnÞúk edaysarbnÞúkBRgayelIFñwmmanragepSg² EdlnaM[eyIgBi)akkñúgkaredaHRsay dUcenHeyIgeRbI

viFanbMElgbnÞúkenaH[eTACaragctuekaNEkg. k> karbMElgBIragRtIekaN mkragctuekaNEkg

eqq

S

B1(20×45)

B2 (20×30)

C (20×20)



qqe 32

= x> karbMElgbnÞúkBIragctuekaNBñaymkragctuekaNEkg

qqe

])(

341[ 2

Laqqe −=

K> karRbmUlbnÞúkBIelIkRmalxNÐmkelIFñwm edIm,IgayRsYl kñúgkarbMElgbnÞúkBIelIkRmalxNÐmkelIFñwm eyIgGaceRbInUvrUbmnþxageRkam S - RbEvgtamTisxøI L - RbEvgtamTisEvg

LSm =

sRmab;FñwmxøI BC bnÞúkenAelIkRmal = w KitCa 2/ mkN RkLaépÞbnÞúkmkelIFñwm =

4

2S KitCa 2m

45o 45o

45o 45o

A

D C

B

S

L



bnÞúkmkelIFñwm = 32

SwSw→ KitCa mkN /

sRmab;FñwmEvg AB bnÞúkenAelIkRmal = w KitCa 2/ mkN RkLaépÞbnÞúkmkelIFñwm = )2(

442

22

mmSSSL −

=− KitCa 2m

bnÞúkmkelIFñwm = )2

3(3

2mSw − KitCa mkN / ¬bnÞúkBRgayesμ I¦

1>6> eRKOgbgÁúMénrcnasm<½n§§ebtugGarem: ebtugGarem:CasmÖar³EdlRtUveKRbIR)as;esÞIrRKb;GKar rYmbBa©ÚlTaMgGKarmYyCan; nigeRcInCan;. rcna

sm<½n§énGKarEdleFVIBIebtugGarem:rYmman³ - kRmalxNÐ ( slab ) CaeRKOgbgÁúMbnÞHedk EdlrgnUvbnÞúkbBaÄr k¾dUcCabnÞúkedk. CaTUeTAkRmas;

rbs;kRmalxNÐmanTMhMtUcCagq¶ayebIeRbobeFobeTAnwgbeNþay b¤TTwgrbs;kRmal. - Fñwm ( beam ) CaeRKOgbgÁúMEdlmanRbEvgEvg edk b¤eRTt CamYynwgTTwg nigCeRmAkMNt;mYy.

tYnaTIcMbgrbs;FñwmKWRTbnÞúkmkBIkRmalxNÐ nigxøÜnvapÞal;. - ssr ( column ) CaeRKOgbgÁúMd¾sMxan; EdlmantYnaTIRTbnÞúkEdlmkBIFñwm b¤kRmalxNÐ. vaGac

RbQmnwgkmøaMgcMp©it nigkmøaMgcMp©itrYmbBa©Úlm:Um:g;. - eRKag ( frame ) CaeRKOgbgÁúMEdlpSMeLIgedayman Fñwm nigssr b¤pSMeLIgedayman kRmalxNÐ Fñwm

nigssr. vaGacCaeRKagsþaTickMNt; b¤eRKagsþaTicminkMNt;. - RKwH ( footing ) rYmman eCIgtag b¤RKwHCab; EdlRTssr nigbBa¢ÚnbnÞúkeTAdIedaypÞal;. - CBa¢aMg ( wall ) CaeRKOgbgÁúMbnÞHbBaÄr EdlRbQmnwgkmøaMgTMnaj k¾dUcCakmøaMgedk kñúgkrNIdUcCa

CBa¢aMgeRkamdI.

B C B C



1>7> CMhanénkarKNnaeRKOgbgÁúMBIebtugGarem: eRkayeBlEdlbøg;sßabtükmμ RtUv)anseRmcTTYlyk visVkrcab;epþImkMNt;nUvRbB½n§rcnasm<½n§d¾l¥

mYy edayFananUvsuvtßiPaB nigsißrPaBrbs;GKar. KMniténkarbegáItKMrUrcnasm<½n§epSg² k¾RtUv)anykmk BicarNa edIm,ITTYl)anlkçN³esdækic©x<s; edayQrelImUldæansmÖar³ niglkçxNÐdI. CaTUeTA lT§pl TaMgenHTTYl)anBI³

- begáItCaKMrUrcnasm<½n§eRKOgbgÁúMEdlRTRTg;bnÞúk - kMNt;nUvRbePTepSg²KñaénbnÞúkEdlmanGMeBIelIGKar - viPaKrcnasm<½n§eRKOgbgÁúMedayeRbIkMuBüÚT½r b¤edayéd edIm,IkMNt;nUvm:Um:g;Gtibrma kmøaMgkat;TTwg

kmøaMgrmYl kmøaMgtamG½kS nigkmøaMgepSg²eTot - kMNt;smamaRténeRKOgbgÁúM nigkMNt;nUvbrimaNEdkEdlRtUvkar - begáItnUvbøg;rcnasm<½n§ nigkarlMGitlkçN³bec©keTsedIm,IeFVIkarsagsg;


T.Chhay 12 Properties of Reinforced Concrete

II.lkçN³énebtugGarem:

2>1> ktþaCH\T§iBldl;ersIusþg;ebtug CaTUeTAebtugCasmÖar³ EdlekItBIkarrYmpSMeLIgeday f μbMEbk xSac; sIum:gt¾ nigTwk EtkñúgkrNIxøH Rb

ePTepSg²énTwkfñaMKImIk¾RtUv)anbEnßmedIm,IehtuplepSg². smÖar³TaMgenH)anlaypSMKña rYcRtUv)ancak;cUl kñúgBum< Tuk[kkrwgedIm,I[ersIusþg;rbs;vaekIneLIgCabnþbnÞab;. ersIusþg;rbs;ebtugvaGaRs½yeTAelIktþaCa eRcIn ehIyvaGacERbRbYlsRmab;karplitdUcKña. ktþacMbgsMxan;²EdlCH\T§iBldl;ersIusþg;ebtugman³

- pleFobTwkelIsIum:gt¾ (water-cement ratio)³ vaCaktþaEdlsMxan;CageK EdlCH\T§iBleTAelIersIu-sþg;rbs;ebtug. edIm,IseRmcnUvGIuRdakm μrbs;sIum:gt¾ pleFobTwkelIsIum:gt¾ EdlRtUvkarcM)ac;RtUvesI μnwg 25.0 KitCam:as;;. pleFobTwkelIsIum:gt¾ EdlmantémøFMCag b¤es μ Inwg 35.0 edayK μanlayTwkfñaMKImI RtUv)aneRbI sRmab;ebtugedIm,ImUlehtugayRsYleFVIkar. enAeBlEdlpleFobTwkelIsIum:gt¾mantémøkan;EtFM enaHersIu-sþg;ebs;ebtugkan;EtmantémøtUc.

- lkçN³ nigsmamaRténsmasPaBénebtug³ ebtugCakarrYmpSMeLIgeday fμbMEbk xSac; sIum:gt¾ nig Twk. karekIneLIgnUvbrimaNsIum:gt¾ nigkareRbIR)as;nUvf μbMEbkEdlmanlkçN³ÉksNæan eFVI[ersIusþg;ebtug ekIneLIg. TwkfñaMKImIiBiessk¾RtUv)anbEnßmedIm,IplitnUvebtugEdlmanKuNPaB nigersIusþg;tamtRmUvkar.

- viFIlay nigkarEfTaM³ kareRbIR)as;nUvm:asIunlayebtug nigry³eBlRtwmRtUvkñúgkarlaysuT§EtCYy sRmalnUv\T§iBlEdlb:HBal;dl;ersIusþg;ebtug. dUcKña kareRbIR)as;nUvm:asIunbgðab;ebtug (vibrator) edIm,IeFVI [ebtughab;ENn CYy[PaKryrn§es<atkñúgebtugxiteTArktémøGb,brma. pleFobrn§es<at %5 eFVI[ ersIusþg;ebtugFøak;cuH %30 . karEfTaMebtugk¾CaktþamYyd¾sMxan;Edlman\T§iBlelIersIusþg;rbs;ebtugEdr. TaMgsMeNIm nigsItuNðPaBsuT§Etman\T§iBledaypÞal;eTAelIGIuRdatkmμrbs;sIum:gt¾. ry³eBlénkarmansM eNImkan;EtEvg ersIusþg;kan;EtekIneLIg. RbsinebIsItuNðPaBkñúgGMLúgeBlénkarEfTaMekInx<s;CagsItuNð- PaBkñúgGMLúgeBlénkarcak;ebtug CalT§plebtugmanersIusþg;tamtRmUvkarmun 28éf¶ .

- Gayuebtug³ ersIusþg;rbs;ebtugekIneLIgtamGayurbs;va ehIyGIuRdakmμrbs;sIum:gt¾enAEtbnþrab;Ex. kñúgkarGnuvtþ ersIusþg;ebtugRtUv)ankMNt;edaykareFVIBiesaFn_eTAelIsMNakKMrUragsIuLaMg b¤KUb enAGayu 7éf¶ nig28éf¶. CaTUeTA ersIusþg;rbs;ebtugenAGayu 28éf¶esμ Inwg 1.3dgeTA 1.7dgénersIusþg;ebtugenAGayu 7éf¶ . sRmab;sIum:gt¾B½rElnFm μta ersIusþg;ekIneLIgtameBledayeFobnwgersIusþg;enAGayu 28éf¶RtUv)anbgðajkñúg taragxageRkam³


lkçN³énebtugGarem: 13 T.Chhay

Gayu 7 éf¶ 14éf¶ 28 éf¶ 3 Ex 6 Ex 1 qñaM 2 qñaM 5 qñaM pleFobersIusþg; 0.67 0.86 1 1.17 1.23 1.27 1.31 1.35

- lkçxNÐénkardak;bnÞúk³ ersIusþg;ebtugrgkarsgát; RtUv)ankMNt;edaykarBiesaFkarsgát;bMEbksM

NakKMrUragsIuLaMg b¤KUbkñúgry³eBlBIr bInaTI. eRkamGMeBIénbnÞúkGcié®nþy_rab;qñaM ersIusþg;ebtugRtUv)ankat; bnßyRbEhl %30 . eRkamGMeBIénbnÞúkGcié®nþy_ 1éf¶ersIusþg;ebtug)at;bg;RbEhl %10 . kñúgkrNIEdl rcnasm½<n§rgnUvbnÞúkdEdl² GMeBIDINamic nigGMeBIb:HTgÁic vaRtUv)aneKykmkBicarNakñúgkarKNnaeRKOgbgÁúM ebtugGarem:.

- rUbrag nigxñatrbs;sMNakKMrU³ xñatTUeTArbs;sMNakKMrUebtugEdleKeRbIsRmab;TsSn_TaynUversIusþg; ebtugGarem:KW ragsIuLaMgEdlmanGgát;p©it cm15 nigkm<s; cm30 nigragKUbEdlmanRTnug cm15 . enAeBl EdleKyksMNakKMrUragsIuLaMgmkeFVIBiesaFn_EdlmanxñatepSgKña eKsegáteXIjfaxñatkan;EtFM ersIusþg;kan; EtFøak;. xageRkamCataragbgðajBIersIusþg;rbs;sMNakKMrUebtugbTdæanEdlmankm<s;es μ InwgBIrdgGgát;p©it eFobnwgxñat cmcm 3015 × .

xñatsIuLaMg cm ersIusþg;eFob 105× 09.1 2010× 06.1 3015× 00.1 4020× 96.0 6030× 91.0 9045× 86.0

12060× 84.0 18090× 82.0

eBlxøHsMNakKMrUragsIuLaMgbTdæanminRtUv)anykmkeFIVkarBiesaF. pleFobkm<s;elIGgát;p©itrbs; sMNakKMrUkan;EtFM ersIusþg;kan;EtTabtamkarkt;sMKal;BIkareFVIBiesaFn_. edIm,ITTYl)annUversIusþg;smmUl eTAnwgersIusþg;sMNakKMrUbTdæaneKRtUvKuNnwgemKuNkMEn EdlmanbgðajkñúgtaragxageRkam³ pleFobkm<s;elIGgát;p©it 2 1.75 1.5 1.25 1.1 1 0.75 0.5 emKuNkMEnersIusþg; 1.00 0.98 0.96 0.93 0.90 0.87 0.7 0.5

ersIusþg;eFobnwgsMNakKMrUbTdæan 1.00 1.02 1.04 1.06 1.11 1.18 1.43 2.00



TMnak;TMngersIusþg;énsMNakKMrUragsIuLaMg nigragKUbsRmab;ersIusþg;rgkarsgát;epSg² bgðajkñúg taragxageRkam³

ersIusþg;rgkarsgát; 2/ mmN

7 15.5 20 24.5 27 34.5 37 41.5 45 51.5

pleFobersIusþg; sMNaksIuLaMgelIsMNakKUb

0.77 0.76 0.81 0.87 0.91 0.93 0.94 0.95 0.96 0.96

CaTUeTAeKsnμt; )('1.1)('85.0)(' prismefcubefcylinderf ccc ==

2>2> ersIusþg;rgkarsgát; kñúgkarKNna eK)ansnμt;faebtugCasar³FatuEdlrgnUvkugRtaMgsgát; minEmnkugRtaMgTaj. dUecñH

ersIusþg;rgkarsgát;CalkçN³vinicä½yKuNPaBrbs;ebtug. sMNakKMrUsRmab;ykmkeFVIkarBiesaFmanTRmg;Ca sIuLaMg KUb nigRBIs.

sMNakKMrUEdlmanTRmg; KUbEdlmanRTnug cm15 b¤ cm20 RtUv)aneKeRbIenAcRkPBGg;eKøs GaLWm:g; nigEpñkxøHrbs;GWr:ub.

sMNakKMrURBIs RtUv)aneRbIenARbeTs)araMg rusSI nigRbeTsdéTeTot ehIyCaTUeTAmanmuxkat; 3077 ×× b¤ 501010 ×× edayeKykvaeTAsgát;epþk. muneKykvaeTABiesaF sMNakKMrURtUv)aneKEfTaMedaysMeNIm nigykeTABiesaFenAGayu 28 éf¶eday

GnuvtþbnÞúkekIneLIgrhUtdl;vaEbk. karEbkrbs;ebtugGacekIteLIgedaysar kugRtaMgTaj kugRtaMgkat; kugRtaMgsgát; b¤bnSMénkugRtaMgTaMgenH.



karEbkrbs;sMNakKMrUebtugmanbIy:agdUcxageRkam³ a. eRkamGMeBIénkmøaMgsgát;tamG½kS sMNakKMrUGacEbkedaykmøaMgkat; b. sMNakKMrU)anEbkedaymanlkçN³CaCYr² dUcCaeRcok. karEbkEbbenH ekIteLIgEtcMeBaHebtug

EdlmanersIusþg;x<s; c. ekIteLIgedaysarbnSMénkmøaMgkat; nigkmøaMgeRcok.

2>3> ersIusþg;rgkarTaj ebtugCasmÖar³RsYy EdlvamanminGacRbQmnwgkugRtaMgTaj)an ehIyvaRtUv)aneKykmkBicarNa

sRmab;bBaðaeRbH kmøaMgkat; nigkmøaMgrmYl. karBiesaFedaypÞal;elIersIusþg;rgkarTajminGaceFVIeTA)an edaykartRmg;min)anl¥ nigbBaða

]bkrN_sRmab;cab;. dUecñHkarBiesaFedayminpÞal; edIm,IQaneTAkMNt;ersIusþg;rgkarTajman karBiesaF edayeRcok nigkarBiesaFedaykarkac;bM)ak;.

karBiesaFedayeRcok RtUv)aneFVIelIsMNakKMrUragsIuLaMgbTdæan cm3015× . sMNakKMrURtUv)andak; epþk rYceRbIkmøaMgsgát;elIkþaRTnab;rhUtdl;eRcokEbkCaBIrbMENk.

karBiesaFedaykac;bM)ak; RtUv)aneFVIeLIgelIsMNakKMrUragRBIs cm701515 ×× dak;KgelITRmEdl mancm¶ay cm60 BIKña ehIyeKeRbIbnÞúkedIm,Ikac;bM)ak;BIr Edlmancm¶ay cm10 BIG½kS.

CaTUeTAersIusþg;rgkarTajmantémøes μ Inwg %10 énersIusþg;rgkarsgát; mann½yfaersIusþg;rgkarTaj tUcCagersIusþg;rgkarsgát; 10dg.

2>4> ersIusþg;rgkarkat; kmøaMgkat;suT§kRmnwgCYbRbTHenAkñúgeRKOgbgÁúMebtugGarem:Nas; eRBaHCaTUeTAvaEtgEtekIteLIgeRkam

GMeBIénkmøaMgtamG½kS. eRKOgbgÁúMEdlrgnUvkmøaMgkat;suT§KW)ak;CaBIrcMENk. dUecñHeRKOgbgÁúMebtugRtUvEtrwg RKb;RKan;edIm,ITb;nwgkmøaMgkat;.

ersIusþg;rgkarkat;RtUv)anKitedaymantémøFMCag %30%20 → énersIusþg;rgkarTaj b¤esμ Inwg %12 énersIusþg;rgkarsgát;.



2>5> m:UDuleGLasÞicrbs;ebtug m:UDuleGLasÞic CalkçN³emkanicd¾sMxan;mYyrbs;ebtug Edl)anBIkarBiesaFkarsgát;elIsMNakKMrU

ragsIuLaMg. m:UDuleGLasÞic)anBIpleFobrvagkugRtaMg nigbERmbRmYlrageFob.

strainunit stressunit

=cE xageRkamCarUbmnþsamBaØsRmab;karKNna m:UDuleGLasÞicrbs;ebtug

cc fwE '043.0 5.1= Edl w - m:as;maDrbs;ebtug cf ' - ersIusþg;rgkarsgát;sMNakKMrUsIuLaMg kñúgkrNI 3/2320 mkgw = eK)an

cc fE '4700=

2>6> emKuNBr½sug b¤pleFobBr½sug emKuNBr½sug μ CapleFobrvagbERmbRmYlragtamTTwg nigbERmbRmYltambeNþay. emKuNenH

ERbRbYlcenøaHBI 20.015.0 → . emKuNBr½sugRtUv)aneKeRbIsRmab;rcnasm½<n§sþaTicminkMNt;. CaTUeTA sRmab;ebtug eK)ankMNt;ykemKuNBr½sugmFümEdlmantémøesμ I 18.0 .

2>7> m:UDulénPaBrwg b¤m:UDulkmøaMgkat; m:UDulénPaBrwgrbs;ebtugRtUv)ankMNt;edaysmIkarxageRkam³

)1(2 μ+= c

cEG

RbsinebI 61

=μ cc EG 43.0=⇒

2>8> pleFobm:UDul pleFobm:UDul n CapleFobrvagm:UDuleGLasÞicrbs;Edk nigm:UDuleGLasÞicrbs;ebtug.

c

s

EEn =

edaym:UDuleGLasÞicrbs;Edkmantémøefr MPaEs 200000= ehIym:UDuleGLasÞicrbs;ebtugGaRs½ynwgersIusþg;rgkarsgát; cc fE '4700=

cfn

'42

=⇒ Edl cf ' KitCa MPa .



2>9> bERmbRmYlmaDrbs;ebtug ebtugTTYlnUvkarERbRbYlmaDkñúgxN³eBlkkrwg. RbsinebIva)at;sMeNImedaysarrMhYt varYmmaD.

b:uEnþRbsinebIvakkrwgkñúgTwk vanwgrIkmaD. ktþaénkarERbRbYlmaDebtug naM[ekItmankarERbRbYlsMeNIm Rbtikm μKImIrvagsIum:gt¾ nigTwk bERmbRmYlsItuNðPaB nigrgnUvbnÞúk.

2>9>1> karrYmmaD bERmbRmYlmaDebtugEdlrwg minesμ InwgmaDTwkEdl)an)at;bg;enaHeT. rMhYténTwkesrIbegáItnUvkarrYm

maDd¾tictYcbMputesÞIrEtK μan. edaysarEtebtugbnþkarkkrwg TwkRtUv)anhYt ehIymaDénTwksIum:gt¾ERbRbYl bNþal[ebtugrYmmaD.

ktþaCaeRcInEdlCH\T§iBldl;karrYmmaDrbs;ebtug bNþalmkBIbERmbRmYllkçxNÐsMeNIm³ - brimaNsIum:gt¾ nigTwk³ enAkñúgsmamaRténkarlayebtug kalNabrimaNsIum:gt¾ nigTwkkan;Et

eRcIn karrYmmaDkan;EtxøaMg.

- smasPaB nigPaBm:g;pg;rbs;sIum:gt¾³ sIum:gt¾ersIusþg;eLIgx<s;qab; nigsIum:gt¾kemþAtic mankarrYm maDxøaMgCagsIum:gt¾Br½ElnFm μta. sIum:gt¾EdlmanlkçN³m:t;pg;Cag rIkmaDCageRkamlkçxNÐ sMeNIm.

- RbePT brimaN nigcMNat;fñak;fμbMEbk³ TMhMénf μbMEbkkan;EttUc rYmmaDkan;EtxøaMg. brimaNfμbM Ebkkan;EteRcIn rYmmaDkan;Etkat;bnßy.

- TwkfñaMKImI³ TwkfñaMKImIEdlCYy[ebtugkan;Etrav eFVI[ebtugkan;EtrYmmaD.

- brimaNEdkkñúgebtug³ edaysarkarrYmmaDekItelIeRKOgbgÁúMebtugGarem: kugRtaMgTaj)anekItelI ebtug ehIymantémøesμ IKñanwgkugRtaMgsgát;EdlekItmanelIEdk. kugRtaMgTaMgenHRtUv)anbEnßm ehIykøayeTACabnÞúk. dUecñH sñameRbHGacekItmanenAkñúgebtug enAeBlNaEdleKeRbIPaKry EdkeRcIn. karBRgayEdk)anl¥ naM[mankarEbgEckkugRtaMgTajkñúgebtug)anl¥ CYykat; bnßybERmbRmYlkugRtaMgxagkñúg.

CaTUeTA ebtugrYmmaDxøaMgkñúgGMLúgeBlénkarcab;epþImkarkkrwgdMbUg b:uEnþeRkaymkkarrYmmaDenH RtUv)ankat;bnßy. témøénkarrYmmaDsrubsRmab;ebtugFm μtaERbRbYlBI 66 1070010200 −− ×→× . RbsinebI eRKOgbgÁúMmanTRmbgáb;sgçag kugRtaMgTajekIneLIgRbEhl MPa10 . RbsinebIebtugRtUv)anEfrkSasMeNIm Cab;lab;kñúgry³eBlmYyc,as;las;eRkayeBlcak; karrYmmaDRtUv)ankat;bnßy. dUecñHvaCakarsMxan;Nas; EdleKRtUvkarEfTaMebtugsRmab;ry³eBlmYymin[ticCag 7 éf¶.



2>9>2> karrIkmaDedaykarekIneLIgénkemþA ebtugrIkmaDCamYynwgkarekIneLIgénkemþA ehIyrYmmaDCamYynwgkarfycuHénkemþA. emKuNlUt kemþArbs;ebtugmantémøRbEhl c

mmo

510−=α mann½yfaeRKOgbgÁúMmYymanRbEvg m30 lUt)an mm10 sRmab;bERmbRmYlkemþA co33 . RbsinebIeRKOgbgÁúMEdlmanTRmsgçag ehIymin)anBRgwgedayEdk kugRtaMg RbEhl MPa7 GacekIteLIg. sRmab;rcnasm½<n§ebtugGarem:EdlmanRbEvgEvg eKRtUveFVItMNsRmab;karrIkmaD expansion joint

ral;RbEvg mm 6030 → mYy. tMNenHmanTMhMRbEhl mm25 .

2>10> Creep Creep KWCakMhUcRTg;RTayrbs;ebtugeRkamvtþmanénbnÞúkGcié®nþy_. kMhUcRTg;RTayenHekIneLIgeTA

tamry³eBlénkardak;bnÞúk. ebtugCasmÖar³eGLasþÚ)aøsÞic. edaycab;epþImCamYynwgkugRtaMgtUc ebtugekItmanbERmbRmYlrag

eFob)aøsÞicbEnßmBIelIbERmbRmYlrageFobeGLasÞic. rUb 2>5 bgðajBIsIuLaMgebtugrgbnÞúk. kMhUcRTg;RTayxN³KW 1ε Edlesμ InwgpleFobkugRtaMgelIm:U

DuleGLasÞic. RbsinebIkugRtaMgenHenArkSaGMLúgry³eBlmYy vanwgekItmanbERmbRmYlrageFobbEnßm 2ε EdlbNþalBI creep. RbsinebIeKdkbnÞúkenHecj bERmbRmYlrageFobeGLasÞic 1ε nwgRtLb;eTArkPaB edImvij ehIybERmbRmYlrageFobedaysar creep xøHk¾RtLb;eTArkPaBedImEdr EtvaenArkSabERmbRmYlrag eFob)aøsÞicGcié®nþy_ 3ε dUcbgðajkñúgrUb. enAkñúgkrNIenH ( ) 23 1 εαε −= Edlα CaGRtaénkarRtLb;eTArk sPaBedImvijrbs;bERmbRmYlrageFobedaysar creep srub. α mantémøcenøaH 1.0 nig 2.0 .

ktþaEdlCH\T§iBldl; creep rbs;ebtugrYmman³ - kRmitkugRtaMg³ creep ekIneLIgCamYynwgkarekIneLIgénkugRtaMg. - ry³eBlénkardak;bnÞúk³ creep ekIneLIgCamYynwgry³eBlénkardak;bnÞúk. RbEhlCa %80 én

creep ekItmankñúgGMLúgeBlbYnExdMbUg ehIy %90 ekIteLIgeRkayry³eBlRbEhlBIrqñaM. - ersIusþg; nigGayurbs;ebtug³ creep nwgmantémøtUcCagRbsinebIvargbnÞúkenAGayucas;. - lkçxNÐbriyakas³ creep RtUv)ankat;bnßyCamYynwgkarekIneLIgénsMeNIm. - kRmiténkardak;bnÞúk³ creep ekIneLIgCamYynwgkMeNInénkRmiténkardak;bnÞúk. - PaKryEdk nigkarBRgaysrésEdkenAkñúgGgát;ebtugGarem:³ creep nigmantémøtUcCagsRmab;Ggát;

EdlmanPaKryEdkx<s; nigmankarBRgaysrésEdk)anl¥. - TMhMénm:as;ebtug³ creep fycuHCamYynwgkarekIneLIgénTMhMrbs;sMNakKMrU.



- RbePT PaBm:t;pg; nigbrimaNsIum:gt¾³ brimaNsIum:gt¾CH\T§iBly:agxøaMgdl; creep cugeRkayrbs; ebtug. Creep edaysarsIum:gt¾mantémøFMCag creep rbs;ebtug 15dg.

- pleFobTwkelIsIum:gt¾³ creep ekIneLIgCamYynwgkarekIneLIgénpleFobTwkelIsIum:gt¾. - RbePT nigcMNat;fñak;fμbMEbk³ f μbMEbkEdlmanTMhMdUc²KñanwgeFVI[ebtugENnl¥ ehIyvanwgkat;bnßy

creep. - RbePTénkarEfTaMebtug³ karEfTaMebtugedaycMhayTwkEdlmansItuNðPaBx<s; k¾dUcCakareRbIR)as;

nUvTwkfñaMKImIRbePT plasticizer nwgkat;bnßybrimaN creep. Creep minRtwmEtekItmanenAkñúgGgát;rgkarsgát;b:ueNÑaHeT b:uEnþvak¾ekItmanenAkñúgGgát;rgkarTaj

Ggát;rgkarBt; nigGgát;rgkarrmYl. pleFobén creep enAkñúgGgát;rgkarTajelI creep enAkñúgGgát;rgkar sgát;FMCagmYysRmab;BIrs)aþh_dMbUg b:uEnþpleFobenHnwgfycuHsRmab;ry³eBlyUr.

2>11> m:UEDlsRmab;TsSn_TaykarrYmmaD nig creep rbs;ebtug

2>11>1> m:UEDl ACI 209 viTüasßanebtugGaem:ricENnaMm:UEDl ACI 209. m:UEDlenHRtUv)anbegáIteLIgdMbUgenAkñúgqñaM 1970.

m:UEDlenHRtUv)aneRbICaeRcInqñaMkñúgkarDIsajrcnasm½<n§ebtug. m:UEDlenHmanlkçN³samBaØkñúgkareRbI Etva minsUvsuRkit. karKNnakarrYmmaD eKGacKNnakarrYmmaDEdleRbIm:UEDl ACI 209 RbsinebIeKsÁal;)a:ra:Em:Rt niglkçxNÐdUcteTA³ viFI EfTaM ¬ebtugEfTaMedaysMeNIm b¤edaycMhayTwk¦ relative humidity H RbePTsIum:gt¾ rUbragsMNakKMrU bERmbRmYlrageFobedaykarrYmmaDcugeRkay shuε Gayurbs;ebtugeRkayeBlcak; t Gayurbs;ebtugEdl cab;epþIms¶Üt ¬CaTUeTAeKykGayuenAcugbBa©b;énkarEfTaM¦ ct . bERmbRmYlrageFobedaysarkarrYmmaDRtUv)ankMNt;dUcxageRkam ( ) ( )

( ) shushssc

cs KK

ttbttt εε−+

−=

Edl =t Gayurbs;ebtugeRkayeBlcak; ¬éf¶¦ =ct Gayurbs;ebtugEdlcab;epþIms¶Üt ¬éf¶¦ =b témøefrkñúgkarkMNt;bERmbRmYlrageFobedaysarkarrYmmaD GaRs½ynwgviFIEfTaMebtug ¬ 35=b sRmab;ebtugEdlEfTaMedaysMeNIm nig 55=b sRmab;ebtugEdlEfTaMedaycMhayTwk¦ =ssK emKuNkMENrUbrag nigTMhMsRmab;karrYmmaD



=shK emKuNkMEN relative humidity sRmab;karrYmmaD shuε ¬bERmbRmYlrageFobedaysarkarrYmmaDcugeRkay¦ ( )mmmm /10780 6−×= ¬sRmab;ebtug

EdlEfTaMedaysMeNIm nigedaycMhayTwk¦ eKGackMNt;emKuNkMENrUbrag nigTMhMsRmab;karrYmmaDdUcxageRkam

⎟⎠⎞

⎜⎝⎛−=

SVKss 0035.014.1

Edl =V maDrbs;sMNakKMrU ( )3mm =S RkLaépÞrbs;sMNakKMrU ( )2mm emKuNkMEN relative humidity sRmab;karrYmmaDKW

⎩⎨⎧

≤≤−≤≤−

=%H%H..%H%H

K

sh 10081030003804001.040.1

sRmab; sRmab;

Edl =H relative humidity ¬KitCa % ¦ karKNna creep eKGacKNnabERmbRmYlrageFobGaRs½ybnÞúksrub ( )0,tticε enAxN³ t rbs;ebtugEdlrgbnÞúkenA xN³ 0t CamYynwgkugRtaMgσ efr tamrUbmnþxageRkam³ ( ) ( ) ( )00 ,, ttttt ciic εεε += Edl ( ) =0tiε bERmbRmYleGLasÞicedImenAeBlrgbnÞúk ( ) =0,ttcε bERmbRmYledaysar creep enAxN³ 0tt ≥ ( )

0

0cmt

i Et σε =

( ) ( )tCE

tt ccmt

c0

0, σε =

Edl =0cmtE m:UDuleGLasÞicenAGayuénkardak;bnÞúk ¬KitCa MPa ¦

( ) =tCc emKuN creep enAxN³ t CaTUeTA bERmbRmYlGaRs½ybnÞúksrubRtUv)anbgðajedayCab;Tak;TgnwgGnuKmn_ creep ( )0,ttJ EdltMNag [bERmbRmYlrageFobGaRs½ybnÞúksrubenAxN³ t EdlekIteLIgedaykugRtaMgefrÉktþaEdleFVIGMeBItaMgBI xN³ 0t . ( ) ( )

0

1, 0cmt

c

EtCttJ +

=

( ) ( )02/3 '043.0

0tfE ccmt γ=

Edl =γ Tm¶n;maDebtug ( )3/ mkg



( ) =0' tf c ersIusþg;rgkarsgát;rbs;ebtugmFümenAGayuEdlrgbnÞúk ( )

0

0280'

ctbtftf cmc +

=

Edl =28cmf ersIusþg;rgkarsgát;rbs;ebtugenAGayu 28 éf¶ ¬ MPa ¦ b nig c CatémøefrEdlmanbgðajenAkñúgtaragxageRkam.

RbePTsIum:gt¾ ebtugEdlEfTaMedaysMeNIm ebtugEdlEfTaMedaycMhayTwk I 4=b 85.0=c 1=b 95.0=c II 30.2=b 92.0=c 70.0=b 98.0=c

eKGackMNt;emKuN creep ( )tCc dUcxageRkam

( ) cscachcuc KKKCt

ttC 60.0

60.0

10 +=

Edl =cuC emKuN creep cugeRkay 35.2= =chK emKuNkMEN relative humidity sRmab; creep =caK emKuNkMENGayuenAeBlrgbnÞúk =csK emKuNkMENrUbrag nigTMhMsRmab; creep

2>11>2> m:UEDl B3 karKNnakarrYmmaD

)a:ra:Em:RtEdlRtUvkarsRmab;KNnabERmbRmYlrageFobedaysarkarrYmmaDEdleRbIm:UEDl B3 KW ersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28éf¶ lkçxNÐtMEhTaM RbePTsIum:gt¾ relative humidity brimaNTwkkñúgebtug nigrUbragrbs;sMNakKMrU.

emKuNkMEN viFItMEhTaM 0t ¬éf¶¦ H caK chK csK EfTaMedaysMeNIm 1≥ %40≥ AN / AN / AN / 7≥ %40≥ ( ) 118.0

025.1 −t H0067.027.1 − ( )SV /0035.014.1 − EfTaMedaycMhayTwk 1≥ %40≥ ( ) 095.0

013.1 −t H0067.027.1 − ( )SV /0035.014.1 − 7≥ %40≥ AN / AN / AN /



eKGac)a:n;s μanbERmbRmYlrageFobedaykarrYmmaDedayeRbIsmIkarxageRkam ( ) ( )( ) ( )tSKt hshus εε =

Edl =shuε bERmbRmYlrageFobedaykarrYmmaDcugeRkay =hK relative humidity sRmab;karrYmmaD

( ) =tS GnuKmn_eBlsRmab;karrYmmaD eKGacKNnabERmbRmYlrageFobedaykarrYmmaDedayeRbIsmIkarxageRkam ( ) ( )[ ] 628.0

281.2

21 10270019.0 −− ×+−= cmshu fwααε Edl =1α emKuNkMENRbePTsIum:gt¾ =2α emKuNkMENlkçxNÐtMEhTaM =w brimaNTwk ¬ 3/ mkg ¦ =28cmf ersIusþg;rgkarsgát;rbs;ebtugenAGayu 28 éf¶

emKuNkMEN 1α CaGnuKmn_eTAnwgRbePTsIum:gt¾ RbePTsIum:gt¾

1α I 00.1 II 85.0 III 10.1

emKuNkMEN 2α CaGnuKmn_eTAnwgRbePTéntMEhTaM RbePTéntMEhTaM

2α EfTaMedaysMeNIm 75.0 EfTaMedayTwk b¤ %100=H 85.0 RKbkñúgGMLúgtMEhTaM 10.1

GnuKmn_sMeNImsRmab;karrYmmaD sMeNIm

hK %98≤H ( )3100/1 H− %100=H 2.0−

%100%98 ≤≤ H eFVIGaMgETb:ULasüúglIeNEG‘r



eKGackMNt;GnuKmn_eBlsRmab;karrYmmaD ( )tS tamsmIkarxageRkam³ ( )

sh

c

TtttS −

= tanh

Edl =t GayuebtugeRkayeBlcak; ¬éf¶¦ =ct GayuebtugEdlcab;epþIms¶Üt ¬éf¶¦ =shT karrYmmaDBak;kNþal (shrinkage half-time)

( ) ( ) ( )[ ]225.028

08.0 /2085.0 SVKftT scmcsh−−=

Edl =sK emKuNkMENrUbragmuxkat;. eKsnμt; 1=sK RbsinebIRbePTGgát;minRtUv)ankMNt;. tarag xageRkambgðajBItémørbs; sK .

emKuNkMEN sK CaGnuKmn_eTAnwgrUbragmuxkat; rUbragmuxkat; sK kRmal 00.1 sIuLaMg 15.1 RBIskaer 25.1 EsV‘r 30.1 KUb 55.1

karKNna creep GnuKmn_ creep RtUv)an[edaysmIkarxageRkam ( ) ( ) ( )cd tttCttCqttJ ,,,, 00010 ++= Edl =1q bERmbRmYlrageFobxN³ ( ) =00 ,ttC GnuKmn_sRmab; creep EdlpSMeLIgeday aging viscoelastic, nonaging viscoelastic nig

aging flow. ( ) =cd tttC ,, 0 GnuKmn_sRmab; drying creep.

281

6.0

cmEq =

Edl =28cmE m:UDuleGLasÞicrbs;ebtugenAGayu 28 éf¶ 2828 4735 cmcm fE = eKGackMNt;GnuKmn_ ( )00 ,ttC dUcxageRkam³



( ) ( ) ( )[ ] ⎟⎟⎠

⎞⎜⎜⎝

⎛+−++=

04

1.0030200 ln1ln,,

ttqttqttQqttC

Edl =2q )a:ra:Em:Rt aging viscoelastic ( ) =0,ttQ binomial integral =3q )a:ra:Em:Rt nonaging viscoelastic

=4q )a:ra:Em:Rt aging flow

=0t Gayurbs;ebtugenAeBlrgbnÞúk ¬éf¶¦ ( ) ( ) 69.0

285.0

2 104.185 −− ×= cmfcq Edl c brimaNsIum:gt¾ ¬ 3/ mkg ¦

( ) ( ) ( ) ( )

( ) ( )

( )0

0

0/1

0

000 ,

1,tr

tr

trf

f ttZtQ

tQttQ−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

Edl ( )( ) ( ) 9/4

09/2

00 21.1086.0

1tt

tQf +=

( ) ( )[ ]0

1.00

01ln,

tttttZ −+

=

( ) ( ) 87.1 12.000 += ttr

4

23 29.0 ⎟⎠⎞

⎜⎝⎛=

cwqq

67.0

4 103.20 −−

×⎟⎠⎞

⎜⎝⎛=

caq

eKGacKNnaGnuKmn_sRmab; drying creep dUcxageRkam³ ( ) ( ) ( )088

50 ,, tHtHcd eeqtttC −− −=

Edl =5q )a:ra:Em:Rt drying creep

28

6.06

5

10757.0

cm

shu

fq

−×

=ε

Edl =shuε bERmbRmYlrageFobedaykarrYmmaDcugeRkay ( ) ( )⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−= tSHtH

10011

( ) ( )⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−= 00 10011 tSHtH

( )sh

c

TtttS −

= tanh

( )sh

c

TtttS −

= 00 tanh



( ) ( ) ( )[ ]225.028

08.0 /2085.0 SVKftT scmcsh−−=

2>11>3> m:UEDl GL 2000 karKNnakarrYmmaD

)a:ra:Em:RtEdlRtUvkarsRmab;KNnabERmbRmYlrageFobedaysarkarrYmmaDEdleRbIm:UEDl GL 2000

KWersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28éf¶ 28cmf relative humidity H Gayurbs;ebtugenAeBl cab;epþImrYmmaD ct RbePTsIum:gt¾ nigrUbragrbs;sMNakKMrU.

eKGacKNnabERmbRmYlrageFobedaykarrYmmaDedayeRbIsmIkarxageRkam ( ) ( ) ( )tht shus ββεε =

Edl =shuε bERmbRmYlrageFobedaykarrYmmaDcugeRkay ( ) =hβ emKuNkMENsRmab;\T§iBlrbs;sMeNIm ( ) =tβ emKuNkMENsRmab;\T§iBléneBl eKGackMNt; shuε edaysmIkarxageRkam

( ) 62/1

28

1030900 −×⎟⎟⎠

⎞⎜⎜⎝

⎛=

cmshu f

Kε

Edl =K témøefrEdlGaRs½ynwgRbePTsIum:gt¾ =28cmf ersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28 éf¶

témøefr K EdlCaGnuKmn_eTAnwgRbePTsIum:gt¾ RbePTsIum:gt¾ K

I 00.1

II 75.0

III 15.1

eKGackMNt;emKuNkMEN ( )hβ dUcxageRkam ( )

4

10018.11 ⎟

⎠⎞

⎜⎝⎛−=

Hhβ



Edl =H relative humidity ¬°¦ eKGacKNnaemKuNkMEN ( )tβ tamrUbmnþxageRkam

( )( )

2/1

2/12.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

=SVtt

tttc

cβ

Edl =t GayuebtugeRkayeBlcak; ¬éf¶¦ =ct Gayurbs;ebtugenAeBlcab;epþImrYmmaD =SV / pleFobmaDelIRkLaépÞ ¬ mm ¦ karKNna creep

GnuKmn_ creep pSMeLIgedayBIrEpñkKW bERmbRmYlrageGLasÞic nigbERmbRmYlrageday creep. ( ) ( )

28

00

,1,0 cmcmt E

ttE

ttJ φ+=

Edl =0cmtE m:UDuleGLasÞicrbs;ebtugenAeBldak;bnÞúk

=28cmE m:UDuleGLasÞicrbs;ebtugenAGayu 28 éf¶ ( ) =0,ttφ emKuN creep

0043003500 cmtcmt fE +=

Edl =0cmtf ersIusþg;rgkarsgát;Fmümrbs;ebtugenAeBlrgbnÞúk. eKGackMNt;vadUcxageRkam

4/3

4/3

280 btatff cmcmt +

= emKuN a nig b Tak;TgeTAnwgRbePTsIum:gt¾dUcbgðajkñúgtaragxageRkam.

emKuN a nig b EdlCaGnuKmn_eTAnwgRbePTsIum:gt¾ RbePTsIum:gt¾ a b

I 2.8 0.77 II 3.4 0.72 III 1.0 0.92

eKGacKNnaemKuN creep ( )0,ttφ dUcxageRkam

( ) ( ) ( )( )

( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

−+⎟⎟⎠

⎞⎜⎜⎝

⎛+−

−⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

+−−

Φ=5.0

20

025.0

0

0

5.0

03.0

0

3.00

0 /12.0086.115.2

77

142,

SVtttth

tttt

tttttttt cφ

RbsinebI ctt =0 enaH ( ) 1=Φ ct



RbsinebI ctt >0 enaH ( )( )

5.05.0

20

0

/12.01

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

−=ΦSVtt

tttc

cc

100/Hh = ¬ =H relative humidity ¬°¦¦

2>11>4> m:UEDl CEB 90 karKNnakarrYmmaD

)a:ra:Em:RtEdlRtUvkarsRmab;KNnabERmbRmYlrageFobedaysarkarrYmmaDEdleRbIm:UEDl CEB 90

KWersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28éf¶ 28cmf relative humidity H Gayurbs;ebtugenAeBl cab;epþImrYmmaD ct RbePTsIum:gt¾ nigrUbragrbs;sMNakKMrU.

eKGacKNnabERmbRmYlrageFobedaykarrYmmaDedayeRbIsmIkarxageRkam ( ) ( )cscscs tttt ,,

0βεε =

Edl =0csε emKuN notional shrinkage

( ) =cs tt,β emKuNEdlBN’naBIkarekItmankarrYmmaDCamYynwgeBl emKuN notional shrinkage KW

( ) RHcmscs f βεε 280=

Edl ( ) =28cms fε emKuNersIusþg;ebtugénkarrYmmaD ( ) ( ) 628

28 1010

910160 −×⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+= cm

sccmsff βε

=RHβ emKuN relative humidity énemKuN notional shrinkage EdlmanbgðajenAkñúgtaragxag eRkam.

emKuN RHβ sMeNIm

RHβ %90%40 <≤ H

arhβ×− 55.1 %99≥H

25.0 =scβ emKuNEdlGaRs½ynwgRbePTsIum:gt¾ EdlmanbgðajenAkñúgtaragxageRkam =28cmf ersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28 éf¶



emKuN scβ RbePTsIum:gt¾ sþg;darGWr:ub sþg;darGaemric scβ kkrwgyWt SL II 4

kkrwgFmμta b¤elOn R I 5

kkrwgelOn RS III 8

3

1001 ⎟

⎠⎞

⎜⎝⎛−=

Harhβ

karekItmankarrYmmaDGaRs½ynwgeBlRtUv)ankMNt;tamsmIkarxageRkam ( ) ( )

( ) ( )ce

ccsc tth

tttt−+

−=− 24/56.0

β

Edl =t Gayurbs;ebtug ¬éf¶¦ =ct Gayurbs;ebtugenAeBlcab;epþImkarrYmmaD =eh kRmas;RbsiT§PaBedIm,IKitbBa©ÚlpleFobmaDelIRkLaépÞ eKGackMNt;kRmas;RbsiT§PaB eh dUcxageRkam

uAh c

e2

= Edl =cA muxkat;rbs;Ggát;eRKOgbgÁúM ¬ 2mm ¦

=u brimaRtrbs;Ggát;eRKOgbgÁúMEdlb:HCamYynwgbriyakas ¬ mm ¦

karKNna creep GnuKmn_ creep tMNag[kugRtaMgsrubGaRs½ynwgbERmbRmYlrageFobkúñgmYyÉktþakugRtaMg. eKGac

kMNt;vadUcxageRkam. ( ) ( )

28

00

,1,0 cmcmt E

ttE

ttJ φ+=

Edl =0cmtE m:UDuleGLasÞicenAGayuEdlrgbnÞúk

=28cmE m:UDuleGLasÞicenAGayu 28 éf¶ ( ) =0,ttφ emKuN creep

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= tS

cmcmt eEE2815.0

280



=S emKuNGaRs½ynwgRbePTsIum:gt¾ ehIyGackMNt;BItaragxageRkam

emKuN S CaGnuKmn_énRbePTsIum:gt¾ RbePTsIum:gt¾ sþg;darGWr:ub sþg;darGaemric S kkrwgyWt SL II 0.38

kkrwgFmμta b¤elOn R I 0.25

kkrwgelOn RS III 0.20

3 28

28 1021500 cm

cmfE =

eyIgGackMNt;emKuN creep ( )0,ttφ BIsmIkarxageRkam ( ) ( )000 ,, tttt cβφφ =

Edl =0φ emKuN notional creep ( ) =0,ttcβ smIkarEdlBN’naBIkarekItman creep GaRs½ynwgeBleRkayeBlrgbnÞúk ( ) ( )0280 tfcmRH ββφφ = Edl =RHφ emKuNsMeNImbriyasénemKuN notional creep Edl[eday

3 4/16.0100/11e

RH hH−

+=φ

( ) =28cmfβ emKuNersIusþg;ebtugénemKuN notional creep Edl[eday ( )

10/3.5

2828

cmcm f

f =β

( ) =0tβ emKuNGayuebtugenAeBlrgbnÞúkénemKuN notional creep Edl[eday ( ) 2.0

00 1

1t

t+

=β

smIkarEdlBN’naBIkarekItman creep GaRs½ynwgeBleRkayrgbnÞúk ( )0,ttβ RtUv)anKNnaedayeRbI smIkarxageRkam

( )3.0

0

00, ⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

−=

tttttt

Hc β

β

( )[ ] 1500250012.015.1 18 ≤++= HheHβ éf¶



2>11>5> m:UEDl CEB 90-99 m:UEDl CEB 90-99 RtUv)anEkERbBIm:UEDl CEB90. karKNnakarrYmmaD

enAkñúgm:UEDlfμ IenH karrYmmaDsrubrYmmanbgÁúMénkarrYmmaDeday autogenous nig edaysars¶Üt. enA kñúgebtug high-performance karrYmmaDeday autogeneous mantémøFM ehIyeKRtUvBicarNavakñúgkar)a:n; RbmaNkarrYmmaD. viFIf μ IenHpþl;nUvkar)a:n;RbmaNkarrYmmaDénebtugFmμta nigebtug high-performance manlkçN³suRkit.

eKGacKNnabERmbRmYlrageFobedaykarrYmmaDsrubedayeRbIsmIkarxageRkam ( ) ( ) ( )cdsascs ttttt ,, εεε +=

Edl ( ) =tasε autogenous shrinkage enAxN³ t ( ) =cds tt,ε drying shrinkage enAxN³ t

eKGacKNna autogenous shrinkage dUcxageRkam ( ) ( ) ( )tft ascmasas βεε 280

= Edl ( ) =280 cmas fε emKuN notional autogenous shrinkage

( ) =tasβ GnuKmn_edIm,IBN’naeBlevlaEdlekItman autogenous shrinkage eKGacKNnaemKuN notional autogenous shrinkage ( )280 cmas fε dUcxageRkam

( ) 65.2

28

2828 10

10/610/

0

−×⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=cm

cmascmas f

ff αε

Edl =asα emKuNGaRs½ynwgRbePTsIum:gt¾ 800= sRmab;sIum:gt¾kkrwgyWt 700= sRmab;sIum:gt¾kkrwgFm μta b¤elOn 600= sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn

=28cmf ersIusþg;rgkarsgát;mFümrbs;ebtugenAGayu 28 éf¶ ¬ MPa ¦ eKGacKNnaGnuKmn_ ( )tasβ edayeRbIsmIkarxageRkam ( ) ( ) 5.02.01 t

as et −−=β Edl =t Gayurbs;ebtug ¬éf¶¦ eKGackMNt; drying shrinkage ( )cds tt,ε edaysmIkarxageRkam

( ) ( ) ( ) ( )cdsRHcmdscda ttHftt −= ββεε 280,

Edl ( ) =280 cmds fε emKuN notional drying shrinkage



( ) =HRHβ emKuNEdlKitBI\T§iBlrbs; relative humidity mkelI drying shrinkage ( ) =− cds ttβ GnuKmn_edIm,IBN’naeBlevlaEdlekItman drying shrinkage

eKGacKNnaemKuN notional drying shrinkage ( )280 cmds fε BIsmIkarxageRkam ( ) ( )[ ] 610/

128 10110220 282

0

−−+= cmds fdscmds ef ααε

Edl =1dsα emKuNEdlGaRs½ynwgRbePTsIum:gt¾ 3= sRmab;sIum:gt¾kkrwgyWt 4= sRmab;sIum:gt¾kkrwgFm μta b¤kkrwgelOn 6= sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn

=2dsα emKuNEdlGaRs½ynwgRbePTsIum:gt¾ 13.0= sRmab;sIum:gt¾kkrwgyWt 11.0= sRmab;sIum:gt¾kkrwgFmμta b¤kkrwgelOn 12.0= sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn

eKGacKNnaemKuN ( )HRHβ tamrUbmnþxageRkam

⎪⎩

⎪⎨

⎧

×≥

×≤≤⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−

=

1

1

3

%9925.0

%99%10100

155.1

s

sRH

H

HH

β

ββ

sRmab;sRmab;

Edl =H Ambient relative humidity (%)

=1sβ emKuNEdlKitBIkarkkrwgedayxøÜnÉgenAkñúgebtug high-performance eyIgGackMNt;vadUcxageRkam

0.1351.0

281 ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛=

cms f

β

eKGacKNnaGnuKmn_ ( ) ( )( ) ( )

5.0

24/56.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛

−+−

=−ce

ccds tth

ttttβ

Edl =ct GayuebtugenAeBlcab;epþIms¶Üt ¬éf¶¦ ==

uAh c

e2 TMhM notional rbs;Ggát; ¬ mm ¦ Edl cA CaRkLaépÞmuxkat; ¬ 2mm ¦ nig u CabrimaRt

rbs;Ggát;Edlb:HCamYynwgbriyakas ¬ mm ¦

karKNna creep



kugRtaMgsrubGaRs½ynwgbERmbRmYlrageFobkñúgmYyÉktþaénkugRtaMg EdleKGacehAmü:ageTotfa compliance creep b¤GnuKmn_ creep. eKGackMNt;vaedayeRbIsmIkarxageRkam

( ) ( )28

00

,1,0 cmcmt E

ttE

ttJ φ+=

Edl =0cmtE m:UDuleGLasÞicenAGayurgbnÞúk ¬ MPa ¦

=28cmE m:UDuleGLasÞicenAGayu 28 éf¶ ( ) =0,ttφ emKuN creep

TS

cmcmt eEE285.0

280=

S CaemKuNGaRs½ynwgRbePTsIum:gt¾ nigersIusþg;sgát; ehIyeKGackMNt;vaBItaragxageRkam

emKuN S CaGnuKmn_eTAnwgRbePTsIum:gt¾ nigersIusþg;rgkarsgát; ( )MPafcm28 RbePTsIum:gt¾ S

60≤ ersIusþg;FMkkrwgelOn 0.20

kkrwgFmμta nigelOn 0.25

kkrwgyWt 0.30

60> RKb;RbePT 0.20

3 28

28 1021500 cm

cmfE =

eKGacKNnaemKuN creep ( )0,ttφ BIsmIkarxageRkam ( ) ( )000 ,, tttt cβφφ =

Edl =0φ emKuN notional creep ( ) =0,ttcβ smIkarEdlBN’naBIkarekItman creep CamYynwgeBleRkayeBlrgbnÞúk

( ) ( )0280 tfcmRH ββφφ = =RHφ emKuN relative humidity énemKuN notional creep

213 4/16.0100/11 ααφ

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+=

eRH h

H

Edl 7.0

281

35⎥⎦

⎤⎢⎣

⎡=

cmfα

2.0

282

35⎥⎦

⎤⎢⎣

⎡=

cmfα



( ) =28cmfβ emKuNersIusþg;ebtugénemKuN notional creep ( )

10/3.5

2828

cmcm f

f =β

( ) =0tβ emKuNGayuebtugenAeBlrgbnÞúkénemKuN notional creep

( ) 2.00

0 11t

t+

=β

Edl 5.012

92.1,0

,00 ≥⎥⎦

⎤⎢⎣

⎡+

+=

α

TT t

tt éf¶

=0t Gayurbs;ebtugenAeBlrgbnÞúk ¬éf¶¦ =Tt ,0 Gayurbs;ebtugenAeBlrgbnÞúkEdlEktRmUveTAtamsItuNðPaBrbs;ebtug

sRmab; CT o20= / Tt ,0 RtUvKñanwg 0t =α emKuNEdlGaRs½ynwgRbePTsIum:gt¾

1−= sRmab;sIum:gt¾kkrwgyWt 0= sRmab;sIum:gt¾kkrwgFm μta b¤elOn 1= sRmab;sIum:gt¾ersIusþg;FMkkrwgelOn

eKGackMNt;smIkarEdlBN’nakarekItman creep CamYynwgeBleRkayeBlrgbnÞúk ( )0,ttβ eday eRbIsmIkarxageRkam³

( )3.0

0

00, ⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

−=

tttttt

Hc β

β

( )[ ] 3318 1500250012.015.1 ααβ ≤++= HheH

5.0

283

35⎥⎦

⎤⎢⎣

⎡=

cmfα

]TahrN_ 2>1³ KNnabERmbRmYlragedaysarrYmmaD nig creep compliance sRmab;sMNakKMrUebtugEdl [xageRkam. eRbIm:UEDl ACI 209. eK[³ sMeNIm %75=H mmuASVh ce 76/2/2 ===

MPafcm 2.4528 = 3/92.207 mkgw =

46.0/ =cw 73.3/ =ca

35=t éf¶



280 =t éf¶ 8=ct éf¶

3/2405 mkg=γ sIum:gt¾RbePT III

ebtugEfTaMedaysMeNIm

dMeNaHRsay karKNnakarrYmmaD ( ) ( )

( ) shushssc

cs KK

ttbttt εε−+

−=

mmmmshu /10780 6−×=ε

edayebtugEfTaMedaysMeNIm 35=b mmSV 38/ =

( ) 007.1380035.014.10035.014.1 =−=⎟⎠⎞

⎜⎝⎛−=

SVKss

sRmab; %75=H ( ) 65.07501.040.101.040.1 =−=−= HKsh

( ) ( )( ) shushss

c

cs KK

ttbttt εε−+

−=

( )( ) ( )( )( ) mmmm /103.2221078065.0007.1

83535835 66 −− ×=⋅−+

−=

karKNna creep ( ) ( )

0

1, 0cmt

c

EtCttJ +

=

kMNt; 0cmtE

edaysarsIum:gt¾RbePT III nigebtugEfTaMedaysMeNIm 30.2=b / 92.0=c ( ) MPa

ctbtftf cmc 1.45

2892.03.2282.45'

0

0280 =

×+=

+=

( ) ( ) ( ) MPatfE ccmt 8.340581.452405043.0'043.0 2/30

2/30

=== γ kMNt; ( )tCc 35.2=cuC ( ) ( ) 767.0750067.027.10067.027.1 =−=−= HKch ( ) ( ) 844.02825.125.1 118.0118.0

0 === −−tKca



( ) ( ) 007.1380035.014.1/0035.014.1 =−=−= SVKcs ( ) 702.000.1844.0767.035.2

351035

10 60.0

60.0

60.0

60.0

=×××+

=+

= cscachcuc KKKCt

ttC ( ) ( )

MPaEtCttJ

cmt

c 1109.498.34058

702.011, 60

0

−×=+

=+

=

]TahrN_ 2>2³ edayeRbIm:UEDl B3 KNnakarrYmmaD nigGnuKmn_ creep sRmab;sMNakKMrUEdl[enAkñúg ]TahrN_ 2>1. dMeNaHRsay³ KNnakarrYmmaD ( ) ( )( ) ( )tSKt hshus εε = kMNt; shuε edaysIum:gt¾RbePT III 10.11 =α edaysarebtugEfTaMgedaysMeNIm 0.12 =α ( ) ( )[ ] 628.0

281.2

21 10270019.0 −− ×+= cmshu fwααε ( )( ) ( ) ( )[ ] mmmm /10827102702.4592.207019.00.110.1 6628.01.2 −−− ×=×+=

kMNt; hK sRmab; %75=H enaH 578.0

100751

1001

33

=⎟⎠⎞

⎜⎝⎛−=⎟

⎠⎞

⎜⎝⎛−=

HKh

kMNt; ( )tS 0.1=sK edaysareyIgmindwgBIRbePTGgát; ( ) ( ) ( )[ ]225.0

2808.0 /2085.0 SVKftT scmcsh

−−= ( ) ( ) ( )( )[ ] 3.160380.122.458085.0 225.008.0 == −−

( ) 389.03.160835tanhtanh =

−=

−=

sh

c

TtttS

( ) ( )( ) ( ) ( )( )( ) mmmmtSKt hshus /109.185389.0578.010827 66 −− ×=×== εε KNna creep ( ) ( ) ( )cd tttCttCqttJ ,,,, 00010 ++= kMNt; 1q MPafE cmcm 9.318332.4547354735 2828 ==



MPaEq

cm

11085.189.31833

6.06.0 6

281

−×===

kMNt; ( )00 ,ttC 3/452

46.092.207

/mkg

cwwc ===

( ) ( ) ( ) ( ) 69.05.069.028

5.02 102.454524.185104.185 −−−− ×=×= cmfcq

6106.127 −×= ( )

( ) ( ) ( ) ( )182.0

2821.128086.01

21.1086.01

9/49/29/40

9/20

0 =+

=+

=tt

tQf

( ) ( )[ ] ( )[ ] 150.028

28351ln1ln,1.0

0

1.00

0 =−+

=−+

=t

ttttZ

( ) ( ) ( ) 54.108287.1870.1 12.012.000 =+=+= ttr

( ) ( ) ( ) ( )

( ) ( )

( )

148.0150.0182.01182.0

,1,

54.10/1

54.10

54.10/1

0

000

0

0

0

=⎥⎦

⎤⎢⎣

⎡+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=

−− tr

tr

trf

f ttZtQ

tQttQ

( )( ) 646.04

23 1066.146.0106.12729.029.0 −− ×=×=⎟⎠⎞

⎜⎝⎛=

cwqq

( ) 667.067.0

4 1008.81073.33.20103.20 −−−−−

×=×=×⎟⎠⎞

⎜⎝⎛=

caq

( ) ( ) ( )[ ] ⎟⎟⎠

⎞⎜⎜⎝

⎛+−++=

04

1.0030200 ln1ln,,

ttqttqttQqttC

( )( ) ( ) ( )[ ] ( ) ⎟⎠⎞

⎜⎝⎛×+−+×+×= −−−

2835ln1008.828351ln1066.1148.0106.127 61.06.06

MPa11001.22 6−×=

KNna ( )cd tttC ,, 0 ³

6

6.06

28

6.06

5 105.2972.45

10827757.010757.0−

−−

×=×

=×

=cm

shu

fq

ε

( ) 389.0=tS ( ) 339.0

3.160828tanhtanh 0

0 =−

=−

=sh

c

TtttS

( ) ( ) 903.0389.01007511

10011 =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−= tSHtH

( ) ( ) 915.0339.01007511

10011 00 =⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −−= tSHtH

( ) ( ) ( )08850 ,, tHtH

cd eeqtttC −− −= ( )

MPaee 11043.210297 6915.08903.086 −×−×−− ×=−×=



( ) ( ) ( )cd tttCttCqttJ ,,,, 00010 ++= ( ) ( ) ( )

MPa1103.431043.21001.221085.18 6666 −−−− ×=×+×+×=

]TahrN_ 2>3³ edayeRbIm:UEDl GL 2000 KNnakarrYmmaD nigGnuKmn_ creep sRmab;sMNakKMrUEdl[ enAkñúg]TahrN_ 2>1. dMeNaHRsay³ KNnakarrYmmaD ( ) ( ) ( )tht shus ββεε = KNna shuε edaysIum:gt¾RbePT III 15.1=K

( ) ( )( ) mmmmf

Kcm

shu /102.843102.45

3015.19001030900 662/1

62/1

28

−−− ×=×⎟⎠⎞

⎜⎝⎛=×⎟⎟

⎠

⎞⎜⎜⎝

⎛=ε

KNna ( )hβ ³ ( ) 627.0

1007518.11

10018.11

44

=⎟⎠⎞

⎜⎝⎛−=⎟

⎠⎞

⎜⎝⎛−=

Hhβ

KNna ( )tβ ³

( )( ) ( )

367.03812.0835

835/12.0

2/1

2

2/1

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛+−−

=⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

=SVtt

tttc

cβ

( ) ( ) ( ) ( )( )( ) mmmmtht shus /10194367.0627.0102.843 66 −− ×=×== ββεε KNna creep ( ) ( )

28

00

,1,0 cmcmt E

ttE

ttJ φ+=

KNna0cmtE nig 28cmE

280 =t éf¶ 280 cmcmt EE =⇒ MPafE cmcm 3.324092.454300350043003500 2828 =+=+= KNna ( )0,ttφ 8280 =>= ctt éf¶

( )( ) ( )

824.03812.0828

8281/12.0

1

5.05.0

2

5.05.0

20

0 =⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−−

−=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

−=ΦSVtt

tttc

cc

75.0100/75100/ === Hh



( ) ( ) ( )( )

( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

+−−

−+⎟⎟⎠

⎞⎜⎜⎝

⎛+−

−⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

+−−

Φ=5.0

20

025.0

0

0

5.0

03.0

0

3.00

0 /12.0086.115.2

77

142,

SVtttth

tttt

tttttttt cφ

( )( )

( )( )( ) ⎥

⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+−−

−+⎟⎠⎞

⎜⎝⎛

+−−

⎟⎠⎞

⎜⎝⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

+−−

=5.0

22

5.05.0

3.0

3.0

3812.02835283575.0086.115.2

728352835

287

14283528352824.0

773.0= ( ) ( )

MPaEtt

EttJ

cmcmt

1107.543.32409

773.03.32409

1,1, 6

28

00

0

−×=+=+=φ

]TahrN_ 2>4³ edayeRbIm:UEDl CEB 90 KNnabERmbRmYlragedaykarrYmmaD nigGnuKmn_ creep sRmab; sMNakKMrUEdl[enAkñúg]TahrN_ 2>1. dMeNaHRsay³ KNnakarrYmmaD ( ) ( )cscscs tttt ,,

0βεε =

KNna 0csε

8=scβ ( ) ( ) 628

28 1010

910160 −×⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+= cm

sccmsff βε

( ) mmmm /104.5181010

2.459810160 66 −− ×=×⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+=

sRmab; %75=H arhRH ββ 55.1−= ( ) ( ) 578.0100/751100/1 33 =−=−= Harhβ 896.0578.055.155.1 −=×−=−= arhRH ββ ( )( ) ( )( ) mmmmf RHcmscs /102.464896.0104.518 66

280

−− ×−=−×== βεε KNna ( )csc tt −β mm

uAh c

e 762==

( ) ( )( ) ( )

( )( ) ( )

343.08354/7656.0

8354/56.0 22 =

−+−

=−+

−=−

ce

ccsc tth

ttttβ

( ) ( ) ( ) ( )( ) mmmmtttt cscscs /103.159343.0102.464, 660

−− ×−=×−=−= βεε KNna creep ( ) ( )

28

00

,1,0 cmcmt E

ttE

ttJ φ+=



KNna0cmtE nig 28cmE

280 =t éf¶ 280 cmcmt EE =⇒ MPafE cm

cm 3554810

45.22150010

21500 33 2828 ===

KNna ( )0,ttφ 586.1

4/7616.0100/7511

4/16.0100/11

33=

−+=

−+=

eRH h

Hφ

( ) 49.210/2.45

3.510/

3.5

2828 ===

cmcm f

fβ

( ) 488.0281.0

11.0

12.02.0

00 =

+=

+=

ttβ

( ) ( ) ( )( )( ) 927.1488.049.2586.10280 === tfcmRH ββφφ ( )[ ] ( ) ( )[ ] 150037925075012.01765.1250012.015.1 1818 ≤=+×+=++= HheHβ éf¶

( ) 3.02835379

2835,3.03.0

0

00 =⎟

⎠⎞

⎜⎝⎛

−+−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

tttttt

Hc β

β

( ) ( ) 578.03.0927.1,, 000 =×== tttt cβφφ ( ) ( )

MPaEtt

EttJ

cmcmt

1104.4435548

578.035548

1,1, 6

28

00

0

−×=+=+=φ

]TahrN_ 2>5³ edayeRbIm:UEDl CEB 90 fμ I cUrKNnabERmbRmYlragedaykarrYmmaD nigGnuKmn_ creep

sRmab;sMNakKMrUEdl[enAkñúg]TahrN_ 2>1. dMeNaHRsay³ KNnakarrYmmaD ( ) ( ) ( )cdsascs ttttt ,, εεε += KNna ( )tasε 600=asα sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn

( ) 65.2

28

2828 10

10/610/

0

−×⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=cm

cmascmas f

ff αε

mmmm /106.721010/2.456

10/2.45600 665.2

−− ×−=×⎟⎠⎞

⎜⎝⎛

+−=

( ) ( ) ( ) 694.0115.05.0 352.02.0 =−=−= −− eet t

asβ ( ) ( ) ( ) ( )( ) mmmmtft ascmasas /104.50694.0106.72 66

280

−− ×−=×−== βεε



KNna ( )cds tt,ε 61 =dsα sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn

12.02 =dsα sRmab;sIum:gt¾ersIusþg;x<s;kkrwgelOn ( ) ( )[ ] 610/

128 10110220 280

0

−− ×+= cmds fdscmds ef ααε

( ) ( )[ ] mmmme /106.511106110220 6610/2.4512.0 −−− ×=××+= 0.197.0

2.453535 1.01.0

281 ≤=⎟

⎠⎞

⎜⎝⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=

cms f

β sRmab; ( ) %5.9697.0%99%75%40 =<=< H

896.010075155.1

100155.1

33

−=⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−−=

HRHβ

( ) ( )( ) ( )

5.0

24/56.0 ⎟⎟⎠

⎞⎜⎜⎝

⎛

−+−

=−ce

ccds tth

ttttβ

( )( ) ( )

343.08354/7656.0

8355.0

2 =⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

( ) ( ) ( ) ( )cdsRHcmdscds ttHftt −= ββεε 280,

( )( )( ) mmmm /102.157343.0896.0106.511 66 −− ×−=−×= ( ) ( ) ( ) ( ) ( ) mmmmttttt cdsascs /106.207102.157104.50,, 666 −−− ×−=×−+×−=+= εεε

KNna creep ( ) ( )

28

,1,0 cm

c

cmtc E

ttE

ttJ φ+=

KNna0cmtE nig 28cmE

280 =t éf¶ 280 cmcmt EE =⇒ MPafE cm

cm 3554810

2.452150010

21500 33 2828 ===

KNna ( )0,ttφ

836.02.45

3535 7.07.0

281 =⎥⎦

⎤⎢⎣⎡=⎥

⎦

⎤⎢⎣

⎡=

cmfα

950.02.45

3535 2.02.0

282 =⎥⎦

⎤⎢⎣⎡=⎥

⎦

⎤⎢⎣

⎡=

cmfα

415.1950.0836.04/7616.0

100/75114/16.0

100/113213

=⎥⎦⎤

⎢⎣⎡ −+=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+= ααφ

eRH h

H

( ) 49.210/2.45

3.510/

3.5

2828 ===

cmcm f

fβ



5.05.32128298.21

29

2.12.1,0

,00 ≥=⎥⎦⎤

⎢⎣⎡ +

+=⎥

⎦

⎤⎢⎣

⎡+

+=

α

TT t

tt éf¶

( ) 475.05.321.0

11.0

12.02.0

00 =

+=

+=

ttβ

( ) ( ) 674.1475.049.2419.10280 =××== tfcmRH ββφφ 880.0

2.453535 5.05.0

283 =⎥⎦

⎤⎢⎣⎡=⎥

⎦

⎤⎢⎣

⎡=

cmfα

( )[ ] 318 250012.015.1 αβ ++= HheH

( )[ ] 132088.0150035188.025075012.01765.1 18 =×≤=×+×+××= ( ) 307.0

28353512835,

3.03.0

0

00 =⎟

⎠⎞

⎜⎝⎛

−+−

=⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−=

tttttt

Hc β

β

( ) ( ) 515.0307.0678.1,, 000 =×== tttt cβφφ ( ) ( )

MPaEtt

EttJ

cmcmt

1106.4235548

515.035548

1,1, 6

28

00

0

−×=+=+=φ

2>12> m:as;maDebtug m:as;maDrbs;ebtugFm μtakkrwgEdleRbIR)as;sRmab;GKar nigrcnasm½<n§epSg²eTotGaRs½yeTA elIkarlay TMhM nigcMNat;fñak;f μbMEbk pleFobTwkelIsIum:gt¾ nigersIusþg;rbs;ebtug. xageRkamCam:as;maD ebtugEdleKGacykmkBicarNa³

- m:as;maDebtugsuT§EdleRbIf μbMEbkTMhM mm20 ERbRbYlcenøaHBI 3/24002320 mkg→ . sRmab; ebtugEdlmanersIusþg;ticCag MPacmkg 28/280 2 = témø 3/2320 mkg GacRtUv)anykmkeRbI. sRmab; ebtugEdlmanersIusþg;FMCagenH m:as;maDebtugmantémø 3/2400 mkg GacRtUv)anykmkeRbI.

- m:as;maDebtugsuT§EdleRbIf μbMEbkTMhM mmmm 150100 → ERbRbYlcenøaHBI 3/25602400 mkg→ . témømFümes μ Inwg 3/2480 mkg GacRtUv)anykmkeRbI.

- m:as;maDebtugGarem: EdlmanPaKryEdk %5.1%7.0 → mantémøRbEhl 3/2400 mkg . sRmab; ebtugGarem:EdlmanPaKryEdleRcInCagenH m:as;maDrbs;ebtugRtUv)aneKsnμt;RbEhl 3/2500 mkg .

- m:as;maDebtugRsalERbRbYlBI 3/1440320 mkg→ - m:as;maDebtugF¶n;ERbRbYlBI 3/43003200 mkg→



2>13> RbePTEdkeRbIkñúgebtug EdkEdleRbIenAkñúgebtug manCaeRcInRbePTEdlRtUv)ancat;cMNat;fñak;dUcxageRkam³

- EdkmUl (round bars)³ EdkmUlRtUv)aneRbIy:agTUlMTUlayenAkñúgebtug. Ggát;p©itrbs;EdkmUlEdl eKGacrk)anenAelITIpSarmancab;BI mm6 dl; mm36 bUkrYmCamYynwgGgát;p©itBiessBIrRbePTeTot KW mm45 nig mm57 . GaRs½yedayépÞxagrbs;va eKEbgEckvaCaBIrRbePTeTotKW Edkrelag (plain bars) nigEdkfñaMgGMeBA (deformed bars). CaTUeTA EdkrelagRtUv)aneKeRbICaEdkEdlman tYnaTITI2 (secondary reinforcement) b¤CaEdkkg (stirrups and ties). EdkfñaMgGMeBARtUv)aneK pliteLIgCaBiessedIm,IbegáInPaBs¥itrvagebtug nigsrésEdk ehIykat;bnßynUvTTwgsñameRbHrbs; ebtugkñúgtMbn;rgkmøaMgTaj. Ggát;p©itrbs;Edkrelag Gacvas;)anedayRsYl EtsRmab;EdkfñaMgGMeBA Ggát;p©itrbs;vaeKkMNt; edayykGgát;p©itrbs;rgVg;Edk Edl)anBImuxkat;rbs;va. épÞxageRkArbs;EdkfñaMgGMeBAmansNæan CaeRcInRbePTEdlmanbgðajkñúgrUbxageRkam.

- EdksMNaj; (Welded fabrics and mats)³ EdksMNaj;manCaeRcInes‘rIeTAtamRbEvgEdkTTwg nig EdkbeNþay. CaTUeTAvaRtUv)aneKpSaredaydak;EdkbeNþay nigEdkTTwg[EkgKñaRtg;kEnøgkat; Kña.

- kabeRbkugRtaMg (Prestressed concrete wires and strands)³ kabeRbkugRtaMgCaRbePTEdkBiess EdlmanersIusþg;x<s;. kabEdlersIusþg;rgkmøaMgTajx<s;manGgát;p©itCaTUeTA mm5 nig mm7 RtUv )aneKykmkbegáItCakabeRbkugRtaMg EdlmankabxageRkAR)aMmYyB½T§CMuvij kabmYyEdlmanGgát; p©itFMCag. ersIusþg;rbs;kabeRbkugRtaMgGtibrmamantémø MPa1750 b¤ MPa1890 . m:UDuleGLasÞicrbs;srésEdk eTaHrgkarTajkþI rgkarsgát;kþI eKkMNt;yk MPaEs

5102×= . em KuNlUtkemþArbs;srésEdkeKyk cmm o/10 5−=α dUcemKuNlUtkemþArbs;ebtugEdr.



muxkat;Edk )(mm épÞmuxkat;Edk )( 2cm Tm¶n; )/( mkg brimaRt )(cm RB6 0.28 0.222 1.89 RB8 0.64 0.499 2.83

DB12 1.13 0.888 3.77 DB16 2.01 1.58 5.03 DB20 2.84 2.23 5.97 DB25 4.91 3.85 7.86 DB28 6.16 4.83 8.80 DB32 8.04 6.31 10.06


T.Chhay 44 Flexural Analysis of Reinforced Concrete

III. viPaKFñwmebtugGarem:rgkarBt;begáag Flexural Analysis of Reinforced Concrete Beam

3>1> karsnμt; (Assumption)

ebtugGarem:CasmÖar³minEmnrUbFatusac;mYy BIeRBaHvaekIteLIgedaysmÖar³BIrRbePTKW ebtug nig Edk. dUecñH eRKOgbgÁúMebtugGarem:EdlkMNt;edayersIusþg;cugeRkay RtUvkMNt;tamkarsn μt;xageRkam³

- bERmbRmYlrageFobrbs;ebtug nigEdkRtUvEtmantémødUcKña mann½yfaPaBs¥itrvagebtug nigEdk mantémøRKb;RKan;.

- bERmbRmYlrageFobrbs;ebtugRtUvEt smamaRteTAnwgcm¶ayBIG½kSNWt - m:UDuleGLasÞicrbs;Edk RtUvEtyk MPaEs

5102×= . kugRtaMgrbs;EdkkñúgtMbn;eGLasÞicRtUvEt mantémøesμ IplKuNrvagbERmbRmYlrageFobCamYynwgm:UDuleGLasÞic.

- muxkat;Rtg;enAEtRtg;eRkayeBlrgkarBt; - ersIusþg;Tajrbs;ebtugRtUv)anecal BIeRBaHersIusþg;TajebtugmantémøtUcCagersIusþg;sgát;dl;eTA

10dg ehIysñameRbHrbs;ebtugRtUvsnμt;faK μan\T§iBl nigmü:ageTotmuneBleRbH muxkat;ebtugTaMgmUlman RbsiT§PaBkñúgkarTb;nwgm:Um:g;xageRkA.

- bERmbRmYlrageFobGtibrmarbs;ebtugkRmitRtwm 003.0 - rUbragénkarBRgaykugRtaMgsgát;rbs;ebtug sn μt;manragctuekaNEkg

3>2> RbePTénkar)ak;edaykarBt; nigEdnkMNt;sac;lUteFob

3>2>1> kar)ak;edaykarBt; eRKOgbgÁúMrgkarBt; Gac)ak;edaybIkrNIGaRs½yeTAnwgPaKryEdkEdl)andak;enAkñúgmuxkat;ebtug³

- EdkGaceTAdl;cMNuc yield munebtugeFVIkardl;ersIusþg;Gtibrma. kñúgkrNIenH kar)ak;bNþalmkBI sac;lUteFobrbs;EdkmantémøFMCag b¤es μ I 005.0 . muxkat;manbrimaNEdktic ehIyRtUv)aneK[eQμaH fa tension-controlled section .

- EdkGaceTAdl;cMNuc yield GMLúgeBlEdlebtugeFVIkardl;ersIusþg;GtibrmaEdr. muxkat;RtUv)aneK [eQ μaHfa balanced section .

- ebtugGacEbkmuneBlEdlEdkeFVIkardl;cMNuc yield bNþalmkBIPaKryEdkeRcInenAkñúgmuxkat;. kñúgkrNIenHebtug)aneFVIkardl;ersIusþg;Gtibrma ehIymansac;lUteFobGtibrma 003.0 Edr b:uEnþkugRtaMg


viPaKebtugGarem:rgkarBt;begáag 45 T.Chhay

rbs; EdkmantémøticCagersIusþg;KNna Edl ys ff < . sac;lUteFobrbs;EdkmantémøtUcCag b¤esμ I 002.0 . muxkat; enHRtUv)aneK[eQ μaHfa compression-controlled section.

eK)ansnμt;faebtugEbkedaysarkmøaMgsgát; enAeBlEdlbERmbRmYlrageFobrbs;ebtugmantémø 003.0 EtkñúgkarBiesaFtémøenHERbRbYlBI 004.00025.0 → .

kñúgkarKNnaFñwm eKeRCIserIsyk tension-controlled section eday[EdkeFVIkardl;ersIusþg; KNna (design strength) munebtugEbk. sñameRbHrbs;ebtugrIkFMeLIg² EdlCasBaØaRbkasGasnñmuneBl ebtugEbk ehIyrcnasm<½n§)ak;Ebk. kñúgkarKNnaFñwmEdleRCIserIsyk compression-controlled section nig balanced section ebtugEbkPøam² rcnasm<½n§)ak;EbkmYyrMBicedayK μankarRbkasGasnñ. kareRCIserIsmuxkat;EbbenHRtUv )aneCosvag.

3>2>2> EdnkMNt;bERmbRmYleFobsRmab; tension-controlled section nig compression-controlled section

karKNnapþl;[cMeBaHkarKNnaebtugGarem:sRmab; tension-controlled section b¤ compression

controlled section. muxkat;TaMgBIr RtUv)ankMNt;edaybERmbRmYlrageFobrgkarTajsuT§ (net tension

strain (NTS)). elIsBIenHlkçxNÐBIreTot)anekItKW balanced strain condition nig transition region

condition. lkçxNÐTaMgbYnenHRtUv)ankMNt;dUcxageRkam³ - Compression-controlled section Camuxkat;EdlbERmbRmYlrageFobrgkarTajsuT§ (NTS)

sRmab;EdkrgkarTajEpñkxageRkAbMputmantémøtUcCagbERmbRmYlrageFobrgkarsgát; enAeBlEdlbERm bRmYlrageFobrbs;ebtugrgkarsgát;mantémøes μ I 003.0 . krNIenHekIteLIgCaTUeTAcMeBaHssrEdlrgbnÞúk tamG½kS nigm:Um:g;.

- Tension-controlled section Camuxkat;EdlbERmbRmYlrageFobrgkarTajsuT§ (NTS) sRmab; EdkrgkarTaj EpñkxageRkAbMputmantémøFMCag b¤esμ I 005.0 kñúgkrNIEdlebtugmanbERmbRmYlrageFob dl;EdnkMNt; 003.0 .

- muxkat;EdlbERmbRmYlrageFobrgkarTajsuT§ (NTS) sRmab;EdkrgkarTajEpñkxageRkAbMput mantémøsßitenAcenøaH compression-controlled section nig tension-controlled section KWenAcenøaH

005.0002.0 → Camuxkat; transition region



- Balanced strain condition ekItmanenAkñúgmuxkat; enAeBlEdlbERmbRmYlrageFobEdktMbn;Taj mantémøesμ I

s

ys E

f=ε kñúgxN³Edlebtugrgkarsgát;manbERmbRmYlrageFobmantémøes μ I 003.0 .

Section condition Concrete strain Steel strain Note ( )400MPaf y = Compression-controlled 0.003 syt Ef≤ε 002.0≤tε Tension-controlled 0.003 005.0≥tε 005.0≥tε Transition region 0.003 005.0≤≤ tsy Ef ε 005.0002.0 ≤≤ tε Balanced strain 0.003 sys Ef=ε 002.0=sε Transition region 0.003 005.0004.0 <≤ tε 005.0004.0 <≤ tε



3>3> emKuNbnÞúk bnÞúkEdlmanGMeBIelIeRKOgbgÁúMRtUv)anKuNCamYynwgemKuNbnÞúk edIm,IkarBarkar)ak;Pøam² nigpþl; nUvkarKNnamYyEdlmanlkçN³esdækic©. emKuNbnÞúkGaRs½ynwgRbePTbnÞúk nigkarbnSMbnÞúk. emKuNbnÞúk sRmab;bnÞúkGefr KW 6.1 ÉemKuNbnÞúksRmab;bnÞúkefr KW 2.1 . dUecñHkarbnSMbnÞúksRmab;bnÞúkGefr nigbnÞúk efrKW LDU 6.12.1 += Edl U - bnÞúkKNna (ultimate load) L - bnÞúkGefr D - bnÞúkefr



3>4> emKuNkat;bnßyersIusþg; emKuNkat;bnßyersIusþg; φ mantémøtUcCag 1. emKuNkat;bnßyersIusþg;GaRs½ynwgRbePTén eRKOgbgÁúM³

- sRmab;muxkat;rgkarTaj 90.0=φ - sRmab;muxkat;rgkarsgát; k> CamYyEdkkgvNÐ 70.0=φ x> CamYyEdkkgdac;² 65.0=φ - sRmab;ebtugsuT§ 55.0=φ - sRmab;kmøaMgkat; nigkmøaMgrmYl 75.0=φ - sRmab;RTnab;enAelIebtug 65.0=φ - sRmab;KMrU strut and tie 75.0=φ

3>5> karEbgEckkugRtaMgsgát;smmUl kugRtaMgEbgEckkñúgebtugrgkarsgát;enAxN³eBl)ak;RtUv)ansnμt;famanragctuekaNEkg ctu- ekaNBñay ExSekag)a:ra:bUl b¤ragNamYyepSgeTotGaRs½yedaykaryl;RBmKñaenAeBleFVIBiesaFn_.

enAeBlEdlFñwmerobnwg)ak; srésEdk)aneFVIkardl;cMNuc yield mun RbsinebImuxkat;enaHman brimaNEdktic (under-reinforced section) ehIykñúgkrNIenHsrésEdkeFVIkardl;kugRtaMgKNna (design

stress). EtRbsinebImuxkat;manEdkeRcIn enaHebtugnwgEbkmun ehIybERmbRmYlrageFobRtUv)ansnμt;faes μ I 003.0 .

kmøaMgsgát; C ekItmanenAkñúgtMbn;sgát; ehIykmøaMgTaj T ekItmanenAtMbn;TajEdlsßitenARtg;nIv:U Edk. eKsÁal;TItaMgénkmøaMg T BIeRBaHvamanGMeBIRtYtsIuKñanwgG½kSTIRbCMuTm¶n;rbs;Edk. ÉTItaMgrbs;kmøaMg C eKGacsÁal;)an luHNaEteKsÁal;maDéntMbn;sgát; ehIyeBlenaHeKGackMNt;)annUvTItaMgTIRbCMuTm¶n; )an. RbsinebIeKsÁal;TItaMgrbs;kmøaMgTaMgBIr enaHeKGackMNt;nUvRbEvgédXñas; EdlCacm¶ayBIkmøaMgTaj mkkmøaMgsgát;.

RbsinebIebtugEbk enAeBlbERmbRmYlrageFob 003.0' =cε ehIyRbsinebIEdkeFVIkardl;cMNuc yield ¬ ys ff = ¦ enaHmuxkat;Ca balanced section. kmøaMgsgát; C RtUv)ansMEdgedaymaDénbøúkkugRtaMg EdlmanragminÉksNæanekItmanelIépÞctuekaNqñÚt bc .



maDénkugRtaMgsgát;snμt;es μ I )'( 1 cfbcC α= Edl cf '1α CakugRtaMgmFüménbøúkkugRtaMgminÉksNæan TItaMgrbs;kmøaMgsgát; KWmancm¶ay z BIsrésEpñkxagelIbMputEdlGaccat;TukCaEpñkéncm¶ay c

¬cm¶ayBIsrésEpñkxagelImkG½kSNWt¦. cz 2α= 72.01 =α sRmab;ebtugEdlmanersIusþg; MPaf c 28' ≤ .

1α RtUv)ankat;bnßyeday 04.0 ral; MPa7 sRmab;ebtugEdlmanersIusþg; MPaf c 28' > . 425.02 =α sRmab;ebtugEdlmanersIusþg; MPaf c 28' ≤ .

2α RtUv)ankat;bnßyeday 025.0 ral; MPa7 sRmab;ebtugEdlmanersIusþg; MPaf c 28' > . edIm,IsRmYldl;karKNnakmøaMgkñúgénmuxkat; enaH ACI code )anyknUvkugRtaMgEbgEckkñúgmuxkat;

ragctuekaNEkgEdlmantémø cf '85.0 BRgayes μ IelItMbn;sgát;smmUl EdlxNÐedaybnÞat;RsbnwgG½kSNWt EdlmanRbEvg ca 1β= .

85.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 28' ≤ . )

728'(05.085.01−

−= cfβ sRmab;ebtugEdlmanersIusþg; MPafMPa c 56'28 ≤< . 65.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 56' > .

sRmab;muxkat;ragctuekaNEkg RkLaépÞtMbn;sgát;mantémøesμ I ba ehIytémøkugRtaMgBRgayesIμKW cf '85.0 Edlpþl;nUvmaDkugRtaMgsrubesμ Inwg abf c'85.0 ehIyRtUvKñanwgkmøaMgsgát; C . sRmab;muxkat;

epSgBIragctuekaNEkg kmøaMgsrubesμInwgplKuNRkLaépÞtMbn;sgát;CamYynwg cf '85.0 .



3>6> srésEdkrgkmøaMgTajénmuxkat;ctuekaNEkgrgkarBt; PaKryEdkenAkñúgmuxkat;ebtugkñúglkçxNÐ balanced RtUv)aneK[eQμaHfa balanced steel ratio bρ

EdlCapleFobrvagmuxkat;Edk sA nigmuxkat;RbsiT§PaB bd

bdAs

b =ρ Edl b - TTwgmuxkat;eRKOgbgÁúMtMbn;sgát;

d - cm¶ayBIsrésEpñkxageRkAbMputmkTIRbCMuTm¶n;EdkrgkmøaMgTaj ¬km<s;RbsiT§PaB¦ smIkarlMnwgBIr EdlCaeKalkarN_kñúgkarviPaK nigKNnaeRKOgbgÁúMehIymantémøRKb;muxkat; nigRKb;

RbePTbnÞúkKW³ - kmøaMgsgát;RtUvmantémøes μIkmøaMgTaj TC = - ersIusþg;m:Um:g;Bt;xagkñúg nM esμ IeTAnwgplKuNrvagkmøaMgsgát; b¤kmøaMgTajCamYynwgédXñas;

)()( zdTzdCM n −=−= nig nu MM φ= Edl φ emKuNkat;bnßyersIusþg;



kareRbIR)as;nUvsmIkarTaMgenHRtUv)anBnül;sRmab;muxkat;ragctuekaNEkgCamYyEdktMbn;Taj. mux kat;GacCa balanced section muxkat;EdlmanEdktic muxkat;EdlmanEdkeRcIn GaRs½yedaykareRbIR)as;nUv PaKryEdk.

3>6>1> balanced section

CMhanTI1³ BIdüaRkambERmbRmYlrageFob eyIg)an

s

yb

b

Efcd

c 003.0=

−

s

y

b

Efd

c

+=⇒

003.0

003.0

edayCMnYs MPaEs 200000= d

fc

yb )

600600(+

=⇒

CMhanTI2³ BIsmIkarlMnwg eyIg)an TC = ysc fAabf =⇒ '85.0

bffA

ac

ys

'85.0=⇒

Edl a - CaRbEvgbøúkrgkarsgát; mantémøes μ Inwg bc1β edaysarvaCa balanced section dUecñHPaKryEdkRtUv)aneRbIKW

bdAs

b =ρ bdA bs ρ=⇒



CMnYs sA eTAkñúgsmIkarxagelI ybc bdfabf ρ=⇒ '85.0

)('85.0'85.01 b

y

c

y

cb c

dff

dfaf βρ ==⇒

CMnYstémø df

cy

b )600

600(+

= eTAkñúgsmIkarxagelI eyIg)an

)600

600('85.0 1yy

cb ff

f+

= βρ

CMhanTI3³ BIsmIkarlMnwgénm:Um:g;xagkñúg eyIg)an )()( zdTzdCM n −=−=

sRmab;muxkat;ragctuekaNEkg cm¶ay 2az =

)2

()2

( adTadCM n −=−=⇒ sRmab;muxkat; balanced section b¤muxkat;EdlmanbrimaNEdktic

ys fAT = dUecñH )

2( adfAM ysn −=

m:Um:g;kñúgxagelIEdl)anKNna RtUvkat;bnßyedayemKuN φ )

'7.1(

bffA

dfAMc

ysysn −=⇒ φφ

smIkarenH sresredayCab;GBaØat ρ )

'7.11()

'7.1( 2

c

yy

c

yyn f

fbdf

bfbdf

dbdfMρ

ρφρ

ρφφ −=−=⇒ eyIgGacsresrsmIkarxagelIenHCa

2bdRM un =φ Edl )

'7.11(

c

yyu f

ffR

ρρφ −=

pleFobrvagRbEvgbøúkkugRtaMgsgát;smmUl a nig km<s;RbsiT§PaBénmuxkat; d

c

y

ff

da

'85.0ρ

=

3>6>2> PaKryEdkGtibrma PaKryEdkGtibrma maxρ EdlGaceRbIenAkñúgmuxkat;ebtugEdlmanEtEdkrgkmøaMgTaj QrelIeKal

karN_bERmbRmYlrageFobsuT§enAkñúgEdkrgkmøaMgTaj PaKryEdk balanced nigersIusþg;rbs;Edk.



TMnak;TMngrvagPaKryEdkenAkúñgmuxkat; ρ nigbERmbRmYlrageFobsuT§ tε

t

s

y

b

Ef

ερρ

+

+=

003.0

003.0 b¤ 003.0)

003.0( −

+=

b

s

y

tEf

ρρε

sRmab; MPaf y 414= nigsnμt; 00207.0/ =sy Ef

- sRmab;muxkat;rgkmøaMgTaj 005.0≥⇒ tε snμt; 005.0=tε ¬b¤ 375.0≤

tdc ¦

td - cm¶ayBIsrésEpñkxageRkAbMputeTAG½kSEdkTajCYrTI1

008.000507.0

=bρρ

kñúgkrNIEdl maxρρ = bρρ 63375.0max =⇒

PaKryEdkenHeFVI[FñwmmanlkçN³yWtRKb;RKan;munnwg)ak; Casegçb³ sRmab; by MPaf ρρ 5474.0276 max =⇒=

by MPaf ρρ 5905.0345 max =⇒= by MPaf ρρ 6983.0517 max =⇒=

sRmab;muxkat;rgkmøaMgTaj 9.0=φ - sRmab;muxkat;enAkñúgtMbn; transition region snμt; 004.0=tε ¬minRtUvtUcCag 004.0 ¦ b¤ 375.06.0 >>

dc



007.000507.0

=bρρ

kñúgkrNIEdl tmaxρρ = bt ρρ 724.0max =⇒

sRmab;muxkat;enAkñúgtMbn; transition region 9.0<φ )

3250)(002.0(65.0 −+=⇒ tεφ

]TahrN_1³ sRmab;muxkat;dUcbgðajkñúgrUb k> kMNt;muxkat;Edk balanced section x> muxkat;EdkGtibrmaEdlGnuBaØateday ACI Code sRmab; tension-controlled section nigsRmab;muxkat; enAkñúgtMbn; transition region K> TItaMgG½kSNWt nigRbEvgbøúkkugRtaMgsgát;sRmab;muxkat;rgkmøaMgTaj smμtikm μ³ MPaf c 28' = nig MPaf y 400=

dMeNaHRsay³ k> kMNt;muxkat;Edk balanced section

)600

600('85.0 1yy

cb ff

f+

= βρ

eday MPaf c 28' = MPaf y 400= nig 85.01 =β 030345.0)

400600600(

4002885.0 2 =

+=⇒ bρ

muxkat;EdkEdldak;kñúgmuxkat;ebtugedIm,I)anlkçxNÐ balanced KW



2897.786540030345.0 cmbdA bsb =××== ρ x> muxkat;EdkGtibrmasRmab; tension controlled section

bt

s

y

Ef

ρε

ρ )003.0

003.0(max +

+=

sRmab; 005.0=tε 019.0030345.0625.0625.0

008.0005.0

max =×===⇒ bb ρρρ 2

maxmax 4.496540019.0 cmbdA bs =××==⇒ ρ sRmab; 9.0=φ muxkat;EdkGtibrmasRmab;muxkat;kñúgtMbn; transition region

bt

s

y

Ef

ρε

ρ )003.0

003.0(max +

+=

sRmab; 004.0=tε 0217.0030345.0714.0714.0

007.0005.0


maxmax 42.5665400217.0 cmbdA bs =××==⇒ ρ sRmab; 817.0=φ K> TItaMgG½kSNWt nigRbEvgbøúkkugRtaMgsgát;sRmab; tension-controlled section

cmbf

fAa

c

ys 76.20402885.0

4004.49'85.0

maxmax =

×××

==

cm¶ayBIsrésEpñkxagelImkG½kSNWtKW cmac 42.24

85.076.20

1

===β

]TahrN_2³ kMNt;ersIusþg;m:Um:g;KNna nigTItaMgG½kSNWténmuxkat;ctuekaNEkgdUcbgðajkñúgrUbxageRkam. RbsinebIeKeRbIEdk 303DB ersIusþg;ebtug MPaf c 20' = nig MPaf y 400=



dMeNaHRsay³ muxkat;Edk 303DB 2195.21 cmAs =⇒ PaKryEdkeRbIR)as;kñúgebtug 0128.0

5530195.21

=×

==bdAsρ

PaKryEdk balanced kñúgebtug )600

600('85.0 1yy

cb ff

f+

= βρ 021675.0=

RbEvgbøúkkugRtaMgsgát; cmbf

fAa

c

ys 62.16302085.0

400195.21'85.0

=××

×==

TItaMgG½kSNWt cmac 55.1985.062.16

1

===β

bERmbRmYlrageFobEdksuT§ 003.0)003.0

( −+

=

b

s

y

tEf

ρρε 005.00055.0 >=

⇒ tension controlled section 9.0=⇒φ ersIusþg;m:Um:g;xagkñúgKNna

mkNadfAM ysn .25.35610)262.1655(400195.219.0)

2( 3 =×−×××=−= −φφ

]TahrN_3³ kMNt;ersIusþg;m:Um:g;KNna nigTItaMgG½kSNWténmuxkat;ctuekaNEkgdUcbgðajkñúgrUbxagelI. EteKeRbIEdk 323DB vij ersIusþg;ebtug MPaf c 20' = nig MPaf y 400= dMeNaHRsay³ muxkat;Edk 323DB 21152.24 cmAs =⇒ PaKryEdkeRbIR)as;kñúgebtug 0146.0

55301152.24

=×

==bdAsρ

PaKryEdk balanced kñúgebtug )600

600('85.0 1yy

cb ff

f+

= βρ 021675.0=

RbEvgbøúkkugRtaMgsgát; cmbf

fAa

c

ys 91.18302085.0

4001152.24'85.0

=×××

==


1

===β

bERmbRmYlrageFobEdksuT§ 003.0)003.0

( −+

=

b

s

y

tEf

ρρε 005.00044.0 <=

⇒muxkat;enAkñúgtMbn; transition region 85.0)3

250)(002.0(65.0 =−+=⇒ tεφ ersIusþg;m:Um:g;KNna mkNadfAM ysn .43.37310)

262.1655(4001152.2485.0)

2( 3 =×−×××=−= −φφ

sRmab;muxkat;rgkmøaMgTaj 005.0=tε



01355.0021675.0625.0625.0008.0005.0


maxmax 3575.22553001355.0 cmbdAs =××== ρ 21153.24 cm< RbEvgbøúkkugRtaMgsgát; cm

bffA

ac

ys 535.17302085.0

4003575.22'85.0

=×××

==

mkNadfAM ysn .11.37210)2535.1755(4003575.229.0)

2( 3 =×−×××=−=⇒ −φφ

eyIgeXIjfa témøénersIusþg;mantémøesÞIresμ IKña EdleKGacTTYlyk)an.

3>6>3> PaKryEdkGb,brma RbsinebIm:Um:g;Gnuvtþn_mkelIFñwmmantémøtUc ehIyTMhMénmuxkat;FMCagGVIEdlRtUvkarsRmab;Tb;Tl;nwg

m:Um:g; enaHkarKNnanwgbgðaj[eXIjmuxkat;EdktUc b¤k¾K μan. RbsinebImindak;srésEdk Fñwmrgm:Um:g;nwgrg kar)ak;Pøam². ACI Code kMNt;nUvmuxkat;EdkGb,brma minsA

dbf

dbff

A wy

wy

cs

4.14

'min ≥= nig

sRmab;krNIFñwmragGkSr T EdlsøabrgkmøaMgTaj enaHmuxkat;EdkRtUvyktémøtUcCageKrvagsmIkar xagelI nigxageRkam

dbff

A wy

cs 2

'min =

Edl bbw = sRmab;muxkat;ragctuekaNEkg wb CaTTwgsøab

3>7> muxkat;lμm muxkat;EdlmanlkçN³l μm RbsinebIersIusþg;m:Um:g;kñúgénmuxkat;FMCag b¤es μ Im:Um:g;xageRkA

un MM ≥φ . viFIsaRsþGacsegçbdUcxageRkam³ - KNnam:Um:g;xageRkAEdlGnuvtþmkelIeRKOgbgÁúM uM

LDu MMM 6.12.1 += - KNna nMφ sRmab;muxkat;EdlsrésEdkrgkmøaMgTaj

+ RtYtBinitüfa maxmin ρρρ << + kMNt;

bffA

ac

ys

'85.0= nigRtYtBinitü tε sRmab; φ

+ kMNt; )2

( adfAM ysn −=φφ



- RbsinebI un MM ≥φ enaHmuxkat;manlkçN³l μm

]TahrN_4³ eKmanFñwmTRmbgáb;mYyEdlmanRbEvg m5.2 . FñwmenHmanmuxkat;ragctuekaNEkgdUcbgðaj kñúgrUb. FñwmRTbnÞúkefr EdlrYmmanbnÞúkpÞal;xøÜnrbs;vasrub mkN /22 nigbnÞúkGefr mkN /13 . edayeRbI

MPaf c 28' = nig MPaf y 400= cUrepÞógpÞat;fa FñwmenHmansuvtßiPaBRKb;RKan;kñúgkarRTbnÞúkxagelI. dMeNaHRsay³

bnÞúkKNna mkNLDWu /2.47136.1222.16.12.1 =×+×=+=

m:Um:g;KNna mkNLWM uu .5.147

25.22.47

2

22

=== muxkat;Edk

23982.11 cmAs =



PaKryEdkenAkñúgmuxkat;ebtug 012256.0

5.46203982.11

=×

==bdAsρ

PaKryEdk balanced

030345.0)600

600('85.0 1 =+

=yy

cb ff

fβρ

RbEvgbøúkkugRtaMgsgát; cm

bffA

ac

ys 578.9202885.0

4003982.11'85.0

=×××

==

TItaMgG½kSNWt cmac 268.11

85.0578.9

1

===β

bERmbRmYlrageFobEdksuT§

005.000938.0003.0)003.0

( >=−+

=

b

s

y

tEf

ρρε ⇒ tension-controlled section 9.0=φ

ersIusþg;m:Um:g;xagkñúgKNna mkNadfAM ysn .155.17110)

2578.95.46(4003982.119.0)

2( 3 =×−×××=−= −φφ

un MM >φ muxkat;manlkçN³RKb;RKan; ]TahrN_5³ eKmanFñwmmuxkat;mYymanRbEvg m6 . FñwmenHmanmuxkat;dUcbgðajkñúgrUb. edayeRbI

MPaf c 20' = nig MPaf y 400= kMNt;bnÞúkGefrrayes μ IGnuBaØat. FñwmenHminmanbnÞúkefrGVIeRkABITm¶n; xøÜnvaeT.



dMeNaHRsay³ Tm¶n;pÞal;rbs;Fñwm

mkNWD /78.324105.5230 4 =×××= − muxkat;Edk

271875.14 cmAs = RbEvgbøúkkugRtaMgsgát;

cmbf

fAa

c

ys 32.17202085.040071875.14

'85.0=

×××

==

PaKryEdkeRbIR)as;enAkñúgmuxkat;ebtug 009345.0

5.523071875.14

=×

==bdAsρ

PaKryEdk balanced kñúgebtug )

600600('85.0 1

yy

cb ff

f+

= βρ 021675.0=

bERmbRmYlrageFobEdksuT§

005.00086.0003.0)003.0

( >=−+

=

b

s

y

tEf

ρρε ⇒ tension-controlled section 9.0=φ


232.175.52(40071875.149.0)

2( 3 =×−×××=−= −φφ

eday[ nu MM φ= mü:ageTot LDu MMM 6.12.1 +=

LL WW 2.7412.20)6

8(6.1)

8678.3(2.13.232 2

2

+=×+×

= mkNWL /43.29

2.7412.203.232

=−

= ]TahrN_6³ RtYtBinitümuxkat;dUcbgðajkñúgrUbxageRkam edIm,ITb;Tl;nwg m:Um:g;KNna mkN.41 . edayeRbI MPaf c 20' = nig MPaf y 235= . dMeNaHRsay³

muxkat;Edk 23912.3 cmAs =

PaKryEdkeRbIR)as;enAkñúgmuxkat;ebtug



00377.0

45203912.3

=×

==bdAsρ

PaKryEdkGb,brmaeRbIR)as;enAkñúgmuxkat;ebtug 00596.0)00596.0,004756.0max()4.1,

4'

max(min ===yy

c

fff

ρ

minρρ <⇒ 258.65.522000596.0min =××=⇒ sA

dUecñHeKRtUveRbIEdk 22 258.663.7183 cmcmADB s >=⇒ RbEvgbøúkkugRtaMgsgát;

cmbf

fAa

c

ys 274.5202085.0

23563.7'85.0

=××

×==


2274.545(23563.79.0)

2( 3 =×−×××=−= −φφ

un MM >⇒φ dUecñH Edk 183DB RKb;RKan;edIm,ITb;Tl;nwgm:Um:g;KNnaxageRkA .

3>8> bNþúMénEdk enAeBlEdlkarKNnamuxkat;EdkRtUvkarsRmab;ebtugmanbrimaNeRcIn ]TahrN_enAeBlEdl maxρ

RtUv)aneRbI eBlenaHeKBi)akkñúgkarBRgayEdkeTAkñúgmuxkat;ebtug. ACI Code )anGnuBaØat[EdkbeNþayGacdak;CabNþúMEdl manTRmg;dUcbgðaykñúgrUb. bNþúMénEdk

cab;BIbYnGaceFVIeTA)anedaymanEdkkgB½T§CMuvij. kareFVIbNþúMEdkkgenHk¾GacRbRBwtþeTA)ansRmab;ssr.



bNþúMénEdk RtUv)ancat;TukCaEdkmYyedImsRmab; kMNt;KMlatEdk nigkRmas;karBarebtug. Ggát;p©it énEdkeTalRtUv)anbMEbkBIRkLaépÞsmmUlrbs;bNþúMEdk.

segçb³ karkMNt;EdkrgkmøaMgTajsRmab;muxkat;ctuekaNEkg 1> kMNt;PaKryEdkeRbIR)as;enAkñúgebtug

bdAs=ρ

2> kMNt;PaKryEdk balanced )600

600('85.0 1yy

cb ff

f+

= βρ nigPaKryEdkGtibrma

bs

y

Ef

ρρ )008.0

003.0(max

+= sRmab;muxkat;rgkmøaMgTaj. dUcKña kMNt;PaKryEdkGb,brma

)4.1,4

'max(min

yy

c

fff

=ρ

3> RbsinebI maxmin ρρρ << kMNt; bf

fAa

c

ys

'85.0= / c / tε nig 9.0=φ . RbsinebI minρρ <

PaKryEdkEdleRbIR)as;kñúgebtugminRKb;RKan; eTaHCay:agNaPaKryEdkEdleRbIR)as;kñúgebtug RtUvEt minρρ ≥ . RbsinebI maxρρ ≥ enaH 9.0<φ .

4> kMNt;ersIusþg;m:Um:g;xagkñúgKNna )2

( adfAM ysn −= φφ

3>9> muxkat;ctuekaNEkgCamYyEdkrgkmøaMgsgát; enAkñúgmuxkat;ebtug muxkat;EdkEdlTb;nwgm:Um:g;Bt; RtUv)ankMNt;ecjBIbnÞúkxageRkAEdlmanGMeBI elIeRKOgbgÁúM edayeFVIy:agNa[ersIusþg;m:Um:g;xagkñúgFMCag b¤esμ Inwgm:Um:g;xageRkA. b:uEnþenAeBlEdlmux kat;ebtug ¬TTwg nigkm<s;RbsiT§PaB¦ mantémøtUcenaH maxρ RtUv)aneRbI. RbsinebIm:Um:g;xageRkAFMCag ersIusþg;m:Um:g;xagkñúg enaHbrimaNEdksgát; nigEdkTajRtUv)anbEnßm.

Edksgát;RtUv)aneRbI enAeBlEdlmuxkat;ebtugRtUv)ankMNt;edaymUlehtusßabtükmμ. pl RbeyaCn_rbs;Edksgát;KW kat;bnßyPaBdabry³eBlyUr nigedIm,IgayRsYldak;Edkkg.

muxkat;EdkDubmanBIrkrNIEdleKRtUvBicarNa GaRs½yeTAnwgkareFVIrbs;Edkdl;cMNuc yield b¤Gt;.



3>9>1> enAeBlEdksgát;eFVIkardl;cMNuc yield

m:Um:g;xagkñúgGacRtUv)anEckecjCaBIr dUcbgðajkñúgrUb 1uM Cam:Um:g;EdlekItBIkmøaMgsgát;rbs;ebtug

nigkmøaMgTajsmmUlrbs;Edk 1sA sRmab;muxkat;eKal. 2uM Cam:Um:g;bEnßmEdlekItBIkmøaMgsgát;enAkñúg Edksgát; sA' nigkmøaMgTajenAkñúgEdkrgkmøaMgTajbEnßm 2sA .

m:Um:g; 1uM Cam:Um:g;Edl)anBImuxkat;sRmab;EdkrgkarTajeKal

cCT =1 abffA cys '85.01 =⇒

bffA

ac

ys

'85.01=⇒

)2

(11adfAM ysu −= φ

karkMNt; 1uM RtUv[ bdAs1

1 <ρ nigtUcCag b¤esμ I bs

y

Ef

ρρ )008.0

003.0(max

+= sRmab;[muxkat;

rgkarTajeKal. BicarNaelIm:Um:g; 2uM edaysnμt;fa muxkat;Edkrgkarsgát; sA' eFVIkardl;cMNuc yield



)'(22 ddfAM ysu −= φ )'('2 ddfAM ysu −= φ

'd - Cacm¶ayBIsrésEpñkxageRkAbMputeTAG½kSEdkrgkarsgát; kñúgkrNIenH ss AA '2 = begáItnUvkmøaMgesμ IKña EtTisedApÞúyKña m:Um:g;srub esμ InwgplbUkénm:Um:g; 1uM nig 2uM

)]'(')2

([ 121 ddfAadfAMMM ysysuun −+−=+= φφ muxkat;EdksrubEdleRbIsRmab;karTajCaplbUkénbrimaNEdk 1sA nig 2sA dUecñH sssss AAAAA '121 +=+=

sss AAA '1 −=⇒

bffAA

ac

yss

'85.0)'( −

=⇒

dUecñHeK)an )]'(')2

()'[( ddfAadfAAM ysyssn −+−−= φφ

nigeyIgman )008.0

003.0()'( max1

s

y

bEf

+=≤−= ρρρρρ ( )1

sRmab; MPaf y 414= enaH bρρρ 63375.0)'( ≤− / 9.0=φ nig 005.0=tε kar)ak;rbs;FñwmbNþalmkBIEdksrubrgkarTajeFVIkardl;cMNuc yield ehIykarEbkPøam²rbs;ebtugRtUv)an eCosvag.

RbsinebI max1 )'( ρρρρ >−= enHmuxkat;sßitenAtMbn; transition region Edl

)007.0

003.0()'( max,

s

y

btEf

+=≤− ρρρρ kñúgkrNIenH 9.0<φ sRmab; 1uM nig 9.0=φ sRmab; 2uM

enaH eK)an )'('9.0)]

2()'[( ddfAadfAAM ysyssn −+−−= φφ

cMNaMfa bdAA tss max,)'( ρ≤− enAkñúgtMbn;sgát; kmøaMgEdkrgkarsgát;KW )'85.0(' cyss ffAC −=

edayKitfaépÞebtugEdlCMnYsedayépÞEdk sA' enaH )'85.0(''85.0 cyscscys ffAabfCCfAT −+=+==

abfAffAfA cscysys '85.0''85.0' =+−⇒ eday ysc fAabf 1'85.0 =



ysscysys fAAffAfA 1''85.0' =+−⇒ EckGgÁTaMgBIrnwg ybdf

1)'85.01(' ρρρ =−−⇒y

c

ff Edl max

11 ρρ ≤=

bdAs

dUecñH )008.0

003.0()'85.01(' max

s

y

by

c Ef

ff

+=≤−− ρρρρ ( )2

PaKryEdkrgkarTajsrubGtibrma ρ EdleRbIenAkñúgmuxkat;ctuekaNEkg enAeBlEdlEdkrgkar sgát;eFVIkardl;cMNuc yield

)'( max ρρρ +=Max mann½yfa muxkat;EdkrgkarTajsrubeRbIenAkñúgmuxkat;ctuekaN enAeBlEdkrgkarsgát;eFVIkardl;

cMNuc yield )'( max ρρ += bdMaxAs edIm,I[dwgfa Edkrgkarsgát;eFVIkardl;cMNuc yield eyIgRtUvBinitübERmbRmYlrageFob eday[

s

yys E

f=≥ εε '

tamrUbxagelI eyIg)an

y

s

y fEfd

c−

=−

=600

600

003.0

003.0'

')600

600( df

cy−

=⇒

eyIgman abffA cys '85.01 = b:uEnþ sss AAA '1 −= nig '1 ρρρ −=



dUecñHeyIg)an abffAA cyss '85.0)'( =− abfbdf cy '85.0)'( =−⇒ ρρ ))('(85.0)'(

da

ff

y

c=−⇒ ρρ

eday ')600

600(11 df

cay−

== ββ

dUecñH Kfd

dff

yy

c =−

=− )600

600)(')('(85.0)'( 1βρρ

RbsinebI K≥− )'( ρρ enaHEdkrgkarsgát;eFVIkardl;cMNuc yield. eyIgeXIjfa enAeBlEdlbrimaNEdkrgkarTajeKal 1sA ekIneLIg enaH 1T nig 1C k¾mantémøkan;

EtFMEdr ehIyG½kSNWtnwgFøak;cuH eBlenaHbERmbRmYlrageFobrbs;Edkrgkarsgát;k¾ekIneLIg rhUtdl;cMNuc yield.



]TahrN_7³ FñwmctuekaNEkg EdlmanTTwg cm30 nigkm<s;RbsiT§PaB cmd 60= . EdkrgkarTajman 286DB teRmobCaBIrCYr ÉEdkrgkarsgát;man 222DB . kMNt;ersIusþg;m:Um:g;xagkñúgRbsinebIeKeRbI

MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ muxkat;EdkrgkarTaj 293.36 cmAs = PaKryEdkrgkarTaj 02052.0

603093.36

=×

=ρ muxkat;Edkrgkarsgát; 26.7' cmA s = PaKryEdkrgkarsgát; 0042.0

60306.7' =×

=ρ muxkat;EdkrgkarTajeKal 2

1 33.29 cmAs = PaKryEdkrgkarTajeKal 01629.0603033.29

1 =×

=ρ )

600600)(')('(85.0 1

yy

c

fdd

ffK

−= β 01517.0

400600600

606

4002885.0 2 =

−=

eday K≥− )'( ρρ enaHEdkrgkarsgát;eFVIkardl;cMNuc yield sRmab; MPaf c 28' = nig MPaf y 400= 030345.0=⇒ bρ 019.0max =⇒ ρ eday max)'( ρρρ <− 9.0=⇒φ ersIusþg;m:Um:g;xagkñúg

)]'(')2

()'[( ddfAadfAAM ysyssn −+−−= φφ

cmabffAA

ac

yss 43.16'85.0)'(

=⇒−

=⇒

mkNM n .5.69410)]660(4006.7)243.1660(40033.29[9.0 3 =×−××+−××=⇒ −φ

viFImü:ageTot epÞógpÞat;faetIEdkrgkarsgát;eFVIkardl;cMNuc yield b¤enA cmac 33.19

85.043.16

85.0===



sac;lUteFobEdkrgkarsgát; 00207.0003.033.19

633.19003.0'' =×−

=×−

=c

dcsε

sac;lUteFobrbs;Edk 002.0=yε eday ys εε >' ⇒ Edkrgkarsgát;eFVIkardl;cMNuc yield

005.0007.0003.033.19

33.19)660(003.0)( >=×−+

=−

=c

cdttε

b¤ 375.0322.060

33.19<==

dc

muxkat;EdkrgkarTajsrub ss AcmbdMaxA >=+××=+= 2

max 76.41)0042.0019.0(6030)'( ρρ RtwmRtUv

3>9>2> enAeBlEdksgát;eFVIkarmindl;cMNuc yield dUckarbkRsayxagelI RbsinebI K

fdd

ff

yy

c =−

<− )600

600)(')('(85.0)'( 1βρρ

enaHEdksgát;eFVIkarmindl;cMNuc yield eT. enHbgðajfa RbsinebI K<− )'( ρρ EdkrgkarTajeFVI kardl;cMNuc yield mun ebtugmanbERmbRmYlrageFobGtibrma 003.0 ehIyEdkrgkarsgát;k¾eFVIkarmindl; cMNuc yield Edr. pleFob c

d ' kan;EtFM mann½yfakalNaeKdak;Edkrgkarsgát;enACitG½kSNWt enaHsac; lUteFobrbs;Edkrgkarsgát;kan;EttUc.

RbsinebIEdksgát;eFVIkarmindl;cMNuc yield dMeNaHRsayTUeTAGaceFVIeTA)anedayQrelIeKalkarN_ sþaTic.

)'(003.0'c

dcs

−=ε )'(600''

cdcEf sss

−== ε

eday[ cbfC cc 1'85.0 β= ]'85.0)'(600[')'85.0'(' cscsss f

cdcAffAC −

=−= edaysar scys CCfAT +== enaH

]'85.0)'(600[''85.0 1 cscys fc

dcAcbffA −+= β

0''600])''85.0()'600[()'85.0( 21 =−−−+⇒ dAcfAAfAcbf sysscsc β

smIkarenHmanTRmg; 0322

1 =++ AcAcA eRkayeBlKNna c KNna )'(600'

cdcf s

−= KNna ca 1β= KNna ]'85.0)'(600[' css f

cdcAC − nigKNna

cbfC cc 1'85.0 β=



)]'()2

([ ddCadCM scn −+−= φφ enAeBlEdksgát;eFVIkarmindl;cMNuc yield/ ys ff <' nigEdkTajsrubRtUvkarsRmab;muxkat; ctuekaNEkgKW³

)''('' maxmaxy

s

y

sss f

fbdffAbdMaxA ρ

ρρ +=+=

edayEckGgÁTaMgBIrnwg bd eyIg)anPaKryEdk

y

ss

ff

bdMaxAMax ''max ρρρ +≤=

b¤ max)''( ρρρ ≤−y

s

ff

kñúgkrNIenH bffAfA

ac

ssys

'85.0''−

=

)]'('')2

)(''[( ddfAadfAfAM ssssysn −+−−= φφ segçb³ viFIsaRsþviPaKmuxkat;CamYyEdkrgkarsgát; 1> kMNt; ρ / 'ρ / )'( ρρ − dUcKñakMNt; maxρ / minρ 2> kMNt; )

600600)(')('(85.0 1

yy

c

fdd

ffK

−= β

3> RbsinebI K≥− )'( ρρ enaHEdkrgkarsgát;eFVIkardl;cMNucyar ys ff =' . RbsinebI K<− )'( ρρ enaHEdkrgkarsgát;eFVIkarmindl;cMNuc yield ys ff <' .

4> RbsinebIEdkrgkarsgát;eFVIkardl;cMNuc yield k> BinitüemIl minmax )'( ρρρρ ≥−≥ b¤ 005.0≥tε / eRbI 9.0=φ x> kMNt;

bffAA

ac

yss

'85.0)'( −

=

K> kMNt; )]'(')2

()'[( ddfAadfAAM ysyssn −+−−= φφ X> muxkat;EdkrgkarTajGtibrma sA EdlGaceRbIenAkñúgmuxkat;KW

ss AbdMaxA ≥+= )'( max ρρ 5> RbsinebIEdkrgkarsgát;eFVIkarmindl;cMNuc yield

k> KNnacm¶ayG½kSNWt c edayeRbIsmIkar cs CCT += x> kMNt; )'(600'

cdcf s

−=



K> RtYtBinitü max)''( ρρρ ≤−y

s

ff b¤ sMaxA EdlGaceRbIenAkñúgmuxkat; RtUvEtFMCagb¤esμ I sA

Edl)aneRbI s

y

ss A

ffbdMaxA ≥+= )''( max ρρ

X> kMNt; bffAfA

ac

ssys

'85.0''−

= b¤ ca 1β=

g> kMNt; )]'('')2

)(''[( ddfAadfAfAM ssssysn −+−−= φφ ]TahrN_8³ kMNt;ersIusþg;m:Um:g;kñúgénmuxkat;dUcbgðajkñúgrUb edayeRbI MPaf c 35' = / MPaf y 400= . eK eRbIEdkrgkarsgát; 253DB Edl 272.14' cmA s = nigEdlrgkarTaj 306DB Edl 239.42 cmAs = .

dMeNaHRsay³

kMNt; 02125.0573539.42

=×

==bdAsρ / 00738.0

573572.14'' =×

==bdA sρ / 01387.0)'( =− ρρ

eday MPaf c 35' = ⇒ )7

28'(05.085.01−

−= cfβ 8.0)7

2835(05.085.01 =−

−=⇒ β

kMNt; 020355.0)400600

600)(57

5.6)(40035(8.085.0)

600600)(')('(85.0 1 =

−×=

−=

yy

c

fdd

ffK β

eday K<− )'( ρρ enaHEdkrgkarsgát;eFVIkarmindl;cMNuc yield 0357.0)

600600('85.0 1 =+

=yy

cb ff

fβρ

02231.00357.0008.0005.0

max ==ρ

max)'( ρρρ <− muxkat;rgkarTaj 9.0=⇒φ kMNt;cm¶ayG½kSNWt c

abfC cc '85.0= eday cca 8.01 == β ccCc 83303508.03585.0 =×××=⇒



)'85.0'(' csss ffAC −= eday )'(600'

cdcf s

−= 43792)65(883200]3585.0)65(600[1472 −

−=×−

−=⇒

cc

ccCs

NfAT ys 16956004004239 =×== 43792)65(88320083301695600 −

−+=⇒

ccc

⇒ 0574080008561928330 2 =−− cc cmmmc 9.14149 ==⇒

cma 92.119.148.0 =×=⇒ kMNt; )'(600'

cdcf s

−= MPaf s 339

9.145.69.14600' =

−=⇒

kMNt; abfC cc '85.0= kNNCc 17.124112411703502.1193585.0 ==×××=⇒ kMNt; )'85.0'(' csss ffAC −= kNNCs 216.455455216)3585.0339(1472 ==×−=⇒ edIm,IkMNt;ersIusþg;m:Um:g;kñúg eKRtUvKitm:Um:g;eFobG½kSEdkTaj sA

)]065.057.0(216.455)2

1192.057.0(17.1241[9.0)]'()2

([ −+−=−+−= ddCadCM scn φφ mkNM n .38.863=φ

RtYtBinitü 02231.0015.0)40033900738.002125.0()''( max <=−⇒≤− ρρρ

y

s

ff

kMNt;muxkat;EdkTajGtibrma )''( maxy

ss f

fbdMaxA ρρ += 22 39.4299.56)

40033900738.002231.0(5735 cmcmMaxAs >=+×= RtwmRtUv

375.025.05.6957

9.14<=

−+=

tdc RtwmRtUv

005.0009.0003.0 >=−

=c

cdttε muxkat;rgkarTaj

3>10> viPaKmuxkat;GkSret T nigmuxkat;GIu I CaFm μtakRmalxNÐ nigFñwmRtUv)aneKcak;CamYyKña edIm,IbegáItCaeRKOgbgÁúMEtmYy (monolithic

structure). kRmalxNÐmankRmas;esþIgCagFñwm. eRkamGMeBIénkugRtaMgBt; EpñkénkRmalxNÐEdlCaEpñk rbs;FñwmrgnUvkugRtaMgsgát;GaRs½yeTAelITItaMgG½kSNWt. EpñkénkRmalxNÐEdleFVIkarCamYyFñwmRtUv)aneK [eQ μaHfa søab (flange) EdlbgðajkñúgrUbedayépÞ bt . EpñkénFñwmEdlenAsl; EdlbgðajedayépÞ

wbth )( − RtUv)aneK[eQ μaHfa RTnug (stem b¤ web).



sRmab;muxkat;GkSr I mansøabBIr KWsøabrgkarsgát;EdlcUlrYmeFVIkar nigsøabrgkarTajEdlKμanRb siT§PaB BIeRBaHvaenABIeRkamG½kSNWt ehIyEdlminRtUv)aneKykvamkKit. dUecñH karviPaK nigkarKNna Fñwmmuxkat; I manlkçN³dUcKñanwgFñwmmuxkat; T .

3>10>1> TTwgRbsiT§PaB

sRmab;muxkat;GkSr T EdlsøabmanRbEvgEvg kugRtaMgsgát;manragCa):ar:abUl EdltémøGtibrma sßitenAelIFñwm ehIytémøGb,brmasßitenAcm¶ay x BImuxrbs;Fñwm. ehIykugRtaMgk¾ERbRbYlBIsrésEpñkxag elIsøab mksrésEpñkxageRkamsøab BIGtibrmamkGb,brma.

témøbERmbRmYlenHGaRs½yeTAnwgTItaMgG½kSNWt. kugRtaMgsmmUl CakugRtaMgBRgayesμ ImanGMeBIelITTwgsøabsmmUl eb . TTwgRbsiT§PaB eb RtUv)an

eKkMNt;edayGnuKmn¾eTAnwg³



- RbelaHElVg 1s - TTwgRTnug wb - TMnak;TMngrvagkRmas;kRmalxNÐ nigkm<s;srubrbs;Fñwm - lkçxNÐTRmrbs;Fñwm ¬samBaØ b¤Cab;¦ - lkçxNÐbnÞúk ¬BRgayes μ I b¤cMcMNuc¦ - pleFobrvagRbEvgFñwmcenøaHm:Um:g;sUnü nigTTwgRTnug nigcm¶ayrvagRTnug

ACI Code )ankMNt;nUvTTwgRbsiT§PaBedaykMNt;yktémøGb,brmaénsmIkarxageRkam³ -

4Lbe = Edl L CaRbEvgFñwm

- we btb +=16 Edl t kRmas;kRmalxNÐ nig wb TTwgRTnug - bbe = Edl b cm¶ayBIcenøaHG½kSkRmalxNÐ muxkat;ragGkSr T b¤muxkat;ragGkSr I GacRtUvviPaKCaragctuekaNEkg b¤ragGkSr T GaRs½yelITI

taMgG½kSNWt.

3>10>2> muxkat;GkSret T RtUv)anKitCaragctuekaNEkg kñúgkrNIenH km<s;énbøúkkugRtaMgsmmUl a sßitenAkñúgsøab ta ≤ begáIt)anCaépÞkugRtaMgsgát;es μ I

nwg abe . muxkat;ebtugBIeRkamG½kSNWtRtUv)aneKsnμt;faK μanRbsiT§PaB ehIymuxkat;RtUv)aneKKitfaman EdkrgkarTaj Edl)anBnül;BIxagelI edayRKan;EtCMnYs b eday eb .

dUecñH ec

ys

bffA

a'85.0

=

nig )2

( adfAM ysn −= φφ



RbsinebI km<s; a ekIneLIgeday ta = enaH )2

( tdfAM ysn −= φφ

kñúgkrNIenH ec

ys

bffA

t'85.0

= b¤ y

ecs f

tbfA '85.0=

sRmab;karviPaKenH maxss AA ≤ nig 005.0≥tε

3>10>3> viPaKmuxkat;ragGkSret T kñúgkrNIenH G½kSNWtsßitenAelIRTnug. EpñkxøHrbs;ebtugenAkñúgRTnugmanRbsiT§PaBkñúgkarTb;Tl;

nwgm:Um:g;xageRkA. kmøaMgsgát; )](['85.0 tabtbfC wec −+= TItaMgrbs; C sßitenAelITIRbCMuTm¶n;rbs;épÞragGkSr T enAcm¶ay z BIsrésEpñkxageRkAbMput.



karviPaKmuxkat;ragGkSr T manlkçN³RsedogKñanwgkarviPaKmuxkat;ebtugEdlEdkrgkarsgát;

edaycat;TuképÞebtug tbb we )( − smmUleTAnwgEdksgát; sA' . karviPaKenHEckecjCaBIrEpñkdUcbgðajkñúg rUbxageRkam³

- muxkat;eKalragctuekaNEkg dbw nigmuxkat;Edk 1sA . kmøaMgsgát; wc abfC '85.01 = nigkmøaMg ys fAT 11 = ehIyRbEvgédXñas; )

2( ad − .



- muxkat;Edlmansøabebtugsgxag 2/])[(2 tbb we −× begáIt)anCakmøaMgsgát;edayKuNCamYy cf '85.0 nigRbEvgédXñas;es μ Inwg )

2( td − . RbsinebI sfA Camuxkat;EdkTajEdlbegáItkmøaMges μ Inwg

kmøaMgsgát;EdlbegáItedayebtugsøabsgxag dUecñH y

wecsf f

bbtfA )('85.0 −=

muxkat;Edksrub sA EdleRbIkñúgmuxkat;GkSr T KW³ sfss AAA += 1 b¤ sfss AAA −=1 muxkat;GkSr T sßitkñúgsßanPaBlMnwg dUecñH 11 TC = / 22 TC = nig TTTCCC ++=+= 2121 BicarNaelIsmIkar 11 TC = sRmab;muxkat;eKalctuekaNEkg eK)an

wcys abffA '85.01 = b¤ wcysfs abffAA '85.0)( =− dUecñH

wc

ysfs

bffAA

a'85.0

)( −=

cMNaMfa wb RtUv)aneRbIedIm,IkMNt; a . ersIusþg;énm:Um:g;kñúgénmuxkat;CaplbUkénm:Um:g;BIr 1uM nig 2uM

21 uun MMM +=φ )

2()()

2(11

adfAAadfAM ysfsysu −−=−= φφ

Edl sfss AAA −=1 nig wc

ysfs

bffAA

a'85.0

)( −=

)2

(2tdfAM ysfu −= φ

)]2

()2

()[( tdfAadfAAM ysfysfsn −+−−= φφ BicarNaelImuxkat;RTnug dbw / sac;lUteFobsuT§ tε GackMNt;BI a / c nig td dUcxageRkam³ RbsinebI

1βac = nig cmhdt 5.6−= bnÞab;mk

cdc t

t)(

003.0−

=ε

sRmab;muxkat;rgkarTajenAkñúg RTnug/ 005.0≥tε . karKNnaersIusþg;m:Um:g;kñúgsRmab;muxkat;GkSr T b¤muxkat;GkSr I

GacKNnaedayeRbIsmIkarxagelI EteKcaM)ac;RtUvRtYtBinitülkçxNÐxageRkam³ - PaKryEdkTajsrubeFobRkLaépÞRbsiT§PaBRTnugRtUvFMCag b¤esμ I minρ

minρρ ≥=db

A

w

sw

yy

c

fff 4.1

4'

min ≥= ρ

- RtYtBinitü bERmbRmYlrageFobsuT§FMCag b¤esμ I 005.0≥tε sRmab;muxkat;rgkarTaj



- muxkat;EdkGtibrma sMaxA enAkñúgmuxkat;GkSr T RtUvEtFMCag b¤esμ I muxkat;EdkEdl)aneRbI sA sRmab;muxkat;rgkarTaj CamYy 9.0=φ

))(()( max webdbflangeAMaxA wsfs ρ+= )()]('85.0[1

max dbbbtff

MaxA wwcy

s ρ+−=

PaKryEdkeFobnwgRTnug )( max dbA

dbA

w

sf

w

sw +≤= ρρ

maxρρρ ≤−⇒ fw smIkarTUeTAsRmab;KNna sMaxA enAkñúgmuxkat;GkSr T enAeBl ta > GackMNt;tam

])[('85.0 wwec abtbbfC +−= sRmab; 003.0=cε nig 005.0=tε / 375.0

005.0003.0003.0

=+

=dc sRmab;RTnug

dUecñH dca 11 375.0 ββ == muxkat;EdkGtibrmaesμ Inwg

yfC

dUecñH ]375.0)[('85.0 1 dbtbbffMaxA wwe

y

cs β+−=

segçb³ viFIsaRsþviPaKmuxkat;GkSret T b¤GkSrGil L páab; 1> kMNt;TTwgRbsiT§PaB eb nigkMNt; maxρ / minρ 2> kMNt;

ec

ys

bffA

a'85.0

=

3> RbsinebI ta < enaHmuxkat;eFVIkarCaragctuekaNEkg - kMNt; )

2( adfAM ysn −= φφ

cMNaMfa³ 1β

ac = nig 005.0)(003.0 ≥−

=cdc t

tε sRmab;muxkat;rgkarTaj 9.0=φ

- RtYtBinitü minρρ ≥=db

A

w

sw

- swwcy

s Adbbbtff

MaxA ≥+−= )()]('85.0[1maxρ

4> RbsinebI ta > enaHmuxkat;eFVIkarCaragGkSret k> kMNt;

y

wcsf f

bbtfA )('85.0 −=



x> kMNt; bffAA

ac

yss

'85.0)'( −

=

K> RtYtBinitü maxρρρ ≤− fw eFobnwgRkLaépÞRTnug Edl

dbA

w

sw =ρ nig

dbA

w

sff =ρ

b¤RtYtBinitü swwey

cs Adbtbb

ffMaxA ≥+−= ]375.0)[('85.0 1β / sRmab; 9.0=φ

X> kMNt; wc

ysfs

bffAA

a'85.0

)( −=

g> kMNt; )]2

()2

()[( tdfAadfAAM ysfysfsn −+−−= φφ ]TahrN_9³ FñwmebtugGarem:EdlmanRbEvg m5.4 ehIymanKMlatBImYyeTAmYyRbEvg m2 . FñwmenHRTkM ralxNÐEdlmankRmas; cm10 . kMNt;nUversIusþg;m:Um:g;kñúgrbs;FñwmkNþal. eKeRbI MPaf c 20' = nig

MPaf y 400= .

dMeNaHRsay³ kMNt;TTwgRbsiT§iPaB

cmbLbtb we 5.112}200;4

450;251016min{};4

;16min{ =+×=+=



kMNt;km<s;bøúkkugRtaMg

ec

ys

bffA

a'85.0

= / 272.14 cmAs =

tcma <=×××

= 08.35.1122085.0

40072.14 dUecñHeyIgRtUvKNnaCaragctuekaNEkgEdlmanTTwg cmbe 5.112= PaKryEdkGb,brma

yy

c

fff 4.1

4'

min ≥= ρ 0035.0min =⇒ ρ

PaKryGtibrma 01355.0)600

600(

'85.0625.0 1max =

+×=

yy

c

fff

βρ

PaKryEdkeFobnwgépÞRkLaRTnug 0035.001472.04025

72.14>=

×==

dbA

w

swρ


1

===β

bERmbRmYlrageFobsuT§rbs;Edk 9.0005.003.0)62.3

62.340(003.0)(003.0 =⇒>=−

=−

= φεc

cdtt

KNna )2

( adfAM ysn −= φφ mkNmmN .81.203.203807232)2

8.30400(40014729.0 ==−××= epÞógpÞat;muxkat;Gtibrma swwc

ys Adbbbtf

fMaxA ≥+−= )()]('85.0[1

maxρ 222.37 cmMaxA = sA> RtwmRtUv

]TahrN_10³ KNnaersIusþg;m:Um:g;kñúgénmuxkat;GkSr T dUcbgðajkñúgrUb edayeRbI MPaf c 25' = nig MPaf y 400= .

dMeNaHRsay³ eK[ cmbb e 90== / cmbe 25= / cmd 43= nig 293.36 cmAs =



KNna tcmbf

fAa

ec

ys >=××

×== 72.7

902585.040093.36

'85.0

eday ta > sikSaCaragGkSr T

KNna y

wcsf f

bbtfA )('85.0 −= 217.24 cm=

21 76.12 cmAAA sfss =−=⇒

epÞógpÞat; tε cm

bffA

webawc

ys 6.9252585.0

40076.12'85.0

)( 1 =××

×==

cmwebac 29.11)(

1

==β

cmdt 8.455.652 =−= 9.0005.000917.0)(003.0 =⇒>=

−= φε

ccdt

t RtYtBinitü 22

minmin 93.3676.343250035.0 cmcmdbA ws <=××== ρ RtwmRtUv KNna )]

2()

2()[( tdfAadfAAM ysfysfsn −+−−= φφ

)2

70430(4002417)2

96430(400)24173693[(9.0 −×+−−=nMφ mkNmmNM n .173.519.519172920 ==φ

3>11> TMhMénmuxkat;FñwmGkSr T Éeka eBlxøH FñwmGkSr T Éeka RtUv)aneRbIedIm,IbEnßmépÞrgkarsgát;. muxkat;enHRtUv)aneKeRbIsRmab;Fñwm EdleKcak;TukCamun.

ACI Code )anENnaMnUvTMhMmuxkat;sRmab;GkSr T ÉekadUcxageRkam³ - kRmas;søab t RtUvFMCag b¤esμ IBak;kNþalTTwgRTnug wb - TTwgsrubrbs;søab b RtUvEttUcCag b¤es μ IbYndgTTwgRTnug wb



3>11> muxkat;GkSr L páab; Fñwmmuxkat;GkSr L páab;CaFñwmEdlRTkRmalxNÐEpñkxageKbMput. TTwgRbsiT§PaBrbs;muxkat;enHRtUv

)ankMNt;nUvtémøGb,brmaénsmIkarxageRkam³ -

12)( Lbb we ≤−

- tbb we 6)( ≤− -

2)( lbb we ≤−

Edl L - RbEvgFñwm l - KMlatFñwm


T.Chhay 82 Flexural Design on Reinforced Concrete Beams

IV. karKNnaFñwmebtugGarem:rgkarkac;begáag

4>1> km<s;RbsiT§PaBsRmab;Fñwm nigkRmalxNÐ Fñwmmankm<s;x<s; b¤TabGaRs½yeTAnwgRbEvgrbs;Fñwm nigbnÞúkxageRkAEdlvaRtUvRT. edIm,IepÞógpÞat;

CamYYyPaBdab xageRkamenHCarUbmnþsRmab;kMNt;km<s;FñwmGaRs½y nwgRbEvgFñwm. TTwgFñwmRtUv)ankMNt;ecjBIkm<s;rbs;Fñwm edaykMNt;enAcenøaH dd

21

31

→ .

4>2> muxkat;ctuekaNEkgCamYyEdkrgkarTaj xageRkamCarUbmnþsRmab;karKNnamuxkat;rgkarTaj

)600

600('85.0 1yy

cb ff

f+

= βρ

)008.0

003.0(max

s

y

bEf

+= ρρ

sRmab; MPaf y 400= bρρ 625.0max =⇒

ehIy 85.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 28' ≤ . )

728'(05.085.01−

−= cfβ sRmab;ebtugEdlmanersIusþg; MPafMPa c 56'28 ≤< . 65.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 56' > .

témøénbERmbRmYlrageFobrbs;Edkkan;EtFM bgðajBIPaBsVitrbs;ebtugGarem:kan;EtFM )ann½yfaenA eBlmuxkat;ebtugkan;EtFMCamYyPaKryEdkticPaBsVitkan;EtFM pÞúymkvijenAeBlmuxkat;ebtugkan;EttUcCa

kRmalxNÐ mYyTis L/24 L/28 L/10 L/20

Fñwm L/18.5 L/21 L/8 L/16


karKNnaFñwmebtugGarem:rgkarkac;begáag 83 T.Chhay

mYyPaKryEdkkan;EtFMenaHPaBsVitrbs;ebtugkan;EttUc. xageRkamCataragbgðajBIPaKryEdksMNUmBr GaRs½yersIusþg;ebtug nigersIusþg;Edk.

taragTI1³ PaKryEdksMNUmBr sρ )(' MPaf c )(MPaf y sρ%

20 235 1.4 400 1.2 28 400 1.4 500 1.2 35 400 1.6 500 1.4

bERmbRmYlrageFobEdksuT§ tε edIm,IeGaymuxkat;rgkarTajRtUv)ankMNt;FMCag 005.0 enaH

9.0=φ . )

3250)(002.0(65.0 −+= tεφ bERmbRmYlrageFobEdksuT§ tε enAcenøaH 005.0004.0 → .

smIkarKNnaersIusþg;m:Um:g;kñúgmanTRmg;dUcxageRkam³ 2bdRMM uun ==φ

Edl nc

yyu R

ff

fR φρ

φρ =−= )'7.1

1(

Edl 9.0=φ sRmab; tension-controlled section nig 9.0<φ sRmab;muxkat;enAkñúgtMbn; transition region dUcenH )

'7.1(

bffA

dfAMMc

ysysun −== φφ

dUcKña )'7.1

(2

c

yyun f

fbdfMM

ρφρφ −==

kñúgkrNIEdleyIgsÁal;m:Um:g;KNnaxageRkA nigsÁal;ersIusþg;smÖar³ eyIgenAsl;GBaØatbIeTotEdl minTan;sÁal; kñúgenaHmanTTwgFñwm b km<s;RbsiT§PaB d nigPaKryEdk ρ . dMeNaHRsayGaceFVIeTA)anluH RtaEteyIgRtUveFVIkarsnμt;cMeBaHGBaØatBIr. CaTUeTA ρ RtUv)ansn μt; ¬edayeRbI maxρ ¦ nigdUcKña b k¾RtUv)an snμt;.

xageRkamCaviFIsaRsþkñúgkaredaHRsayedaysÁal; uM / cf ' nig yf ³ - RbsinebI ρ RtUv)ansnμt; ¬edayeGayenAcenøaH max2

1 ρ nig bρ21 ¦ enaHeyIgGackMNt;

)'7.1

1(c

yyu f

ffR

ρφρ −=



u

u

RMbd =⇒ 2

CaTUeTApleFob bd ERbRbYlBI 32 → ¬eKniymyk 2 ¦

dUcenH eKGackMNt; b nig d dUcKña eyIg)an bdAs ρ=

- RbsinebI b nig d RtUv)aneGay enaHPaKryEdkEdlRtUvkarkMNt;tamrUbmnþxageRkam³ )

'7.1411('85.0

2bdfM

ff

c

u

y

c

φρ −−=

bdAs ρ=⇒ - RbsinebI b RtUv)ansnμt;bEnßmBIelI ρ enaHeKRtUv

KNna )'7.1

1(c

yyu f

ffR

ρφρ −=

KNna bR

Mdu

u=

RbsinebI 2=bd enaH 3

2bR

Mdu

u=

bdAs ρ=⇒

4>3> KMlatEdk nigRsTab;karBarEdk 4>3>1> KMlatEdk



srésEdkRtUv)anteRmobedaymanKMlaty:agticbMputes μ InwgGgát;p©itEdk b:uEnþminRtUvtUcCag mm25 edIm,IeGayeKGacbgðab;ebtug)any:aggayRsYlkñúgeBlcak;ebtug. KMlatEdksRmab;karteRmobEdkbBaÄr EdlmaneRcInCagmYyRsTab; minRtUvmantémøtUcCag mm25 Edr. RbsinebIKMlatEdkmanTMhMtUcenaHl,ay ebtugminGacB½T§CMuvijEdk)anl¥eT.

4>3>2> RsTab;karBarEdk

RsTab;karBarEdk Casac;ebtugEdlenAcenøaHépÞxageRkA nigépÞrbs;Edk. eKcaM)ac;RtUvkarRsTab;kar BarEdkeRBaHvamanplRbeyaCn_bYny:ag³

- edIm,Ietags¥itsrésEdkeTAnwgebtugEdleFVIeGaysmÖar³TaMgBIreFVIkarCamYyKña. \T§iBlrbs;PaB s¥itGaRs½yeTAnwgkRmas;RsTab;karBar.

- edIm,IkarBarsrésEdkeTAnwgERcHsIuEdk. - edIm,IkarBarkar)at;bg;ersIusþg;EdkEdlbNþalmkBIkemþA. kRmas;RsTab;karBar mm20 GacTb;

Tl; nwgePøIgeqH)an 1em:ag. - sRmab;yandæan eragcRk cMNtrfynþ RsTab;karBarbEnßmRtUv)aneKdak;BIelIkRmalxNÐEfmeTot

edIm,IkarBarkarswkercrwlEdlbNþalmkBIcracrN_. kRmas;RsTab;karBarEdkGaRs½yeTAnwgmCÄdæanEdleRKOgbgÁúMenaHsßitenA. xageRkamCatarag bgðajBIkRmas;RsTab;karBarGb,brma³

mCÄdæan kRmas;karBarEdk )(mm ebtugcak;pÞal;nwgdI 75 ebtugcak;pÞal;nwgdI b¤halxül; + Ggát;p©itEdkFMCag mm16 50 + Ggát;p©itEdktUcCag mm16 35 ebtugmincak;pÞal;nwgdI b¤minhalxül; - kRmalxNÐ CBa¢aMg + Ggát;p©itEdkFMCag mm36 35 + Ggát;p©itEdktUcCag mm36 20 - Fñwm ssr 35 - kRmalekag



+ Ggát;p©itEdkFMCag mm20 20 + Ggát;p©itEdktUcCag mm20 15

4>3>3> TTwgGb,brmarbs;muxkat;ebtug

smIkarTUeTAedIm,IkMNt;TTwgGb,brmarbs;muxkat;ebtugGacsresrdUcxageRkam³ )(2)(2)1(min karBarEdkRsTab;Edkkg ++−+= φsnnDb

Edl n - cMnYnEdkbeNþay D - Ggát;p©itEdkEdlFMCageK s - KMlatEdk

4>3>4> km<s;Gb,brmarbs;muxkat;ebtug

km<s;rbs;muxkat;ebtugRtUv)ankMNt;edayGaRs½ynwgRsTab;Edk. - EdkmYyRsTab;³ mmDdh 50

211 ++= - EdkBIrRsTab;³ mmDdh 6022 ++=

]TahrN_1³ kMNt;muxkat;Edk nigmuxkat;ebtugedIm,ITb;Tl;nwgm:Um:g;KNna mkN.490 edayeRbIPaKryEdk Gtibrma maxρ sRmab;muxkat;rgkarTaj. sm μtikm μ³ MPaf c 20' = nig MPaf y 400= . dMeNaHRsay³ eday MPaf c 20' = / MPaf y 400= / 85.01 =β nig 9.0=φ sRmab; tension-controlled section

)600

600('85.0 1yy

cb ff

f+

= βρ



021675.0)400600

600(4002085.0 2 =

+=bρ

01355.0625.0)008.0

003.0(max ==

+= b

s

y

bEf

ρρρ

MPaff

fRc

yyu 1.4)

207.140001355.01(40001355.09.0)

'7.11( max

max(max) =××

−××=−=⇒ρ

φρ 36

6

(max)

2 105.1191.410490 mm

RMbdu

u ×=×

==⇒

dUcenHsRmab;karsnμt; b / kMNt; d nig bdAs ρ= mmb 200= / mmd 773= / 295.20 cmAs =

mmb 250= / mmd 5.691= / 242.23 cmAs = mmb 300= / mmd 630= / 261.25 cmAs = ¬ 256DB ¦ mmb 400= / mmd 5.546= / 262.29 cmAs =

* kareRCIserIskm<s;RbsiT§PaBGaRs½ynwgktþaxageRkam³ - km<s;bnÞb;³ TTwgrbs;muxkat;tUcpþl;nUvkm<s;FñwmFM Edlkat;bnßylMhkm<s;. elIsBIenH FñwmeRCA

ceg¥ótkat;bnßyersIusþg;m:Um:g;edaykarxUcRTg;RTayxag lateral deformation. - brimaN nigkarBRgaysrésEdk³ Fñwmceg¥ótRtUvkarsrésEdkeRcInCagmYyRsTab; dUcenHvabegáIt

km<s;Fñwm. - kRmas;CBa¢aMg³ RbsinebIbøúksIum:gt_RtUv)aneRbI TTwg b RtUv)aneRCIserIsesμ InwgkRmas;CBa¢aMg.

sRmab; GKarCBa¢aMgxagRkas;CagCBa¢aMgkñúg. * kareRCIserIsmuxkat;EdkGaRs½ynwgktþaxageRkam³

- karteRmobEdkRKb;RKan;enAkñúgmuxkat; CaTUeTA mYyRsTab; b¤BIrRsTab; nigbMeBjtamlkçxNÐ ACI

Code sRmab;KMlatEdkGb,brma. - épÞmuxkat;EdkeRCIserIsRtUvmantémøEk,rbMputépÞsrésEdktRmUvkar

dUcenHeyIgeRCIserIsyk mmb 300= / mmd 630= / 261.25 cmAs = ¬ 25@6 DB ¦ RtUvteRmobBIrRsTab; kMNt;km<s;Fñwm mmmmDdh 715602563060 =++=++= dUcenHyk mmh 750= mmd 665=⇒ ]TahrN_2³ edaHRsay]TahrN_1 edayeRbI ρ RbEhl %1 nig cmb 35=



dMeNaHRsay³ eday MPaf c 20' = / MPaf y 400= / 01355.0max =ρ sRmab; tension-controlled section

)'7.1

1(c

yyu f

ffR

ρφρ −= MPaRu 1765.3)

207.140001.01(40001.09.0 =

××

−××=⇒ 3

62 154257830

1765.310490 mm

RMbd

u

u =×

==⇒

sRmab; cmb 35= mmd 665=⇒ 2275.235.663501.0 cmAs =××=

edayeRCIserIs 284DB mYyRsTab; 262.24 cmAs = epÞógpÞat;TTwg mmsnnDb 95)1(min +−+= edayyk Ds =

cmmmmmDb 3529195287957min <=+×=+=⇒ epÞógpÞat; kMNt;km<s;Fñwm mmmmDdh 72950

22866550

2min =++=++= yk cmh 75= edayEdkEdldak;mantémøFMCagEdkKNna dUcenHeyIgGacbnßykm<s;FñwmBI cmcm 7275 → sRmab;karERbRbYlkm<s;Fñwm 22 62.2424.24)

7275(275.23 cmcmAs <==

mmd 65664720 =−= RtYtBinitüersIusþg;m:Um:g;

0098.07235

62.24=

×=ρ maxρ< ⇒ tension-controlled section

cmbf

fAa

c

ys 55.16352085.0

40062.24'85.0

=××

×==



MPamkNmmNadfAM ysn 490.083.508.10083.508)2

5.165656(40024629.0)2

( 6 >=×=−×××=−= φφ

RtYtBinitüsac;lUteFobEdksuT§ tε 003.0)005.0( −=

b

tρρε

021675.0)400600

600(4002085.0 2 =

+=bρ

452.0021675.0

0098.0==

bρρ

005.0008.0003.0452.0005.0

>=−=tε epÞógpÞat; mü:ageTot 47.19

85.055.16

85.0===

ac 375.03.0

6.6547.19

<==td

c epÞógpÞat;

]TahrN_3³ kMNt;muxkat;EdksRmab;muxkat;eGayxageRkam cmb 25= nig cmh 50= EdlTb;nwgm:Um:g; KNna mkNMu .200= . smμtikmμ³ MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³ edaysnμt;Edk 25DB mYyRsTab; =d cmmm 4343070500 ==−

eday MPaf c 28' = / MPaf y 400= / 85.01 =β )600

600('85.0 1yy

cb ff

f+

= βρ



030345.0)400600

600(4002885.0 2 =

+=bρ

019.0625.0)008.0

003.0(max ==

+= b

s

y

bEf

ρρρ

)'7.1

411('85.02bdf

Mf

f

c

u

y

c

φρ −−= edaysn μt; 9.0=φ

max2

6

01356.0)430250289.07.1

10200411(400

2885.0 ρρ <=××××

××−−

×=

⇒ tension-controlled section BitR)akd 258.14432501356.0 cmbdAs =××== ρ

225 9.425 cmADB s =⇒

325

==⇒s

s

AAn

dUcenH 27.14253 cmDBAs == ]TahrN_4³ kMNt;muxkat;EdkcaM)ac;sRmab; cmb 35= RbsinebIvaRbQmnwgm:Um:g;KNna mkNMu .425= . smμtikm μ³ MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³ sRmab; MPaf c 28' = / MPaf y 400= / 85.01 =β

030345.0=bρ / 019.0max =ρ sRmab;muxkat;rgkarTaj 9.0=φ edayeRbI 019.0max =ρ

MPaff

fRc

yyu 75.5)

287.1400019.01(400019.09.0)

'7.11( max

max(max) =××

−××=−=⇒ρ

φρ 36

6

(max)

2 10913.7375.5

10425 mmR

Mbdu

u ×=×

==

sRmab; cmdcmb 4635 =⇒= 259.304635019.0 cmAs =××=⇒

edayeRbIEdk 32φ 4edIm 2154.32324 cmDB = EdkRtUv)anteRmobmYyCYr ⇒ mmsnnDb 95)1(min +−+= edayyk sD = mmmmmmDb 35031995327957min <=+×=+=⇒ RtwmRtUv km<s;Fñwm mmmmDdh 52650

23246050

2=++=++= yk cm53



BiPakSa³ edaysarsrésEdkeRbIR)as; 2154.32 cm FMCagsrésEdktRmUvkar 259.30 cm

max02.04635

154.32 ρρ >=×

=⇒ bERmbRmYlrageFobEdksuT§ 004.00046.0003.0)005.0( >=−=

b

t

ρρε

⇒muxkat;sßitkñúgtMbn; transition region 9.0867.0)

3250)(002.0(65.0 <=−+=⇒ tεφ

cmbf

fAa

c

ys 44.15352885.0

400154.32'85.0

=××

×==

mkNmkNmmNadfAM ysn .425.86.426.1086.426)2

4.154460(4004.3215867.0)2

( 6 ≈=×=−××=−=φφ

eyIgeXIjfa sRmab;bMErbMrYlmuxkat;Edk 2546.159.30154.32 cm=− RbEhl %5 enaHersIusþg;m:Um:g;man témøRbEhlKña edaysar φ fycuH. dUcenHkarKNnamuxkat;edayeGaymuxkat;rgkarTaj 9.0=φ man lkçN³esdækic©.

4>4> muxkat;ctuekaNEkgCamYyEdkrgkarsgát; RbsinebIm:Um:g;KNnamantémøFMCagersIusþg;m:Um:g;kñúg enaHmuxkat;RtUv)armuxkat;EdkbEnßmsRmab;tMbn;

rgkarTaj nigrgkarsgát;. srésEdkrgkarsgát;pþl;nUvkmøaMgsgát;bEnßmeTAelIkmøaMgsgát;rbs;ebtug. k> edaysnμt;EdkrgkarTajmanmYyRsTab; viFIsaRsþKNnasRmab;muxkat;ctuekaNEkgCamYyEdkrgkarsgát; enAeBleKsÁal; uM / cf ' / b / d

nig 'd mandUcxageRkam³ - KNnaPaKryEdk balanced bρ nigPaKryEdkGtibrma maxρ edayeRbIsmIkarxageRkam³

)600

600('85.0 1yy

cb ff

f+

= βρ nig )008.0

003.0(max

s

y

bEf

+= ρρ

kMNt;muxkat;EdkGtibrmasRmab;rgkarTaj bdAs max1 ρ= - KNna (max)uR edayeRbI maxρ )9.0( =φ

)'7.1

1( maxmax(max)

c

yyu f

ffR

ρφρ −=

- KNnaersIusþg;m:Um:g;kñúgEdlekItedaysarmuxkat;EdkrgkarTaj 1uM edayeRbI (max)uR 2

(max)1 bdRM uu =



+ RbsinebI uu MM <1 enaHRtUvkarEdkrgkarsgát; + RbsinebI uu MM >1 enaHminRtUvkarEdkrgkarsgát;eT. KNnaPaKryEdk ρ tamrUbmnþ

)'7.1

411('85.02bdf

Mf

f

c

u

y

c

φρ −−= nigKNna bdAs ρ= .

- KNna 12 uuu MMM −= CaersIusþg;m:Um:g;EdlekItBIEdkrgkarsgát; - KNna 2sA BI )'(22 ddfAM ysu −= φ nigbnÞab;mkKNna 21 sss AAA += - KNnakugRtaMgenAkñúgEdkrgkarsgát;dUcxageRkam

+ KNna ys fc

dcf ≤−

= )'(600' + b¤KNna s'ε BIdüaRkambMErbMrYlrageFob nig sss Ef '' ε= . RbsinebI ys εε =' enaHEdkrgkar sgát; yield ehIy ys ff =' . + KNna sA' BI )'('22 ddfAM ssu −=φ .RbsinebI ys ff =' enaH 2' ss AA = . EtebI ys ff <' enaH 2' ss AA > ehIy )

'(' 2

s

yss f

fAA = .

- eRCIserIsmuxkat;EdksRmab; sA nig sA' edIm,IeGaysmlμmnwgTTwg b . CaTUeTA Edk sA eRcIn teRmobCaBIrRsTab; É sA' eRcInteRmobCamYyRsTab;.

- KNna mmdh 65+= sRmab;EdkrgkarTajmYyRsTab; nig mmdh 90+= sRmab;Edkrgkar TajBIrRsTab;. RtYtBinitüfa max)]'('[ ρρρ <−

y

s

ff edayeRbI d fμ I b¤RtYtBinitü

sy

ss A

ffbdA ≥+= )]'('[ max(max) ρρ eday

bdAs=ρ nig

bdA s''=ρ . karRtYtBinitüenHmincaM)ac;eT

RbsinebI maxρ RtUv)aneRbIenAkñúgmuxkat;eKal. - RbsinebIcaM)ac; eKRtUvKNnaersIusþg;m:Um:g;énmuxkat;cugeRkay nMφ ehIyeRbobeFobCamYy uM

edayeGay un MM ≥φ . - RtYtBinitübERmbRmYlrageFobEdksuT§ 005.0003.0)( ≥

−=

ccdt

tε x> edaysnμt;EdkrgkarTajmanBIrRsTab; kúñgkrNIEdkrgkarTajmanBIrRsTab; eKGacsnμt;fa mmhd 90−= nig

mmdmmhdt 2565 +=−= . eKmanviFIBIry:agkñúgkarkMNt;muxkat;srésEdk³ - vIFITI1³ edaysn μt; sac;lUteFobEdksuT§enAnIv:UTIRbCMuTm¶n;EdkTajes μ I 005.0 b¤ 005.0=sε

enAnIv:U d . kñúgkrNIenH bERmbRmYlrageFobEdksuT§ sRmab;srésEdkRsTab;eRkambMputman témøFMCag 005.0 .



005.0003.0)( >−

=c

cdttε . dUcenHeyIgedaHRsaydUckrNIxagelI EdkrgkarTajmanmYyRs

Tab;. - vIFITI2³ edaysn μt; 005.0=tε enAnIv:UEdkRsTab;eRkameK td . kñúgkrNIenH bERmbRmYlrag

eFobEdkeFobenAnIv:UTIRbCMuTm¶n;EdkTajmantémøtUcCag 005.0 ³ 005.0003.0)( <−

=c

cdtsε

EdlenAEtGacTTYlyk)an. dMeNaHRsaytamviFITI2enH segçbdUcxageRkam³ + KNna mmhdt 65−= / tdc )

83(= nig ca 1β=

+ KNnakmøaMgsgát;enAkñúgebtug ysc fATabfC 111 '85.0 === kMNt; 1sA . KNna )

2(11

adfAM ysu −= φ . bdAs1

1 =ρ / 9.0=φ + KNna 12 uuu MMM −= edaysn μt; mmd 65'= + KNna 2sA BI )'(22 ddfAM ysu −= φ eday ys ff =' . muxkat;EdkrgkarTajsrub 21 sss AAA += + KNnakugRtaMgenAkñúgEdkrgkarsgát;dUcxageRkam

× KNna ys fc

dcf ≤−

= )'(600' × b¤KNna s'ε BIdüaRkambMErbMrYlrageFob nig sss Ef '' ε= . RbsinebI ys εε =' enaHEdkrg karsgát; yield ehIy ys ff =' . × KNna sA' BI )'('22 ddfAM ssu −=φ . RbsinebI ys ff =' enaH 2' ss AA = . EtebI

ys ff <' enaH 2' ss AA > ehIy )'

(' 2s

yss f

fAA = .

]TahrN_5³ eKmanFñwmmYymanmuxkat; cmb 25= nigkm<s; cmh 55= EdlRtUvRTnUvm:Um:g;Bt;KNna mkNMu .300= . KNnasrésEdktRmUvkar. sm μtikm μ MPaf c 20' = nig MPaf y 345= .

dMeNaHRsay³ - kMNt;ersIusþg;m:Um:g;EdlekItBIEdkrgkarTajCaeKalsRmab;lkçxNÐ tension-controlled section

sRmab; MPaf c 20' = nig MPaf y 345= / 85.01 =β 0266.0)

345600600(

3452085.0)

600600('85.0 2

1 =+

=+

=yy

cb ff

fβρ

0157.0)008.0200000

345003.0(0266.0)

008.0

003.0(max =

+=

+= s

y

bEf

ρρ

MPaff

fRc

yyu 1.4)

207.13450157.01(3450157.09.0)

'7.11( max

max(max) =××

−××=−=ρ

φρ



edaysnμt;EdkrgkarTajmanBIrRsTab; mmmmhd 4609055090 =−=−=

MPaMmkNmmNbdRM uun 300.89.216.1089.2164602501.4 622(max) =<=×=××==⇒φ

dUcenHmuxkat;enHRtuvkarEdkrgkarsgát;edIm,ITb;Tl;nwgm:Um:g;EdlenAsl;. - KNna 1sA / 1uM nig 2uM

2max1 06.1846250157.0 cmbdAs =××== ρ

mkNMM nu .89.2161 == φ 2

12 11.8389.216300 cmMMM uuu =−=−=⇒ - KNna 2sA nig sA' Edl)anBI 2uM edaysnμt; cmd 6'=

)'(22 ddfAM ysu −= φ 22

62

2 69.6669)60460(3459.0

1011.83)'(

cmmmddf

MAy

us ==

−×××

=−

=φ

EdkrgkarTajsrub 221 75.2469.606.18 cmAAA sss =+=+=

Edkrgkarsgát; 22 69.6' cmAA ss == eFVIkardl; yield

- RtYtBinitüEdksgát;eFVIkardl; yield 001725.0

200000345

200000=== y

y

fε

eday mmbf

fAa

c

ys 6.1462502085.0

3451806'85.0

1 =××

×==

mmac 47.17285.0

6.1461

===β

ys εε >=×−

= 00196.0003.0)47.172

6047.172(' eFVIkardl; yield - RtYtBinitü tε edayeyIgeRbI maxρ nig uR mkeRbIsRmab;edaHRsay edayeGaybERmbRmYlrageFobEdksuT§enAnIv:UTIRbCMu Tm¶n;Edk 005.0=sε . dUcenHeyIgRtUvkMNt; tε sRmab;EdkenARsTab;eRkameKbMput.

mmdt 49060550 =−= 005.00055.0003.0)

47.17247.172490(003.0)( >=

−=

−=

ccdt

tε RtwmRtUv dUcenH EdktRmUvkarsRmab;karTaj 275.24 cmAs = eRbI 255DB sRmab;karsgát; 269.6' cmA s = eRbI 222DB



]TahrN_6³ eKmanFñwmmYymanmuxkat; cmb 30= nigkm<s; cmh 50= EdlRtUvRTnUvm:Um:g;Bt;KNna mkNMu .400= . KNnasrésEdktRmUvkar. sm μtikm μ MPaf c 28' = nig MPafy 400= .

dMeNaHRsay³ manBIrviFIsaRsþ vIFITI1³ - kMNt;ersIusþg;m:Um:g;Gtibrmaénmuxkat;EdlmanEtEdkrgkarTajCaeKal sRmab; MPaf c 28' = / MPaf y 400= / 85.01 =β

030345.0=bρ / 019.0max =ρ sRmab; tension-controlled section 9.0=φ

MPaff

fRc

yyu 75.5)

287.1400019.01(400019.09.0)

'7.11( max

max(max) =××

−××=−=⇒ρ

φρ

edaysnμt; mmhd 4109050090 =−=−= EdkmanBIrRsTab; MPammNbdRM uu 290.1029041030075.5 622

1 <×=××==⇒ dUcenHRtUvkarEdksgát; - KNna ,1sA ,2uM 2sA nig sA

2max1 37.234130019.0 cmbdAs =××== ρ

mkNMMM uuu .11029040012 =−=−= )'(22 ddfAM ysu −=φ edaysnμt; mmd 60'=

226

2 73.8873)60410(4009.0

10110 cmmmAs ==−××

×=⇒



muxkat;EdkTajsrub 221 1.3273.837.23 cmAAA sss =+=+=

eRbIEdk 305DB - RtYtBinitüEdkrgkarsgát;eFVIkardl; yield b¤Gt;

)600

600)('('85.0' 1yy

c

fdd

ffK

+=≥− βρρ

00444.0)400600

600)(41060(

4002885.0 2 =

+=K

KbdAs <=

×==− 019.0

413037.23' 1ρρ

⇒ Edkrgkarsgát;eFVIkarmindl; yield eT dUcenH ys ff <' - KNna sf ' ³

ys fc

dcf ≤−

= )'(600' kMNt; c BI 2

1 37.23 cmAs = mm

bffA

ac

ys 92.1303002885.0

4002337'85.0

1 =××

×==

mmac 02.15485.092.130

1

===β

ys fMPaf ≤=−

= 3.366)02.154

6002.154(600' - KNna sA' BI )'(''2 ddfAM ssu −= φ

226

53.9953)60410(3.3669.0

10110' cmmmA s ==−××

×= eRbIEdk 252DB

eyIgeXIjva eKarBtamlkçxNÐ max)''( ρρρ ≤−

y

s

ff

- RtYtBinitübERmbRmYlrageFobEdksuT§ tε enAnIv:UEdkRsTab;xageRkam ¬eRBaHeyIgsnμt;fa bERmbRmYlrag eFobEdksuT§ sε enAnIv:UTIRbCMuTm¶n;Edk¦

mmdt 44060500 =−= 005.00056.0003.0)

02.15402.154440(003.0)( >=

−=

−=

ccdt

tε RtwmRtUv



vIFITI2³ edayeRbIEdkrgkarTajBIrRsTab; nigsac;lUteFobEdksuT§enARsTab;eRkambMput 005.0=tε

- KNna mmdt 44060500 =−= BIdüaRkambERmbRmYlrageFob 375.0

008.0003.0

003.0003.0

==+

=ttd

cε

mmdc t 165375.0 ==⇒ mmca 25.14085.0 ==⇒

- kmøaMgsgát;kñúgebtug kNNabfC c 385.1001100138530025.1402885.0'85.01 ==×××==

¬sRmab;muxkat;manEdkrgkarTajCaeKal¦ eday 11 TC = 221

1 03.252503400

1001385 cmmmfTA

ys ====⇒

mmd 41090500 =−= mkNmmNadfAM ysu .25.306.1025.306)

225.140410(40025039.0)

2( 6

11 =×=−×××=−= φ 0203.0

413003.251

1 =×

==bdAsρ

- eday 1uu MM > dUcenHmuxkat;RtUvkarEdkrgkarsgát; mkNMu .75.9325.3064002 =−=



226

22 44.7744

)60410(4009.01075.93

)'(9.0cmmm

ddfMAy

us ==

−×××

=−

=⇒

muxkat;EdkrgkarTajsrub 221 47.3244.703.25 cmAAA sss =+=+= eRbIEdk 305DB

- RtYtBinitü Edkrgkarsgát;eFVIkardl; yield b¤Gt; 00444.0)

400600600)(

41060(

4002885.0 2 =

+=K

K<=− 1)'( ρρρ ⇒ Edkrgkarsgát;eFVIkarmindl; yield eT dUcenH ys ff <' MPa

cdcf s 82.381)

16560165(600)'(600' =

−=

−=

KNna sA' BI 2uM 22

62 79.7779

)60410(82.3819.01075.93

)'('9.0' cmmm

ddfMAs

us ==

−×××

=−

=⇒ eRbIEdk 252DB

- RtYtBinitüersIusþg;m:Um:g;kñúg 2325.35305 cmDBAs == 281.9252' cmDBA s == 2

1 515.25' cmAAA sss =−= )]'('')

2([ 1 ddfAadfAM ssysn −+−= φφ

mmNM n .1018.430)]60410(82.381981)2

25.140410(4005.2551[9.0 6×=−××+−××=φ eyIgeXIjfa 0045.0003.0)

165165410(003.0)( =

−=

−=

ccd

sε

4>5> KNnamuxkat;GkSret T kñúgkarKNnamuxkat;GkSr T edaysÁal;m:Um:g;KNna uM / kRmas;søab t nigTTwgsøab b . kRmas;

rbs;RTnug wb ERbRbYlBI cmcm 5020 → . GBaØatBIreTotEdlRtUvkarKNnaKW km<s;RbsiT§PaB d nigmux kat;Edk sA . eKmanBIkrNIEdlCYbRbTH³

- enAeBleKsÁal; d + RtYtBinitüfa muxkat;eFVIkarCaragctuekaNEkg b¤GkSret T edaysnμt; ta =

KNnaersIusþg;m:Um:g;sRmab;søabTaMgmUl )

2()'85.0( tdbtfM cnf −=φφ

RbsinebI nfu MM φ> enaH ta > KNnaCaragGkSret T. RbsinebI nfu MM φ< enaH ta < KNna CaragctuekaNEkg.

+ RbsinebI ta < enaHKNna )'7.1

411('85.02bdf

Mf

f

c

u

y

c

φρ −−= / KNna bdAs ρ= .

epÞógpÞat; minρρ ≥w .



+ RbsinebI ta > enaHKNna sfA sRmab;Epñksøabsgxag ¬>>>¦ ywcsf ftbbfA /)('85.0 −=

)2

(2tdfAM ysfu −= φ

m:Um:g;EdlTb;edayRTnugKW 21 uuu MMM −=

KNna 1ρ edayeRbI 1uM / wb nig d )

'7.1411('85.0

21

1 dbfM

ff

wc

u

y

c

φρ −−=

nigKNna dbA ws 11 ρ= muxkat;Edksrub sfss AAA += 1 bnÞab;mkRtYtBinitü maxss AA ≤ dUcKña RtUvRtYtBinitü minρρ ≥=

dbAw

w

+ RbsinebI ta = enaH y

cs f

btfA '85.0φ=

- enAeBleKminsÁal; d nig sA karKNnaRtUveFVItamviFIsaRsþxageRkam + snμt; ta = nigKNnabrimaNEdksrub sftA EdlRtUvkarsRmab;Tb;nwgkmøaMgsgát;kñúgsøab

TaMgmUl bt

y

csft f

btfA '85.0=

+ kMNt; d BI sftA nig ta = tamrUbmnþxageRkam³ )

2( tdfAM ysftu −=φ

× RbsinebI eKyktam d KNnarkeXIjenaH sfts AA = nig mmdh 65+= sRmab; EdkmanmYyRsTab; b¤ mmdh 90+= sRmab;EdkmanBIrRsTab;.

× RbsinebI eKyk 1d fμ IFMCag d KNnaenaHmuxkat;eFVIkarCaragctuekaNEkg. ehIy )

'7.1411('85.0

2bdfM

ff

c

u

y

c

φρ −−= / KNna bdAs ρ= .

× RbsinebI eKyk 21d fμ ItUcCag d KNnaenaHmuxkat;eFVIkarCaragGkSr T. ehIy muxkat;EdkcugeRkay sA FMCag sftA . kñúgkrNIenH eKRtUveFVIdUckrNIxagelIedIm,IkMNt; muxkat; sA .



]TahrN_7³ eKmanFñwmmYymanGkSr T EdlmanRTnug cmbw 25= RbEvgsøab cmb 100= kRmas;søab cmt 10= nigkm<s;RbsiT§PaB cmd 37= . kMNt;muxkat;EdkcaM)ac; edIm,ITb;nwgm:Um:g; mkNMu .375= .

smμtikm μ MPaf c 20' = nig MPafy 400= . dMeNaHRsay³

- RtYtBinitüG½kSNWt edaysnμt; cmta 10== mmNtdbtfM cn .106.489)

2100370(10010002085.09.0)

2('85.0 6×=−××××=−= φφ

eday un MM >φ ⇒muxkat;manlkçN³CactuekaNEkg - kMNt;muxkat;EdkrgkarTaj

00845.0)3701000209.07.1

10375411(400

2085.0)'7.1

411('85.02

6

2 =××××

××−−

×=−−=

bdfM

ff

c

u

y

c

φρ

2265.313710000845.0 cmbdAs =××== ρ edayeRbI 2325.35305 cmDB = - RtYtBinitü 0035.0

4004.10382.0

3725325.35

min ==>=×

== ρρdb

Aw

sw

swwey

cs Acmdbtbb

ffA >=+−= 2

1max 41.44]375.0)[('85.0 β

dUcKña cmbf

fAa

c

ys 31.81002085.0

400325.35'85.0

=×××

==

cmac 78.985.031.8

1

===β

nig 005.000835.0)78.9

78.937(003.0 >=−

=sε

]TahrN_8³ RbB½n§kRmalxNÐdUcbgðajkñúgrUb EdlpÁúMeLIgedaykRmalxNÐEdlmankRmas; cmt 8= EdlRT edayFñwmRbEvg cmL 430= EdlmanKMlatBIKña cml 300= KitBIG½kSmkG½kS. FñwmmanRTnug cmbw 35=



nigkm<s;RbsiT§PaB cmd 47= . kMNt;muxkat;EdkcaM)ac;edIm,ITb;nwgm:Um:g;KNna mkNMu .575= . smμtikm μ MPaf c 20' = nig MPafy 400= . dMeNaHRsay³

- kMNt;RbEvgsøab

⎪⎩

⎪⎨

⎧ +

=

l

Lbt

bw

e 4

16

min⎪⎩

⎪⎨

⎧

=

=+×

=

mm

mmmm

3000

10754

430016303508016

min

dUcenH mmbe 1075= - RtYtBinitüTItaMgG½kSNWt edaysnμt; ta =

)2

('85.0 tdbtfM cn −= φφ mkNmkNmmNM n .575.794.565.794.565)

280470(8010752085.09.0 <==−××××=φ

eday un MM <φ ⇒ muxkat;manlkçN³CaragGkSr T dUcenH ta > . - kMNt;muxkat;EdksrubsRmab;Tb;Tl;CamYykmøaMgsgát;kñúgsøab

22456400

80)3501075(2085.0)('85.0 mmf

tbbfAy

wcsf =

−××=

−=

mmNtdfAM ysfu .10188.380)2

80470(40024569.0)2

( 62 ×=−××=−=⇒ φ

⇒ )'7.1

411('85.02

11 dbf

Mf

f

wc

u

y

c

φρ −−=

0077.0470350209.07.1

10812.194411(400

2085.02

6

1 =××××

××−−

×=ρ



enaH 211 67.1247350077.0 cmdbA ws =××== ρ

⇒muxkat;EdkTajsrub 223.3756.2467.12 cmAs =+= eRbI 306DB BIrRsTab; - km<s;srubrbs;muxkat; mmh 56090470 =+=

swwey

cs Acmdbtbb

ffA >=+−= 2

1max 87.50]375.0)[('85.0 β

- RtYtBinitü tε / cmbf

fAa

c

ys 278.95.1072085.0

40039.42'85.0

=×××

==

cmac 91.1085.0

278.9

1

===β

cmdt 50656 =−= 005.00107.0)

91.1091.1050(003.0 >=

−=⇒ tε

]TahrN_9³ sRmab;RbB½n§kRmalxNÐmYy EdlmanTTwgsøabRbEvg cmbe 122= TTwgRTnug 40=wb ehIy kRmalxNÐmankRmas; cmt 10= . KNnamuxkat;GkSr T edIm,IrgnUvm:Um:g;KNna mkNMu .1100= . smμtikm μ MPaf c 20' = nig MPaf y 400= .



dMeNaHRsay³ - edaysarminsÁal;km<s;RbsiT§PaB eyIgeGay ta = kMNt;muxkat;Edk sftA sRmab;søabTaMgmUl

285.51400

101222085.0'85.0 cmf

btfAy

csft =

×××==

eGay )2

( tdfAM ysftu −= φ KNna d

mmtfA

Mdysft

u 3.6392

10040051859.0

1011002

6

=+××

×=+=⇒

φ

eyIgeXIjfa RbsinebI cmd 93.63= enaH sfts AA = - RbsinebI cmd 93.63> / eyIgsnμt;yk cmd 67= enaH ta < muxkat;manlkçN³CaragctuekaNEkg PaKryEdkRtUv)anKNnatamrUbmnþxageRkam³

)'7.1

411('85.02dbf

Mf

f

wc

u

y

c

φρ −−=

⇒ 006.06701220209.07.1

101100411(400

2085.02

6

=××××

××−−

×=ρ

enaHmuxkat;Edk 204.4967122006.0 cmbdAs =××== ρ - RbsinebI cmd 93.63< / eyIgsnμt;yk cmd 60= enaH ta > muxkat;manlkçN³CaragGkSret T .

285.34400

)40122(102085.0)('85.0 cmf

bbtfAy

wcsf =

−×××=

−=

mmNtdfAM ysfu .10690)2

100600(40034859.0)2

( 62 ×=−××=−= φ

mkNMu .41069011001 =−=

sRmab;muxkat;EdkrgkmøaMgTajeKal cmbw 40= / cmd 60= nig mkNMu .4101 = MPa

dbMR m

kN

w

uu 85.22.2847

60.04.0410

2221 ==

×==

⇒ 0088.0)209.07.1

85.2411(400

2085.0)'7.1

411('85.01 =

×××

−−×

=−−=c

u

y

c

fR

ff

φρ

211 12.2160400088.0 cmdbA ws =××== ρ

21 97.5512.2185.34 cmAAA sfss =+=+=⇒

eRbIEdk 227.56327 cmDB = - RtYtBinitü tε

cmbf

fAa

wc

ys 42.12402085.0

40012.21'85.0

1 =××

×==



cmac 6.1485.042.12

85.0===

cmdt 63=

005.00099.0003.0 >=⎟⎠⎞

⎜⎝⎛ −

=⇒c

cdttε tension-controlled section

- KNnamuxkat;EdksrubGtibrma )]60040085.0375.0100)4001220[(

4002085.0]375.0)[('85.0 1max ×××+−=+−= dbtbb

ffA wwe

y

cs β

222max 27.5636.676736 cmcmmmAs >== RtwmRtUv


viFIKNnaepSgeTot 105 T.Chhay

V. viFIKNnaepSgeTot

Alternative Design Methods 5>1> esckþIepþIm (Introduction)

enAkñúgemeronTI3 nigTI4 karviPaK nigkarKNnaGgát;ebtugBRgwgEdkRtUv)anBnül;edayQrelIeKal karN_Edlpþl;[eday ACI Code 318-05. viFIKNnadéTRtUv)anbgðajenAkñúg]bsm<½n§ Appendix B én ACI Code edayeyageTAtamemKuNbnÞúkEdl[enAkñúg]bsm<½n§ Appendix C. viFIKNnaepSgeTotenH KWCaeKalkarN_énkarviPaK nigkarKNnaenAkñúg ACI Code 318-99. vamanlkçN³RsedogKñaxøHeTAnwg viFI Edl)anBnül;BImun elIkElgEtvaeRbIemKuNbnÞúk nigemKuNkat;bnßyersIusþg; φ xusKña. smIkarviPaK nig smIkarKNnaeKalEdlmanenAkñúgemeronmun nwgRtUv)aneRbIenATIenH. enAeBleKeRbI Appendix B edIm,I KNna eKRtUvCMnYsnUvGVIEdlRtUvKñaenAkñúg Code enaH.

5>2> emKuNbnÞúk (Load Factors)

RbsinebIersIusþg;TRmUvkar required strength RtUv)antageday U ehIykmøaMgxül; nigkmøaMgrBa¢ÜydIRtUv )antageday W nig E erogKña enaHtam ACI Code, Appendix C ersIusþg;TRmUvkar U KYrEtCatémøEdlFM CageKkñúgcMeNambnSMbnÞúkxageRkam³

1> sRmab;krNIbnÞúkefr bnÞúkGefr nigbnÞúkxül; LDU 7.14.1 += (5-1a)

WLDU 6.1()7.14.1(75.0 ++= b¤ )0.1 E (5-1b)

WDU 6.1(9.0 += b¤ )0.1 E (5-1c)

2> enAeBlbnÞúkxül; W minRtUv)ankat;bnßyedayemKuNTisedA directionality factor W3.1 Gac RtUv)aneRbICMnYs W6.1 . enAeBlEdlbnÞúkrBa¢ÜydIRtUv)anQrenAelIbnÞúkeFVIkar service forces enaH

E4.1 GacRtUv)aneRbICMnYs[ E0.1 . 3> kñúgkrNIEdlbnÞúksm<aFdI H RtUv)anbBa©ÚleTAkñúgkarKNna

HLDU 7.17.14.1 ++= (5-2a) enAeBlEdlbnÞúkefr D nigbnÞúkGefr L kat;bnßy\T§iBlrbs; H enaH HDU 7.19.0 += (5-2b)

sRmab;bnSMbnÞúkén D / L b¤ H LDU 7.14.1 +=


T.Chhay 106 Alternative Design Methods

4> RbsinebITm¶n; nigbnÞúksm<aFEdl)anmkBIsarFaturav F RtUv)anbBa©ÚleTAkñúgkarKNna FLDU 4.17.14.1 ++= (5-3a)

enAeBlEdlbnÞúkefr D nigbnÞúkGefr L kat;bnßy\T§iBlrbs; F enaH FDU 4.19.0 += (5-3b)

sRmab;bnSMbnÞúkén D / L b¤ F LDU 7.14.1 +=

sm<aFbBaÄrénsarFaturavKYrRtUv)anKitCabnÞúkefr. 5> enAeBlEdl\T§iBlTgÁic impact effects RtUv)anrab;bBa©Úl enaHvaRtUv)anKitbBa©ÚleTAkñúgbnÞúkGefr. 6> enAeBlEdl structural effects T énsRmut differential settlement, creep, karrYmmaD

(shrinkage) b¤ bNþÚrsItuNðPaB mantémøFM vaKYrRtUv)anrab;bBa©ÚleTAkñúgbnSMbnÞúkén )7.14.14.1(75.0 LTDU ++= (5-4a)

TDU 4.14.1 += (5-4b)

smIkar (5-1a) RtUv)aneRbICaTUeTA. emKuNbnÞúkefres μ Inwg 4.1 nigemKuNbnÞúkGefres μ Inwg 7.1 . sRmab;bnÞúkefr nigbnÞúkGefrcMcMNuc DP nig LP enaHbnÞúkcMcMNucemKuN LDU PPP += dUcKña

LDU MMM += Edl DM nig LM m:Um:g;bnÞúkefr nigm:Um:g;bnÞúkGefrerogKña.

5>3>emKuNkat;bnßyersIusþg; (Strength-Reduction Factor φ ) ersIusþg; nominal strength énmuxkat;RtUv)ankat;bnßyedayemKuN φ edIm,IKitsRmab;kar)at;bg;

ersIusþg;enAkñúgsmÖar³d¾tictYc small adverse variations in material strength karplitEdleFIVeLIgedayéd artisanry TMhMxñat karRKb;RKg nigkRmiténkarRtYtBinitü. emKuN φ CaEpñkmYyénemKuNsuvtßiPaB.

bTdæan ACI Code, Section C.3 (Appendix C) kMNt;nUvtémøxageRkamedIm,IeRbIR)as;³ - sRmab;muxkat;rgkarTaj 90.0=φ

- sRmab;muxkat;rgkarsgát; k> CamYyEdkkgvNÐ 70.0=φ x> CamYyEdkkgFm μta 65.0=φ - sRmab;kmøaMgkat; nigkmøaMgrmYl 75.0=φ - sRmab;RTnab;enAelIebtug 65.0=φ - sRmab;karBt;enAelIebtugsuT§ b¤enAelIebtugEdlmanbrimaNEdkGb,brma yf/4.1 ³ 65.0=φ



sRmab;muxkat;EdlsßitenAkñúgtMbn; transition region rvagmuxkat;rgkarTaj tension-controlled

section nigmuxkat;rgkarsgát; compression-controlled section enaH φ GacnwgekIneLIgCabnÞat;rhUtdl; 9.0 .

eKk¾GaceRbIemKuNkat;bnßyersIusþg; φ sRmab;ssr ¬b¤muxkat;Edlman 005.0<tε ¦ edayvaERb RbYleTAtamkrNIxageRkam³

1> enAeBlEdl gcnu AfPP '1.0≥= φ enaH 7.0=φ sRmab;ssrEdkkgFm μta nig 75.0=φ sRmab;EdkkgvNÐ½. krNIekIteLIgCaTUeTAsRmab;muxkat;rgkarsgát; compression control.

gA Camuxkat;eBj. 2> rvagtémø gc Af '1.0 b¤ nPφ ¬mYyNaEdltUcCag¦ nigsUnü ehIy uP sßitenAkñúgtMbn;Taj

tension control zone nig φ FMCag 7.0 ¬b¤ 75.0 ¦. ACI Code, Section C3.2 kMNt;fa sRmab;Ggát;Edlman yf minFMCag MPa400 CamYyEdksIuemRTI nigCamYycm¶ayrvagEdk rgkarsgát; nigkarTaj )'( dd − minRtUvticCag h7.0 ¬ h =km<s;srubrbs;muxkat;¦ nig

sdhd −= enaHtMél φ RtUv)anekIneLIgCabnÞat;eTArk 9.0 . sRmab;tMbn; transition region, φ RtUv)ankMNt;edayviFan linear interpolation rvag 7.0 ¬b¤

75.0 ¦ nig 9.0 . rUb 5>1 bgðajBIbMErbMrYlrbs; φ sRmab;Edk MPa400 . smIkarbnÞat;mandUcxageRkam³ tεφ 6757.0 += sRmab;muxkat;EdkkgFmμta (5-5)

tεφ 5065.0 += sRmab;muxkat;Edkkgv½NÐ (5-6)

mü:agvijeTot φ enAkñúgtMbn; transition region GacRtUv)ankMNt;CaGnuKmn_eTAnwg )/( cdt sRmab;Edk MPa400 dUcxageRkam³

⎟⎠⎞

⎜⎝⎛+=

cdt20.037.0φ sRmab;muxkat;EdkkgFmμta (5-7)

⎟⎠⎞

⎜⎝⎛+=

cdt15.050.0φ sRmab;muxkat;EdkkgvNÐ (5-8)

Edl c Cakm<s;G½kSNWtenAersIusþg; normal strength.



5>4> muxkat;ctuekaNEkgCamYyEdkrgkarTaj (Rectangular Sections with Tension Reinforcement) BIkarviPaKénmuxkat;ctuekaNEkgEdkrgkarTaj smIkarxageRkamRtUv)anbMEbk Edl cf ' nig yf

KitCa MPa ³

⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

yy

cb ff

f600

600'85.0 1βρ

RbsinebIPaKryEdkGtibrmaRtUv)ankMNt; bρ75.0 enaH

⎟⎟⎠

⎞⎜⎜⎝

⎛

+==

yy

cb ff

f600

600'6375.075.0 1max βρρ (5-9)

enHbgðajfa bρρ 75.0max = FMCag bρρ 634.0max = Edl)an[enAkñúgemeronTI3 sRmab;Edk MPa400 .

sRmab; MPaf c 28' ≤

⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

yy

cff

f600

600'542.0maxρ (5-10)

85.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 28' ≤ . )

728'(05.085.01−

−= cfβ sRmab;ebtugEdlmanersIusþg; MPafMPa c 56'28 ≤< .



65.01 =β sRmab;ebtugEdlmanersIusþg; MPaf c 56' > . PaKryEdkénmuxkat; balanced section bρ nigPaKryEdkGtibrmaGnuBaØat maxρ GacRtUv)an

KNnasRmab;témøepSgKñaén cf ' nig yf dUcbgðajenAkñúgtarag 5>1. PaKryEdkKNnaEdlesñIeLIgsRmab; maxρρ ≤ k¾RtUv)anbgðajenAkúñgtarag 5>1.

taragTI5>1³ PaKryEdkEdlRtUv)anesñIreLIg sρ )(' MPaf c )(MPaf y sρ%

20 235 1.4 400 1.2 28 400 1.4 500 1.2 35 400 1.4 500 1.2

smIkarm:Um:g;KNnaRtUv)anbMEbkenAkñúgemeronmunmanTRmg;dUcxageRkam³ 2bdRMM uun ==φ (3-21)

Edl nc

yyu R

ff

fR φρ

φρ =⎟⎟⎠

⎞⎜⎜⎝

⎛−=

'7.11 (3-22)

nig 9.0=φ . sRmab;muxkat;rgkarTaj (tension-controlled section) / 005.0≥tε

⎟⎟⎠

⎞⎜⎜⎝

⎛−==

bffA

dfAMMc

ysysun '7.1

φφ (3-19a)

dUcKña ⎟⎟⎠

⎞⎜⎜⎝

⎛−==

c

yyun f

fdbdfMM

'7.12 ρ

φφ (3-20)

eyIgeXIjfasRmab;eRkABIm:Um:g;emKuN uM / cf ' / yf eKmanGBaØatbIenAkñúgsmIkarenHKW b / d nig ρ . dUcenHeKminGacedaHRsaysmIkarenH)aneT Tal;EtGBaØatBIrRtUv)ansnμt;. CaTUeTA eKeRcInsnμt; ρ ¬edayeRbI maxρ ¦ nig b k¾RtUv)ansnμt;Edr. edayQrelIkarBiPakSaBIxagedIm krNIxageRkamRtUv)anbegáIt eLIgenAeBl uM / cf ' / yf RtUv)ansÁal;³

1> RbsinebI ρ RtUv)ansnμt; enaH uR GacRtUv)anKNnaBIsmIkar (3-22) Edl[ 2bd uu RM /= . GñkKNnaGaceRbI ρ rhUtdl; maxρ EdlbegáItmuxkat;ebtugEdkrgkarTajGb,brma. RbsinebI eRbI minρ vanwgbegáItmuxkat;ebtugGtibrma. RbsinebI b RtUv)ansnμt;bEnßmBI elI ρ enaH d Gac RtUv)anKNnadUcxageRkam³

bRMd

u

u= (5-11)

RbsinebI 2/ =bd enaH 3 )/2( uu RMd = nig 2/db = bgçittémøeTArktémøEdlFM.



2> RbsinebI d nig b RtUv)an[ enaHPaKryEdkRtUvkar ρ GacRtUv)anKNnaedaysmIkar (3-20)

eKTTYl)an

3> ⎥⎥⎦

⎤

⎢⎢⎣

⎡−−= 2'7.1

411'85.0bdf

Mf

f

c

u

y

c

φρ (5-12)

⎥⎦

⎤⎢⎣

⎡−−=

c

u

y

cf

Rf

f'85.0

211'85.0

nig bdAs ρ= Ca]TahrN_/ RbsinebI mkNMu .72.275= / mmb 300= / mmd 450= / MPaf c 20' = nig

MPaf y 400= enaH 0154.0=ρ BIsmIkar (5-12) nig 220794503000154.0 mmbdAs =××== ρ enA eBlEdleK[ b nig d eKKYrEtBinitüemIlfaetIeKRtUvkarEdkrgkarsgát; b¤Gt; eRBaHEt d tUc. eKGacedaH Rsayva)andUcxageRkam³

k> KNna maxρ nig ( )[ ]cyyu fffR '7.1/1 maxmaxmax, ρφρ −= x> KNna == 2

max,max, bdRM unφ ersIusþg;m:Um:g;Gtibrmarbs;muxkat;EdkrgkarTaj. K> RbsinebI max,nu MM φ< enaHvaminRtUvkarEdkrgkarTajeT. KNna ρ nig sA BIsmIkar (5-

12)

X> RbsinebIeKsÁal; ρ nig b KNna uR ³

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

c

yyu f

ffR

'7.11

ρφρ

KNna d BIsmIkar (5-11)

bRMd

u

u= nig bdAs ρ=

]TahrN_TI1³ kMNt;muxkat;EdkcaM)ac;sRmab;muxkat;EdlmanTTwg mmb 250= nigkm<s;srub mmd 700= ¬rUbTI5>2¦ RbsinebIvargnUvm:Um:g;emKuNxageRkA mkN.312 . eK[ MPaf c 28' = nig MPaf y 400= . dMeNaHRsay

1> snμt;eRbIEdk 25DB mYyRsTab; ¬epÞógpÞat;enAeBleRkay¦ mmd 65050700 =−= . 2> RtYtBinitüemIlfaetImuxkat;RtUvkarEdksgát; b¤Gt;. eRbobeFobersIusþg;m:Um:g;KNnaénmuxkat; ¬eday

eRbI maxρ ¦ CamYym:Um:g;KNna. sRmab; MPaf c 28' = nig MPaf y 400= / 02276.0max =ρ . MPa

ff

fRc

yyu 63.6

'7.11 max

max =⎟⎟⎠

⎞⎜⎜⎝

⎛−=ρ

φρ



ersIusþg;m:Um:g;KNnaénmuxkat;ebtugEdkrgkarTajKW

mkNmkNbdRM un .312.3.7001065025063.6 622max/max, >=×××== −φ

dUcenH maxρρ < enaHvaCamuxkat;EdlmanEtEdkrgkarTaj. 3> KNna ρ BIsmIkar (5-12) edIm,ITTYl)an 0089.0=ρ / 6502500089.0 ××== bdAs ρ

21446mm= eRbIEdk 253DB ( )21472mmAs = . muxkat;cugeRkayRtUv)anbgðajenAkñúgrUbTI 5>2. 4> epÞógpÞat; tε ³

mma 96.982502885.0

4001472=

×××

= mmac 4.116

85.0==

005.00137.0003.0 >=−

=c

cdttε 9.0=φ

5>5> muxkat;ctuekaNCamYynwgEdkrgkarsgát ; (Rectangular Sections with Compression Reinforcement) muxkat;ebtugEdkrgkarTaj singly reinforced section EdlmanersIusþg;m:Um:g;GtibrmaenAeBlEdl

maxρ rbs;EdkRtUv)aneRbI. RbsinebIm:Um:g;emKuNFMCagersIusþg;m:Um:g;kñúg ¬krNImuxkat;RtUv)ankMNt;¦ enaHeK RtUvkarmuxkat;EdkDub doubly reinforced section edaybEnßmEdkTaMgenAkñúgtMbn;sgát; nigtMbn;Taj. viFI saRsþsRmab;KNnamuxkat;ctuekaNEkgCamYyEdksgát; enAeBlEdleKsÁal; uM / cf ' / b / d nig 'd Rtuv)ansegçbenAkñúgemeronTI4. karEdlxusKñamanEtmYyKW bρρ 75.0max = RtUv)aneRbIenAkñúgkarKNnaenH³

⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

yy

cff

f600

600'6375.0 1max βρ (5-9)



dUcKña RtUvepÞogpÞat; 005.0≥tε sRmab; 9.0=φ . ]TahrN_TI2³ muxkat;FñwmRtUv)ankMNt;eday mmb 300= nigkm<s;srub mmh 500= ehIyrgnUvm:Um:g;emKuN

mkNMu .5.447= . kMNt;muxkat;EdkcaM)ac;edayeRbI MPaf c 28' = nig MPaf y 400= . ¬eyagtamrUb 5>3¦.

dMeNaHRsay³

1> kMNt;ersIusþg;m:Um:g;KNnaénmuxkat;EdkeTal. sn μt; 018.0=ρ . dUcenH MPaRu 5.5= . sRmab; EdkBIrRsTab; mmd 41090500 =−=

mkNbdRM uu .4.277104103005.5 6221 =×××== −

m:Um:g;KNnaKW mkNmkNMu .4.277.5.447 >= dUcenHeKRtUvkarEdksgát; 2> KNna 1sA / 2uM / 2sA nig sA

21 2214410300018.0 mmbdAs =××== ρ

mkNMMM uuu .1.1704.2775.44712 =−=−= )'(22 ddfAM ysu −= φ snμt; mmd 50'=

)50410(4009.0101.170 26 −=⋅ sA 2

2 5.1312 mmAs = 2

21 5.35265.13122214 mmAAA sss =+=+= ¬ 286DB ¦ 3> epÞógpÞat;PaB yield rbs;Edkrgkarsgát;. Edkrgkarsgát; yield RbsinebI

⎟⎟⎠

⎞⎜⎜⎝

⎛

−⎟⎠⎞

⎜⎝⎛=≥−

yy

cfd

dffK

600600''85.0' 1βρρ

0185.0400600

60041050

40028)85.0( 2 =⎟

⎠⎞

⎜⎝⎛

−⎟⎠⎞

⎜⎝⎛=K

KbdAs <=

×==− 018.0

4103002214' 1ρρ

dUcenH Edkrgkarsgát;Gt; yield ³ ys ff <'



4> KNna sf ' ³ ( )[ ] ys fcdcf ≤−= /'600' / kMNt; 1sA ³ 2

1 2214mmAs = mm

bffA

ac

ys 1243002885.0

4002214'85.0

1 =××

×==

mmac 9.14585.0

124

1===

β

MPaMPaf s 4004.3949.145509.145600' <=

−=

5> KNna sA' BI )'(''2 ddfAM ssu −= φ )50410(4.394'9.0101.170 6 −=⋅ sA

dUcenH 21331' mmA s = b¤KNna sA' BI ( ) 22 1331'/' mmffAA syss == ¬ 253DB ¦

6> epÞógpÞat; 003.0⎟

⎠⎞

⎜⎝⎛ −

=c

cdttε

mmdhdt 45050500' =−=−= 005.0006.0003.0

9.1459.145450

>=⎟⎠⎞

⎜⎝⎛ −

=tε 9.0=φ

375.0324.0450

9.145<==

tdc (OK)

7> epÞógpÞat; nMφ cugeRkay/ 25.3694 mmAs = / 26.1472' mmA s = / 2

1 9.2221 mmAs = / mma 5.124= nig mmc 5.146= ( ) mkNM n .15.518504104.3946.1472

25.1244104009.2221 =−×+⎟⎠⎞

⎜⎝⎛ −×=

epÞógpÞat; tε / mmdt 450= 005.0006.0003.0 >=⎟

⎠⎞

⎜⎝⎛ −

=c

cdttε

9.0=φ mkNmkNM n .5.447.3.46615.5189.0 >=×=φ

5>6> karKNnamuxkat;GkSret (Design of T-Section) kñúgkarKNnamuxkat;GkSret enAeBlEdleKsÁal;m:Um:g;emKuN uM kRmas;søab T TTwg b RtUv)an

kMNt;BIkarKNnakRmalxNÐ ehIykarkMNt;rbs; ACI Code sRmab;TTwgsøabRbsiT§PaB b RtUv)an[enAkñúg emeronTI3. kRmas;RTnug wb GacRtUv)ansn μt;edayERbRbYlBI mm500200 → TMhMEdlRtUv)aneRbIKWsßitenA



cenøaH mm400300 → . GBaØatBIrRtUvkarkMNt;CacaM)ac;KW d nig sA . CMhanénkarKNnaRtUv)ansegçbenA kñúgemeronTI4. ]TahrN_TI3³ muxkat;FñwmGkSret RtUv)anbgðajenAkñúgrUbTI4 manTTwgRTnug mmbw 250= TTwgsøab mb 1= kRmas;søab mmt 100= nigkm<s;RbsiT§PaB mmd 370= . kMNt;muxkat;EdkcaM)ac;RbsinebIm:Um:g;emKuN

mkN.420 . eK[ MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³

1> KNnaTItaMgTItaMgGkS½NWt Edlmuxkat;GacmanragctuekaN. snμt;km<s;rbs;bøúksgát; mma 100= Edl mmta 100== enaH ( ) mkNmkNtdbtfM cn .420.44.685

2'85.0 >=⎟

⎠⎞

⎜⎝⎛ −= φφ

m:Um:g;KNnaEdlsøabebtugGacRT)anFMCagm:Um:g;emKuNEdlmanGMeBIelIva. dUcenH muxkat;eFVIkar manragctuekaN.

2> kMNt;muxkat;EdkTaj edayKitmuxkat;manragctuekaNEdl mmb 1000= MPa

bdMR u

u 06.33701000

42000000022 =

×==

BIsmIkar (5-12) sRmab; MPaRu 07.3= nig 0092.0=ρ 2340437010000092.0 mmbdAs =××== ρ

eRbI 286DB / 25.3694 mmAs = ¬BIrRsTab;¦ 3> epÞógpÞat;fa min/ ρρ ≥= dbA wsw / 00333.00363.0)375250/(3404 min =>=×= ρρw 4> epÞógpÞat; 003.0⎟

⎠⎞

⎜⎝⎛ −

=c

cdttε mmdt 375=

mma 21.5710002885.0

4003404=

×××

= mmc 3.6785.021.57

==



005.00135.0 >=tε 9.0=φ

5>7> viFI strut and tie (Strut and Tie Method)

5>8> 5>7>1> esckþIepþIm (Introduction)

ACI Code, Appendix A/ ENnaMnUvviFImYyepSgeTot eRkABIviFIEdl)anBnül;BIxagedImenAkñúgem eronTI 3. viFIenHeK[eQ μaHfa strut and tie model. viFIepSgenHRtUv)anGnuvtþy:agmanRbsiT§PaBenAkñúg tMbn;Edldac; discontinuity enAkñúgeRKOgbgÁúM dUcCatMbn;TRm tMbn;EdlbnÞúkGnuvtþ b¤tMbn;Edlmuxkat;FrNI maRtpøas;bþÚrPøam²dUcCa brackets nig portal frames. enAkñúgtMbn;TaMgenH muxkat;rabes μ IminrkSaenArabesμ I eRkayeBlrgkarBt; ¬dUcGVIEdl)ansnμt;enAkñgemeronTI3¦ ehIyvaRtUv)aneK[eQμaHfa tMbn; D (D-region)

¬rUbTI5>5 a¦. tMbn;epSgeTotebs;Fñwmsþg;da RTwsþIbTFñwmmUldæan nigTMnak;TMng linear strain relationship

RtUv)anGnuvtþ. tMbn;TaMgenHRtUv)aneK[eQ μaHfa tMbn; B (B-region) ¬rUbTI5>5 a¦. edayQrelIeKalkarN_ St. Venant PaBdac;KñaenAkñúgkarEbgEckkugRtaMgenAkúñgtMbn; D ¬Edl bNþalmkBIragFrNImaRt b¤lkçxNÐbnÞúk¦bgðajfakugRtaMgbNþalmkBIbnÞúktamGkS½ nigm:Um:g;Bt; kar BRgaykugRtaMgesÞIrEtmanlkçN³CabnÞat;enAcm¶ayRbEhlnwgkm<s; h rbs;Ggát;BIcMNucdac; ¬rUbTI5>5 b nig c¦. RbsinebItMbn; D BIrCan;Kña b¤CYbKña BYkvaGacRtUv)anKitCatMbn; D EtmYy. pleFobrvagRbEvgGtibrma nigkm<s;es μ Inwg 2 EdlbegáItmMuGb,brma o5.26 rvag strut and tie ¬b¤RbEhl o25 ¦.

enAkñúgKMrU strut and tie ¬rUbTI5>6¦ cMNucEdlkmøaMgbICYbKñaenAtMN D RtUv)aneK[eQ μaHfa cMNuc node nigmaDebtugEdlenACMuvijcMNuc node RtUv)anehAfatMbn;cMNuc nodal zone. kmøaMgEdlmanGMeBIenA elIcMNuc node GacERbRbYleTAtamkmøaMgTaj nigkmøaMgsgát;énbnSMepSg² dUcCa CCC −− / TCC −− /

TTC −− / TTT −− ¬rUbTI 5>7¦. rUbTI5>8 bgðajBIRbePTtMbn;cMNuc typical nodal zone sRmab;kar GnuvtþbnÞúkepSg² cMENkÉrUbTI 5>9 bgðajBI extended nodal zone sRmab;srésEdkmYy b¤eRcInRsTab;.



KMrU strut and tie (Strut and Tie Model)

KMrU strut and tie GacRtUv)anbgðajedayKMrU truss CamYynwgkmøaMgeFVIGMeBIenAelIcMNucepSg². \LÚv BicarNanUv truss EdkEdl)anbgðajenAkñúgrUbTI 5>10. edaysarEtvamanlkçN³sIuemRTI Rbtikm μenAcMNuc A nig B esμ IKña kNRR BA 20== nigBIlMnwgéntMN A nig D kmøaMgTajenAkñúg kNAB 20= enAeBlEdl kmøaMgsgát;enAkñúg AD b¤ kNBD 3.28= . Ggát; AB RtUv)anKitCa tie cMENkÉ AD nig BD RtUv)ancat;Tuk Ca strut. kmøaMgenAkñúgGgát;epSg²eTotesμ IsUnü. edayeRbobeFob truss enHCamYyFñwmbtugenAkñúgrUbTI 5>6a

eyIgGaceXIjfaRkLaépÞPaKeRcInén ACD nig BED nigRkLaépÞEdlenABIxageRkam nodal zone D min manRbsiT§PaB nigeFVIkarCa filler. kmøaMgenAkñúg strut sRmab;lkçxNÐbnÞúkenH FMCagkmøaMgenAkñúg tie. kñúg krNIenH vamanRkLaépÞebtugRKb;RKan;edIm,IeFVIkarCa strut ¬rUbTI5>6a¦. eKRtUvkarCacaM)ac;nUvsrésEdk edIm,IeFVIkarCa tie sRmab; AB . karcgP¢ab;d¾RtwmRtUvrbs; tie mansar³sMxan;Nas;sRmab;karKNnaRbkb edaysuvtßiPaB. karcgP¢ab;KYreFVIeLIgenAtMbn; nodal zone.





5>7>2> viFIsaRsþKNnatam ACI (ACI Design Procedure)

edayQrelI ACI Code, Section A.2 karKNnatMbn; D-region rab;bBa©ÚlnUvCMhanxageRkam³ - kMNt; nigbMEbknUvtMbn;nImYy² - kMNt;kmøaMgpÁÜbEdlmanGMeBIelIEdntMbn; D-region nImYy² - eRCIserIsKMrU truss edIm,IbBa¢ÚnkmøaMgpÁÜbenAkñúgtMbn; D-region. G½kSén strut nig tie KYrRtYtsIuKñaCa

mYynwgtMbn;sgát; compression field nigtMbn;Taj tension field.



- kMNt;TTwgRbsiT§PaBrbs; struts nig nodal zones edayQrelIersIusþg;ebtug ersIusþg;Edk nigKMrU truss Edl)aneRCIserIs.

- epÞógpÞat;lkçxNÐeFVIkar serviceability condition EdleyageTAtamtRmUvkarrbs; ACI Code. PaBdabrbs;Fñwmx<s; deep beam GacRtUv)anKNnaedayeRbIkarviPaKeGLasÞic elastic analysis. lkçxNÐRKb;RKgsñameRbHén ACI Code, Section 10.6.4 KYrRtUv)anepÞógpÞat;edaysnμt;fa tie

RtUv)aneRsabenAkñúgRBIsebtug eyagtam RA.4.2 .



5>7>3> tRmUvkarsRmab;karKNna (Design Requirement)

tRmUvkarKNnasRmab; struts nig tie GacRtUv)ansnμt;dUcxageRkam³ 1> KNna struts, ties nigtMbn; nodal zone

un FF ≥φ (5-13)

Edl =uF kmøaMgenAkñúg struts, ties nigtMbn; nodal zone Edl)anBIbnÞúkemKuN =nF ersIusþg; nominal strength rbs; struts, ties nigtMbn; nodal zone

75.0=φ sRmab;TaMg struts nig tie

2> ersIusþg;rbs; struts ³ ersIusþg;sgát; nominal compressive strength rbs; struts EdlK μanEdk beNþay nsF KYrEttUcCagtémø nsF enAcugTaMgBIrrbs; struts ³

cscens AfF = (5-14)

Edl =csA RkLaépÞmuxkat;enAcugmçagrbs; struts =cef ersIusþg;sgát;RbsiT§PaBrbs;ebtugEdltUcCagenAkúñg struts b¤ nodal zone.

ssce ff '85.0 β= (5-15) Edl =sβ sRmab; struts manrUbragCaRBIs =sβ sRmab; struts EdlTTwgRtg;muxkat;kNþalGgát;FMCag TTwgenAcMNuc node

(bottle-shaped struts) CamYybrimaNEdkRKb;;RKan;edIm,ITb;nwg kugRtaMgTaj tamTTwg.

λβ 6.0=s dUcGVIEdl)anerobrab;xagelI edayK μanbrimaNEdkRKb;;RKan;edIm,ITb;nwg



kugRtaMgTajtamTTwg ¬ 0.1=λ sRmab;ebtugTm¶n;Fm μta normal-weight

concrete, 0.85 sRmab;ebtugxSac;Tm¶n;Rsal sand-lightweight concrete nig 0.75 sRmab;ebtugTm¶n;RsalTaMgGs; lightweight concrete¦.

4.0=sβ sRmab; struts enAkñgGgát;Taj b¤søab 6.0=sβ sRmab;krNIepSgeTotTaMgGs;

3> EdkExVg struts ¬rUbTI5>11¦³ sRmab; MPaf c 35' ≤ témø 75.0=sβ GacRtUv)aneRbIRbsinebI G½kSrbs; struts RtUv)anExVgedayRsTab;Edk

003.0sin ≥∑ iis

sisb

A γ (5-16)

Edl =siA RkLaépÞmuxkat;EdksrubenAKMlat is enAkñúgRsTab;TI i Edlkat; strut enAmMu iα CamYyG½kSrbs; strut. =is KMlatEdkenAkñúgRsTab;TI i Edlkat; strut enAmMu iα CamYyG½kSrbs; strut . =sb TTwgGgát; =1α mMurvagG½kSrbs; strut nigr)arenAkñúgRsTab;TI i énr)arEdlkat;Kñaeday strut.

4> Edkrgkarsgát;enAkñúg struts ³ Edkrgkarsgát;GacRtUv)aneRbIedIm,IbegáInersIusþg;rbs; strut

sscscens fAAfF ''+= (5-17)

Edl =nsF ersIusþg;én strut BRgwgedayEdkbeNþay =sA' RkLaépÞénEdksgát;enAkñúg strut



=sf ' kugRtaMgenAkñúg sA' ¬ ys ff =' sRmab; MPa500400 → ¦ 5> ersIusþg;rbs; tie ³ersIusþg; nominal strength én tie, ntF KW³

)( psetpytsnt ffAfAF Δ++= (5-18)

Edl =tsA RkLaépÞEdkminrgeRbkugRtaMgenAkñúg tie

=tpA RkLaépÞEdkeRbkugRtaMg =sef kugRtaMgRbsiT§PaBeRkayeBl)at;bg;enAkñúgEdkrgeRbkugRtaMg

=Δ pf karbegáInkugRtaMgeRbkugRtaMgEdlbNþalmkBIbnÞúkemKuN 0=tpA sRmab;Ggát;minrgeRbkugRtaMg

pypse fff ≤Δ+ )( (5-19) eKGacGnuBaØat[yk MPaf p 400=Δ sRmab; bonded prestressed reinforced b¤

MPaf p 70=Δ sRmab; unbonded prestressed reinforced . dUcKña EdnkMNt;x<s;énkarGnuvtþ sRmab;TTwgrbs; tie GacRtUv)anykdUcxageRkam

)/(max, scentt bfFw = (5-20)

6> ersIusþg;rbs;tMbn; nodal zones³ ersIusþg; nominal compression strength éntMbn; nodal zones

nnF KYrEtesμ I nzcenn AfF = (5-21)

Edl =nzA RkLaépÞxagebs; nodal zone b¤muxkat;rbs; nodal zone EdlEkgeTAnwg kmøaMgpÁÜbenAelImuxkat;

7> Confinement enAkñúgtMbn; nodal zones: y:agehacNas;Edk confinement RtUv)anpþl;[enA kñúgtMbn; nodal zone nig\T§iBlrbs;vaRtuv)anKaMRTedaykarBiesaF nigkarviPaKenaHkugRtaMg rgkarsgát;RbsiT§PaBKNnaenAelIépÞéntMbn; nodal zone EdlbNþalmkBIkmøaMg strut nigkmøaMg tie minKYrelIsBI témøxageRkam³

cnce ff '85.0 β= (5-22)

Edl 0.1=nβ enAkñúgtMbn; nodal zone EdlP¢ab;eday strut b¤ bearing areas b¤TaMgBIr ¬ CCC −− node¦.

8.0=nβ enAkñúgtMbn; nodal zone Edlf<k;P¢ab; tie mYy ¬ TCC −− node¦. 6.0=nβ enAkñúgtMbn; nodal zone Edlf<k;P¢ab; tie BIr b¤eRcIn ¬ TTC −− node¦.

karGnuvtþénviFI strut and tie method sRmab;Fñwmx<s;manenAkñúgemeronTI8 ]TahrN_TI6.


PaBdab nigsñameRbH 123 T.Chhay

VI. PaBdab nigsñameRbH

6>1> sñameRbHenAkñúgeRKOgbgÁúMebtug (Deflection of Structural Concrete Members) Ggát;ebtugrgkarBt;RtUv)anKNnasRmab;suvtßiPaB nigkareRbIR)as; (serviceability) . Ggát;Edl)an

KNnaedayeKarBtamsmIkar nigkarkMNt;EdlEcgedaybTdæan ACI Code nwgmansuvtßiPaB. dUcenH dUc karBnül;kñúgemeronmun TMhMGgát;nImYy²Edl)ankMNt; k¾dUcbrimaNEdkcaM)ac;edIm,IrkSanUvlT§PaBm:Um:g;kñúg es μ I b¤FMCagm:Um:g;xageRkA. enAeBlEdl TMhMmuxkat;cugeRkayRtUv)anKNna FñwmRtUv)anepÞógpÞat;sRmab;lkç xNÐbeRmIbRmas; (serviceability) dUcCasñameRbH nigPaBdab. edIm,IkarBarnUvsñameRbH nigPaBdabelIslb; eKcaM)ac;manPaBrwgRkajrbs;Ggát;RKb;RKan;.

kareRbIR)as; ACI Code provision Edl)anBicarNanUvTMnak;TMng nonlinear relationship rvag stress nig strain enAkñúgebtug )anpþl;CalT§plnUvmuxkat;tUcCagmuxkat;EdlKNnadayRTwsþIeGLasÞic. bT dæan ACI Code ,Section 9.4 TTYlsÁal;nUvkareRbIR)as;EdkEdlman yield strength rhUtdl; MPa560 nig kareRbIR)as;nUvebtugersIusþg;x<s;. kareRbInUvebtug nigEdkersIusþg;x<s;pþl;CalT§plnUvmuxkat;tUcCag ehIy karbnßynUvPaBrwgRkajTb;nwgkarBt;rbs;Ggát; )an[PaBdabekInFMCag.

PaBdabEdlGacGnuBaØatRtUv)ankMNt;edayktþaepSg²dUcCa RbePTGKar rUbragrbs;GKar vtþman rbs;Bidan nigCBa¢aMg karxUcxatrMBwgTukEdlbNþalBIPaBdabelIslb; nigRbePT nigTMhMrbs;bnÞúkcl½t.

bTdæan ACI Code , Section 9.5 kMNt;bBa¢ak;kRmas;Gb,brmasRmab;Ggát;rgkarBt;mYyTis one-

way flexural members nigkRmalxNÐmYyTis dUcbgðajkñúgtaragTI 1. témøTaMgGs;kñúgtaragKWsRmab; Ggát;EdlminRT b¤EdlminP¢ab;eTAnwgCBa¢aMgxNÐ b¤sMNg;epSgeTotEdlTMngeFVI[xUcxatedayPaBdabFM.

taragTI1³ kRmas;Gb,brmarbs;Fñwm nigkRmalxNÐmYyTis ¬ L RbEvgElVg¦

Ggát; Yield

Strength

)(MPaf y TRmsamBaØ cugmçagCab; cugsgçagCab; Cantilever

275 25/L 30/L 35/L 5.12/L 350 22/L 27/L 31/L 11/L

kRmalxNÐtan;mYyTis

400 20/L 24/L 28/L 10/L 275 20/L 23/L 26/L 10/L 350 18/L 5.20/L 5.23/L 9/L

Fñwm b¤kRmalxNÐ ribbed mYyTis

400 16/L 5.18/L 21/L 8/L


T.Chhay 124 Deflection and Control of Cracking

kRmas;Gb,brmaEdlbgðajenAkñúgtaragTI1 RtUv)aneRbIsRmab;Ggát;EdlplitBIebtugTm¶n;Fmμta normal-weight concrete, 3/2320 mkgW = nigsRmab;EdkEdlman yield strength dUcbgðajkñúgtarag. témøRtUv)anEktRmUvsRmab;krNIebtugTm¶n;Rsal b¤ yield strength rbs;EdkxusBI MPa400 dUcxageRkam³

- sRmab;rbtugTm¶n;RsalEdlmanTm¶n;maDsßitkñúgcenøaH 33 /1900/1400 mkgmkg − témøenAkñúg taragsRmab; MPaf y 400= RtUvKuNnwg )0003125.065.1( cW− b:uEnþminRtUvtUcCag 09.1 . Edl

cW Cam:as;maDebtug. - sRmab; yield strength rbs;EdkxusBI MPa400 témøenAkñúgtaragsRmab; MPaf y 400= RtUvKuN

nwg )5.689/4.0( yf+ .

6>2> PaBdabxN³ (Instantaneous Deflection) PaBdabrbs;Ggát;ekIteLIgCacMbgedaysarbnÞúkefrbUknwgbnÞúkGefrmYyEpñk b¤TaMgGs;. PaBdab

EdlekIteLIgPøam²bnÞab;BIGnuvtþbnÞúkeK[eQμaHfa PaBdabPøam² (immediate deflection) b¤PaBdabxN³ (instantaneous deflection) . eRkambnÞúkEdlGnuvtþsßitesßr PaBdabnwgekIneLIgKYr[kt;sMKal;CamYynwg eBl. eKmanviFIepSg²sRmab;KNnaPaBdabenAkñúgeRKOgbgÁúMsþaTickMNt; nigsþaTicminkMNt;. karKNnaPaB dab instantaneous deflection KWQrelI elastic behavior énGgát;rgkarBt;. PaBdabeGLasÞic ΔCaGnu-Kmn_eTAnwgbnÞúk W ElVg L m:Um:g;niclPaB I nigm:UDuleGLasÞicrbs;smÖar³ E ³

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎠⎞

⎜⎝⎛=Δ

EIMLK

EIWL

EIWLf

23α (6-1)

Edl =W bnÞúksrubenAelIElVg ehIy α nig K CaemKuNEdlGaRs½yeTAnwgdWeRkénPaBbgáb;rbs; TRm bERmbRmYlm:Um:g;niclPaBtambeNþayElVg nigkarBRgaybnÞúk. ]TahrN_ PaBdabGtibrmaénbnÞúk BRgayes μ IenAelIFñwmTRmsamBaØKW³

EIwL

EIWL

3845

3845 43

==Δ (6-2)

Edl =W bnÞúksrubenAelIElVg wL= ¬bnÞúkBRgayes μ IelImYyxñatRbEvg × ElVg¦. PaBdabrbs;Fñwm CamYynwglkçxNÐbnÞúk niglkçxNÐTRmepSg² edayCab;GnuKmn_eTAnwgbnÞúk ElVg nig EI RtUv)an[enAkñúg ]bsm<½n§ C nigenAkñúgesovePAviPaKeRKOgbgÁúM.

edaysareKsÁal; W nig L enaHeKRKan;EtKNnam:UDuleGLasÞic E nigm:Um:g;niclPaB I énGgát;eb tug b¤PaBrwgRkajTb;karBt;rbs;Ggát; EI . 6>2>1> m:UDuleGLasÞic (Modulus of Elasticity)

bTdæan ACI Code , Section 8.5 kMNt;bBa¢ak;fa eKGacykm:UDuleGLasÞicrbs;ebtug cE



ccc fWE '043.0 5.1= sRmab;témø cW enAcenøaH 3/1400 mkg eTA 3/2500 mkg (6-3) cc fE '4780= sRmab;ebtugTm¶n;Fm μta normal-weight concrete 3/2320 mkgWc =

CaTUeTAm:UDuleGLasÞicRtUv)ankMNt;edayebtugsMNakKMrYsIuLaMgrgbnÞúkkñúgry³eBlxøI short-term

loading of concrete cylinder. enAkñúgGgát;BitR)akd creep EdlbNþalmkBIbnÞúkEdlGnuvtþmkelICab; lab; ¬y:agehacNas;k¾manbnÞúkefr¦ man\T§iBleTAelIm:UDulenAEpñkrgkarsgát;énGgát;. sRmab;Epñkrgkar Taj m:UDulenAkñúgEpñkTajRtUv)ansnμt;dUcKñanwgm:UDulenAkñúgEpñksgát; enAeBlEdltémø stress mantémøtUc. enAeBl stress FM m:UDuleGLasÞicfycuHCaxøaMg. elIsBIenH m:UDuleGLasÞicERbRbYltambeNþayElVgEdl bNþalmkBIbERmbRmYlénm:Um:g;nigkmøaMgkat;TTwg. 6>2>2> pleFobm:UDuleGLasÞic (Modular Ratio)

pleFobm:UDuleGLasÞic cs EEn /= EdlRtUv)aneRbIenAkñúgkarbMElgRkLaépÞ dUcEdl)anBnül;enA kñúgemeronTI2 EpñkTI10. vaRtUv)anKitCacMnYnKt; EtminGactUcCag 6 . ]TahrN_ enAeBlEdl

MPaf c 5.17' = enaH 10=n MPaf c 20' = enaH 9=n MPaf c 30' = enaH 8=n MPaf c 35' = enaH 7=n

sRmab;ebtugTm¶n;Fm μta (normal-weight concrete) n Gacykesμ I cf '/42 . 6>2>3> m:Um:g;eRbH (Cracking moment)

dMeNIrkarénkar)ak;rbs;FñwmTRmsamBaØrgbnÞúkRtUv)anBnül;enAkñúgkfaxNÐ 3>3. enAeBlbnÞúk Gnuvtþn¾tUc ¬ekItmanm:Um:g;tUc¦ nig stress enAsrésrgkarTajeRkAbMputnwgmantémøtUcCagm:UDuldac; (modulus of rupture) rbs;ebtug cr ff '623.0= . RbsinebIeKbegáInbnÞúkrhUtdl;kugRtaMgTaj (tensile

stress) xiteTACitkugRtaMgdac;mFüm rf enaHsñameRbHnwgcab;epþImekIteLIg. RbsinebIkugRtaMgTajFMCag rf muxkat;nwgeRbH ehIykrNImuxkat;eRbHnwgcab;epþImekIteLIg. enHmann½yfaeKmanbIkrNIRtUvBicarNa³

- enAeBlEdlkugRtaMgTaj tf tUcCag rf muxkat;Gt;eRbHTaMgmUlRtUv)anBicarNaedIm,IKNnalkçN³ rbs;muxkat;. enAkñgkrNIenH m:Um:g;niclPaB gI RtUv)aneRbI³ 12/3bhI g = Edl =bh muxkat;ebtugTaMg mUl.

- enAeBlEdlkugRtaMgTaj tf es μ Inwg cr ff '623.0= sñameRbHnwgcab;epþImekItman ehIym:Um:g;Edl begáItnUvkugRtaMgenHRtUv)aneK[eQ μaHfa m:Um:g;eRbH (cracking moment) . edayeRbIrUbmnþkugRtaMgBt;

gcrr I

cMf = b¤ cI

fM grcr = (6-4)



Edl cr ff '623.0= / =gI m:Um:g;niclPaBmuxkat;l¥eBj nig =c cm¶ayBIG½kSNWteTAsrésrgkar TajEpñkxageRkAbMput. ]TahrN_ sRmab;muxkat;ctuekaNEkg 12/3bhI g = nig 2/hc =

- enAeBlEdlm:Um:g;xageRkAFMCagm:Um:g;eRbH (cracking moment) crM enaHkrNImuxkat;eRbHnwgcab; epþImekIteLIg ehIyebtugenAkñúgtMbn;rgkarTajRtUv)anecal. muxkat;eRbHbMElg (transformed cracked

section) RtUv)aneRbIedIm,IKNnam:Um:g;niclPaBeRbH (cracking moment of inertia) crI edayeRbIRkLaépÞ ebtugenAkñgtMbn;sgát; nigRkLaépÞEdkbMElg (transformed steel area) snA . ]TahrN_6>1³ muxkat;ebtugctuekaNEkgRtUv)anBRgwgedayEdk 283DB enAkñúgmYyCYr ehIymanTTwg

mm300 nigkm<s;srub mm650 cMENk mmd 585= ¬rUb 6>1¦. cUrKNnam:UDuldac; (modulus of

rupture) rf / m:Um:g;niclPaBmuxkat;l¥eBj gI nigm:Um:g;eRbH crM edayeRbI MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ 1> m:UDuldac; modulus of rupture MPaff cr 28.3'623.0 == 2> m:Um:g;niclPaBénmuxkat;l¥eBj ( ) 4933 1087.612/65030012/ mmbhI g ⋅=== 3> m:Um:g;eRbH mkNcIfM grcr .3.69325/1087.628.3/ 9 =⋅×==

6>2>4> m:Um:g;niclPaB (Moment of inertia)

edayKuNm:Umg;niclPaBeTAnwgm:UDuleGLasÞiceyIgTTYl)anPaBrwgRkajTb;nwgkarBt;rbs;Ggát;. eRkambnÞúktUc m:Um:g;GtibrmaEdlekItmannwgmantémøtUc ehIy tensile stress enAsrésrgkarTajxageRkA bMputnwgmantémøtUcCagm:UDuldac;rbs;ebtug. enAkñúgkrNIenH muxkat;eRbHbMElgeBj (gross transformed

cracked section) nwgmanRbsiT§PaBkñúgkarpþl;nUvPaBrwgmaM. enAxN³bnÞúkeFVIkar b¤bnÞúkFM sñameRbHenAtMbn; TajEdl)anmkBIkarBt;nwgekIteLIg. enARtg;muxkat;eRbH TItaMgG½kSNWtsßitenAx<s; b:uEnþenARtg;muxkat;



kNþalcenøaHsñameRbHenAelIbeNþayFñwm TItaMgG½kSNWtsßitenATab ¬Ek,rEdkrgkarTaj¦. manEtTItaMgTaMg BIrenHeT Edlmuxkat;eRbHbMElgmanRbsiT§PaBkñúgkarkMNt;PaBrwgRkajrbs;Ggát;. dUcenH m:Um:g;niclPaB RbsiT§PaBERbRbYly:agxøaMgtambeNþayElVg. enATItaMgm:Um:g;Bt;Gtibrma enaHEpñkebtugeRbHenAtMbn;rgkar TajminRtUv)anKitkñúgkarKNnam:Um:g;niclPaB. enARtg;cMNucrbt; kugRtaMgtUc ehIymuxkat;TaMgmUlGacnwg mineRbH. sRmab;sßanPaBenH nigenAkñúgkrNIsRmab;FñwmEdlmanFñwmERbRbYl dMeNaHRsayd¾RtwmRtUvman lkçN³sμ úKsμaj.

rUb 6>2 a bgðajBIExSekagbnÞúk-PaBdabrbs;FñwmebtugEdlRtUv)aneFVIBiesaFn_rhUtdl;)ak;. Fñwm RtUv)anRTedayTRmsamBaØ manRbEvg ft17 nigrgnUvbnÞúkcMcMNucBIrEdlmancm¶ayBIKña ft5 edaysIuemRTInwg G½kS. FñwmRtUv)anrgnUvkardak;bnÞúkBIrCMu³ TImYy ¬ExSekag 1cy ¦ ExSekagbnÞúk-PaBdabCabnÞat;Rtg;eLIgelI dl;bnÞúk KP 7.1= enAeBlEdlFñwmcab;epþImekItmansñameRbH. bnÞat; a bgðajnUvTMnak;TMngbnÞúk-PaBdab edayeRbIm:Um:g;niclPaBsRmab;muxkat;bMElgGt;eRbH. eKGacemIleXIjfaPaBdabBitR)akdrbs;FñwmeRkam bnÞúkEdltUcCagbnÞúkeRbH ¬edayQrelImuxkat;Gt;eRbHsac;mYy homogeneous cracked section¦ mantémø Ek,reTAnwgPaBdabEdl)anmkBIkarKNna ¬bnÞat; a ¦. ExSekag 1cy bgðajnUvExSekagPaBdabBitR)akd enAeBlEdlbnÞúkekIneLIgrhUtdl;Bak;kNþalbnÞúkcugeRkay (ultimate load). CRmal (slop) rbs;ExSekag enARKb;nIv:UbnÞúkTaMgGs; mantémøtUcCagCRmalrbs;bnÞat; a edaysarEtsñameRbHekItman ehIyEpñkEdl eRbHénmuxkat;ebtug)ankat;bnßynUvPaBrwgRkajrbs;Fñwm. bnÞab;mkbnÞúkRtUv)andkecjPaBdabEdlenA esssl; (residual deflection) RtUv)anGegáteXIjmanenAkNþalElVgFñwm. enAeBlmansñameRbHkarsnμt; BIkarRbRBwtþeTArbs;muxkat;Gt;eRbHeRkambnÞúktUcminRtUv)anykmkGnuvtþ.

sRmab;karGnuvtþbnÞúkCMuTIBIr PaBdab ¬ExSekag c ¦ )anekIneLIgkñúgkRmitFMCagbnÞat; a edaysar EtersIusþg;rbs;srésebtugTajRtUv)an)at;bg;. enAeBlbnÞúkekIneLIg TMnak;TMngrvagbnÞúk nigPaBdabRtUv )anbgðajedayExSekag 2cy . RbsinebIbnÞúkenACMuTImYyekIneLIgdl;bnÞúkcugeRkay enaHExSekag 1cy nwgcab; ykKnøgExSekag 2cy enARtg;bnÞúkRbEhl uP6.0 . ExSekag c bgðajBIdMeNIrkarBitR)akdrbs;FñwmsRmab; karbEnßmbnÞúk b¤kardkbnÞúk.

bnÞat; b bgðajBITMnak;TMngrvagbnÞúk nigPaBdabedayQrelImuxkat;bMElgeRbH. eKeXIjfa PaB dabEdlKNnaedayQrelIeKalkarN_hñwg xusKñaBIPaBdabBitR)akd. rUb 6>2 b bgðajBIbERmbRmYlPaB rwgRkaj EI rbs;FñwmCamYynwgkarekIneLIgénm:Um:g;. bTdæan ACI Code, section 9.5 ENnaMnUvsmIkaredIm,I kMNt; m:Um:g;niclPaBRbsiT§PaBEdleRbIenAkñúgkarKNnaPaBdabenAkñúgm:Um:g;rgkarBt;. m:Um:g;niclPaB



RbsiT§PaBEdl[eday ACI Code (Eq. 9.8) edayQrelIsmIkarEdlesñIedayelak Branson nwgRtUv)an KNnadUcxageRkam³

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1 (6-5)

Edl =eI m:Um:g;niclPaBRbsiT§PaB =crM m:Um:g;eRbH/ ⎟⎟

⎠

⎞⎜⎜⎝

⎛

t

gr

YIf (6-6)

=rf m:UDuldac;rbs;ebtug cr ff '623.0= (6-7)

=aM m:Um:g;K μanemKuNGtibrmarbs;Ggát;enAxN³EdlPaBdabkMBugRtUv)anKNna =gI m:Um:g;niclPaBrbs;muxkat;ebtugl¥eBjeFobG½kSTIRbCMuTm¶n; edayecalEdl =crI m:Um:g;niclPaBénmuxkat;bMElgeRbH =tY cm¶ayBIG½kSTIRbCMuTm¶n;edayecalEdkeTAépÞrgkarTaj. xageRkamCakarkMNt;edaybTdæan³ 1> sRmab;FñwmCab; m:Um:g;niclPaBRbsiT§PaBGacRtUv)anyktémømFüménm:Um:g;niclPaBénmuxkat;

Edlmanm:Um:g;viC¢man nigGviC¢manFMCageK. 2> sRmab;ebtugTm¶n;Rsal m:UDuldac; rf edIm,IeRbIenAkñúgsmIkar (6-6) es μ Inwg

⎟⎠⎞

⎜⎝⎛=

556.0623.0 ct

rff Edl c

ct ff '556.0

≤ (6-8a)

Edl ctf CaersIusþg;TajedaykarbMEbk (splitting tensile strength). enAeBlEdleKGt;sÁal; ctf enaH rf GacRtUv)anKitdUcxageRkam³

cr ff '465.0= (6-8b) sRmab;ebtugeFVIBIxSac;Tm¶n;Rsal (sand-lightweight concrete)

cr ff '532.0= (6-8c) 3> sRmab;Ggát;RBIs eI GacyktémøEdlTTYl)anBIsmIkar (6-5) enAkNþalElVgsRmab;FñwmTRm

samBaØ nigFñwmCab; nigenATRmsRmab;Fñwm cantilever (ACI Code, section 9.5.2) . cMNaMfa eI Edl)anmkBIkarKNnatamsmIkar (6-5) pþl;nUvtémøEdlsßitenAcenøaHm:Um:g;nicl PaBl¥eBj gross moment of inertia gI nig m:Um:g;niclPaBeRbH cracked moment of inertia

crI edayGnuKmn_eTAnwgkRmiténpleFob a

crMM . Ggát;ebtugEdlmanbrimaNEdkeRcIn Gacnwg



man eI xiteTACit crI b:uEnþsRmab;Ggát;EdlmanRTnug flanged member Gacnwgman eI xiteTA Cit gI .

4> sRmab;FñwmCab; témøRbEhléntémømFümén eI sRmab;Ggát;RBIs b¤minRBIs edIm,IeFVI[lT§pl

kan;EtRbesIreLIgmandUcxageRkam³ - sRmab;FñwmEdlmancugsgçagCab; )(15.07.0 Average 21 eeme IIII ++= (6-9) - sRmab;FñwmEdlmancugmçagCab; )(15.085.0 Average conme III += (6-10)



Edl em II = enAkNþalElVg É eee III =21, enAcugFñwmsgçag nig econ II = enARtg;cug Cab;. eI GacyktémømFümén eI enARtg;muxkat;Edlmanm:Um:g;viC¢man nigGviC¢manFM. eKKYr eRbI moment envelope kñúgkarKNnatémøviC¢man nigGviC¢manén eI . enAkñúgkrNIEdlFñwmrg bnÞúkcMp©itFM manEt eI kNþalElVgKYrRtUv)aneRbI.

6>2>5> lkçN³rbs;muxkat; (Properties of sections)

edIm,IKNnam:Um:g;niclPaBmuxkat;eBj gross section nigmuxkat;eRbH cracked section eKcaM)ac;RtUv KNnacm¶ayBIsrésrgkarsgát; compression fiber eTAG½kSNWt neutral axis ¬ x b¤ kd ¦.

1> m:Um:g;niclPaBeBj gI ¬ecalmuxkat;EdkTaMgGs;enAkñúgebtug¦ a. sRmab;muxkat;ctuekaNEkgEdlmanTTwg b nigkm<s;srub h enaH 12/3bhIg = . b. sRmab;muxkat; T-section EdlmanTTwgsøab b TTwgRTnug wb nigkRmas;RTnug t KNna y

cm¶ayBIG½kSTIRbCMuTm¶n;eTAcMNucx<s;bMputrbs;søab³ ( )

)(2

)(2

2

thbbttththbbt

yw

w

−+

⎥⎦⎤

⎢⎣⎡

+−

−+⎟⎟⎠

⎞⎜⎜⎝

⎛

= (6-11)

bnÞab;mkeTotKNna ( ) ( )

⎥⎦⎤

⎢⎣⎡ −

+⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+=

33212

323 yhbtybtybtbtI wwg (6-11a)

2> m:Um:g;niclPaBeRbH crI ³ yk =x cm¶ayBIG½kSNWtmksrésrgkarsgát;eRkAbMput ¬ kdx = ¦ a. muxkat;ctuekaNEkgCamYyEtnwgEdkrgkarTaj sA

i. KNna x BIsmIkarxageRkam 0)(

2

2=−− xdnAbx

s (6-12) ii. KNna 23 )(3/ xdnAbxI scr −+= (6-12a)

b. muxkat;ctuekaNEkgCamYyEdkrgkarTaj sA nigEdkrgkarsgát; sA' i. KNna x ³ 0)()'(')1(

2

2=−−−−+ xdnAdxAnbx

ss (6-13) ii. KNna 223 )()'(')1()3/( xdnAdxAnbxI sscr −+−−+= (6-13a)

c. T-section CamYyEdkrgkarTaj sA i. KNna x ³ ( ) 0)(

2)

2(

2=−−

−+− xdnAtxbtxbt sw (6-14)



ii. KNna ( ) 2323

)(3212

xdnAtxbtxbtbtI swcr −+⎥⎥⎦

⎤

⎢⎢⎣

⎡ −+

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+= (6-14a)

6>3> PaBdabry³eBlyUr (Long-term Deflection) PaBdabrbs;Ggát;ebtugEdkBRgwgbnþekIneLIgeRkambnÞúkEdlGnuvtþsßitesßr ebIeTaHbICavayWtebI

eRbobeFobCamYyeBlk¾eday. karrYmmaD nig creep CamUlehtueFVI[ekItmanPaBdabbEnßmEdleK[eQμaH fa PaBdabry³eBlyUr long-term deflection. varg\T§iBlCacMbgBIsItuNðPaB sMeNIm Gayurbs;ebtug enAxN³énkardak;bnÞúk karEfTaMebtug brimaNEdkrgkarsgát; nigdg;sIuetbnÞúkefr. bTdæan ACI Code,

Section 9.5 esñIfa y:agehacNas;témøEdlTTYledaykarviPaKd¾RtwmRtUvmYy KWPaBdabry³eBlyUrbEnßm sRmab;Ggát;rgkarBt;ebtugFm μta nigebtugTm¶n;RsalKYr)an TTYlBIkarKuNPaBdabPøam²CamYyemKuN

'501 ρζλ

+=Δ (6-15)

Edl =Δλ emKuNsRmab;PaBdabbEnßmEdlbNþalmkBI\T§iBlry³eBlyUr bdA s /''=ρ sRmab;muxkat;enAkNþalElVgrbs;FñwmTRmsamBaØ b¤FñwmCab;

b¤sRmab;muxkat;enATRm rbs;Fñwm cantilever . =ζ emKuNGaRs½yeBl time-dependent factor

sRmab;bnÞúkefrEdlGacnwgykdUcbgðajkñúg taragTI 6>2. emKuN Δλ RtUv)aneRbIedIm,IKNnaPaBdabEdlbNþalmkBIbnÞúkefr nigEpñkxøHénbnÞúkGefrEdlnwg

sßitenAzitezrsRmab;ry³eBlmYyRKb;RKan;edIm,IbegáItnUvPaBdabGaRs½ynwgeBlmYyKYr[kt;sMKal;. em KuN Δλ CaGnuKmn_eTAnwglkçN³smÖar³ EdlsMEdgeday ζ niglkçN³muxkat; sMEdgeday )'501( ρ+ . enAkñúgsmIkar (6-15) \T§iBlrbs;Edkrgkarsgát;KWTak;TgeTAnwgRkLaépÞebtugCagTak;TgeTAnwgpleFob rvagEdksgát;elIEdkTaj.

ACI Code Commentary, section 9.5 bgðajnUvExSekagedIm,IKNna ζ sRmab;ry³eBlticCag 60 Ex. témøTaMgenHRtUv)anKNnadUcbgðajkñúgtaragTI 6>2.

PaBdabsrubesμ InwgplbUkPaBdabPøam² nigPaBdabbEnßmry³eBlyUr. ]TahrN_ PaBdabbEnßm ry³eBlyUrsrubrbs;FñwmrgkarBt;CamYy 01.0'=ρ enAry³eBl 5 qñaMesμ InwgplKuN Δλ CamYynwgPaBdab Pøam² Edl 33.1)01.0501/(2 =×+=Δλ .



tarag 6>2 emKuNGaRs½yeBlsRmab;PaBdabry³eBlyUr ry³eBl ¬Ex¦ 1 3 6 12 24 36 48 60 ζ 5.0 0.1 2.1 4.1 7.1 8.1 9.1 0.2

6>4> PaBdabGnuBaØat (Allowable Deflection) GaRs½yeTAtambTdæan ACI Code, Section 9.5 PaBdabminRtUvelIstémødUcxageRkam ³

- 180/L sRmab;PaBdabPøam²EdlbNþalmkBIbnÞúkGefrsRmab;dMbUlerobesμ IEdlminRTGgát;Edl TMngeFVIxUcxat.

- 360/L sRmab;PaBdabPøam²EdlbNþalmkBIbnÞúkGefrsRmab;kRmalxNÐEdlminRTGgát;Edl TMngeFVIxUcxat.

- 480/L sRmab;EpñkénPaBdabsrubEdlekIteLIgeRkayBIkarP¢ab;Ggát; dUcCaplbUkPaBdabry³ eBlyUrEdlbNþalmkBIbnÞúkefrTaMgGs; nigPaBdabPøam²EdlbNþalmkBIbnÞúkGefrbEnßm sRmab;kRmalxNÐ b¤dMbUlEdlRTGgát;EdlTMngnwgeFVI[xUcxat.

- 240/L sRmab;EpñkénPaBdabsrubEdlekIteLIgeRkayBIGgát;RtUv)anP¢ab; sRmab;kRmalxNÐ b¤ dMbUlEdlminRTGgát;EdlTMngnwgeFVI[xUcxat.

6>5> PaBdabEdlbNþalmkBIbnSMbnÞúk (Deflection Due to Combinations of Load) RbsinebIFñwmrgnUvbnÞúkeRcInRbePT ¬BRgayes μ I BRgayminesμ I b¤bnÞúkcMcMNuc¦ b¤rgnUvm:Um:g;cug enaH

PaBdabGacRtUv)anKNnasRmab;bnÞúk b¤kmøaMgtamRbePTmYy²EdlGnuvtþmkelIFñwmdac;edayELkBIKña ehIy PaBdabsrubRtUvKNnaedayviFItRmYtpl superposition. enHmann½yfaPaBdabmYy²RtUveFVIplbUknBVnþCa mYyKñaedIm,ITTYl)anPaBdabsrub. PaBdabrbs;bnÞúkeRkambnÞúkmYy²RtUv)anbgðajenAkñúgtarag 6>3.

]TahrN_6>2³ KNnaPaBdabxN³kNþalElVgsRmab;FñwmTRmsamBaØdUcbgðajkñúgrUb 6>3 EdlRTnUvbnÞúk efrBRgayes μ I mkN /85.5 nigbnÞúkGefr mkN /75.8 rYmnwgbnÞúkefrcMcMNuc kN25.22 enARtg;kNþal ElVg. eK[ MPaf c 28' = / MPaf y 400= / mmb 330= nig mmd 530= nigkm<s;srub mm630 ¬ 8=n ¦. dMeNaHRsay³

1> epÞógpÞat;km<s;Gb,brmaGaRs½yeTAtambTdæan ACI Code tarag 6>1 km<s;srubGb,brma mmL 5.762

1612200

16===



edaysarkm<s;srubEdleRbIR)as; mmmm 5.762630 < dUcenH eKRtUvkarepÞógpÞat;PaBdab.



2> PaBdabenAkNþalElVgEdlbNþalmkBIbnÞúkBRgayKW

ecIEwL

3845 4

1 =Δ

PaBdabenAkNþalElVgEdlbNþalmkBIbnÞúkcMcMNucKW

ecIEPL

48

3

2 =Δ

edaysarEteKsÁal; w / P nig L dUcenHeKRtUvKNnam:UDuleGLasÞic cE nigm:Um:g;niclPaBRbsiT§PaB eI .

3> m:UDuleGLasÞicrbs;ebtugKW MPaEc 4.25293284780 ==

4> m:Um:g;niclPaBRbsiT§PaB

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1

kMNt;témøTaMgGs;enAGgÁxagsþaM mkNPLwLMa .5.339

42.1225.22

82.12)85.575.8(

48

22=

×+

+=+=

4933

1088.612

)630(33012

mmbhIg ⋅===

t

grcr Y

IfM = eday MPaff cr 3.328623.0'623.0 === mmhYt 315

2==

mkNMcr .1.72315

1088.63.3 9=

⋅×=

m:Um:g;niclPaBénmuxkat;bMElgeRbH crI RtUv)anKNnadUcxageRkam³



kMNt;TItaMgG½kSTIRbCMuTm¶n;sRmab;muxkat;eRbHedaysmIkarm:Um:g;énmuxkat;bMElgeFobG½kSTIRbCMu Tm¶n;eTA 0 yk == kdx cm¶ayBIG½kSTIRbCMuTm¶n;

0)(2

2=−− xdnAbx

s 8==c

sEEn 23041mmAs =

01289384024328165 2 =−+ xx mmx 38.215= ( ) 492

32

3105.3)38.215530(30418

338.215330)(

3mmxdnAbxI scr ⋅=−×+=−+=

CamYynwgGgÁTaMgGs;Edl)anKNna eyIgTTYl)an 499

39

31053.3105.3

5.3391.7211088.6

5.3391.72 mmIe ⋅=⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+⋅⎟

⎠⎞

⎜⎝⎛=

5> KNnaPaBdabBIbnÞúkepSg²

1Δ ¬bNþalmkBIbnÞúkrayesμ I¦ecIE

wL384

5 4=

( ) mm2.471053.34.25293384

1220085.575.859

4

1 =⋅××

×+=Δ

2Δ ¬bNþalmkBIbnÞúkcMcMNuc¦ecIE

PL48

3=

mm43.91053.34.2529348

12200222509

3

2 =⋅××

×=Δ

PaBdabPøam²srub mm63.5643.92.4721 =+=Δ+Δ= 6> eRbobeFobtémøEdl)anmkBIkarKNnaCamYyPaBdabGnuBaØat³

PaBdabPøam²Edl)anmkBIbnÞúkGefrBRgayesμ I mkN.75.8 esμ Inwg =+× )85.575.8/(2.4775.8 mm29.28 . RbsinebIGgát;CaEpñkmYyrbs;kRmalxNÐEdlminRT b¤P¢ab;eTAnwgCBa¢aMgxNÐ b¤Ggát;epSg²eTot

EdlGacTMngeFVI[xUcxatedaysarPaBdabFM enaHPaBdabPøam²GnuBaØatEdlbNþalmkBIbnÞúkGefresμ Inwg mmmmL 29.289.33

36012200

360>==

EtRbsinebIGgát;CaEpñkénkRmalxNÐdMbUl nigRsedogKñaeTAGVIEdl)anerobrab;xagelI enaHPaBdab Pøam²GnuBaØatEdlbNþalmkBIbnÞúkGefrKW mmmmL 29.288.67

18012200

180>== . témøGnuBaØatTaMgBIrFM

CagPaBdabBitR)akd mm29.28 EdlbNþalmkBIbnÞúkGefrBRgayesμ I.



]TahrN_6>3³ kMNt;PaBdabry³eBlyUr long-term deflection rbs;FñwmenAkñúg]TahrN_6>2 RbsinebIem KuNGaRs½yeBl time-dependent factor esμ Inwg 0.2 . dMeNaHRsay³

1> bnÞúkEdlGnuvtþGcié®nþy_bNþal[manPaBdabry³eBlyUrKWekItmkBIbnÞúkGefr EdlrYmmanbnÞúk efrBRgayesμ I mkN /85.5 nigbnÞúkefrcMcMNuc kN25.22 EdlGnuvtþn;enAkNþalElVg. PaBdabbNþalmkBIbnÞúkBRgayes μ I mm9.18)85.575.8/(2.4785.5 =+×= PaBdabCaGnuKmn_bnÞat;eTAnwgbnÞúk w ehIytémøepSgeTot ¬ L / cE / eI ¦dUcKña PaBdabbNþalmkBIbnÞúkcMcMNuc mm43.9= PaBdabsrubEdlbNþalmkBIbnÞúkzitezr sustained load mm33.2843.99.18 =+=

2> sRmab;PaBdabry³yUrbEnßm PaBdabPøam²RtUv)anKuNnwgemKuN Δλ

012

'501 +=

+=Δ ρ

ζλ

kñúgkrNIenH 0' =sA dUcenH 0.2=Δλ PaBdabry³eBlyUrbEnßm mm66.5633.282 =×=

3> PaBdabry³eBlyUrsrubCaplbUkrvagPaBdabPøam²CamYynwgPaBdabry³eBlyUrbEnßm mm29.11366.5663.56 =+

4> PaBdabbNþalmkBIbnÞúkefrCamYynwgPaBdabry³eBlyUrbEnßmEdlbNþalmkBIkarrYmmaDnig creep KW mm8566.5633.28 =+

]TahrN_6>4³ KNnaPaBdabxN³ nigPaBdabenAry³eBl 1qñaM enAcugTMenrrbs;Fñwm cantilever dUcbgðaj kñúgrUbTI 6>4. FñwmmanRbEvg m1.6 nigRTbnÞúkefrBRgayesμ I mkN /85.5 bnÞúkGefrBRgayesμ I mkN /85.5 bnÞúkefrcMcMNuc kNPD 35.13= enAcugTMenr nigbnÞúkGefrcMcMNuc kNPL 8.17= EdlGnuvtþenAcm¶ay m05.3 BITRmbgáb;. eK[ MPaf c 28' = / MPaf y 400= / mmb 300= / mmd 550= / nigkm<s;muxkat;srub

mm635 ¬srésEdkrgkarTajKW 256DB nigEdkrgkarsgát; 252DB ¦. dMeNaHRsay³

1> km<s;Gb,brma mmmmL 6355.7628

61008

>== dUcenHeKRtUvepÞógpÞat;PaBdab. PaBdabGtibrmarbs;Fñwm cantilever KWsßitenAcugTMenr. PaBdabenAcugTMenrKWdUcxageRkam³ PaBdabEdlbNþalmkBIbnÞúkBRgay



EIwL8

4

1 =Δ PaBdabEdlbNþalmkBIbnÞúkefrcMcMNucenAcugTMenr

EILPD

3

3

2 =Δ PaBdabGtibrmaenAcugTMenrEdlbNþalmkBIbnÞúkGefrcMcMNucenA ma 05.3= BIcugbgáb;

)3(6

2

3 aLEIaPL −=Δ b¤ )

231(

3

3

ab

EIaPL +

2> m:UDuleGLasÞicrbs;ebtugTm¶n;RsalKW MPaEc 4.25293284780 ==

3> m:Um:g;GtibrmaenAcugbgáb; mkNPPwLM LDa .5.2458.1705.35.131.6

21.685.505.31.6

2

22=×+×+

×=++=

4> m:Um:g;niclPaBeBj ¬Etebtug¦ 49

33104.6

12635300

12mmbhIg ⋅=

×==

5> mkNYIf

Mt

grcr .5.66

2635

104.628623.0 9=

⋅×==

6> kMNt;TItaMgG½kSNWt bnÞab;mkkMNt;m:Um:g;niclPaBénmuxkat;bMElgeRbH. Kitm:Um:g;énmuxkat; eFob G½kSTIRbCMuTm¶n;nigdak;[vaes μIsUnü. eRbI 8=n edIm,IKNnamuxkat;bMElgrbs; sA nig eRbI

7)1( =−n sRmab;KNnamuxkat;bMElgrbs; sA' . yk xkd = ( ) 0)()'(')1(

2

2=−−−−+ xdnAdxAnxb ss

01337044030434150 2 =−+ xx



sRmab;muxkat;enH mmx 875.213= 49223 108.3)()'(')1(

3mmxdnAdxAnxbI sscr ⋅=−+−−+=

7> m:Um:g;niclPaBRbsiT§PaBKW

gcra

crg

a

cre II

MMI

MMI ≤

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛=

33

1

993

93

1085.3108.35.245

5.661104.65.245

5.66⋅=⋅

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−+⋅⎟

⎠⎞

⎜⎝⎛=eI

8> KNnaPaBdabeRkambnÞúkepSg²EdlmanGMeBIelIFñwm

1Δ ¬bNþalBIbnÞúkBRgayesμ I mkN /7.11 ¦ mm8.201085.34.252938

61007.119

4=

⋅×××

=

1Δ ¬bNþalBIbnÞúkefr¦ mm4.10=

2Δ ¬bNþalBIbnÞúkefrcMcMNuc¦enAcugTMenr mm5.101085.34.252933

6100135009

3=

⋅×××

=

3Δ ¬bNþalBIbnÞúkGefrcMcMNuc¦enA m05.3 BIcugbgáb;

3Δ mm3.41085.34.252936

)305061003(3050178009

2=

⋅××−×××

= PaBdabPøam²srub mm6.353.45.108.20321 =++=Δ+Δ+Δ=Δ

9> PaBdabbEnßmry³eBlyUr esμ InwgplKuNrvagPaBdabPøam²CamYynwgemKuN Δλ sRmab;ry³eBl 1qñaM 4.1=ζ

006.0550300

982'' =×

==bdA sρ

077.1006.0501

4.1=

×+=Δλ

PaBdabPøam²srub sΔ EdlbNþalmkBIbnÞúkzitezr sustained load ¬enATIenHmanEtbnÞúkefr mkN /85.5 nig kNPD 35.13= enAcugTMenr¦

mms 9.205.104.10 =+=Δ PaBdabry³eBlyUrbEnßm mm5.229.20077.1 =×=

10> PaBdabry³eBlyUrsrubCaplbUkrvagPaBdabPøam²CamYynwgPaBdabry³eBlyUrbEnßm EdlekItBIkarrYmmaD nig creep .

mm1.585.226.35 Total =+=Δ ]TahrN_6>5³ KNnaPaBdabxN³enAkNþalElVgrbs;FñwmenAkñúgrUb 6>5 EdlFñwmenHmanRbEvg m8.9 . FñwmenHRtUv)anbnþedayTRmCaeRcInEdlmanRbEvgElVgepSg²Kña. düaRkamm:Um:g;Bt;nigmuxkat;rbs;FñwmenA



kNþalElVg nigTRmk¾RtUv)anbgðaj. FñwmenHRTbnÞúkefrBRgayesμI mkN /3.61 nigbnÞúkGefr mkN /5.52 . eK[ MPaf c 20' = / MPaf y 400= nig 2.9=n .

m:Um:g;enAkNþalElVg mkNM D .260= mkNM LD .650)( =+ m:Um:g;enATRmxageqVg A mkNM D .75.242= mkNM LD .5.569)( =+ m:Um:g;enATRmxagsþaM B mkNM D .293= mkNM LD .735)( =+

dMeNaHRsay³ 1> Fñwm AB rgnUvm:Um:g;viC¢manEdleFVI[dabcuHeRkamenAkNþalElVg nigm:Um:g;GviC¢manenAcugTaMgBIr

EdleFVI[dabeLIgelIenAkNþalElVg. dUcEdl)anBnül;BIxagedIm PaBdabCaGnuKmn_eTAnwg m:Um:g;niclPaBRbsiT§ eI . enAkñúgFñwmCab; témørbs; eI EdlRtUv)aneRbICatémømFümsRmab;tMbn;m:U m:g;viC¢man nigm:Um:g;GviC¢man. dUcenHmuxkat;bInwgRtUv)anBicarNa muxkat;enAkNþalElVg nigmuxkat; enATRmTaMgBIr.

2> KNna eI ³ sRmab;RkLaépÞeBjénmuxkat;TaMgGs; mmkd 356= nig 410102.5 mmIg ⋅= dUcKña MPaff cr 8.2'623.0 == nig MPafE cc 8.21376'4780 == sRmab;RKb;muxkat;. témørbs;

kd / crI nig crM sRmab;muxkat;eRbH/ eI sRmab;EtbnÞúkefr ¬edayeRbI aM sRmab;bnÞúkefr¦ nig eI sRmab;bnÞúkefr nigbnÞúkGefr ¬edayeRbI aM sRmab;bnÞúkefr nigbnÞúkGefr¦RtUv)anKNna

nigbegáItCa taragdUcxageRkam³

muxkat; kd ¬ mm ¦ crI ¬ 4mm ¦ crM ¬ mkN. ¦ eI ¬ 4mm ¦ ¬bnÞúkGefr¦

eI ¬ 4mm ¦ ¬ LLDL + ¦

kNþalElVg 8.169 101012.2 ⋅ 226 101014.4 ⋅ 101025.2 ⋅ TRm A 281 101052.1 ⋅ 409 10102.5 ⋅ 101088.2 ⋅ TRm B 320 101084.1 ⋅ 409 10102.5 ⋅ 101042.2 ⋅ cMNaMfa enAeBlEdlFñwmrgEtbnÞúkefr ehIypleFob acr MM / FMCag 0.1 enaH eI es μ Inwg gI .

3> kMNt;témømFümrbs; eI BIsmIkar (6.9) ( ) ( ) 4101010

1 1037.21042.288.215.01025.27.0)average( mmIe ⋅=++⋅= sRmab;bnÞúkefr nigbnÞúkGefr

( ) 41010 1065.21042.288.25.0)sections endfor average( mmIe ⋅=+= ( ) 4101010

2 1045.21065.21025.25.0)average( mmIe ⋅=⋅+⋅= sRmab;EtbnÞúkefr



410102.5)sections endfor average( mmIe ⋅= ( ) 4101010

3 1067.4102.51014.45.0)average( mmIe ⋅=⋅+⋅=



4> KNnaPaBdabPøam²enAkNþalElVg

1Δ ¬bNþalmkBIbnÞúkBRgay¦eEI

wL3845 4

= ¬cuHeRkam¦

2Δ ¬bNþalmkBIm:Um:g;enAcMNuc A / AM ¦e

AEI

LM16

2−= ¬eLIgelI¦

3Δ ¬bNþalmkBIm:Um:g;enAcMNuc B / BM ¦e

BEI

LM16

2−= ¬eLIgelI¦

PaBdabsrub 321 Δ−Δ−Δ=Δ PaBdabsRmab;bnÞúkefrBRgayes μ I mkN /3.61 edayyk mkNDLM A .75.242)( = /

mkNDLM B .293)( = nig 4103 1067.4 mmIe ⋅= CMnYseTAkñúgsmIkarxagelI eyIgTTYl)an³

mm1.48.15.14.7 =−−=Δ ¬cuHeRkam¦ PaBdabEdlbNþalBIbnSMbnÞúkefr nigbnÞúkGefrRtUv)anKNnaedayykbnÞúkefrbUknwgbnÞúkGefr

mkN /8.113= / mkNLLDLM A .5.569)( =+ / mkNLLDLM B .735)( =+ nig 410

2 1045.2 mmIe ⋅= mm2.114.85.61.26 =−−=Δ ¬cuHeRkam¦

PaBdabPøam²EdlbNþalBIEtbnÞúkGefrKW mm1.71.42.11 =− ¬cuHeRkam¦. RbsinebIkarkMNt;PaBGnuBaØatiKW mmL 4.20480/9800480/ == enaHmuxkat;KWRKb;RKan;. cMNucmYycMnYnEdlTak;TgnwglT§pl³ 1> RbsinebIeKeRbIEt eI énmuxkat;kNþalElVg 4101025.2 mmIe ⋅= enaHPaBdabEdlbNþalmkBI

bnÞúkefr nigbnÞúkGefrRtUv)anKNnaeday KuNtémøEdlTTYl)ankñúgCMhanTI4 CamYynwgpl eFobéntémø eI TaMgBIr³ Δ ¬bnÞúkefr + bnÞúkGefr¦ mm2.12

1025.21045.22.11 10

10=

⋅⋅

×= PaBxusKñamantémøtUc RbEhl %8 .

2> RbsinebI 1eI mFüm RtUv)aneRbI 4101 1037.2 mmIe ⋅= enaH

Δ ¬bnÞúkefr + bnÞúkGefr¦ mm8.111025.21037.22.11 10

10=

⋅⋅

×= . PaBxusKñamantémøtUcRbEhl %5 .

3> edIm,IPaBgayRsYleKGacRbI eI énmuxkat;kNþalElVg elIkElgEteKRtUvkartémøCak;lak;.



6>6> sñameRbHenAkñúgGgát;rgkarBt; (Cracks in Flexural Members)

karsikSaBIkarkekItsñameRbH kareFVIkarrbs;sñameRbHenAeBlbnÞúkekIneLIg nigkarRtYtBinitüsñameRbH mansar³sMxan;Nas;sRmab;karKNnaeRKOgbgÁúMebtugEdkBRgwgd¾Cak;lak;mYy. enAkñúgGgát;rgkarBt; sñam eRbH ekIteLIgeRkambnÞúkeFVIkar working load nigedaysarebtugexSayTb;nwgkarTaj enaHEdkRtUv)andak; enAtMbn;TajEdleRbH edIm,ITb;nwgkarTajEdlbgáeLIgedaykmøaMgxageRkA.

sñameRbHedaykarBt;ekIteLIgenAeBlEdlkugRtaMgenAsrésrgkarTajxageRkAeKbMputmantémøelIsBI m:UDuldac;rbs;ebtug (modulus of rupture of concrete) . CamYynwgkareRbIR)as;EdkBRgwgEdlmanersIusþg; x<s; (high-strength reinforcing bars) sñameRbHGacnwgekItmaneRcInenAelIGgát;ebtugGarem:. CamYynwgkar eRbIR)as;EdkrgkarTajx<s; high-tensile steel manRbeyaCn_CaeRcIn b:uEnþeKminGacecosputBIsñameRbHEdl eKmincg;)anenaHeT. sñameRbHEdlmanTMhMFM² )anGnuBaØat[manERcHsIuEdk b¤eFVI[mankarRCabTwkEdleFVI [)at;bg;esaP½NPaBrbs;eRKOgbgÁúM.

sñameRbHekItmanenAelIebtug enAeBlEdlrn§tUc²EdlminGackMNt;)anekItmanenAkñúgFñwmebtugEdlCa lT§plénkugRtaMgTajxagkñúg. kugRtaMgkñúgTaMgenHGacnwgbNþalmkBIkrNImYy b¤eRcInCagmYyénkrNIxag eRkam³

- kmøaMgxageRkA dUcCa kmøaMgTajtamG½kSedaypÞal; kmøaMgkat;TTwg m:Um:g;Bt; b¤m:Um:g;rmYl - karrYmmaD - creep - karrIkmaDxagkñúgEdlCalT§plBIkarpøas;bþÚrlkçN³rbs;smasFatupSMebtug

CaTUeTA sñameRbHRtUv)anEbgEckCaBIrRbePTFM²KW³ sñameRbHbnÞab;bnSM (secondary cracks) nig sñameRbHcMbg (main cracks).

6>6>1> sñameRbHbnÞab;bnSM (secondary Cracks)

sñameRbHbnÞab;bnSM CasñameRbHd¾tUc²ekItmanenAdMNak;kaldMbUgénkareRbH EdlekIteLIgedaykar rIkmaDxagkñúg nigkarRbTajKñaénsmasFatuebtug nigedaykugRtaMgEdl)anBIkarBt;tUcbNþalmkBITm¶n; pÞal;rbs;Ggát; nigbnÞúkefrdéTeTot. sñameRbHmanbIRbePTKW³

- sñameRbHedaykarrYmmaD (shrinkage cracks) CasñameRbHsMxan; BIeRBaHvaCH\T§iBlelITRmg;ragrbs; kareRbHEdlekIteLIgedaybnÞúkenAkñúgGgát;rgkarBt;. enAeBlEdlBYkvaekIteLIg BYkvabegáItnUv Knøgd¾exSayenAkñúgebtug. enAeBlEdlbnÞúkRtUv)anGnuvtþsñameRbHcab;epþImelcecjrUbragenAelI



muxkat;EdlexSayCageK dUcCatambeNþayEdkBRgwg. cMnYn sñameRbHEdlekIteLIgRtUv)ankMNt; edaybrimaNénkarrYmmaDrbs;ebtug nigvtþmanénkarbgáb;TRm. eKBi)akkñúgkarRKb;RKgsñameRbH edaykarrYmmaDenHNas;.

- sñameRbHbnÞab;bnSMedaykarBt; (secondary flexural cracks) CaTUeTAvamanKMlatFM² ehIysñam eRbHmYy²minman\T§iBlkñúgkarbegáItsñameRbHdéTeToteT. vaRtUv)anrMBwgnwgekItmaneRkambnÞúktUc dUcCabnÞúkefr. enAeBlbnÞúkRtUv)anGnuvtþCabnþbnÞab;eTAelIFñwmsamBaØ kugRtaMgTajekItmanenA srésxageRkam ehIyenAeBlEdlvaFMCagkugRtaMgTajEdlekItBIkarBt;rbs;ebtug sñameRbHcab; epþImekIteLIg. vacab;epþImrIkFMCabnþbnÞab; niglatsn§wgeTAkan;G½kSNWt. vaCakarBi)akkñúgkarTsSn_ TaynUvmuxkat;EdlsñameRbHbnÞab;bnSMcab;epþImekItman BIeRBaHebtugminEmnCasmÖar³rUbFatusac; mYy (homogeneous material) nigsmÖar³rUbFatues μ Isac; (isotropic material). elak Salinger nigelak Billing )an):an;RbmaNkugRtaMgEdkmunkareRbHRtwmEtBIRbEhl MPa42 eTA MPa49 . TMhMeRbHdMbUgRtUv)anrMBwgRbEhl mm025.0 enAsrésTajxageRkAbMputrbs;ebtug. enAeBlsñameRbHRtUv)anbegáIt kugRtaMgTajrbs;ebtugenAmuxkat;eRbHfycuHdl; 0 ehIysrésEdk TTYlnUvkmøaMgTajTaMgGs;. enAkñúgxN³enH vaekItmankarsNþkrvagsrésEdk nigebtugedaysar Etebtug nigEdkmansac;lUtxusKña niglatsn§wgeTAdl;muxkat;Edlebtug nigEdkman strain es μ IKña. rUbTI6>6 bgðajBIKMrUénkarEbgEckkugRtaMgrvagsñameRbHenAkñúgGgát;eRkamkmøaMgTajtamG½kS.



- sñameRbHbnÞab;bnSMERcH (corrosion secondary cracks) ekIteLIgenAeBlsMeNImmansarFatuKImIdUc CasUdüÚmkørY (sodium chloride NaCl ) kabUnDIG‘uksIut (carbon dioxide 2CO ) nig]s μ ½nG‘uksIuEsn RCabcUleTAkñúgépÞebtug ehIybegáItCaERcHsIuEdk. bnSMG‘uksIutEdlbegáItedaykarxUcxatrbs;Edk RKbdNþb;nUvbrimaNeRcInCagEdk nigCRmujsm<aFemkanicEdlbnþlatsn§wgsñameRbHkan;EtFM. sñameRbHRbePTenHmaneRKaHfñak;EdlGaceFVI[eRKOgbgÁúM)ak;. kar)ak;dMbUlenA Muskegan enArdæ Michigan kñúg qñaM 1955 bNþalmkBIERcHsIuEdk RtUv)anraykarN_eday Shermer. karrIkraldal énsñameRbH nigkarpÞúHebtug (spalling of concrete) enAelIs<an San Mateo-Hayward kñúgGMLúg eBl 7qñaM enArdæ California RtUv)anraykarN_eday Stratfull. sñameRbHedayERcHGacRtUv)an bBaÄb;edayeRbInUvviFIsaRsþsagsg;RtwmRtUv nigebtugEdlmanKuNPaBx<s;.

6>6>2> sñameRbHcMbg (Main Cracks)

sñameRbHcMbg (main cracks) ekIteLIgenAdMNak;kalbnÞab;BIsñameRbHbnÞab;bnSM (secondary

cracks). vaRtUv)anbegáIteLIgedayPaBxusKñaén strain enAkñúgEdk nigebtugenAelImuxkat;eRbH. karRbRBwtþ eTArbs;sñameRbHcMbgpøas;bþÚrenABIrdMNak;kalepSgKña. enAeBlEdlEdkrgkugRtaMgTajtUc cMnYnsñameRbH ekIneLIg b:uEnþTMhMsñameRbHenAmanTMhMtUc EtenAeBlEdlkugRtaMgTajekIneLIg va)aneTAdl;dMNak;kal lMnwg. enAeBlEdlkugRtaMgekIneLIgkan;Etx<s; dMNak;kalTIBIrénkareRbHekIteLIg ehIyTMhMeRbHrIkFM b:uEnþ BuMmankarekIneLIgnUvcMnYnsñameRbHKYr[kt;sMKal;eT. CaTUeTAsñameRbHmYy b¤BIrcab;epþImBRgIkTMhMFMCagsñam eRbHdéT EdlbegáItCasñameRbHeRKaHfñak; ¬rUbTI 6>7¦.

sñameRbHenAkñúgFñwm nigeRKOgbgÁúMrgkarTaj Edl)ansikSaedayGñkGegátkarTsSn_TayBITMhMsñam eRbH nigkarRKb;RKgsñameRbHCacMENkénbBaðaEdlRtUvsikSa.

TaMgenHRtUv)anBiPakSaenATIenH CamYynigtRmUvkarrbs;bTdæan ACI Code. - ebIeyagtamRTwsþIsñameRbHEdlmaneRsc TMhMsñameRbH (crack width) nigKMlatsñameRbH (crack

spacing) GaRs½yeTAelIeRcInktþa EdlrYmmanPaKryEdk karBRgayEdkenAkñúgmuxkat;ebtug kug RtaMgBt;rbs;EdkenAbnÞúkeFVIkar service load kRmas;ebtugkarBarEdk niglkçN³rbs;sarFatupSM ebtug. smIkarepSg²sRmab;TsSn_TayTMhM nigKMlatsñameRbHenAkñúgGgát;ebtugGarem:RtUv)an bgðajenAkñúgsnñisiT§sþIGMBIkarkekItkaretags¥it nigkarkekItsñameRbHenAkñúgebtugBRgwgedayEdk Symposium on Bond and Crack Formation in Reinforced Concrete enA Stockholm RbeTs Sweden kñúgqñaM 1957. elak Chi nigelak Kirstein )anbgðajsmIkarsRmab;TMhMeRbH nigKMlat



sñameRbHCaGnuKmn_eTAnwgRkLaépÞRbsiT§PaBrbs;ebtugEdlenACMuvijEdk³ RkLaépÞebtugmUlEdl manGgát;p©ites μ IGgát;EdkbYndgRtUv)aneRbIedIm,IKNnaTMhMeRbH. smIkardéTeTotRtUv)anbgðajenA TsvtSr_eRkay ²eTot.

elak Gergely nigelak Lutz bgðajnUvrUbmnþxageRkamsRmab;kMNt;TMhMeRbH³

63 1011 −×= cs AdfW β (6-16) Edl β / A nig sf RtUv)ankMNt;BIxagedIm nig =cd kRmas;karBarebtugEdlRtUv)anvas;BIsrés

TajEpñkxageRkAbMputeTAG½kSEdkCitCageK. témø β GacRtUv)anykRbEhl 2.1 sRmab;Fñwm nig 35.1 sRmab;kRmalxNÐ. cMNaMfa sf KitCa MPa nig W KitCa mm .

pleFobrvagTMhMsñameRbHGtibrmaelITMhMsñameRbHmFümRtUv)anrkeXIjsßitenAcenøaH 5.1 nig 0.2 Edl)anraykarN_edayGñkGegátCaeRcIn. témømFümeKGaceRbI 75.1 .



- TMhMeRbHEdlGacGnueRKaH (tolerable crack width) ³ eKminGaceCosputBIkarkekItsñameRbHenAelI Ggát;ebtugGarem:)aneT. eTaHbICamankarsikSa nigkarsagsg;y:agykcitþTukdak;y:agNak¾eday k¾vaenAEtkekItnUvsñameRbHb:unsréssk;Edr. CaTUeTAsñameRbHRtUv)anvas;enAelIépÞrbs;ebtug b:uEnþ Cak;EsþgsñameRbHmantaMgBInIv:UEdkemø:H EdlCakEnøgekItmanERcHsIuEdk. tRmUvkaresaP½NPaBCH \T§iBldl;TMhMsñameRbHGnuBaØat. sñameRbHEdlGacemIleXIjedayEPñkTeTmanTMhMRbEhl

mm15.0 vaGaRs½yeTAnwg texture rbs;épÞebtug. témøepSg²sRmab;sñameRbHGnuBaØatenAnIv:UEdk RtUv)anesñIeLIgedayGñkGegátCaeRcIn EdlvasßitenAcenøaH 25.0 nig mm40.0 sRmab;Ggát;xagkñúg nigsßitenAcenøaH 15.0 nig mm25.0 sRmab;Ggát;xageRkA. TMhMsñameRbH mm40.0 sRmab;Ggát;xag kñúg nig mm32.0 sRmab;Ggát;xageRkA eRkamlkçxNÐs¶ÜtGacRtUv)anGnueRKaH.

- karRKb;RKgsñameRbH (crack control) eRcInekItmanenAelIGgát;ebtugGarem:EdleRbIEdkersIusþg;x<s; (high-strength steel) . sñameRbHkan;EtFMekItmaneRkambnÞúkeFVIkar edaysarEtkugRtaMgGnuBaØat x<s;. karRKb;RKgsñameRbHGaRs½yeTAnwgTMhMsñameRbHGnuBaØat . vaCakarRbesIrEdlmansñameRbH tUc²EteRcIn CaCagmansñameRbHFM²Ettic. sñameRbHbnÞab;bnSM (secondary crack) RtUv)ankat; bnßyedaykarRKb;RKgnUvbrimaNkMe)areRbgTaMgGs; pleFobTwkelIsIum:gt¾ PaBRCabTwkrbs;f μ bMEbknigebtug kRmiténkarEfTaMebtug niglkçxNÐbgák;cug (end-restraint condition).

ktþaEdlTak;TgnwgkarRKb;RKgsñameRbHcMbg KWkugRtaMgEdk PaBetags¥itrbs;ebtug kar BRgayEdk Ggát;p©itEdk PaKryEdk kRmas;karBarebtug niglkçN³rbs;sarFatupSMebtug. edIm,I CYykat;bnßyTMhMsñameRbH eKRtUveFVI[ktþaEdl)anerobrab;xagelIy:agehacmYymanlkçN³kan;Et l¥.

6>7 tRmUvkarrbs;bTdæan ACI Code (ACI Code Requirement)

edIm,IRKb;RKgsñameRbHenAkñúgGgát;ebtugGarem: bTdæan ACI Code, chapter 10 kMNt;nUvtRmUvkarxag eRkam³

1> manEtEdk deformed bar RtUv)anGnuBaØat[eRbICaEdkem (main reinforcement) 2> EdkrgkarTajKYrEtRtUv)anBRgayenAtMbn;TajGtibrma (ACI Code, section 10.6.3) 3> enAeBlEdlsøabrbs;muxkat;sßiteRkamkarTaj EpñkénEdkemKYrRtUv)anBRgayenAkñúgcMeNamtémø

EdltUcCageKkñúgcMeNamTTwgsøabRbsiT§PaB (effective flange width) nigmYyPaKdb;énElVg one-tenth of the span (ACI Code, section 10.6.6).



4> ersIusþg;KNna (design yield strength) rbs;EdkminKYr[elIsBI MPa560 (ACI Code, section

9.4). 5> KMlatGtibrma s BIEdkEdlmancm¶ayeTAépÞebtugrgkarTajCitCageK sRmab;FñwmebtugGarem: nigkM

ralxNÐmYyTisRtUv)ankMNt; cs Cfs 5.2/105000 −= (6-17)

b:uEnþminRtUvFMCag )/280(300 sf Edl =sf kugRtaMgKNnaenAkñúgEdkeRkambnÞúkeFVIkarRtUv)ankMNt;edaypleFobrvagm:Um:g;

K μanemKuN nigplKuNrvagRkLaépÞEdk nigRbEvgédXñas;kñúg )/( jdAMf ss = . ¬mü:ag vijeTot eKGaceRbI 3/2 ys ff = edaysarEtkareRbItémøRbEhlrbs; djd 87.0= ¦.

=cC kRmas;ebtugkarBarEdk (clear cover) BIépÞrgkarTajCitbMputeTAépÞEdkrgkar Taj.

=s KMlatKitBIG½kSénEdkrgkarTajEdlCitCageKeTAépÞebtugrgkarTaj. karkMNt;enHRtUv)aneRbIsRmab;EtFñwmebtugGarem: nigkRmalxNÐmYyTisEdlsßitenAkñúglkç

xNÐbrisßanFmμta. karkMNt;KMlatminTak;TgnwgTMhMEdkeT EdlvanaM[mankareRbIR)as;TMhMEdktUc CagedIm,IbMeBjlkçxNÐKMlat. sRmab;krNIFñwmebtugGarem:EdleRbIEdk MPaf y 420= nig

mmCc 50= . enaHKMlatGtibrma s RtUv)anKNnadUcxageRkam³ snμt; MPafs 28042066.0 =×=

( ) mms 250505.2280/105000 =×−= EdldUcKñaeTAnwg mm300)280/280(300 =

6> enAkñúgbTdæanBImun karRKb;RKgsñameRbHRtUv)anQrelIemKuN Z EdlkMNt;dUcxageRkam³ mmkNAdfZ cs /313 ≤= sRmab;Ggát;enAxagkñúg (6-18)

mmkNZ /26≤ sRmab;Ggát;enAxageRkA (6-19)

Edl =sf kugRtaMgBt;enAbnÞúkeFVIkar nigGacykes μ I 3/2 yf / A nig cd CatMbn;TajRbsiT§PaB rbs;ebtug nigkRmas;ebtugkarBarEdk erogKña. smIkarenHQrelIsmIkar (6-16) edaysnμt;TMhMsñameRbH RtUv)ankMNt;Rtwm mm40.0 sRmab;Ggát;enAxagkñúg nig mm32.0 sRmab;Ggát;enAxageRkA. edIm,ITTYl)an Z tUc eKRtUvbnßykRmas;karBarebtug. kRmas;ebtugminRtUvelIsBI mm50 .

7> Edkxag skin reinforcement skA sRmab;Fñwmkm<s;eRCA Edlmankm<s;RbsiT§PaB mmd 900≥ srésEdkesþIgKYrRtUv)anbEnßmenAEk,répÞbBaÄrkñúgtMbn;TajedIm,IRKb;RKgsñameRbHenAelIRTnug



BIelIEdkem. bTdæan ACI Code, section 10.6.7 )anbriyayBIEdkbEnßmEdlCaEdkxag skin

reinforcement skA . EdkxagKYrRtUv)anBRgayesμ IelIépÞTaMgsgçagsRmab;cm¶ay 2/d Ek,rEdk rgkarTajbMput. KMlat skS rvagEdkbeNþayénEdkxagminKYrFMCagtémøEdltUcCageKkñúgcMeNamtémø 6/d /

mm300 nig )750/(1000 −dAb Edl bA CaRkLaépÞénmuxkat;EdkmYy² KitCa 2mm ¬rUbTI6>8¦.

⎪⎩

⎪⎨

⎧

−=

)750/(1000300

6/min

dA

dS

b

sk

Edkxag k¾GacRtUv)anKitbBa©ÚlkñúgkarKNnaersIusþg; (strength) edayQrelIkarKNnakugRtaMg stress nigbERmbRmYlrageFob (strain). elIsBIenH EdkxagsrubenAépÞTaMgsgçagénGgát; minKYrelIsBIBak; kNþalmuxkat;EdkrgkarTajsrub sA eT.

eyagtamrUbTI 6>8 RbsinebI mmb 400= / mmd 950= nigeRCIserIsEdk 10DB ¬ =bA 278mm ¦CaEdkxag enaHKMlatrbs;Edk 10DB EdlCaEdkbeNþayKYryktémøtUcCageKkñúgcMeNam

mm300 / mm1586/950 = nig mm390)750950/()781000( =−× . dUcenH eyIgeRCIserIsykKMlat mm150 . EdkxagKYrRtUv)anBRgayedayEdk 10DB kñúgKMlat mm150 elIkm<s; 2/d sRmab;xagmYy²

¬rUb TI 6>8¦. RkLaépÞsrubEdkxagsRmab;épÞTaMgBIr 2468786 mm=×= EdltUcCag 40215.05.0 ×=sA 25.2010 mm= .

taragxageRkampþl;nUvKMlatGtibrmaenAelIépÞmYy² skS RkLaépÞEdkxagGb,brmamYy² bA . km<s;Fñwm d / mm 800 900 1000 1100 1200 1300 1400 1500

KMlatGtibrma skS / mm 150 150 150 175 200 200 225 250 bA ¬Gb,brma¦/ 2mm 5.7 5.22 5.37 25.61 90 110 25.146 5.187



]TahrN_6>6³ muxkat;FñwmTRmsamBaØRtUv)anbgðajenAkñúgrUb 6>9

a. epÞógpÞat;muxkat;EdktamtRmUvkarrbs; ACI Code b. kMNt;TMhMeRbHEdlnwgGacekItman c. epÞógpÞat;emKuN Z tamsmIkar (6-18)

eK[ MPaf c 28' = / MPaf y 400= nigEdkkg 10DB . dMeNaHRsay³

1> rUb 6>9 muxkat; a ³ a. sRmab; 283DB / 21847mmAs = / kRmas;ebtugkarBarEdk mmCc 462/2860 =−= / snμt;

MPaff ys 26440066.066.0 =×== / KMlatGtibrma mms 7.282465.2264/105000 =×−= EdltUcCag mm2.318)264/280(300 = .

KMlatEdlpþl;[ mm90)6060300(5.0 =−−= edayKitBIG½kSEdkeTAG½kSEdk EdltUcCag mm7.282 .

b. sRmab;muxkat;enH mmdc 60= . RkLaépÞebtugrgkarTajRbsiT§PaBsRmab;EdkmYyKW ( ) 2120003/602300 mmA =×=

KNnaTMhMsñameRbHtamsmIkar (6-16) 63 1011 −×= cs AdfW β

edayGgát;enHCaFñwmenaH 2.1=β nig MPafs 240= mmW 28.01060120002402.111 63 =⋅×××= −



EdltUcCag mm40.0 nig mm32.0 sRmab;Ggát;xagkñúg nigsRmab;Ggát;xageRkA. c. tamsmIkar (6-18)

mmkNAdfZ cs /5.21106012000240 333 =⋅×== − EdltUcCag mmkN /31 nig mmkN /26 sRmab;Ggát;xagkñúg nigsRmab;Ggát;xageRkA.

2> rUb 6>9 muxkat; b ³ a. karKNnaKMlatEdkmanlkçN³RsedogKñacMNuc a xagelI. b. sRmab;muxkat;enH mmdc 60= ehIyEdkRtUv)andak;CaBIrRsTab;. TIRbCMuTm¶n;rbs;EdkKW mm90

BIsrésxageRkam. RkLaépÞebtugrgkarTajRbsiT§PaBsRmab;EdkmYyKW ( ) 290006/902300 mmA =×=

mmW 26.0106090002402.111 63 =⋅×××= − RKb;RKan; c. tamsmIkar (6-18)

mmkNAdfZ cs /5.1910609000240 333 =⋅×== − RKb;RKan; karBiPakSa eyIgGaceXIjfaKMlat s enAkñúgsmIkar (6-17) CaGnuKmn_énkugRtaMgkñúgEdkTaj b¤CaGnuKmn_eday minpÞal;énbERmbRmYlrageFobenAkñúgEdkTaj sss Ef ε×= ehIy sE sRmab;Edkes μ I MPa5101.2 ⋅ . dUcKñaKM latk¾GaRs½ynwgkRmas;ebtugkarBarEdk cC . karekIneLIgnUvkRmas;ebtugkarBar vanwgkat;bnßy KMlat EdlvaminTak;TgeTAnwgTMhMEdkEdleRbIenAkñúgmuxkat;eT.



enAkñúg]TahrN_enH TMhMsñameRbHEdlrMBwgTukRtUv)anKNnaedaysmIkar (6-16) edIm,Ipþl;[nisiSt nigvisVkrnUvtRmUvkarRKb;RKgsñameRbH nigTMhMsñameRbH. CaTUeTATMhMsñameRbHRtUv)anvas;enAelIFñwmEdl eFVIkarBiesaFn_enAkñúgmnÞIrBiesaFn_ b¤k¾enAkñúgeRKOgbgÁúMCak;EsþgEdlsßiteRkambnÞúk EdleFVI[mansñameRbH eRKaHfñak;ekIteLIgenAkñúgFñwm nigkñúgkRmalxNÐ ehIyEdlRtUvkarkarBiesaFn_. RbsinebITMhMsñameRbHEdl )anvas;mun nigeRkaykardak;bnÞúkFMCag yield strain rbs;Edk enaHEdkemnwgmanlkçN³)øasiÞc nig KμanRb siT§PaB. eKGacvas;TMhMeRbHCak;Esþg)anedaybnÞat;sRmab;vas;sñameRbHEdleKGacrkTij)an. eRkABI kugRtaMgEdk nigkRmas;ebtugkarBarEdk W enAGaRs½ynwgktþaTIbIKW A EdlCaRkLaépÞebtugrgkarTajBT§½CMu vijEdkrgkarTajmYy. ]TahrN_6>7³ KNnaFñwmTRmsamBaØEdlmanRbEvg m3.7 RTnUvbnÞúkefrBRgayesμ I mkN /9.21 nigbnÞúk GefrBRgayes μ I mkN /2.17 . eRCIserIsmuxkat;EdkRKb;RKan; nigepÞógpÞat;KMlatEdkedIm,IbMeBjlkçxNÐ ACI Code. eK[ mmb 400= / MPaf c 28' = / MPaf y 400= PaKryEdk %8.0 nigkRmas;ebtugkar BarEdk mmCc 50= .

dMeNaHRsay³

1> sRmab;PaKryEdk %8.0=ρ / MPaRu 7.2= ¬ 9.0=φ ¦. m:Um:g;emKuNxageRkAKW 8/2wLMu = nig mkNw /8.532.176.19.212.1 =×+×=

mkNMu .624.3488/3.78.53 2 =×= 2bdRM uu = mmd 568= 26.1817568400008.0 mmAs =××=

eRbI 283DB ¬ 23.1847 mmAs = ¦mYyCYr. km<s;srubrbs;muxkat;Fñwm mmh 650= . CaTUeTA

mmd 5862/2850650 =−−= ¬rUbTI6>10¦



2> KNnabnÞúkeFVIkar (service load) nigm:Um:g;eFVIkar (service moment) mkNw /1.392.179.21 =+=

mkNMu .5.2608/3.71.39 2 =×= 3> KNnakm<s;G½kSNWt kd nigRbEvgédXñas; jd tamsmIkar (6-12)

0)(2/)( 2 =−− kddnAkdb s 8=n 23.1847 mmAs = mmd 586= mmkd 4.174= mmkddjd 9.5273/ =−= 9.0586/9.527 ==j

cMNaMfa eKGacyktémøRbEhlrbs; 87.0=j kñúgkrNIEdl kd minRtUv)anKNna. 4> KNnakugRtaMg sf

jdfAM ss ⋅⋅= MPafs 267)9.5273.1847/(105.260 6 =×⋅=

5> KNnaKMlat s tamrUbmnþ (6-17) mms 3.268505.2267/105000 =×−=

EdltUcCag mm6.314)267/280(300 = KMlatEdl[ ( ) mmmm 8.23013664644005.0 <=−−=


RbEvgEdkbgán; b¤RbEvgEdkRCYs 153 T.Chhay

VII. RbEvgEdkbgáb; b¤RbEvgEdkRCYs

7>1> esckþIepþIm lkçN³bnSúIKñarvagEdk nigebtug enAkñúgeRKOgbgÁúMebtugGarem:QrelIeKalkarN_ PaBs¥itrvagsmÖar³

TaMgBIreRkayebtugkkrwg. RbsinebIsrésEdkEdlmanmuxkat;mUlRtg;RtUv)anbgáb;enAkñúgebtug caM)ac;eKRtUv mankmøaMgmYyRKb;RKan;edIm,ITajsrésEdkenaHecjBIebtug. RbsinebIRbEvgbgáb;énsrésEdkenAkñúgebtug manRbEvgEvgRKb;RKan; enaHsrésEdkGaceFVIkardl;cMNuc yield edayTukRbEvgxøHrbs;srésEdkenAkñúg ebtug. kmøaMgs¥itGaRs½yeTAnwgPaBkkitrvagEdk nigebtug. kmøaMgkkitTTYl\T§iBlCacMbgbNþalBIPaB eRKIménépÞxagrbs;srésEdk karlayebtug karRskmaD nigkRmas;ebtugeRsabEdk. EdkfñaMgGMeBA (deformed bar) pþl;nUvPaBs¥itl¥CagEdkmUl. ersIusþg;ebtugkan;EtFM PaBs¥itkan;EtFM. kRmas;ebtugeRsab Edkkan;EtRkas; kugRtaMgPaBs¥itrbs;Edkkan;EtFM.

CaTUeTA ersIusþg;PaBs¥itTTYl\T§iBlBIktþaxageRkam³ - ersIusþg;rbs;Edk yf / RbEvgbgáb;kan;EtEvg sRmab; yf kan;EtFM - KuNPaB nigersIusþg;sgát;rbs;ebtug cf ' / kalNa cf ' kan;EtFM enaHRbEvgbgáb;kan;xøI - muxkat;Edk KMlat nigTItaMgrbs;EdkenAkñúgmuxkat;ebtug. EdkbeNþayEdldak;kñúgKMlatbBaÄr

FMCag cm30 manersIusþg;s¥itTabCag GaRs½yedaykarrYmmaD nigkarRskrbs;ebtugGMLúgeBl dMeNIrkarkkrwgrbs;ebtug. dUcKña KMlatEdkkan;EtFM pþl;nUversIusþg;s¥itkan;EtFM eRBaHvapþl;nUv épÞebtugRKb;RKan;CMuvijEdk.

- kRmas;ebtugeRsabEdk. kRmas;kan;EttUc bgá[mankareRbH. - karxÞb;EdkbeNþayedayEdkTTwg. karxÞb;EdkbeNþayedayEdkTTwg b¤EdkkgRKb;RKan;

karBarkarpÞúHEbkebtugCuMvijEdkbeNþay.

7>2> karbegáItkugRtaMgs¥it

7>2>1> PaBs¥itedaykarBt; eKmanFñwmmYyRbEvg dx rgnUvbnÞúkBRgayes μI. eday[m:Um:g;EdlekIteLIgenAEpñkmçagCa 1M nig

mçageTotCa 2M ehIy 1M mantémøFMCag 2M . m:Um:g;nwgbegáItnUvkmøaMgsgát; nigkmøaMgTajxagkñúg. eday 21 MM > enaH 21 TT > dUcKña 21 CC > .


T.Chhay 154 Development Length of Reinforcing Bars

enAmuxkat;NamYyenaH jdMT =

Edl jd CaédXñas;

jddMdTTT ==− 21

b:uEnþ OdxuTT ∑+= 21 Edl u CakugRtaMgs¥itmFüm

O∑ CaplbUkbrimaRténmuxkat;r)arenAEpñkrgkarTaj dUcenH

jddMOdxuTT =∑=− 21

OjddxdMu

∑×=⇒

1

Eteday Vdx

dM=

OjdVu∑

=⇒ (7.1)

mü:ageTotedIm,IsRmYlkñúgkarKNna j RtUv)ansnμt;es μ Inwg 87.0 dUcenH

OdVu∑

=87.0

edayersIusþg;énPaBs¥it RtUv)ankat;bnßyedayemKuN 85.0=φ enaH

OdVUn ∑

=87.0φ

(7.2)

7>2>2> karBiesaFsRmab;RbsiT§PaBPaBs¥it

karBiesaFedIm,IkMNt;lT§PaBkugRtaMgs¥itGaceFVIeLIgedayeRbI pullout test ¬rUbTI 7>2¦. kar BiesaFenH kMNt;lT§PaBs¥iténépÞEdkRbePTepSg²edayeFobeTAnwgRbEvgbgáb;. kugRtaMgTajEbkEckes μ I



CMuvijsrésEdkenARtg;muxkat;Cak;lak; nigERbRbYltambeNþayRbEvgbgáb; nigenARtg; radial distance BIépÞrbs;srésEdk. b:uEnþkarBiesaFenHmin)ansMEdgBIPaBs¥itRbsiT§PaBenAkñúgépÞrbs;srésEdkenAkñúg Ggát;rgkarBt;eT eRBaHkugRtaMgERbRbYltamkm<s;rbs;muxkat;ebtug. RbePTTIBIrénkarBiesaFGacGnuvtþ)ancMeBaHEdkbgáb; ¬rUbTI 7>3¦. enAkñúgkarBiesaFenH eKbegáIn kmøaMg P bnþicmþg² ehIyeKkt;RtacMnYn KMlat nigTMhMsñameRbH. kugRtaMgs¥itERbRbYltambeNþayRbEvg srésEdkcenøaHsñameRbH. bERmbRmYlrageFobrbs;srésEdkmantémøGtibrmaenARtg;muxkat;eRbH ehIy fycuHenARtg;muxkat;kNþalrvagmuxkat;eRbH. eKk¾GaceFVIkarBiesaFeTAelIGgát;rgkarBt; edIm,IsikSaBIRbsiT§PaBénPaBs¥ittambeNþayépÞrbs;Edk Taj. karviPaKkugRtaMgs¥itrbs;srésEdkRtUv)anbgðajrYcmkehIyenAkñúgkfaxNÐ 7>2>1. RbEvgbgáb; (development length) CaRbEvgrbs;srésEdknImYy² edIm,IbegáIt yield strength eBj eljedaymin[rbUtedaysarersIusþg;s¥it (bond strength). RbsinebIsrésEdkminmanRbEvgbgáb;RKb;RKan; enaHkugRtaMgs¥itenAkñúgtMbn;Tajrbs;FñwmnwgmantémøFM ehIyvanwgeFVI[mansñameRbH nigrEhkkRmas;ebtug karBarEdkCMuvijEdkrgkarTaj. RbsinebIkarrEhkebtugbnþdl;cugsrésEdk Fñwmnwg)ak;. cMNaMfa KMlattUcrvagEdkrgkarTaj nigkRmas;ebtugkarBarEdkenAEpñkxag nig)atrbs;FñwmmantémøtUcnwgkat;bnßy ersIusþg;s¥itrbs;srésEdk.



7>3> RbEvgbgáb;sRmab;tMbn;Taj

7>3>1> RbEvgbgáb;mUldæan dl RbsinebIsrésEdkbgáb;kñúgebtugrgkmøaMgTaj T enaHkmøaMgTajenaHRtUvTb;edaykugRtaMgs¥itrvag

srésEdk nigebtug. kmøaMgTajGtibrmaRtUvmantémøes μ Inwg ys fA Edl sA muxkat;srésEdk. kmøaMgenH



RtUv)anTb;edaykmøaMgkñúg dnOlU Edl nU kugRtaMgs¥itcugeRkaymFüm dl RbEvgbgáb;Edk nigO brimaRt srésEdk )( Dπ . kmøaMgTaMgBIrenHRtUvEtesμ IKñaedIm,ImanlMnwg.

dnys OlUfA =

OUfA

ln

ysd =⇒ (7.3)

eday 4

2b

sdA π

= nig bdO π=

n

ybd U

fdl

4=⇒ (7.4)

mann½yfa RbEvgbgáb;GaRs½ynwg muxkat;Edk ersIusþg;rbs;Edk nigkugRtaMgs¥itEdlCaGnuKmn_eTA nwg cf ' .

)21('5.0 −=

bcn d

cfU

)21('

5.0

−=⇒

b

b

c

yd

dc

dff

l (7.5)

eday[ bdc 5.1= b

c

yd d

ff

l'

5.0= (7.6)

smIkarRbEvgbgáb;sRmab;tMbn;Taj Edl)anBIkareFVIBiesaFn_ ehIyRtUv)ansRmYledayKN³kmμkarKW b

b

trc

yd d

dKcf

fl

)('109

+=

αβγλ (7.7)

Edl 5.2≤+

b

tr

dKc

α emKuNTItaMgsrésEdk β emKuNRTnab;Edk γ emKuNTMhMEdk λ emKuNTm¶n;ebtug c KMlatEdk b¤RTnab;ebtugkarBarEdk c RtUvmantémøtUckñúgcMeNamkrNITaMgBIrxageRkam³ - cm¶aytUcCageK Edlvas;BIépÞebtugmkG½kSEdk - mYydgknøHénKMlatEdk EdlKitBIG½kSmkG½kS



trK snÞsSn_EdkTTwg

snfA

K yttrtr 10=

trA muxkat;EdkTTwg ytf ersIusþg;EdkTTwg

s KMlatEdkGtibrmarbs;EdkTTwgKitBIG½kSmkG½kS n cMnYnEdkTTwg cMNaM³ 1¦ ( ) btrb dKc /+ minKYrFMCag 5.2 edIm,IFanasuvtßiPaBdl;kardac;edaykarrbUt. 2¦ témørbs; cf ' minRtUvFMCag MPa3.8 . 3¦ trK RtUv)aneKsnμt;mantémøesμ IsUnüedIm,IsRmYldl;karKNna.

7>3>2> emKuN ACI Code sRmab;KNna dl sRmab;srésEdkrgkarTaj

1¦ α emKuNTItaMgsrésEdk 3.1=α sRmab;EdkEdldak;manKMlatx<s;Cag cm30 BIEdkbgáb;

1=α sRmab;krNIepSgeTot 2¦ β emKuNRTnab;Edk 5.1=β sRmab;Edklab epoxy-coating ehIymanRTnab;ebtugkarBarEdktUcCag bd3 nigman

KMlatEdktUcCag bd6 2.1=β sRmab;Edklab epoxy-coating krNIepSgeTot 1=β sRmab;EdkminmanlabfñaMkarBar 3¦ γ emKuNTMhMEdk 8.0=γ sRmab;EdkEdlmanGgát;p©ittUcCag b¤es μ I mm19 1=γ sRmab;EdkEdlmanGgát;p©itFMCag b¤esμ I mm22



4¦ λ emKuNTm¶n;ebtug 3.1=λ sRmab;ebtugRsal ¬RbsinebIeKsÁal;ersIusþg;TajedaykarrEhkrbs;ebtugTm¶n;Rsal

ctf eRbI ctc ff /'56.0=λ b:uEnþ 1≥λ ¦ 1=λ sRmab;ebtugFmμta 5¦ ACI Code GnuBaØat[eRbI 0=trK eTaHbICamanvtþmanEdkTTwgk¾eday. enAkñúgkrNIenH

)/('109

bc

y

b

d

dcff

dl αβγλ

=

témørbs; cf ' minRtUvFMCag MPa3.8 . 6¦ sR CaemKuNkat;bnßyEdlbNþalBIbrimaNEdkelIs. ACI Code, section 12.2.5 GnuBaØat[ kat;bnßy dl edayemKuN sR enAeBlEdlEdkenAkñúgGgát;rgkatBt;elIstRmUvkarénkarviPaK

elIkElgEtkEnøgEdleKRtUvkarCaBiessnUvkarf<k; b¤RbEvgbgáb;sRmab; yf b¤srésEdkRtUv)an sikSaKNnaedayBicarNa\T§iBlrBa¢ÜydI.

( )( )[pþl;

tRmUvkars

ss A

AR =

7¦ sRmab;RKb;krNITaMgGs; RbEvgbgáb; dl minRtUvtUcCag mm300 .

7>3>3> rUbmnþsRmYlsRmab; dl ACI Code, section 12.2.2 GnuBaØat[eRbIrUbmnþsRmYlsRmab;KNnapleFob bd dl / . vaQrelI

PaBCak;EsþgEdlkrNIsagsg;bc©úb,nñeRbIKMlat nigRsTab;ebtugkarBarEdkCamYynwgEdkxÞb; (confining

reinforcement) dUcCaEdkkg (stirrup and tie) EdleFVI[témø ( ) btrb dKc 5.1≥+ . elIsBIenH karBiesaF bgðajfa eKGackat;bgßyRbEvgbgáb; dl %20 sRmab;EdkEdlmanGgát;tUcCag b¤esμ I mm19 . edayQrelI karsnμt;TaMgenH nigsnμt;fa ( ) btrb dKc 5.1=+ enaHsmIkar 7.7 RtUv)ansRmYldUcxageRkam³

1¦ sRmab;srésEdkEdlmanGgát;p©itFMCag b¤esμ I mm22

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'53αβλ (7.8)

sRmab;srésEdkEdlmanGgát;p©ittUcCagb¤es μ I mm19

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'2512αβλ (7.9)

pleFob bd dl / enAkñúgsmIkar 7.9 es μInwg %80 énpleFob bd dl / enAkñúgsmIkar 7.8. eKeRbI smIkarTaMgenHkñúgkrNIEdleKCYblkçxNÐmYykñúgcMeNamlkçxNÐTaMgBIrxageRkam³



k¦ KMlatBIépÞEdkeTAépÞEdkEdlRtUvbgáb; b¤RCYsminRtUvtUcCag bd / RsTab;ebtugkarBarEdkmin RtUvtUcCag bd ehIyEdkkgEdldak;elIRbEvg dl minRtUvtUcCagtémøGb,brmaEdl[eday kUd.

x¦ KMlatBIépÞEdkeTAépÞEdkEdlRtUvbgáb; b¤RCYsminRtUvtUcCag bd2 / RsTab;ebtugkarBarEdk minRtUvtUcCag bd .

2¦ sRmab;krNIdéTeTot témørbs; bd dl / enAkñúgsmIkar 7.8 nig 7.9 RtUvKuNnwg 5.1 edIm,IeFVI[va smmUleTAnwgsmIkar 7.7.

smIkarTaMgenHmanlkçN³gayRsYlkñúgkareRbIR)as;sRmab;lkçxNÐTUeTAEdlBak;B½n§nwgkarsikSa KNna nigkarsagsg;. ]TahrN_ sRmab;RKb;eRKOgbgÁúMebtugTm¶n;Fmμta ( )0.1=λ srésEdkEdlminlab epoxy-coating ( )0.1=β EdkEdlmanGgát;p©itFMCag b¤esI μ mm22 ( )0.1=γ enaHsmIkar 7.8 køayCa

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'53 (7.10)

eKeRbIsmIkarenH RbsinebIvaeKarBlkçxNÐ k¦ nig x¦ b:uEnþsRmab;krNIdéTeTot eKRtUvKuN bd dl / CamYynwg 5.1 b¤

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'109 (7.11)

sRmab;lkçxNÐdUcKña nigsRmab;srésEdkEdlmanGgát;p©ittUcCag b¤esμ I mm19 smIkar 7.9 køayCa

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'2512 (7.12)

eKeRbIsmIkarenH RbsinebIvaeKarBlkçxNÐ k¦ nig x¦ b:uEnþsRmab;krNIdéTeTot eKRtUvKuN bd dl / CamYynwg 5.1 b¤

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'2518 (7.13)

kñúgkarsikSaKNna nigkarsagsg;GKarebtugGarem: eKniymeRbI MPaf c 28' = nig MPaf y 400= . Rbsin ebIeKCMnYstémøTaMgenHeTAkñúgsmIkarxagelI enaH smIikar 7.10 køayCa bd dl 45= ¬Ggát;p©itEdk mm22≥ ¦ (7.10a)

smIikar 7.11 køayCa bd dl 5.67= ¬Ggát;p©itEdk mm22≥ ¦ (7.11a)

smIikar 7.12 køayCa bd dl 36= ¬Ggát;p©itEdk mm19≤ ¦ (7.12a)

smIikar 7.13 køayCa bd dl 54= ¬Ggát;p©itEdk mm19≤ ¦ (7.13a)



témøepSgeTotrbs;pleFob bd dl / RtUv)anbgðajenAkñúgtarag 7>1. tarag 7>2 bgðajBIRbEvgbgáb; dl sRmab;srésEdkepSg² ¬enAeBl MPaf y 400= nig MPaf c 20' = nig MPa30 ¦ sRmab;krNIeKarB lkçxNÐ nigkrNIepSgeTot. tarag 7>1 témørbs; bd dl / sRmab;témøepSg²én cf ' nig yf ¬EdkrgkarTaj¦

MPaf y 235= MPaf y 400=

mm19≤ mm22≥ mm19≤ mm22≥ cf ' ( )MPa

eKarB

lkçxNÐ krNIepSg

eTot eKarB

lkçxNÐ krNIepSg

eTot eKarB

lkçxNÐ krNIepSg

eTot eKarB

lkçxNÐ krNIepSg

eTot 21 24.6 36.9 30.7 46.1 41.9 62.9 52.4 78.6 28 21.3 32.0 26.6 39.9 36.3 54.5 45.4 68.1 35 19.1 28.7 23.8 35.7 32.5 48.9 40.6 60.9 42 17.4 26.1 21.8 32.7 29.6 44.4 37.0 55.5

tarag 7>2 RbEvgbgáb; ( )mmld sRmab;EdkrgkarTaj nig MPaf y 400= ( )0.1=== λβα

RbEvgbgáb; ( )mmld sRmab;EdkrgkarTaj MPaf c 20' = MPaf c 30' = elxsMKal;

rbs;Edk

Ggát;p©itrbs; srésEdk ( )mm

eKarB lkçxNÐ

krNIepSg eTot

eKarB lkçxNÐ

krNIepSg eTot

10M 11.3 485 728 396 594 15M 16.0 687 1031 561 842 20M 19.5 1046 1569 854 1281 25M 25.2 1352 2028 1104 1656 30M 29.9 1605 2408 1310 1965 35M 35.7 1915 2873 1564 2346

7>4> RbEvgbgáb;sRmab;tMbn;sgát; dcl RbEvgbgáb;sRmab;tMbn;sgát;RtUv)aneKKitfamanRbEvgxøICagRbEvgbgáb;sRmab;tMbn;Taj eRBaHkmøaMg

xøH RtUv)anbBa¢ÚneTAebtugedaysrésEdk nigmü:ageTotvaminmansñameRbHenAtMbn;TMBk;. RbEvgbgáb; dcl sRmab;tMbn;sgát;RtUv)ankMNt;eday

c

ybdc f

fdl

'24.0

= yb fd043.0≥ (7.14)



ehIyvaminRtUvmantémøtUcCag cm20 . eKGackat;bnßyRbEvgbgáb; dcl edayKuNnwg =sR ¬ sA tRmUvkar¦ / ¬ sA Edlpþl;[¦. sRmab;Ggát;rgkarsgát;ebtugGarem:EdlmanEdkkgv½NÐGgát;p©itFMCag mm6 nigKMlat tUcCag b¤es μ I mm100 eKGacKuN dcl énsmIkar 7.14 eday 75.0=slR . CaTUeTA ( )≥×= slsdcd RRll b¤

mm200 . tarag 7>3 nig 7>4 [témørbs; bdc dl / enAeBl 400=yf . tarag 7>3 témørbs; bd dl / sRmab;témøepSg²rbs; cf ' nig yf ¬Edkrgkarsgát;¦/ dcl Gb,brma= mm200

ycybdc fffdl 043.0'/24.0/ ≥= ( )MPaf c'

( )MPaf y 21 28 32≥

235 12.3 10.6 10.1 400 21 18.1 17.2

tarag 7>4 RbEvgbgáb;mUldæan ( )mmldc sRmab; Edkrgkarsgát; ( )MPaf y 400=

RbEvgbgáb; ( )mmldc enAeBl =cf ' elxsMKal; rbs;Edk

Ggát;p©itrbs; srésEdk ( )mm ( )MPa21 ( )MPa28 ( )MPa32≥

10M 11.3 237 204 200 15M 16.0 336 290 275 20M 19.5 410 353 335 25M 25.2 529 456 4.33 30M 29.9 628 541 514 35M 35.7 750 646 614

7>5> segçbkarKNna dl kñúgtMbn;Taj edaysnμt;karsagsg;Fm μta ( ) 5.1/ ≥+ btrb dKc .

1¦ RbsinebIeKeKarBlkçxNÐmYykñúgcMeNamlkçxNÐTaMgBIrxageRkam³ k¦ KMlatBIépÞEdkeTAépÞEdk bd≥ / RsTab;ebtugkarBarEdk bd≥ ehIyKMlatEdkkgminRtUvtUcCagtémø

Gb,brmaEdl[edaykUd. x¦ KMlatBIépÞEdkeTAépÞEdk bd2≥ / RsTab;ebtugkarBarEdk minRtUvtUcCag bd . enaH

sRmab;EdkEdlmanGgát;p©itFMCag b¤esμ I mm22 / ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'53αβλ (7.8)

sRmab;EdkEdlmanGgát;p©ittUcCag b¤esμ I mm19 / ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

b

d

ff

dl

'2512αβλ (7.9)

2¦ sRmab;krNIepSgeTot KuNpleFobxagelInwg 5.1 .



3¦ cMNaMfa MPaf c 69' ≤ ehIy 7.1≤αβ témørbs; ,α β nig λ RtUv)anBnül;BIxagedIm. 4¦ sRmab;EdkkBa©úM eTaHbICakñúgtMbn;TajkþI kñúgtMbn;sgát;kþI eKRtUvbegáIn dl %20 sRmab;kBa©úMEdkbI nig %33

sRmab;kBa©úMEdkbYn. kBa©úMEdkmYyRtUv)aneKBicarNaCaEdkeTalEdlmanGgát;p©it nigRkLaépÞsmmUleTA nwgRkLaépÞsrubrbs;EdkTaMgGs;kñúgmYykBa©úM. eKeRbIGgát;p©itsmmYlenHedIm,IRtYtBinitüKMlat nigRs-

Tab;ebtugkarBarEdk.

]TahrN_ 7>1³ rUb 7>5 bgðajBImuxkat;FñwmebtugGarem:TRmsamBaØEdlman 254DB Edlh‘¿uB½T§edayEdk kg 150@10DB . kMNt;RbEvgbgáb;rbs;EdkRbsinebIFñwmenHplitBIebtugTm¶n;Fm μta ehIyEdkminmanlab epoxy. MPaf c 21' = nig MPaf y 400= .

dMeNaHRsay 1¦ RtYtBinitülkçxNÐKMlat nigRsTab;ebtugkarBarEdk

k¦ mmdb 25= x¦ RsTab;ebtugkarBarEdk bdmm >=−= 5.475.1260 K¦ KMlatrvagsrésEdk bdmm >=−

−= 3525

3120300

X¦ EdkbeNþayRtUv)ancgxÞb;edayEdkkg 10DB . dUcenH FñwmenHeKarBtamlkçxNÐ. enaH

c

y

b

d

ff

dl

'53αβλ

= ¬sRmab;srésEdkEdlmanGgát;p©it mm22> ¦ (7.8)

2¦ témørbs;emKuN³ sRmab;EdkxageRkam 0.1=α / sRmab;Edkminmanlab epoxy 0.1=β nigsRmab; ebtugTm¶n;Rsal 0.1=λ . ehIyBinitüemIlfa MPaMPaf c 3.858.421' <== .



4.52215

4003=

××

=b

d

dl

dUcenH mmld 1310254.52 =×= yk mm1350 . cMNaMfa RbsinebIeKeRbIrUbmnþTUeTAsRmab;KNna bd dl / ¬smIkar 7.7¦ edaysnμt; 0=trK enaH

( )bbc

y

b

d

dcff

dl

/'53αβλ

= (7.8)

enAkñúg]TahrN_enH 0.1=== λβα . ehIy =bc cm¶aytUcCageKBIG½kSrbs;EdkeTAépÞebtugEdlCitbMput ( )1c b¤Bak;kNþalénKMlatBIG½kSeTAG½kS srésEdk ( )2c . mmc 601 = ( ) mmc 30

31203005.0

2 =−

= ¬lub¦ ( ) 5.12.125/30/ <==+ btrb dKc / dUcenH eRbI ( ) 5.1/ =+ btrb dKc . dUcenH cybd ffdl '5/3/ αβλ= dUc CMhanTI 2 nig mmld 1350= . cMNaMfa³ RbsinebIEdkminRtUv)ancgxÞb;edayEdkkg témørbs; dl RtUvKuNnwg 5.1 ¬ =<= bdmms 235

mm50 ¦. ]TahrN_ 7>2³ eFVI]TahrN_ 7>1 eLIgvij RbsinebIFñwmenHplitBIebtugfμbMEbkTm¶n;Rsal srésEdklab fñaM epoxy ehIy sA tRmYvkartamkarviPaKKW 21800mm . dMeNaHRsay³ 1¦ témørbs;emKuN³ 0.1=α ¬EdkeRkam¦/ 5.1=β ¬EdklabfñaM¦/ 3.1=λ ¬ebtugfμTm¶n;¦ nig =sR ¬ sA

tRmUvkar¦ sA/( pþl;[ 92.05.1962/1800) == . témørbs; 5.1=β edaysarRTnab;ebtugkarBarEdktUc Cag mmdb 753 = . RtYtfa 7.15.15.10.1 <=×=αβ .

2¦ c

ys

b

d

ffR

dl

'53 αβλ

= ¬sRmab;srésEdk mm22> ¦ ( )( )( ) 94

2154003.15.192.03

=×

= mmld 2350=

]TahrN_ 7>3³ ssrebtugGarem:man 328DB EdlRtUvbgðÚtcUlkñúgeCIgtag. kMNt;RbEvgbgáb;EdlcaM)ac; sRmab;bgáb;cUlkñúgRKwH. eRbI MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³ RbEvgbgáb;kñúgtMbn;sgát;KW



ybc

ybdc fd

ffd

l 043.0'

24.0≥=

mmldc 45528

4002524.0=

××= ¬lub¦

dcl Gb,brmaKW mm43040025043.0 =×× b:uEnþvaminGactYcCag mm200 eT. edaysarvaminmanemKuN déTeTotdUcenH mmld 455= .

7>6> muxkat;eRKaHfñak;enAkñúgGgát;rgkarBt; muxkat;eRKaHfñak;sRmab;RbEvgbgáb;EdkenAkñúgGgát;rgkarBt;KW • enARtg;cMNuckugRtaMgGtibrma • enARtg;cMNucEdlEdkbeNþayrgkarTajRtUv)anbBaÄb; b¤Bt; • enARtg;épÞrbs;TRm • enARtg;cMNucrbt;Edlm:Um:g;bþÚrsBaØa muxkat;eRKaHfñak;sRmab;KMrUFñwmCab;rgbnÞúkBRgayes μ IRtUv)anbgðajenAkñúgrUbTI 7>6. muxkat; nig

RbEvgbgáb;RtUv)anBnül;dUcxageRkam³ 1¦ muxkat;eRKaHfñak;sRmab;Edkm:Um:g;GviC¢manmancMnYnbI³ muxkat;TI ! KWenARtg;épÞTRm Edlm:Um:g;

GviC¢man k¾dUcCakugRtaMgmantémøGtibrma. eKRtUvRtYtBinitüRbEvgbgáb;cMnYnBIrKW 1x nig 2x . muxkat; @ Camuxkat;EdlcMENkénEdkm:Um:g;GviC¢manxøHRtUv)anbBaÄb;. edIm,IbegáItkmøaMgTaj

eBjelj srésEdkRtUv)anbgðÚtcm¶ay 2x muneBlEdlbBaÄb;va. enAeBlcMENkénsrésEdk RtUv)anbBaÄb; srésEdkEdlenAsl;begáItkugRtaMgGtibrma.

muxkat; # enARtg;cMNucrbt;. eKRtUvbgðÚtsrésEdkenHcm¶ay 3x BImuxkat; #³ 3x RtUvEtFMCag b¤esμ Inwgkm<s;RbsiT§PaB d b¤ bd12 b¤ 16/1 énRbEvgElVgcenøaHépÞssrxagkñúg edayykmYy NaEdlmantémøFMCageK. eyagtam ACI Code, section 12.12.3 y:agehacNas;k¾ 3/1 én brimaNsrésEdksrubEdlpþl;[sRmab; m:Um:g;GviC¢manenARtg;TRmRtUvbgðÚtcm¶ay 3x BIcMNuc rbt;.

2¦ muxkat;eRKaHfñak;sRmab;Edkm:Um:g;viC¢manmancMnYnbI³ muxkat;TI $ Camuxkat;Edlmanm:Um:g;viC¢man k¾dUcCakugRtaMgGtibrma. eKRtUvRtYtBinitüRbEvgbgáb;cMnYnBIrKW 1x nig 2x . RbEvg 1x CaRbEvg bgáb; dl EdlkMNt;eday ACI Code, section 12.11 nigdUckarbgðajBIxagelI. RbEvg 2x FMCag b¤esμ Inwg d b¤ bd12 .



muxkat; % Camuxkat;EdlcMENkénEdkm:Um:g;viC¢manxøHRtUv)anbBaÄb;. edIm,IbegáItkmøaMgTaj eBjelj srésEdkRtUv)anbgðÚtcm¶ay 2x . srésEdkEdlenAsl;nwgbegáItkugRtaMgGtibrma edaysarcMENkénsrésEdkRtUv)anbBaÄb; . eyagtam ACI Code, section 12.11.1 enARtg;épÞ TRm ¬muxkat; !¦ y:agehacNas;k¾ 4/1 énsrésEdkm:Um:g;viC¢manenAkñúgGgát;Cab;RtUvbgðÚtcUl eTAkñúgTRm. sRmab;Ggát;samBaØ y:agehacNas;k¾ 3/1 én brimaNsrésEdksrubEdlpþl;[ sRmab;m:Um:g;viC¢manRtUvbgðÚtcUlTRm.

enARtg;cMNucrbt; ¬muxkat; ^¦ RtUvGnuvtþedayeKarBtam ACI Code, section 12.11.3.

]TahrN_ 7>4³ FñwmCab;mankarlMGitsrésEdkdUcbgðajkñúgrUbTI 7>7. m:Um:g;Bt;GtibrmaviC¢man nigGviC¢mank¾RtUv)anbgðaj. eyIgRtYvRtYtBinitüRbEvgbgáb;enARKb;muxkat;eRKaHfñak;TaMgGs;. eK[³ MPaf c 21' = / MPaf y 276= / =b

mm300 / mmd 460= nigRbEvgElVg mL 2.7= .



dMeNaHRsay³ muxkat;eRKaHfñak;KW (1) enARtg;épÞrbs;TRmsRmab;EdkrgkarTaj nigEdkrgkarsgát; ¬muxkat; !¦ (2) enARtg; cMNucEdlEdkTajRtUv)anbBaÄb;enAkñúgElVg ¬muxkat; @ nig %¦ (3) enARtg;cMNucrbt; ¬muxkat; # nig ^¦ nig (4) enARtg;kNþalElVg ¬muxkat; $¦. 1¦ BIrUbTI 7>7 RbEvgbgáb;sRmab;Edkm:Um:g;GviC¢manKW³ 283DB RtUv)anbBaÄb;enARtg;cm¶ay mx 35.1= BI épÞrbs;TRm b:uEnþEdkbIeTotRtUv)anbgðÚtdl;cm¶ay m8.1 BIépÞTRm.

k¦ kMNt;RbEvgbgáb;sRmab;EdkxagelI



Ggát;p©itEdkm:Um:g;GviC¢man mmdb 28= RsTab;ebtugkarBarEdk bdmm >=−= 46

22860

cm¶ayBIépÞeTAépÞEdk bdmm 262282

120300>=−

−=

dUcenH c

y

b

d

ff

dl

'53αβλ

= ¬sRmab; mmdb 22≥ ¦

eday 3.1=α ¬sRmab;EdkxagelI¦/ 0.1=β / 0.1=λ enaH ( ) mmld 131528

2152763.13

==

x¦ epÞógpÞat;RbEvgbgáb; dlmmx >=13501 (O.K) K¦ RbEvgbgáb; 2x EdlbgðÚtBIcMNucEdlminRtUvkar 283DB ( ) mmddx b 46012;max2 == X¦ epÞógpÞat;RbEvgbgáb; 4x dlmmx >=−= 135045018004 (O.K) g¦ ecjBIcMNucrbt; ¬muxkat; #¦ eKRtUvbgðÚtbrimaNEdky:agtic 3/1 énbrimaNEdksrubcm¶ayy:ag

tic d b¤ bd12 b¤ 16/L BIcMNucrbt;enH. EdkEdlbgðÚthYscMNucrbt;KW 283DB dUcenHRKb;RKan;. epÞógpÞat; mmxx 46023 ==

eyIgman mmmm 46080010001800 >=− (O.K) 2¦ Edkrgkarsgát;enARtg;épÞTRm ¬muxkat; !¦ KWEdkEdlmanmuxkat; mm25 ³ RbEvgbgáb; 5x esμ Inwg mm

ffd

lc

ybdc 361

212762524.0

'24.0

=××

== yk mm370

dcl Gb,brma mmfd yb 29727625043.0043.0 =××== b:uEnþvaminRtUvtUcCag mm200 . dcl Edlpþl;[ mmmm 370380 >= O.K.

3¦ RbEvgEdkbgáb;sRmab;srésEdkm:Um:g;viC¢man³ 253DB RtUv)andak;cm¶ay m8.1 BIkNþalElVg ehIy EdkEdlenAsl;RtUv)anbgðÚtdl;TRm. RbEvgbgáb; 6x BIkNþalElVgKW

( ) mmmmld 18001011215/282763 <=×××= O.K. 7x ( ) mmdd b 46012;max == RKb;RKan;

eKGackMNt;TItaMgCak;EsþgkñúgkarbBaÄb;EdkenAkñúgElVgedayeRbIdüaRkamm:Um:g;ersIusþg; (moment-

resistance diagram) EdlnwgBnül;enAkñúgkfaxNÐ 7>9.



7>7> TMBk;; ¬ACI Code, section 12.5 nig 7.1¦ TMBk;RtUv)aneRbIenAxagcugr)ar enAeBlEdlRbEvgbgáb;Rtg;EdlvaRtUvkarmantémøtUcCagRbEvgbgáb;

caM)ac;. )ann½yfa r)arEdlmanTMBk;xagcug RtUvkarRbEvgbgáb;xøICagr)arRtg;. Ggát;p©itGb,brmarbs;BMnt; Edlvas;BIépÞxagkñúgrbs;TMBk; bD ERbRbYleTAtamGgát;p©itrbs;r)ar³

- sRmab; 2510 DBDB − / bb dD 6= - sRmab; 3628 DBDB − / bb dD 8= - sRmab; 5843 DBDB − / bb dD 10= RbEvgbgáb;sRmab;r)arEdlmanTMBk;RtUv)ankMNt;edayrUbmnþxageRkam³

bc

yhb d

ff

l'

24.0=

CaTUeTA bc

ydh d

ff

l'

24.0 βλ=

Edl β emKuNRTnab;Edk

2.1=β sRmab;Edklab epoxy-coating

1=β sRmab;EdkminmanlabfñaMkarBar λ emKuNTm¶n;ebtug

3.1=λ sRmab;ebtugRsal 1=λ sRmab;ebtugFmμta

RbEvgbgáb;rbs;r)arEdlmanTMBk;RtUv)anKuNCamYyemKuNsRmab;krNIxageRkam³ - r)arEdlmanGgát;p©ittUcCag mm36 EdlmanTMBk;Bt;mMu o90 Bak;edayEdkkgbBaÄr b¤edkEdl

manKMlatminFMCag bd3 RbEvgbgáb;RtUvKuNCamYy 8.0 . - r)arEdlmanGgát;p©ittUcCag mm36 EdlmanRTnab;karBarEdkxagFMCag cm6 RbEvgbgáb;RtUv

KuNCamYy 7.0 . eKeRbIemKuNdUcKñasRmab;TMBk; o90 enAeBlkRmas;ebtugkarBarEdkenAxag TMBk;FMCag mm50 .

- r)arEdlmanGgát;p©ittUcCag mm36 EdlmanTMBk;Bt;mMu o180 Bak;edayEdkkgbBaÄrehIyman KMlatminFMCag bd3 RbEvgbgáb;RtUvKuNCamYy 8.0 .

- enAeBlminRtUvkareRbIEdkTMBk; eKGacKuNRbEvgbgáb;sRmab;EdkelIsedayemKuNpleFob



( )( )[pþl;

tRmUvkars

ss A

AR =

- enAeBleKeRbIEdkTMBk;mankRmas;ebtugkarBarEdkxagelI xageRkam nigxag tUcCag mm60 enARtg;cugminCab;rbs;Ggát; eKRtUvdak;EdkkgedayKMlattUcCag b¤es μ I bd3 . elIsBIenH eKminGaceRbIemKuN 8.0 )aneT.

RbEvgbgáb; dhl sRmab;EdkfñaMgGMeBArgkarTajminRtUvtUcCag bd8max( / )150mm . cMNaMfa TMBk; minmanRbsiT§PaBsRmab;Edkrgkarsgát;eT.

karlMGitBITMBk; o90 nig o180 RtUv)anbgðajenAkñúgrUbTI 7>8. eKRtUvkarTMhMEdlbgðajkñúgrUbedIm,I karBarkarrEhk nigkarpÞat;ebtug. rUbTI 7>9 a bgðajBIkarlMGitBITMBk; enARtg;cugminCab;CamYynwgkRmas; ebtugkarBarEdktUcCag mm60 EdlGackarBarkarpÞat;ebtug. kareRbIEdkkgbiTCitKWcaM)ac;sRmab;karsikSa KNnad¾RtwmRtUv. rUbTI 7>9 b nig c bgðajBIkardak;EdkkgbBaÄr nigEdkkgedk. rUbTI 7>10 bgðajBIkar BRgaykugRtaMgtambeNþayTMBk; o90 eRkamGMeBIkmøaMgTaj P .



]TahrN_ 7>5³ KNnaRbEvgbgáb;EdlRtUvkarsRmab;EdkxagelIEdlmanGgát;p©it mm25 rbs;Fñwmkugs‘ul dUcbgðajenAkñúgrUbTI 7>11 EdlbgðÚtcUleTAkñúgssrRbsinebIsrésEdkenaH k¦ Rtg; x¦ manTMBk; o90 enAxagcug K¦ manTMBk; o180 enAxagcug



EdkRtUv)ancgxÞb;edayEdkkgEdlmanGgát;p©it 150@10DB ehIymankRmas;ebtugkarBarEdk mm40 nigKMlatBIépÞEdkeTAépÞEdk mm50 . eRbI MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ k¦ EdkRtg;³ EdkmanGgát;p©it mmdb 25= . edaysarKMlatBIépÞEdkeTAépÞEdk bd2= nigkRmas;ebtugkar

BarEdkFMCag bd ehIyEdkRtUvxÞb;edayEdkkg dUcenHvaeKarBlkçxNÐ k¦ nig x¦. eKGaceRbIsmIkar 7.10 edIm,IKNna dl . mmld 1134= sRmab;EdkxagelI 3.1=α dUcenH mmld 1474= .

x¦ EdkEdlmanTMBk; o90 ³ sRmab;EdkEdlmanGgát;p©it mmdb 25= RbEvgbgáb; cybhb ffdl '/24.0= mm454= . edaysarminmankarEktRmUv enaH mmdmml bdh 2008454 =>=

karlMGitRtUv)anbgðajenAkñúgrUbTI 7>11. eKmineRbIemKuN 3.1=α sRmab;Ggát;EdlmanTMBk;eT. c¦ EdkEdlmanTMBk; o180 ³ RbEvgbgáb; hbl mm454= dUckarKNnaxagelI. edaysarminmankarEktRmUv

enaH mmdmml bdh 2008454 =>= karlMGitRtUv)anbgðajenAkñúgrUbTI 7>11.

7>8> kartEdk enAeBlEdlEdkmanRbEvgxøI eKcaM)ac;RtUvtvaedaydak;bRBa¢ÜsKñanUvRbEvgmYysmRsbedIm,IbBa¢Únkug

RtaMgénPaBs¥itBIr)armYyeTAr)armYy. kartEdkGaceFVIeLIgedaykartbRBa¢Üsmux nigkarpSa. kartEdk edaykarbRBa¢ÜsminGaceFVIeTA)aneT sRmab;r)arEdlmanGgát;p©itFMCag mm36 . sRmab;tMNpSaRtUveFVIeLIg eday[TwkbnSamanersIusþg;esIμ %125 énersIusþg;rbs;Edk.



kartEdkminRtUv)anGnuBaØt[eFVIenARtg;muxkat;Edlmanm:Um:g;GtibrmaeT. elIsBIenH eKk¾RtUveCos

vagkartEdkRtg;TItaMgEtmYykEnøg edIm,IeCosvagkarFøak;exSayrbs;muxkat;ebtug kareTIsETgEdk nigkar Bi)akcak;ebtug.

k> kartEdkenAtMbn;rgkarTaj stl RbEvgtEdk dst ll = RtUv)aneRbIenAeBlEdlmuxkat;EdkticCagBak;kNþalRtUv)ant nigmuxkat;Edk

eRbIR)as;esμ I2dgmuxkat;RtUvkarTaMgGs;elIRbEvgEdlt. RbEvgtEdk dst ll 3.1= RtUv)aneRbIenAeBlNa EdlkartEdkeFVIeLIgenATItaMgEtmYy EtCasMNUmBr eKminRtUvtEdkenAkEnøgdUcKñaeLIy. sRmab;RKb;krNI RbEvgtEdkminRtUvmantémøtUcCag cm30 .

x> kartEdkenAtMbn;rgkarsgát; scl RbEvgtEdkenAtMbn;sgát; scl RtUvmantémøFMCag b¤es μ IRbEvgbgáb;enAtMbn;rgkarsgát;.

bysc dfl 0724.0= sRmab; MPaf y 400≤ bysc dfl )2413.0( −= sRmab; MPaf y 400>

sRmab;RKb;krNI RbEvgtEdkminRtUvmantémøtUcCag cm30 . RbsinebIebtugEdlykmkeRbIman ersIusþg;tUcCag MPa20 enaHRbEvgtEdkRtUvKuNnwg 3.1 . sRmab;ssrEdlmanEdkkgragCarWus½r enaH RbEvgtEdkRtUvKuNnwg 75.0 EtsRmab;EdkkgFmμtaRtUvKuNnwg 83.0 b:uEnþminRtUvtUcCag cm30 .

]TahrN_ 7>6³ KNnaRbEvgbRBa©ÜssRmab; 256DB EdkrgkarTajxageRkam ¬CaBIrCYr¦ KMlatBIépÞEdkeTA épÞEdk mm60 nigkRmas;karBarebtug mm40 sRmab;krNIxageRkam³ k¦ enAeBleKtbRBa©ÜsEdkbIedIm nig sA( pþl;[ sA/() tRmYvkar 2) > x¦ enAeBleKtbRBa©ÜsEdkbYnedIm nig sA( pþl;[ sA/() tRmUvkar 2) <



K¦ enAeBleKtbRBa©ÜsRKb;srésEdkTaMgGs;Rtg;TItaMgEtmYy. eK[ MPaf c 35' = nig MPaf y 400= . dMeNaHRsay³ k¦ sRmab; 25=bd ehIy 0.1==== λγβα ¬smIkar 7.8¦/ MPaMPa 3.89.535 <= bd dl 6.40= BIeRBaHvaeKarBlkçxNÐ k¦ nig x¦. mmld 1015256.40 =×= . sRmab; sA( pþl;[ /)

sA( tRmYvkar 2) > / mmmmll dst 30010150.1 >== ¬Gb,brma¦. EdkEdlRtUvbRBa©ÜstUcCagEdksrub Bak;kNþal.

x¦ mmld 1015= dUckarKNnaxagelI. edaysar sA( pþl;[ sA/() tRmUvkar 2) < / mmll dst 13203.1 == EdlFMCag mm300 .

K¦ mmmmlst 3001320 >= . ]TahrN_ 7>7³ KNnaRbEvgbRBa©ÜssRmab; 32DB Edkrgkarsgát;enAkñúgssrEdleRbIEdkkgFm μta enA eBl MPaf c 35' = nigenAeBl k¦ MPaf y 400= x¦ MPaf y 550= . dMeNaHRsay³ k¦ sRmab; 32=DB / mmldb 52032

3540024.0 =××= . RtYtBinitü ( )( ) mmlsc 927400320724.0 =≥ .

dUcenH mmlsc 930= . x¦ mmldb 520= dUckarKNnaxagelI. RtYtBinitü ( ) mmlsc 1520322455013.0 =−×≥ .

dUcenH mmlsc 1550= .

7>9> karbBaÄb;Edk ersIusþg;m:Um:g;enAkñúgFñwmCaGnuKmn_eTAnwgkm<s;RbsiT§iPaB d / TTwgFñwm b / nigmuxkat;Edk sA sRmab;

karEdleKsÁal;ersIusþg;Edk yf nigersIusþg;ebtug cf ' . sRmab;FñwmEdlmanTTwg nigkm<s;efr enaHmuxkat; EdkERbRbYleTAtamm:Um:g;Bt;EdlmanGMeBItambeNþayFñwm. dUcenHeKcaM)ac;RtUvbBaÄb;Edk enAkEnøgNaEdl eKminRtUvkarvaedIm,ITb;Tl;nwgkugRtaMgBt;. sRmab;krNIxøH dUcCaFñwmCab; EdksRmab;m:Um:g;viC¢man RtUv)aneK Bt;eLIgelIedaymMu o45 edIm,Ipþl;CaEdkrgkmøaMgTajsRmab;m:Um:g;GviC¢manenAelITRm.

ersIusþg;m:Um:g;rbs;FñwmrgkarTajenARKb;muxkat;TaMgGs;RtUv)ankMNt;eday )

2( adfAM ysu −= φ



édXñas; )2

( ad − ERbRbYlBImuxkat;mYyeTAmuxkat;mYytambeNþayFñwm dUckarERbRbYlbrimaNsrés EdkEdr eTaHCay:agenHk¾eday eyIgeXIjfabERmbRmYlédXñas;mantUcbMput ehIyminmantémøxusKñaeRcInBI muxkat;m:Um:g;GtibrmaeT. dUcenH eKGacsnμt;faersIusþg;m:Um:g;sRmab;muxkat;smamaRtnwgkmøaMgTaj b¤mux kat;srésEdk edayKitTaMgRbEvgTMBk;.

edIm,IkMNt;TItaMgénkarbBaÄb;Edk eKRtUvKUrdüaRkamm:Um:g;EdlekItBIkmøaMgxageRkAmuneK. düaRkam ersIusþg;m:Um:g;RtUv)anKUrenAelIRkaPicEtmYy edIm,IbgðajTItaMgsrésEdkxøHEdlminRtUvkarRbEvgEvgCag tRmUvkar. ersIusþg;m:Um:g;cugeRkaysRmab;srésEdkmYysrésKW³

)2

( adfAM ysbub −= φ

Edl bf

fAa

c

ys

'85.0=

sbA - muxkat;EdkmYysrés cMNucRbsBVrvagbnÞat;ersIusþg;m:Um:g; CamYydüaRkamm:Um:g;xageRkA bgðajBITItaMgEdleyIgGacbBaÄb;

Edk)an. b:uEnþeKcaM)ac;RtUvbEnßmRbEvgEdkedIm,IPaBs¥itCamYyebtug. ACI Code )ankMNt;faRKb;Edk EdlbBaÄb;RtUvbEnßmRbEvges μ Inwgkm<s;RbsiT§PaBrbs;Fñwm b¤ bd12 ¬edayyktémømYyNaEdlFMCageK¦ elIsBIenH ACI Code )ankMNt;fay:agticNas; 3/1 énsrésEdksRmab;m:Um:g;viC¢manRtUvbgðÚseTAkñúg TRmsRmab;FñwmTRmsamBaØ.



edIm,IgayRsYlkñúgkarbgðajBIkarbBaÄb;Edk rUb 7>13 bgðajFñwmTRmsamBaØrgbnÞúkBRgayesμ I mux kat;rbs;va nigdüaRkamm:Um:g;. ExSekagm:Um:g;Bt;manrag)a:ra:bYlEdlmanm:Um:g;GtibrmaenAkNþalElVg

mkN.272 . edaysarFñwmBRgwgeday 254DB enaHersIusþg;m:Um:g;rbs;srésEdkmYyedImKW ⎟

⎠⎞

⎜⎝⎛ −=

2adfAM ysbub φ

mmbf

fAa

c

ys 3.1283002185.0

3501963'85.0

=××

×==

mkNMub .6.73102

3.1285403504919.0 6 =⋅⎟⎠⎞

⎜⎝⎛ −××= −



dYcenH ersIusþg;m:Um:g;rbs;EdkbYnsrésKW mkN.4.294 EdlFMCagm:Um:g;xageRkA mkN.272 . Rbsin ebIRbsinebIeyIgKUrdüaRkamm:Um:g;[RtUvmaRtdæanenAelIExSeKal AA− eyIgeXIjfaeKGacbBaÄb;srésEdk TImYyenARtg;cMNuc a srésEdkTIBIrenARtg;cMNucb nigsrésEdkTIbIenARtg;cMNuc c ehIysrésEdkTIbYn enARtg;TRmcug A . cMNucTaMgenHCaTItaMgsRmab;bBaÄb;EdktamRTwsþI. b:uEnþ eKcaM)ac;begáItEpñkénersIusþg;xøH rbs;srésEdkedayPaBs¥it dUckarBnül;BIxagelI. ACI Code kMNt;[EdkEdlbBaÄb;TaMgGs;bnþeday RbEvgEdlesμ Inwgkm<s;RbsiT§PaB d rbs;Fñwm b¤ bd12 edayyktémømYyNaEdlFMCageK BIcMNucbBaÄb;tam RTwsþI ,a ,b nig c . Code, section 12.11.1 k¾kMNt;Edrfa y:agehacNas; 3/1 énEdkm:Um:g;viC¢manRtUv)an bnþcUleTAkñúgTRmsRmab;FñwmsamBaØ. dUcenH sRmab;]TahrN_Edlerobrab;enATIenH eKRtUvbgðÚtEdkBIrsrés eTAkñúgTRm ehIydüaRkamersIusþg;m:Um:g;Edl)anbgðajenAkñúgrUbTI 7>13 RtUvekþabdüaRkamm:Um:g;xageRkARKb; cMNucTaMgGs;. srésEdknImYy²TTYl)anlT§PaBTb;Tl;nwgbnÞúkeBjeljenARtg;cm¶ay dl BIcugrbs;va. sRmab;FñwmCab; eKRtUvBt;srésEdkenARtg;cMNucEdlRtUvkar nigeRbIvaedIm,ITb;Tl;nwgm:Um:g;GviC¢man enARtg;tMN. y:agehacNas;k¾eKRtUvbnþEdk 3/1 énEdkm:Um:g;GviC¢manTaMgGs;Edlpþl;[sRmab;m:Um:g;GviC¢-manBIcMNucrbt;cm¶ayEdlesμ Inwgkm<s;RbsiT§PaB ,d b¤ bd12 b¤ 16/L edayyktémømYyNaEdlFMCageK. eKk¾eRbI bent bar edIm,ITb;Tl;nwgEpñkxøHrbs;kugRtaMgkmøaMgkat;enAkñúgFñwmpgEdr. düaRkamersIusþg; m:Um:g;sRmab;FñwmCab;KMrURtUv)anbgðajenAkñúgrUbTI 7>14. ]TahrN_ 7>8³ sRmab;FñwmTRmsamBaØEdlbgðajenAkñúgrUbTI 7>15 cUrsikSaKNnaFñwmEdlrgbnÞúkKNna xageRkA nigsg;düaRkamersIusþg;m:Um:g;. dUcKña bgðajBITItaMgEdlGacbBaÄb;Edk. eRbI mmb 250= / pl eFobEdkKW 018.0 / MPaf c 21' = / MPaf y 280= . dMeNaHRsay³ sRmab; 018.0=ρ / MPaRu 90.3= ehIy 2bdRM uu = eday mkNMu .8.176= enaH mmd 426= yk mmh 500= 21980440250018.0 mmAs =××= eRbI 254DB km<s;RbsiT§PaBCak;Esþg mmd 60440500 =−= mma 2.123

2502185.02805.1963

=×××

=



ersIusþg;m:Um:g;sRmab;EdkmYyedIm MPaadfAM ysur 8.4610

22.1234402804919.0

26 =⋅⎟

⎠⎞

⎜⎝⎛ −××=⎟

⎠⎞

⎜⎝⎛ −= −φ

ersIusþg;m:Um:g;sRmab;EdkbYnedIm mkNMur .2.187=



düaRkamersIusþg;m:Um:g;RtUv)anbgðajenAkñúgrUbTI 7>15. cMNaMfa eKGacBt;srésEdk b¤bBaÄb;srésEdkenA cm¶ay mm440 ¬b¤ bd12 edayykmYyNaEdlFMCageK¦ bnÞab;BIcMNucEdleKminRtUvkarsrésEdk ¬tam RTwsþI¦. RbEvgbgáb; dl sRmab; mmdb 25= KW mmdb 9207.36 = . cMNucbBaÄb;EdkTImYy nigTIBIrenARtg; cMNuc A nig B b:uEnþcMNucCak;EsþgKWenARtg;cMNuc 'A nig 'B cm¶ay mm450 BIcMNuc A nig B . BI 'A RbEvg dl

mm920= fyeRkayRtUv)aneFVIedIm,IbegáItdüaRkamersIusþg;m:Um:g;. cugrbs;EdkEdlenAsl;BIreTotRtUvbgðÚt cYleTAkñúgTRm Rtg;cMNuc 'C . CaTUeTA eKmineRbIEdkEdlbBaÄb;enAkñúgElVgRtg;cMNuc 'A nig 'B Ca bent bar edIm,ITb;Tl;kmøaMgkat;eT.


T.Chhay 180 Shear and Diagonal Tension

VIII. kmøaMgkat;TTwg nigkmøaMgTajGgát;RTUg Shear and Diagonal Tension

8>1> esckþIepþIm enAeBlEdlFñwmTRmsamBaØrgnUvbnÞúk m:Um:g;Bt; nigkmøaMgkat;TTwgnwgekIteLIgelIRbEvgFñwm. edIm,IRT

nUvbnÞúkenHedaysuvtßiPaB FñwmRtUv)aneFVIkarKNnaeLIgedIm,ITb;nwgkmøaMgTaMgBIrRbePTenH. karKNnasRmab; karBt;RtUv)aneFVIeLIgdMbUgeK edIm,IkMNt;muxkat;Fñwm nigEdkemcaM)ac; dUcEdl)anENnaMBIemeronmun.

bnÞab;mkFñwmRtUv)anKNnaedIm,ITb;nwgkmøaMgkat;TTwg. kñúgkrNIEdlEdkkgminRtUv)andak; enaHFñwm nwg)ak;edaykmøaMgkat;TTwg. kar)ak;edaykmøaMgkat;TTwg ekIteLIgedaymanPaBdabtUc nig)at;bg;nUv lkçN³yWt ehIymin)anRbkasGasnñenAmuneBl)ak;eT. sRmab;kar)ak;edaykarBt;begáag ekIteLIgeday karekIneLIgnUvPaBdabbnþicmþg² nigmansñameRbH dUcenHvamankarpþl;sBaØaRbkasGasnñmuneBl)ak;cug eRkay. karKNnasRmab;kmøaMgkat;TTwg RtUv)aneFVIeLIgedIm,IFananUvkar)ak;edaykmøaMgkat;TTwgekIteLIg eRkaykar)ak;edaykarBt;begáag.

8>2> kugRtaMgkmøaMgkat;enAkñúgFñwmebtugGarem:

rUbmnþTUeTAsRmab;kugRtaMgkmøaMgkat;TTwgenAFñwmrUbFatusac;mYy (homogenous beam) karBRgay kugRtaMg


kmøaMgkat; nigkmøaMgTajGgát;RTUg 181 T.Chhay

IbVQ

=ν ¬*>!¦ Edl V - kmøaMgkat;srubenAmuxkat;EdlRtUvsikSa Q - m:Um:g;sþaTiceFobG½kSNWténmuxkat;EdlxNÐedaybnÞat;EdlRtUvsikSakugRtaMgkmøaMgkat;

I - m:Um:g;niclPaBénmuxkat;eFobG½kSNWt b - TTwgFñwménmuxkat;EdlRtUvsikSakugRtaMgkmøaMgkat;

karBRgaykugRtaMgm:Um:g;Bt; nigkmøaMgkat;TTwgGaRs½yeTAnwgRTwsþIbTeGLasÞicsRmab;muxkat;Fñwm ctuekaN dUcbgðajkñúgrUbTI8>2.

kugRtaMgm:Um:g;Bt;

IMcf =

Edl kugRtaMgkmøaMgkat;enARKb;cMNucTaMgGs;RtUv)anKNnatamrUbmnþkugRtaMgkmøaMgkat;

IbVQ

=ν kugRtaMgkmøaMgkat;GtibrmasßitenAelIGkSNWt nigmantémøes μ I av5.1 ¬kmøaMgkat;TTwgmFüm¦ Edl

bhV

a =ν . ExSekagkmøaMgkat;TTwgmanrag):ar:abUl.

sRmab;FñwmebtugsésEdkrgkarTaj (singly reinforced concrete beam) karBRgaykugRtaMg kmøaMg kat;TTwgenAelIGk½SNWtmanrag):ar:abUl. enAeRkamGk½SNWt kugRtaMgkmøaMgkat;TTwgGtibrmamantémøefr ehIy)anrkSatémøenHRtwmnIv:UEdkrgkarTaj BIeRBaHvaK μankarpøas;bþÚrkmøaMgTajBIcMNucGk½SNWtehIymü:ag eTotkmøaMgTajkñúgebtugRtUv)anecal. kugRtaMgkmøaMgkat;TTwgmantémøesμ IsUnü enAeRkamnIv:UEdk ¬rUbTI8> 3¦.



sRmab;ebtugsrésEdkEdlmanEdkrgkarsgát; nigmuxkat;GkSret karBRgaykugRtaMgkmøaMgkat; TTwgRtUv)anbgðajkúñgrUbTI8>3. eyIgsegÁteXIjfa kmøaMgkat;TTwgesÞIrEtTaMgGs; RtUv)anTb;edayRTnug EdlsøabTb;nwgPaKrytUcbMput. sRmab;karGnuvtþesÞIrTaMgGs; eKecalnUvlT§PaBTb;kmøaMgkat;TTwgrbs; søab.

eyagtamrUbTI8>1 edayykFñwmmYykMNat;tUc dx mkviPaK eyIgeXIjfa m:Um:g;Bt;enAcugsgxagén

kMNat; 1M nig 2M minmantémøesμ IKñaeT. edaysar 21 MM < dUcenHedIm,IrkSalMnwgsRmab;kMNat; dx kmøaMg sgát; 2C RtUvmantémøFMCag 1C ¬rUbTI8>4¦. dUcenHkugRtaMgkmøaMgkat;TTwg v ekItmanenAelImux kat;edk

1aa − b¤ 1bb − ¬rUbTI8>4 a¦. kugRtaMgkmøaMgEkg (normal stresses) nigkugRtaMgkmøaMgkat;TTwg (shear

stresses) enAelIGgát;tUcenAkRmitnIv:U 1aa − b¤ 1bb − RtUv)anbgðajenAkñúg¬rUbTI8>4 b¦. cMNaMfa kugRtaMg kmøaMgEkg (normal stresses) enAnIv:UénG½kSNWtKW 0 b:uEnþkmøaMgkat;TTwgmantémøGtibrma. kmøaMgkat;TTwg edkesμ InwgkmøaMgkat;TTwgbBaÄr dUcbgðajenAkñúg ¬rUbTI8>4 b¦. enAeBlEdl kugRtaMgkmøaMgEkgmantémø es μ IsUnü b¤tUc enaHkrNIkmøaMgkat;TTwgsuT§GacekItman. kñúgkrNIenH kugRtaMgTajGtibrma tf manGMeBI tammMu o45 ¬rUbTI8>4 c¦.



kugRtaMgTajsmmUleTAnwgkugRtaMgem dUcbgðajkñúgrUbTI 8>4 d. kugRtaMgemenHRtUv)aneKehAfa kug RtaMgTajGgát;RTUg. enAeBlkugRtaMgTajGgát;RTUgmantémøes μ IersIusþg;Tajrbs;ebtug sñameRbHGgát;RTUg ekIteLIg. karviPaKy:agsegçbenHBnül;BIKMniténkmøaMgTajGgát;RTUg nigsñameRbHGgát;RTUg. kareFVIkarCak; EsþgmanlkçN³sμ úKsμajCag ehIyvaTTYl\T§iBlBIktþaepSg². sRmab;bnSMénGMeBIénkmøaMgkat;TTwg nig kmøaMgEkgenAcMNucNamYyenAkñúgFñwm kmøaMgTajGgát;RTUg (principal stresses) Gtibrma nigGb,brma pf RtUv)an[edaysmIkarxageRkam³

22

22vfff p +⎟

⎠⎞

⎜⎝⎛±= ¬*>@¦

Edl =f GaMgtg;sIueténkugRtaMgEkgEdlbNþalmkBIkarBt; =v kugRtaMgkmøaMgkat; kar)ak;edaykmøaMgkat;TTwgenAkñúgFñwmebtugPaKeRcInTMngCaekIteLIgenAkEnøgEdlkmøaMg

kat;TTwgGtibrma CaTUeTAenAEk,rTRménGgát;. PsþútagTImYyénkar)ak;EdlKYr[P½yxøayKWkarekIteLIgnUv sñameRbHGgát;RTUg.

8>3> kareFVIkarrbs;FñwmedayK μanEdkkmøaMgkat;TTwg ebtugexSaykñúgkarTaj ehIyFñwmGac)ak;RbsinebImuxkat;EdkminRtwmRtUvRtUv)anpþl;[. kugRtaMg

TajekItmanenAkñúgFñwmbNþalmkBIkmøaMgTajtamG½kS kmøaMgBt; kmøaMgkat;TTwg kmøaMgrmYl b¤bnSMénbnÞúk TaMgenH. TItaMgénsñameRbHenAkñúgFñwmebtugGaRs½ynwgTisedAénkugRtaMgem (principal stresses). bnSMénkug RtaMgkmøaMgEkg normal stress nigkugRtaMgkmøaMgkat;TTwg begáIt)ankmøaMgTajtamGgát;RTUg (diagonal

tension) GtibrmaEdlsßitenARbEhlcm¶ay d BImuxénTRm. kareFVIkarrbs;FñwmebtugGarem:edaymanb¤KμanEdkkmøaMgkat;TTwg RtUv)anBiesaFeRkamGMeBIénkarekIn

eLIgénbnÞúkdUc)anerobrab;enAkñúgemeronTI3. enAkñúgkarBiesaFFñwm sñameRbHbBaÄrEdlekItBIkarBt;ekIteLIg enAelImuxkat;Edlmanm:Um:g;Bt;Gtibrma enAeBlEdlkugRtaMgTajenAkñúgebtugelIsBIm:UDuldac; (module of

rupture) rbs;ebtug b¤ cr ff '623.0= . sñameRbHeRTtenAkñúgRTnugekItmanenAkñúgdMNak;kalbnÞab;enATI taMgEk,rTRm.



sñameRbHeRTtEdlekItmanenAkñúgFñwmEdlminTan;)aneRbHBIdMbUg CaTUeTARtUv)aneK[eQ μaHfa sñam

eRbHkmøaMgkat;RTnug (web-shear crack). RbsinebIsñameRbHeRTtcab;epþImenABIelIsñameRbHEdlekItBIkar Bt;EdlmanRsab; ehIyrIksayenAkñúgFñwm enaHsñameRbHRtUv)aneK[eQ μaHfa sñameRbHkmøaMgkat;rgkarBt; (flexural-shear crack) rUbTI8>5. sñameRbH web-shear crack ekItmanenAkñúgFñwmEdlmankmøaMgkat;FM nig



m:Um:g;Bt;tUcenAkñúgRTnugesþIg. vaCasñameRbHminFmμtaehIyGacekItmanenAEk,rcMNucrbt;énFñwmCab; b¤Ek,r TRménFñwmsamBaØ.

sñameRbH flexural-shear crack CaRbePTsñameRbHFm μtaEdleKGaceXIjmanenAelIFñwm. dMbUgsñam eRbH flexural crack ekItmanbBaÄrenAelIFñwm bnÞab;mksñameRbHeRTtcab;epþImekItmanBIelIkMBUlénsñameRbH flexural crack enAeBlEdlkugRtaMgkmøaMgkat;TTwgekItmanenAkñgtMbn;enaH. enAkñugtMbn;EdlmankugRtaMg kmøaMgkat;TTwgFM FñwmRtUvEtBRgwgedayEdkkg stirrup b¤EdkBt; (bent bar) edIm,IeFVI[FñwmmanlkçN³sVit (ductile) Edlmin)ak;b¤ dac;. edIm,IeCosvagkar)ak;edaykmøaMgkat; munkar)ak;edaykarBt; emKuNsuvtßiPaB FMRtUv)anpþl;[edIm,ITb;nwgkar)ak;edaykmøaMgkat;TTwg. ACI Code kMNt;emKuNkat;bnßyersIusþg;

75.0=φ sRmab;kmøaMgkat;TTwg. ersIusþg;kmøaMgkat;TTwgenAkñúgGgát;ebtugGarem:RtUv)anekIteLIgedaybnSMénkmøaMgemkanicxageRkam

¬rUbTI8>5¦³ - ersIusþg;kmøaMgkat;TTwgénebtugminTan;eRbH zV - karepÞrkmøaMgkat;TTwgrvagGnþrépÞ (interface shear transfer) aV EdlbNþalmkBIkarbgçaMKñarvag

fμbMEbktambeNþayépÞd¾KRKatrbs;sñameRbH - GMeBIrbs;FñÚr (arch action) - GMeBIEdkf<k; (dowel action) dV EdlbNþalmkBIersIusþg;énr)arEdkbeNþayeTAkmøaMgkat;TTwg

tamTTwg (transverse shearing force) bEnßmeTAelIkmøaMgTaMgenH EdkkmøaMgkat;TTwg (shear reinforcement) begáInersIusþg;kmøaMgkat;TTwg

sV edayGaRs½yeTAelIGgát;p©it nigKMlatEdkkgEdleRbIenAkñúgGgát;ebtug. RbsinebIEdkkmøaMgkat;TTwg minRtUv)andak;enAkñúgFñwmragctuekaN enaHsmamaRténkmøaMgkat;TTwgEdlTb;edaykmøaMgemkanicepSg²KW³ BI %20 eTA %40 eday zV / BI %35 eTA %50 eday aV / BI %15 eTA %25 eday dV .

8>4> \T§iBlm:Um:g;eTAelIersIusþg;kmøaMgkat; sRmab;FñwmTRmsamBaØeRkamGMeBIbnÞúkBRgayesμ I muxkat;kNþalElVgrgnUvm:Um:g;Bt;FM nigkmøaMgkat;

TTwgtUc b¤esμ IsUnü EdlpÞúyBImuxkat;enAEk,rTRmEdlm:Um:g;Bt;mantémøtUc ÉkmøaMgkat;TTwgmantémøFM ¬rUbTI 8>1¦. kmøaMgkat;TTwg nigm:Um:g;mantémøFMenAEk,rTRmkNþalsRmab;FñwmCab;. enATItaMgEdlkmøaMgkat;TTwg FM nigm:Um:g;Bt;tUc enaHvanwgmankareRbHedaykarBt;tictYc ehIykugRtaMgmFüm bdVv /= . kugRtaMgkmøaMg TajtamGgát;RTUgCakugRtaMgEdleRTtedaymMuRbEhl o45 ¬rUbTI8>4 c ¦. sñameRbHGgát;RTUgGacrMBwgfanwg ekItman enAeBlEdlkugRtaMgkM;laMgTajGgát;RTUgEdlsßitenAEk,rtMbn;G½kSNWtxiteTACit b¤elIsersIusþg;



kmøaMgTajrbs;ebtug. CaTUeTA ersIusþg;kmøaMgkat;TTwgcugeRkay (ultimate shear strength) ERbRbYlcenøaHBI cf '29.0 nig cf '42.0 . eRkayBIkarBiesaFn_eTAelIFñwmCaeRcInGMBIkmøaMgkat;TTwg nigkmøaMgTajtam

Ggát;RTUg eK)anrkeXIjfaenAkñúgtMbn;EdlmankmøaMgkat;TTwgFM nigm:Um:g;Bt;tUc enaHsñameRbHkmøaMgTaj Ggát;RTUgRtUv)anbegáIteLIgenAeBlkmøaMgkat;TTwgmFüm

dbfV wccr '29.0= ¬*>#¦ Edl wb CaTTwgRTnugmuxkat;GkSret b¤TTwgmuxkat;ctuekaN d Cakm<s;RbsiT§PaBrbs;Fñwm enATItaMgEdlkmøaMgkat;TTwg nigm:Um:g;Bt;mantémøFM enaHsñameRbHedaykarBt; (flexural crack)

RtUv)anekIteLIgdMbUg. enAdMNak;kalTImYy sñameRbHxøHBt;kñúgTisedAGgát;RTUgenAeBlEdlkugRtaMgkmøaMg TajGgát;RTUg EdlsßitenABIcugxagelIénsñameRbHTaMgenaHFMCagkugRtaMgkmøaMgTajrbs;ebtug. RbsinebIeK [m:Um:g;FMmanGMeBIelIFñwm sRmab;muxkat;EdlmanbrimaNEdkRKb;RKan; enaHkmøaMg nominal shear force enA eBlEdlsñameRbHekItmanRtUv)an[dUcxageRkam

dbfV wccr '16.0= ¬*>$¦



témøenHKWtUcCagtémøEdl[edaysmIkar ¬*>#¦ eRcInCagBak;kNþalenAeBlEdlm:Um:g;Bt;mantémø tUc. enHmann½yfam:Um:g;Bt;FMkat;bnßytémørbs;kugRtaMgkmøaMgkat;TTwgenAeBlEdlsñameRbHekIteLIg. smIkarxageRkamRtUv)anesñIeLIgedIm,ITsSn_TaynUvkugRtaMg nominal shear stress enAeBlEdlsñamGgát; RTUgRtUv)anrMBwgfaekItman³

cu

uwc

wcr f

MdVf

dbVv '29.02.17'16.0 ≤⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+== ρ ¬*>%¦

ACI Code, Section 11.3.2 )anyksmIkarenHsRmab;KNnakmøaMg nominal ultimate shear force EdlTb;edayebtug

dbfdbM

dVfV wcw

u

uwcc '29.0)2.17'16.0( ≤+= ρ ¬*>^¦

Edl dbA wsw /=ρ / d Cakm<s;RbsiT§PaBrbs;muxkat;Fñwm/ wb CaTTwgRTnugsRmab;muxkat;GkSr et b¤TTwgénmuxkat;ctuekaN É uV nig uM CakmøaMgkat;TTwgcugeRkay (ultimate shearing force) nigm:Um:g; Bt;cugeRkay (ultimate bending moment) EdlekIteLIgkñúgeBldMNalKñaenAelImuxkat;sikSa.

témøén uu MdV / minRtUvFMCag 0.1 sRmab;smIkar ¬*>^¦. RbsinebI uM mantémøFMenAkñúgsmIkar ¬*>^¦ enaHtYTIBIrnwgmantémøtUcesÞIEtesμ IsUnü enaH cv xiteTArk cf '16.0 . RbsinebI uM mantémøtUc enaH tYTIBIrnwgmantémøFM ehIytémø cf '29.0 lub. eRkABIsmIkar ¬*>^¦ ACI Code, Section 11.3.1GnuBaØat[ KNnaersIusþg;kmøaMgkat;rbs;ebtugdUcxageRkam³

dbfV wcc )'17.0(= ¬*>&¦ 1> kñúgkrNIsRmab;kmøaMgsgát;tamG½kS uN

dbfdbM

dVfV wcwm

uwcc '29.0)2.17'16.0( ≤+= ρ ¬*>*¦

⎟⎠⎞

⎜⎝⎛ −

−=8

4 dhNMM uum

Edl db

A

w

sw =ρ

=h km<s;srubrbs;Fñwm uu MdV / GacFMCag 0.1 b:uEnþ cV minRtUvFMCag

g

ucwc A

NfdbV45.3

1)'29.0( += ¬*>(¦

Edl gA CaRkLaépÞTaMgGs; (gross section) KitCa 2mm mü:agvijeTot cV GacRtUv)anKNnaeday



cg

uwc f

AN

dbV ')145.02( += ¬*>!0¦

2> kñúgkrNIsRmab;kmøaMgTajtamG½kS uN

cg

uwc f

ANdbV ')58.02( += ¬*>!!¦

Edl uN mantémøGviC¢mansRmab;kmøaMgTaj RbsinebI cV GviC¢man enaH cV RtUv)anykesμ IsUnü.

8>5> FñwmmanEdkkmøaMgkat; EdkEdleRbIedIm,ITb;nwgkmøaMgkat; EdleKeRbIGacmaneRcInRbePTepSg²

a. Edkkg EdleKeRbIedaydak;EkgeTAnwgEdkbeNþay ¬Edkem¦ b¤RtUv)aneKdak;eRTt mMuEdl eKniymeRbI o45 . EdkkgEdleKniymeRbImanmuxkat; 10DB nig 12DB .

b. EdkBt; EdlCaEpñkmYyrbs;EdkbeNþayEdleKBt;eLIg ¬enAkEnøgEdleKbBaÄb;¦ edaymMu o30 nig o60 CaTUeTA o45 .

c. bnSMrvagEdkkg nigEdkBt; d. sMNaj;Edk CamYynwgsMNaj;EkgeTAnwgG½kS e. EdkkgvNÐ EdleKeRbIsRmab;ssr ersIusþg;kmøaMgkat;TTwgrbs;FñwmebtugGarem:RtUv)anbegáIneLIgedaykareRbInUvEdkkmøaMgkat;TTwg.

munnwgekItnUvsñameRbHGgát;RTUg EdkkmøaMgkat;TTwgCYyersIusþg;kmøaMgkat;TTwgtictYcbMput. eRkayeBlEdl sñameRbHkmøaMgkat;TTwgekIteLIg EdkkmøaMgkat;TTwgbegáInersIusþg;kmøaMgkat;rbs;Fñwm ehIykmøaMgkúñgmþg eTotEdlekIteLIgenAmuxkat;eRbH. enAeBlbrimaNEdkkmøaMgkat;TTwgtUc kar)ak;EdlekIteLIgedaysar EdkenARTnugeFVIkardl; yield GacnwgekIteLIg b:uEnþRbsinebIbrimaNEdkkmøaMgkat;TTwgFM enaHkar)ak;eday shear-compression failure GacnwgekIteLIg TaMgenHCaGVIEdleyIgKYreCosvag.

ebtug Edkkg (stirrups) nigEdkdgErk (bent bars) eFVIGMeBIrYmKñaedIm,ITb;nwgkmøaMgkat;TTwg. edaysarersIusþg;rgkarsgát;x<s; ebtugedIrtYCaGgát;rgkarsgát;Ggát;RTUgénRbB½n§Fñwm cMENkÉEdkkgedIrtYCa Ggát;rgkarTajbBaÄr. kmøaMgsgát;Ggát;RTUg k¾dUcCabgÁúMkmøaMgbBaÄrrbs;va mantémøes μ InwgkmøaMgTajenAkñúg Edkkg. EdkBt;dgErk (bent-up reinforcement) k¾edIrtYdUcCaGgát;TajenAkñúg truss Edr ¬rUbTI *>^¦.



CaTUeTA karcUlrYmrbs;EdkkmøaMgkat;TTwgeTAkñúgersIusþg;kmøaMgkat;TTwgrbs;FñwmebtugGarem:

GacRtUv)anBiBN’nadUcxageRkam³ - vaTb;Tl;EpñkxøHénkmøaMgkat;TTwg/ sV - vabegáInGaMgtg;sIueténkmøaMgkat;rvagGnþrépÞ/ aV ¬rUbTI *>%¦/ edayTb;Tl;nwgkarrIkFMénsñam

eRbHeRTt (inclined crack). - vabegáInnUvkmøaMgf<k; (dowel force)/ dV ¬rUbTI *>%¦/ enAkñúgEdkbeNþay - GMeBITb; (confining action) rbs;EdkkgeTAelIebtugGacbegáInersIusþg;rbs;va - GMeBITb; (confining action) rbs;EdkkgeTAelIebtugbegáInnUvsmtßPaBrgVilénsnøak;)øasÞic

(rotation capacity of plastic hinge) EdlekItmanenAkñúgeRKOgbgÁúM indeterminate structure

eRkambnÞúkcugeRkay nigbegáInRbEvgEdl yield GacekItmanenAelIva. eday nV CaersIusþg;kmøaMgkat;rbs;muxkat;ebtugGarem:enaH



scn VVV += ¬*>!@¦ Edl cV - ersIusþg;kmøaMgkat;)anBIebtug

sV - ersIusþg;kmøaMgkat;)anBIEdk RbsinebI uV kmøaMgkat;Edl)anBIbnÞúkxageRkAenaH

)( scnu VVVV +=≤ φφ ¬*>!#¦ Edl LDu VVV 6.12.1 += nig 75.0=φ

sV RtUv)anKNnaedaykarviPaK truss ¬rUbTI *>&¦. sRmab;sñameRbH o45 niges‘rIénEdkkg b¤ EdkdgErk. kmøaMgkat;bBaÄr sV esμ InwgplbUkbgÁúMkmøaMgbBaÄrénkmøaMgTajEdlekItmanenAkñúgEdkeRTt

αsinytvs fnAV = ¬*>!$¦ Edl vA -muxkat;kat;EdkkmøaMgkat;CamYyKMlat s

ytf - ersIusþg;EdkkmøaMgkat;

eday 211 aaaans +=

otgaaaad 45141 == ¬BIRtIekaN 41aaa ¦ αtgaaaad 241 == ¬BIRtIekaN 21aaa ¦

)cot1()cot45(cot αα +=+=⇒ ddns o )cot1( α+=⇒

sdn

eKTTYl)an )cos(sin)cot1(sin αααα +=+=s

dfAs

dfAV ytvytv

s ¬*>!%¦ sRmab;krNIEdkkgbBaÄr o90=α



sdfA

V ytvs = b¤

s

ytv

VdfA

s = ¬*>!^¦

sRmab;krNIEdkkgbBaÄr o45=α

sdfA

V ytvs 4.1= b¤

s

ytv

VdfA

s 4.1= ¬*>!&¦

sRmab;krNIEdkdgErkEtmYy b¤RkumEdkenAmYykEnøg αsinytvs fAV = b¤

αsinyt

sv f

VA = ¬*>!*¦

sRmab; o45=α

yt

sv f

VA 4.1= ¬*>!(¦

8>6> tRmUvkarrbs ; ACI Code sRmab;karKNnakmøaMgkat;TTwg

8>6>1> muxkat;eRKaHfñak;sRmab;karKNnaersIusþg;kmøaMgkat;TTwgmFüm Critical section for nominal shear strength calculation

ACI Code, Section 11.1.3 GnuBaØat[ykmuxkat;eRKaHfñak;sRmab;karKNnaersIusþg;kmøaMgkat; mFümenAcm¶ay d BIépÞmuxénTRm. karENnaMenHQrenAelIPaBCak;EsþgEdlsñameRbHeRTtdMbUgeKTMngCa ekIteLIgenAelIFñwmRtg;cm¶ay d BITRmEdleRcInelcecjenAeBleFVIBiesaFn_. muxkat;eRKaHfñak;enHRtUv)an GnuBaØat enAkñúglkçxNÐEdlRbtikm μTRmbBa¢ÚnkmøaMgsgát;eTAkñúgtMbn;cug bnÞúkRtUv)anGnuvtþenAelI b¤enAEk,r kMBUlénGgát;ehIyK μanbnÞúkcMcMNucGnuvtþenAcenøaHépÞénTRm nigTItaMgénmuxkat;eRKaHfñak;. bTdæank¾kMNt;Edr faEdkkmøaMgkat;TTwgRtUv)andak;enAcenøaHépÞénTRm nigcm¶ay d .

8>6>2> muxkat;EdkGb,brmasRmab;EdkkmøaMgkat;TTwg vtþmanrbs;EdkkmøaMgkat;TTwgenAkñúgFñwmebtugTb;Tl;nwgkarrIkraldalénsñameRbHeRTt. mü:agvij

eTot PaBsVit (ductility) ekIneLIg ehIyva)anRbkasGasnñmuneBl)ak;. RbsinebIKμanEdkkmøaMgkat;TTwg enaHFñwmmanlkçN³RsYyehIy)ak;edaymin)anR)ab;mun. dUcenH muxkat;EdkkmøaMgkat;TTwgRtUv)ankMNt; eday Code. ACI Code, Section 11.5.5 tRmUvEdkkgTaMgGs;[manRkLaépÞEdkkmøaMgkat;TTwgGb,brma

vA es μ Inwg

yt

w

yt

wcv f

sbf

sbfA 35.0'062.0 ≥= ¬*>@0¦

Edl wb CaTTwgénRTnug nig s CaKMlatrbs;Edkkg. eKRtUvkarbrimaNEdkkmøaMgkat;TTwgGb,-brmaenAeBlEdl cu VV φ5.0> elIkElg



- kRmalxNÐ nigeCIgtag - rnUtebtug - FñwmEdlmankm<s;tUcCag ;250max{ mm 5.2 dgkRmas;énsøab; ; 5.1 énTTwgRTnug} RbsinebI 35.0'062.0 =cf enaH MPaf c 9.31' = . enHman½yfaenAeBlEdl MPaf c 32' < enaH

témøGb,brma ytwv fsbA /35.0= manlkçN³lub EtenAeBlEdl MPaf c 32' ≥ enaHtémøGb,brma =vA

ytwc fsbf /'062.0 manlkçN³lub. karekIneLIgnUvRkLaépÞEdkkmøaMgkat;TTwgsRmab; MPaf c 32' ≥ KWedIm,IkarBarCamunnUvkar)ak;edaykmøaMgkat;TTwg (shear failure )Pøam² enAeBlEdlekItmansñameRbHeRTt.

vaCakarGnuvtþmYyd¾Fm μtakñúgkardMeLIgkRmas;kRmalxNÐ kRmas;eCIgtag b¤km<s;Fñwmrak;edIm,IbegáIn lT§PaBTb;Tl;nwgkmøaMgkat;TTwg. EdkkgGacnwgK μan\T§iBlenAkñúgGgát;rak; edaysartMbn;rgkarsgát;rbs; vamankm<s;tUcEmnETn nigminmanTMBk;RKb;RKan;EdlRtUvkarsRmab;Edkkg. sRmab;FñwmEdlminrak; eKmin RtUvkarEdkkmøaMgkat;TTwgenAeBlEdl cu VV φ5.0< .

RkLaépÞEdkkmøaMgkat;TTwgGb,brmaGacnwgRtUv)anTTYledayeRbIEdkkg 10DB dak;enAKMlatGti-brma maxS . RbsinebI MPaf yt 400= ehIyEdkkg 10DB manragGkSr U ¬eCIgBIr¦RtUv)aneRbI enaH smIkar ¬*>@0¦køayeTACa

w

ytv

wc

ytv

bfA

bf

fAS

35.0)'062.0(max ≤= ¬*>@!¦

sRmab; MPaf c 32' < / ww bbS /17940035.0/400157max =×= sRmab; MPaf c 32' = / wbS /179000max = ¬*>@@¦ sRmab; MPaf c 35' = / wbS /171200max = sRmab; MPaf c 42' = / wbS /156250max = RbsinebIeKeRbIEdk 12DB manragGkSr U enaH sRmab; MPaf c 32' < / wbS /258250max = sRmab; MPaf c 32' = / wbS /25750max = ¬*>@#¦ sRmab; MPaf c 35' = / wbS /246450max = sRmab; MPaf c 42' = / wbS /224950max = RtUvcgcaMfa maxS minRtUvFMCag mm600 b¤ 2/d eT. taragTI 1 pþl;nUv maxS edayQrelIsmIkar ¬*>@@¦ nig ¬*>@#¦. KMlatcugeRkayKYrEtRtUvrMkil

eTArktémøEdltUc. ]TahrN_ mmS 515max = køayeTACa mmS 500max = . taragTI1> témørbs; cmbfAS wytv 6035.0/max == . enAeBlEdl MPaf yt 400= nig MPaf c 32' <



wb )(cm 25 30 35 40 45 50 55 60 wb maxS )(cm 10DB 60 55 50 40 35 35 30 25 wb/179400

maxS )(cm 12DB 60 60 60 60 55 50 45 40 wb/258250

8>6>3> kmøaMgkat;TTwgGtibrmaEdlTb;edayEdkkmøaMgkat;TTwg sV edIm,IkarBarkar)ak; shear-compression failure EdlebtugGacEbkedaykugRtaMgkmøaMgkat;TTwgFM

nigkugRtaMgkmøaMgsgát;enAkñúgtMbn;eRKaHfñak; enABIelIkMBUlénsñameRbHGgát;RTUg ACI Code, Section

11.5.6.8, tRmUv[ dbfV wcs '67.0≤ . RbsinebI dbfV wcs '67.0> enaHeKRtUvtMelIgmuxkat;ebtug. edayQrenAelIkarkMNt;enH³

RbsinebI MPaf c 20' = enaH dbV ws 3≤ b¤ MPadbV ws 3/ ≤ RbsinebI MPaf c 28' = enaH dbV ws 5.3≤ b¤ MPadbV ws 5.3/ ≤ RbsinebI MPaf c 35' = enaH dbV ws 4≤ b¤ MPadbV ws 4/ ≤

8>6>4> KMlatEdkkgGtibrma edIm,IFanafasñameRbHGgát;RTUgRtUvkat;Edkkgy:agehacmYy enaH ACI Code, Section 11.5.4 tRmUv

fa KMlatrvagEdkkgminKYrelIs 2/d b¤ mm600 RbsinebI dbfV wcs '33.0≤ ¬edayQrelIkarsnμt;fa sñameRbHGgát;RTUgekItmantammMu o45 niglatsn§wgtamcm¶ayedkRbEhlcm¶ay d . enAkñúgtMbn;kmøaMgkat; TTwgFM Edl dbfV wcs '33.0> KMlatEdkkgGtibrmacenøaHEdkkgminRtUvFMCag 4/d . karkMNt;enHcaM )ac;edIm,IFana[sñameRbHGgát;RTUgkat;Edkkgy:agehacbI. enAeBlEdl dbfV wcs '67.0> karkMNt; énKMlatGtibrmaminRtUv)anGnuvtþ ehIyTMhMrbs;muxkat;ebtugKYrRtUv)andMeLIg.

karkMNt;TIBIrsRmab;KMlatGtibrmaénEdkkg k¾GacTTYl)anBIlkçxNÐmuxkat;EdkkmøaMgkat;TTwg Gb,brma. vA Gb,brma RtUv)anTTYlenAeBlKMlat s Gb,brma ¬smIkar *>@!¦.

karkMNt;TIbIsRmab;KMlatGtibrmaesμ Inwg mm600 enAeBlEdl dbfV wcs '33.0≤ niges μ Inwg mm300 enAeBlEdl dbfVdbf wcswc '67.0'33.0 ≤< . témøtUcCageKénKMlatGtibrmaRtUv)anyk

mkeRbI. tRmUvkarKMlatGtibrmaén ACI Code FanaKMlatCitKñarbs;EdkkgedIm,Icab;EdkrgkarTajbeNþay enAkñúgFñwm edayehtuenHva)anbegáInlT§PaBbgáb;Edkrbs;va dV ¬rUbTI *>%¦.



8>6>5> ersIusþg; yield rbs;EdkkmøaMgkat;TTwg ACI Code, Section 11.5.2. tRmUv[ersIusþg; design yield strength rbs;EdkkmøaMgkat;TTwg minKYrelIs MPa420 . mUlehtuEdlenABIeRkaykarsMercenHKWedIm,IkMNt;TMhMsñameRbHEdlbNþalmkBI kmøaMgTajGgát;RTUg nigedIm,IFanafaEKmrbs;sñameRbHenArkSaépÞb:HCitKñaedIm,IbegáInkmøaMgbBa¢ÚnénkmøaMg kat;rvagGnþrépÞ aV ¬rUbTI *>%¦. sRmab;srésEdkfñaMgGMeBAsRmab;pSar (welded deformed wire fabric)

ersIusþg; design yield strength minKYrelIs MPa560 .

8>6>6> TMBk;rbs;Edkkg ACI Code, Section 11.5.2. tRmUveGayEdkkmøaMgkat;TTwgRtUv)andak;enAEk,rsrésrgkar sgát;eRkAbMput nigsrésrgkarTajeRkAbMputtamEtGaceFVIeTA)an CamYynwgtRmUvkarrbs; code sRmab; kRmas;karBarEdk edaysarEt enAeBlEdlbnÞúkEdlmanGMeBIenAelIFñwmxiteTACitbnÞúkcugeRkay (ultimate

load) sñameRbHkM laMgTaj edaykarBt; (flexural tension crack) bnøayy:ageRCAcUleTAkñúgFñwm. dUcKña edIm,I[EdkkgTTYl)annUversIusþg; yield eBj vaRtUvkarTMBk;Edll¥. enAeBlEdlbnÞúkEdlmanGMeBIelIFñwm xiteTACitbnÞúkcugeRkay (ultimate load) kugRtaMgenAkñúgEdkkg)aneTAdl;kugRtaMg yield rbs;va enAcMNuc EdlsñameRbH Ggát;RTUgkat;cMEdkkgenaH. tRmUvkarrbs; ACI Code sRmab;TMBk;Edkkg/ Section 12.13

dUcxageRkam³ - karBt;nImYy²enAkñúgEpñkCab;énEdkkgGkSr U Fmμta b¤BhuEdkkgGkSr U KYrB½T§CMuvijEdk

beNþay (ACI Code, Section 12.13.3) emIlrUbTI *>*a. - Code GnuBaØat[eRbInUvTMBk; standard o90 / o135 b¤ o180 CMuvijEdkbeNþysRmab;Edkkg

16DB . RbsinebIEdkkg 19DB / 22DB nig 25DB CamYynwg MPaf yt 280> enaH Code,

Section 12.13.2 tRmUvTMBk; standard bUknwgRbEvgbgáb; cytb ffd '/17.0 cenøaHBak;kNþal km<s;Fñwm nigEpñkxageRkAénTMBk;. RbsinebIEdkRtUvBt;edaymMu o90 RbEvgBnøÚtminRtUvtUcCag

bd12 . sRmab;Edk 16DB b¤EdkkgTMhMtUcCagenH RbEvgBnøÚtKW bd6 (ACI Code, Section

7.1) emIlrUbTI *>*. - RbsinebIEdkkgGkSr U DubRtUv)aneRbIedIm,IpÁúMCaEdkkgbiTCit RbEvgRCYs (lap length) minRtUv

tUcCag dl3.1 (ACI Code, Section 12.13.5) emIlrUbTI *>*c . - srésEdkEdlpSar (welded wire fabric) RtUv)aneRbIsRmab;EdkkmøaMgkat;TTwgenAkñúg]sSa-

hkmμplitTukmun (precast industry) . TMBk;lMGitRtUv)anpþl;[enAkñúg ACI Code, Section

12.13.2.3 nigenAkñúgesckþIBnül; (commentary) rbs;va.



- EdkkgbiTCitRtUv)anpþl;[sRmab;FñwmEdlrgnUgkmøaMgrmYl (ACI Code, Section 7.11). - FñwmEdlenAB½T§CMuvijeRKOgbgÁúMRtUveRbIEdkkgbiTCitedIm,IrkSa structural integrity rbs;Ggát;

(ACI Code, Section 7.13.2.2).



8>6>7> EdkkgenAEdlenAEk,rTRm ACI Code, Section 11.1.3 kMNt;faEdkkgkmøaMgkat;TTwgEdlpþl;[enAcenøaHépÞTRm nigmuxkat;

eRKaHfñak; (critical section) EdlsßitenAcm¶ay d BITRmKYrRtUv)anKNnasRmab;kmøaMgkat;TTwg uV dUcKña enAnwgmuxkat;eRKaHfñak;. vaCakarGnuvtþFmμtaedaydak;EdkkgTImYyenAcm¶ay 2/s BIépÞénTRm Edl s CaKMlatEdlKNnaedaysmIkar ¬*>!^¦ sRmab; uV enAmuxkat;eRKaHfñak;.

8>6>8> RbEvgRbsiT§PaBrbs;EdkdgErk manEtbIPaKbYnRtg;cMNuckNþalénEpñkeRTténEdkbeNþayRtUv)anKitfamanRbsiT§PaBsRmab;Edk

kmøaMgkat;TTwg. enHmann½yfa KMlatGtibrmarbs;EdkdgErkKW )'(75.0 dd − . BIrUbTI *>( RbEvgRbsiT§PaB rbs;EdkdgErkKW )'(06.1)')(414.1(75.045sin/)'(75.0 dddddd o −=−=− . KMlatGtibrma s es μ Inwg cm¶ayedkEdl)anBIkarTMlak;cMeNalEkgénRbEvgRbsiT§PaBEdkdgErk. dUcenH

oddS 45cos)'(06.1max −= b¤ )'(75.0707.0)'(06.1max ddddS −=−=

8>7> karKNnaEdkkgbBaÄr eKRtUvkarEdkkg (stirrup) enAeBlEdl cu VV φ2

1> . EdkkgGb,brmaRtUv)aneRbIenAeBlEdl cuc VVV φφ <<2

1 . kñúgkrNIenHeKeRbIEdkkg 10DB EdlRtUv)andak;nUvKMlatGtibrma. enAeBlEdl cu VV φ> eKRtUvkardak;EtEdkkgCamYyKMlattUcCagKMlatGtibrma ehIyGacRtUv)anKNnaedayeRbI

smIkar ¬*>!^¦³ sytv VdfAS /= . EdkkgEdlRtUv)aneRbICaTUeTAenAkñúgmuxkat;ebtugCaEdkkg 10DB nig 12DB GkSr U eCIgBIr

CamYynwg MPaf yt 400= . RbsinebI 10DB RtUv)aneRbIenaH smIkar¬*>!^¦køayCa³

sss

ytv

VVVfA

dS 62800400157

=×

== ¬*>@$¦

RbsinebI 12DB RtUv)aneRbIenaH

sss

ytv

VVVfA

dS 90400400226

=×

== ¬*>@%¦

pleFobKMlatEdkkgelIkm<s;RbsiT§PaB d rbs;Fñwm GaRs½ynwg sV . témøén dS / sRmab;témø epSgKñaén sV enAeBlEdl MPaf yt 400= RtUv)an[enAkñúgtaragTI2 nigtaragTI3 sRmab;Edk 10DB nig Edk 12DB erogKña. témødUcKñaRtUv)anbgðajCadüaRkamdUcenAkñúgrUbTI 8>10 nigrUbTI 8>11.



taragTI2> pleFob dS / sRmab;témø sV ¬ MPaf yt 400= / sVdS /62800/ = ¦ 10DB

sV )(kN 125.6 142.7 190.3 237.9 251.2 285.5 330.5 380.6 418.7 475.8 592.5

dS / 0.5 0.44 0.33 0.264 0.25 0.22 0.19 0.165 0.15 0.132 0.106

taragTI3> pleFob dS / sRmab;témø sV ¬ MPaf yt 400= / sVdS /90400/ = ¦ 12DB

sV )(kN 180.8 225 265 310 361.6 445 490.0 535 665 775 850

dS / 0.5 0.40 0.34 0.29 0.25 0.20 0.18 0.17 0.14 0.12 0.11



tamtarag nigdüaRkamxagelIeyIgGacsnñidæan)anfa³

- RbsinebIeKeRbI 10DB / 2/dS = enAeBlEdl kNVs 6.125≤ . enAeBlEdl sV ekIneLIg dS / fycuHtamExSekageTArktémø 132.0 enAeBl kNVs 8.475= . RbsinebIKMlatGb,brma

RtUv)ankMNt;Rtwm mm75 enaH mmd 568≥ . enAeBlEdl kNVs 2.251> enaH 4/dS ≤ . - RbsinebIeKeRbI 12DB / 2/dS = enAeBlEdl kNVs 8.180≤ . enAeBlEdl sV ekIneLIg

dS / fycuHtamExSekageTArktémø 14.0 enAeBl kNVs 665= . RbsinebIKMlatGb,brma RtUv)ankMNt;Rtwm mm75 enaH mmd 535≥ . enAeBlEdl kNVs 6.361> enaH 4/dS ≤ .

- RbsinebIeKeRbIEdkkgGkSr U MPaf yt 280= enaHeKRtUvKuN dS / edaytémø 10/7 b¤CaTUeTA 400/ytf .

8>8> segçbviFIsaRsþKNnaEdkkgbBaÄr CMhankñúgkarKNnaEdkkgbBaÄrsRmab;kmøaMgkat;TTwg edayeyagtam ACI Code GacRtUv)an

segçbdUcxageRkam³

f. kMNt;kmøaMgkat;KNna uV BIbnÞúkEdlGnuvtþmkelIeRKOgbgÁúM. kmøaMgkat;KNnaRKITicEdl RtUvykmksikSasßitenARbEvg d BImuxénTRm.

g. kMNt; dbfV wcc '17.0φφ = b¤ dbfdbM

dVfV wcwu

uwcc '29.0)2.17'16.0( φρφφ ≤+=

bnÞab;mkKNna cVφ21



h. k> RbsinebI cu VV φ21

< muxkat;minRtUvkarEdkkg x> RbsinebI cuc VVV φφ ≤<

21 eRbImuxkat;EdkkgGb,brma

K> RbsinebI cu VV φ> muxkat;Edkkg RtUvKNnadUcxageRkam i. kMNt;kmøaMgkat;EdlTb;eday Edkkg

φφ cu

sVVV −

=

j. kMNt; dbfV wcc '33.01 = nig 12 2'67.0 cwcc VdbfV == . RbsinebI 2cs VV > dMeLIgmuxkat;.

k. kMNt;KMlatrbs;Edk s

ytv

VdfA

s =1

l. kMNt;KMlatEdkGtibrmaEdlGnuBaØateday ACI Code. KMlatEdkGtibrmaCatémøtUcbMput én 2s nig 3s k> cmds 60

22 ≤= RbsinebI dbfVV wccs '33.01 =≤ cmds 30

42 ≤= RbsinebI 21 csc VVV ≤<

x> cw

ytv

w

ytv

fbfA

bfA

s'

1633 ≥=

m. k> RbsinebI max1 ss < eRbI 1s x> RbsinebI max1 ss > eRbI maxs

n. ACI Code min)ankMNt;nUvKMlatGb,brmaeT. eRkamlkçxNÐFmμta KMlatGb,brma S RtUv)ansnμt;ykesμ Inwg mm75 sRmab; cmd 50≤ nigmanKMlatGb,brmaes μ Inwg mm100 sRmab;FñwmeRCA (deep beam) . RbsinebI S mantémøtUcenaH eKGactMeLIgmuxkat;Edkkg b¤eRbIEdkkgeCIgeRcIn ¬rUbTI 8>8¦.

o. sRmab;muxkat;mUl RkLaépÞEdleRbIsRmab;KNna =cV plKuNGgát;p©itCamYykm<s;RbsiT§PaB d / Edl 8.0=d énGgát;p©it/ ACI Code,

Section11.3.3 . ]TahrN_ 1³ FñwmTRmsamBaØmanmuxkat;ctuekaN cmb 30= / cmd 55= nig cmh 60= ehIyRtUv)anBRgwg eday 254DB . epÞógpÞat;faetImuxkat;enHRKb;RKan; b¤Gt;sRmab;kmøaMgkat;TTwgemKuN (ultimate shear

force) xageRkam. RbsinebIvaminRKb;RKan; cUrKNnaEdkkmøaMgkat;TTwgkñúgTRmg;CaEdkkgGkSr U . eday eRbI MPaf c 28' = nig MPaf yt 400= .



k> kNVu 50= x> kNVu 110= K> kNVu 240= X> kNVu 345= g> kNVu 570= dMeNaHRsay³ CaTUeTA mmbbw 300== / mmd 550= nig ( ) ( ) kNbdfV cc 3.111105503002817.075.0'17.0 3 =××== −φφ kNVc 65.552

1 =φ ( ) ( ) kNbdfV cc 288105503002833.0'33.0 3

1 =××== − ( ) kNbdfV cc 576'67.02 ==

k> kNVkNV cu 565.5550 21 =<= φ / muxkat;RKb;RKan; edayminRtUvkarEdkkmøaMgkat;TTwg.

x> cu VkNV φ21110 >= / b:uEnþvatUcCag kNVc 3.111=φ . eday 0=sV dUcenH muxkat;RtUvkarEdk

kmøaMgkat;TTwgGb,brma. eRbI 10DB CaEdkkgGkSr U enAKMlatGtibrma. 22 157

4102 mmAv =×=

π KMlatGtibrmaCatémøtUcCageKkñúgcMeNam mmdS 2752/2 == yk mm250 ¬lub¦ mmbfAS wytv 598)30035.0/(40015735.0/3 =××== yk mm550 ¬b¤eRbItaragTI1¦ mmS 6004 = dUcenHeRbIEdkkg mmDB 250@10 K> cu VkNV φ>= 240 / RtUvkarEdkkmøaMgkat;TTwg. karKNnaGaceFVIeLIgCaCMhanxageRkam³ KNna ( ) kNVVV cus 6.17175.0/3.111240/)( =−=−= φφ

edaysar 1cs VV < enaH mmdS 6002/max ≤= eRCIserIs 10DB CaEdkkgGkSr U nigKNnaKMlatRtUvkaredayQrelI sV

mmV

dfAS

s

ytv 201171600

5504001571 =

××== yk mm200

KNnaKMlatGtibrma³ mmS 2502 = / mmS 5503 = nig mmS 6004 = dUcenH mmS 250max = edaysar mmSmmS 250200 max =<= dUcenHeRbIEdkkg mmDB 200@10

X> cu VkNV φ>= 345 /RtUvkarEdkkmøaMgkat;TTwg. KNna ( ) kNVVV cus 6.31175.0/3.111345/)( =−=−= φφ

edaysar 1cs VV > enaH mmdS 3004/max ≤= yk mm125 edaysar 21 csc VVV << enaHeKGaceRbIEdkkg edaymincaM)ac;dMeLIgmuxkat;ebtug.



eRCIserIs 10DB CaEdkkgGkSr U nigKNnaKMlatRtUvkaredayQrelI sV mm

VdfA

Ss

ytv 110311600

5504001571 =

××== yk mm100

KNnaKMlatGtibrma³ mmdS 5.1374/2 == yk mm125 / mmS 5503 = nig mmS 3004 = dUcenH mmS 125max = edaysar mmSmmS 125100 max =<= dUcenHeRbIEdkkg mmDB 100@10

g> cu VkNV φ>= 570 / RtUvkarEdkkmøaMgkat;TTwg. KNna ( ) kNVVV cus 6.61175.0/3.111570/)( =−=−= φφ

edaysar 2cs VV > enaHmuxkat;minRKb;RKan;. eKRtUvkardMeLIgTMhMrbs;muxkat;mYy b¤k¾TaMgBIr. cMNaM³ taragTI 2 nigrUbTI 8>10 k¾GacRtUv)aneRbIedIm,IKNnaKMlat S sRmab; K> nig X> )anpgEdr.

1> sRmab; K> kNVs 6.171= BIrUbTI 8>10 ¬b¤taragTI 2> sRmab;EdkkgGkSr U 10DB ¦ eyIg TTYl)an 37.0/ =dS dUcenH mmS 5.2031 = EdltUcCag mmd 2502/ = . cgcaMfa maxS EdlQrelI sV KW 2/d minEmn 4/d eT. dUcKñaBItaragTI 1> eyIgTTYl)an

mmbfAS wytv 55035.0/3 == . 2> sRmab; X> kNVs 6.311= / 18.0/ =dS enaH mmS 1001 = / kNkNVs 2.2516.311 >= enaH

4/max dS = RtUv)aneRbI. ]TahrN_2³ FñwmTRmsamBaØEdlmanRbEvg m2.5 nigmanRbEvgcenøaHssr (clear span) m9.4 edayRTnUv bnÞúkBRgayesμ Iefr mkN /65 nigbnÞúkBRgayesμ IGefr mkN /55 . TMhMrbs;Fñwm nigsrésEdkRtUv)anbgðaj enAkñúgrUbTI 8>12. epÞógpÞat;muxkat;sRmab;kmøaMgkat;TTwg nigKNnaEdkkmøaMgkat;TTwgcaM)ac;. eK[

MPaf c 20' = nig MPaf y 400= . dMeNaHRsay³ eK[ mmbw 350= / mmd 580=

1> KNnakmøaMgkat;TTwgemKuN (ultimate shear) BIbnÞúkxageRkA³ bnÞúkBRgayesμ IemKuN mkN /166556.1652.1 =×+×=

uV ¬enABImuxépÞTRm¦ kN7.4062

9.4166=

×=

KNna uV ¬enAcm¶ayBImuxépÞénTRm¦ kN42.31016658.07.406 =×−=



2> KNna :cVφ

( ) kNdbfV wcc 75.115105803502017.075.0)'17.0( 3 =××== −φφ kNVc 87.572

1 =φ KNna kNdbfV wcc 6.299105803502033.0'33.0 3

1 =×××== − KNna kNVV cc 2.5992 12 ==

3> eday cu VV φ> dUcenHmuxkat;RtUvkarEdkkmøaMgkat;TTwg. cm¶ay 'x EdlenARtg;cm¶ayenHmuxkat; ebtugminRtUvkarEdkkmøaMgkat;TTwg ¬enA cVφ2

1 ¦KW³ mx 10.2

29.4

7.40687.577.406' =⎟

⎠⎞

⎜⎝⎛ −

=

4> KNna ( ) ( ) kNVVV cus 56.25975.0/75.11542.310/ =−=−= φφ . edaysar 1cs VV < enaH mmdS 6002/max ≤= RtUv)anBicarNa ¬b¤eyagtamrUbTI 8>10 b¤taragTI2³ kNVs 2.251> ¦.

5> KNnaEdkkg³ eRCIserIsEdkkgGkSr U 10DB / 2157mmAv = . KNna 1S edayQrelI kNVs 56.259= / mmVdfAS sytv 140/1 == yk mm125 ¬b¤yk 24.0/ =dS BItaragTI2

b¤BIrUbTI 8>10¦



6> KNnaKMlatGtibrma³ mmdS 2902/5802/2 === yk mm250 / mmbfAS wytv 50035.0/3 == ¬b¤eRbItaragTI1¦/ mmS 6004 = . dUcenH mmS 250max = .

7> edaysar mmSmmS 250125 max1 =<= eRbI mmDB 125@10 8> KNna sV sRmab;KMlatGtibrma mm250

kNs

dfAV yts

s 7.14510250

580400157 3 =××

== − kNVs 3.109=φ

kNVV sc 2253.10975.115 =+=+φφ cm¶ay 1x EdlenARtg;cm¶ayenHmuxkat;GaceRbIKMlat mms 250=

mx 09.129.4

7.4062257.406

1 =⎟⎠⎞

⎜⎝⎛ −

=

edaysar 1x mantémøtUc eRbI mms 125= sRmab;cm¶ayFMCag b¤es μ I m09.1 . cMNaMfa RbsinebI 1x Evg KMlatenAcenøaH mm150 eTA mm250 GacRtUv)anbEnßm.

9> EdkkgRtUv)anBRgaydUcxageRkam³ dak;EdkkgTI1enAcm¶ay 2/S BImuxépÞénTRm EdkkgTImYyenA mmS 5.622/1252/ == yk mm50 R)aMbYnEdkkgmanKMlat mmmmS 1125125 == srub mmmm 10901175 > bYnEdkkgmanKMlat mmmmS 1000250 == srub mmmm 24502175 < cMnYnEdkkgsrubsRmab;FñwmKW 28)491(2 =++ . karBRgayEdkkgRtUv)anbgðajenAkñúgrUbTI 8>13 ÉkmøaMggkat;TTwgEdl)anKNnaRtUv)anbgðajenAkñúgrUbTI 8>12.

10> dak;Edkkg 12DB cMnYnBIredIm enABIelImuxkat;FñwmedIm,IedIrtYrCaEdkkgBüÜr.



8>9> kmøaMgkat;TTwgEdlbNþalBIbnÞúkGefr enAkñúg]TahrN_TI2 TaMgbnÞúkefr nigbnÞúkGefrRtUv)ansnμt;faBRgayesμ IeBjtambeNþayFñwm Edl

begáIt)ankmøaMgkat;TTwgsUnüenAkNþalElVg. CaFm μta bnÞúkefrBitCaBRgayeBjelIbeNþayFñwm EtbnÞúk GefrGacGnuvtþeBj b¤k¾GnuvtþEtEpñkxøHrbs;Fñwm EdltRmUv[mankmøaMgkat;TTwgGtibrmaekIteLIgenAkNþal ElVg b¤muxkat;kMNt;NamYy. rUbTI 8>14 a bgðajBIFñwmTRmsamBaØCamYynwgbnÞúkBRgayesμ IGnuvtþeBj beNþayFñwm. kmøaMgkat;TTwgERbRbYlCaragbnÞat;tambeNþayFñwm CamYynwgkmøaMgkat;TTwgGtibrmaenATRm A .

kñúgkrNIEdlbnÞúkGefr LWW 6.12 = kmøaMgkat;TTwgGtibrmamanGMeBIenARtg;TRm A enAeBlEdl 2W GnuvtþeBjElVgFñwm ¬rUbTI 8>14 a ¦. kmøaMgkat;TTwgGtibrmaekItmanenAkNþakElVgRbsinebIbnÞúkGefr

RtUv)andak;EtBak;kNþalFñwm BC ¬rUbTI 8>14 b ¦ EdlbegáIt)an uV enAkNþalElVges μInwg 8/2LW . dUc enH kmøaMgkat;TTwgKNnaRtUv)anbegáIteLIgedaykarbEnßmkmøaMgkat;TTwgGtibrmaEdlbNþalmkBIbnÞúk Gefr ¬EdlRtUv)andak;enAelIRbEvgepSg²énElVg¦ eTAelIkmøaMgkat;TTwgGefr ¬rUbTI 8>14 c ¦. vaCakar GnuvtþFm μtaedayKitkmøaMgkat;TTwgGtibrmaRtg;TRm A es μ Inwg 2/)6.12.1(2/ LWWLW LDu += / b:uEnþ uV enAkNþalElVgesμ I 8/)6.1(8/2 LWLW L= CamYybnÞat;Rtg;ERbRbYltambeNþay AC nig CB dUcbgðajenA kñúg rUbTI 8>14 d. karKNnasRmab;kmøaMgkat;TTwgenAkñúkrNIenHnwgGnuvtþdUcKñanwgkarBnül;kñúg]TahrN_2. RbsinebI karerobrab;xagelIenHGnuvtþeTAFñwmkñúg]TahrN_2 enaH uV ¬enATRm A ¦ kN7.406= nig uV ¬enA kNþalElVg¦ kN9.538/9.4)556.1( =×= .



]TahrN_3³ Fñwm cantilever RbEvg m3 manmuxkat;ctuekaNEkg nigRTnUvbnÞúkemKuNBRgayes μ I nigcMcMNuc ¬bnÞúkpÞal;xøÜnRtuv)anrab;bBa©ÚlrYc¦ dUcbgðajenAkñgrUb 8>15. edayeRbI MPaf c 28' = nig MPaf y 400= KNnaEdkkmøaMgkat;TTwgcaM)ac;sRmab;dak;kñúgFñwmTaMgmUledayeyagtam ACI Code.



dMeNaHRsay³

1> KNnakmøaMgkat;TTwgtambeNþayFñwmEdlbNþalmkBIbnÞúkxageRkA uV ¬enATRm¦ kN3653689380 =++×= udV ¬enAcm¶ay d ¦ kN4.351

300051080365 =−=

uV ¬enAcm¶ay m2.1 xageqVg¦ kN2692.180365 =×−= uV ¬enAcm¶ay m2.1 xagsþaM¦ kN18089269 =−= uV ¬enAcugTMenr¦ kN36=

düaRkamkmøaMgkat;TTwgRtUv)anbgðajenAkñúgrUbTI 8>15. 2> KNna cVφ ³

( ) ( ) kNbdfV cc 2.103105103002817.075.0'17.0 3 =××== −φφ kNVc 6.512

1 =φ edaysar cud VV φ> muxkat;ebtugRtUvkarEdkkmøaMgkat;TTwg. KNna

kNbdfV cc 2.26710510300)2833.0('33.0 31 =××== −

kNVV cc 4.5342 12 ==



cm¶ay x EdlenARtg;enHmuxkat;minRtUvkarEdkkmøaMgkat;TTwg ¬enA kNVc 6.5121 =φ ¦ EdlRtVv)an

vas;BITRm A . mx 8.28.1

361806.511802.1 =⎟⎠⎞

⎜⎝⎛

−−

+=

¬ mm200 BIcugTMenr¦. dUcKña 1x sRmab; cVφ KW m16.2 BI A ¬ mm840 BIcugTMenr¦ 3> Epñk AC ³ kmøaMgkat;TTwgKNna kNVV udu 4.351== . KNna φφ /)( cus VVV −=

kN9.33075.0/)2.1034.351( =−= . edaysarEt 21 csc VVV << enaH 4/max dS ≤ RtUv)an BicarNa ¬b¤epÞógpÞat;edayeRbIrUbTI 8>10¦.

4> KNnaEdkkg³ eRCIserIsEdkkgGkSr U 10DB / 2157mmAv = . KNna 1S ¬QrelI sV ¦ mm

VdfA

Ss

ytv 100330900

5104001571 =

××==

eRbI mm100 ¬b¤TTYl 19.0/ =ds BIrUb 8>10¦. 5> KNnaKMlatGtibrma³ mmdS 5.1274/5104/2 === yk mm125

mmbfA

Sw

ytv 55030035.0400157

35.03 =××

== ¬BItaragTI1 sRmab; mmb 300= ¦

mmS 3004 = dUcenH mmS 125max =

6> eday mmSmmS 125100 max =<= dUcenHeRbIEdkkg mmDB 100@10 7> enAcMNuc C / kmøaMgkat;TTwgKNna cu VkNV φ>= 269 enaH ( ) kNVs 22175.0/2.103269 =−= .

mmVdfAS sytv 145/1 == kNVkNV cs 2.267221 1 =<= mmdS 2552/2 == ¬b¤ mm250 ¦

21 145 SmmS <= enaH mmS 1451 = b¤ mm125 8> edaysarKMlat mm125 nig mm100 mantémøEk,rKña eRbIEdkkg mmDB 100@10 sRmab;Epñk

AC . 9> Epñk BC

A. cu VkNV φ>=180 kNVkNV cs 2.2674.10275.0/)2.103180( 1 =<=−=

B. mmVdfAS sytv 313102400/510400157/1 =××== C. mmdS 2552/5102/2 === ¬b¤tUcCag mmS 5503 = nig mmS 6004 = ¦.

yk mmS 250max = . eRbIEdkkg mmDB 250@10 sRmab;Epñk BC .



10> karBRgayEdkkgedayvas;ecjBITRm A ³ dak;EdkkgTImYyenA mmS 502=

mm120010012 =× mm17502507 =×

srub mm3000 karBRgayEdkkgRtUv)anbgðajenAkñúgrUbTI 8>16. EdkkgsrubmancMnYn 20 .

8>10> kugRtaMgkmøaMgkat;TTwgenAkñúgGgát;Edlmankm<s;ERbRbYl

edaysarEtkugRtaMgkmøaMgkat;TTwg v CaGnuKmn_énkm<s;RbsiT§PaB d dUcenHkugRtaMgkat;TTwgERbRbYl tambeNþayFñwmebtugBRgwgedayEdkCamYynwgkm<s;ERbRbYl. enAkñúgFñwmEbbenH ¬rUbTI 8>17¦ eKBicarNa elIFatuGnnþtUc dx . kmøaMgsgát; C enAelImuxkat;NamYyes μInwgm:Um:g;Eck[édXñas; b¤ yMC /= . edrIevTI mYyén C KW³

2yMdyydMdC −

=

RbsinebI 1C FMCag 2C enaH vbdxdCCC ==− 21 dy

yM

ydM

yMdyydMvbdx 22 −=

−=

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

dxdy

byM

dxdM

ybv 2

1

edaysar jdy = / dxdM / es μ InwgkmøaMgkat;TTwg V nig dxjdd /)( CaCRmal (slope)/

⎥⎦⎤

⎢⎣⎡−= )(

)( 2 jddxd

jdbM

bjdVv nig αtan

)( 2jdbM

bjdVv ±= ¬*>@^¦



Edl V nig M CakmøaMgkat;TTwg nigm:Um:g;xageRkA ehIy α CamMuCRmalénépÞmYyrbs;FñwmeTAnwgépÞmYy eTotrbs;Fñwm. sBaØabUkRtUv)aneRbIenAeBlEdlkm<s;fycuHÉm:Um:g;ekIneLIg b:uEnþsBaØadkRtUv)aneRbIenAeBl km<s;ekIneLIgehIym:Um:g;k¾ekIneLIg. rUbmnþenHRtUv)aneRbIenAeBlEdlmMuCRmaltUc EdlmMu o30≤α .

TRmg;samBaØénsmIkar ¬*>@^¦GacRtUvbegáIteLIgedaysMrYl j enaHeyIgTTYl)an

αtan2bdM

bdVv ±= ¬*>@&¦

sRmab;viFIKNnaersIusþg; smIkarxageRkamGacRtUv)aneRbI α

φφtan2bd

Mbd

Vv uu ±= ¬*>@*¦

sRmab;kmøaMgkat;TTwg αφ tan

dMVV u

un ±= ¬*>@(¦ rUbTI 8>18 bgðajBIFñwm cantilever CamYynwgbnÞúkcMcMNucenAcugTMenr. m:Um:g;nigkm<s; d ekIneLIgkñúg

TisedAeTArkTRm. kñúgkrNIenH sBaØadkRtUv)aneRbIenAsmIkar ¬*>@&¦ ¬*>@*¦ nig¬*>@(¦. dUcKña sBaØadk RtUv)aneRbIsRmab;muxkat; t enAkñúgFñwmTRmsamBaØdUcbgðaj ehIysBaØabUkRtUv)aneRbIsRmab;muxkat; Z Edlm:Um:g;ekIneLIgenAeBlEdlkm<s;fycuH.

enAkñúgkrNICaeRcIn karERbRbYlkm<s;rbs;FñwmekItmanenAelIEpñkrbs;FñwmEdlenAEk,rTRm ¬rUbTI 8>18¦.



karBesaFeTAelIFñwmCamYykm<s;ERbRbYlbgðajfa FñwmEdlmankm<s;FMenATRmCaTUeTA)ak;edaysar

kmøaMgkat;TTwgsgát;. ÉFñwmEdlmankm<s;tUcenATRmCaTUeTA)ak;edaysarPaBKμanesßrPaB EdlbNþalmkBI karraldalénsñameRbHemenAkñúgFñwmeLIgelI ehIybnÞab;mksñameRbHenaHraldaltamTisedkenAelImuxkat; FñwmEpñkxagelI. karBiesaFk¾)anbgðajEdrfa sRmab;FñwmEdlmankm<s;ERbRbYl ¬rUbTI 8>18¦ CamYynwgmMu eRTt α RbEhl o10 nigrgnUvkmøaMgkat;TTwg nigkmøaMgBt; ersIusþg;kmøaMgkat;TTwgrbs;ebtug CVV GacRtUv )anKNnaeday

)tan1( α+= cCV VV ¬*>#0¦ Edl =CVV ersIusþg;kmøaMgkat;TTwgrbs;FñwmCamYynwgkm<s;ERbRbYl ( ) dbfdb

MdVfV wcwu

uwcc '29.02.17'16.0 ≤⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+= ρ ACI Code Eq.11.6

=α mMuEdlbegáIteLIgedayTisrbs;Edk. vaRtUv)anKitfaviC¢mansRmab;FñwmEdlmankm<s;tUc enATRm nigGviC¢mansRmab;FñwmEdlmankm<s;FMenATRm ¬rUbTI 8>18¦



=sd km<s;RbsiT§PaBrbs;FñwmenATRm ACI Code Eq.11.3 CasmIkarRtUv)ansRmYl nigGaceRbIedIm,IKNna cV ³

( ) dbfV wcc '17.0= ¬*>#!¦ ]TahrN_4³ KNnaFñwm cantilever dUcbgðajenAkñúgrUbTI 8>19 eRkamGMeBIbnÞúkemKuN. FñwmenHkm<s;srub enAcugTMenr mm300 ehIyekIneLIgeTArkTRm. edayeRbIPaKryEdk %5.1=ρ / MPaf c 28' = /

MPaf y 400= nig mmb 250= . dMeNaHRsay³

1> uM ¬TRm¦ mkN.2695.2622/5.25.36 2 =×+×= 2> sRmab; %5.1=ρ / MPaRu 72.4=

mmbR

Mdu

5.47725072.4

10269 6=

×⋅

== 217905.477250015.0 mmAs =××= ¬eRbIEdk 283DB ¦ yk mmd 490= / mmh 550= .

3> KNnasRmab;kmøaMgkat;TTwg³ kmøaMgkat;TTwgGtibrmaenATRmKW kN25.1535.25.3662 =×+ .

edaysarmuxkat;FñwmERbRbYl m:Um:g;RtUv)anBicarNakñúgkarKNnakmøaMgkat;TTwg. edaysarkm<s; FñwmekIneLIgCamYym:Um:g;ekIneLIg sBaØadkRtUv)aneRbIenAkñúgsmIkar ¬*>@*¦



)(tan2 αφφ bdM

bdVv uu

u −=

edIm,Irk αtan / yk d enAcugTMenresμ I mm490 nig d enAKl;TRmesμ I mm240 1.0

2500240490tan =

−=α

uv ¬TRm¦ MPa07.11.049025075.0

1026949025075.0

1532502

6=

××

⋅−

××=

4> kugRtaMgkmøaMgTTwgenAcugTMenrKW bdVu φ/ ¬ 0=uM ¦ MPavu 38.1

24025075.062000

=××

= 5> enAcm¶ay mmd 490= BImuxépÞénTRm km<s;RbsiT§PaBKW mm441 ¬BIrUbFrNImaRt¦

kNVu 4.13549.05.3625.153 =×−= uM ¬enAcm¶ay mm490 BITRm¦= mkN.4.198

201.25.3601.262

2=×+×

MPavu 09.144125075.0

1.0104.19844125075.0

104.1352

63=

××

×⋅−

××⋅

=

6> enAkNþalElVg ¬ m25.1 BITRm¦ mmd 365=

kNVu 6.10725.15.3625.153 =×−= mkNM u .106

225.15.3625.162

2=+×=

MPavu 15.136525075.0

1.01010636525075.0

106.1072

63=

××

×⋅−

××⋅

=

dUcKña enAcm¶ay m9.1 BITRm ¬ m6.0 BIcugTMenr¦ mmd 300= kNVu 9.83= kNM u 8.43= kNvu 23.1= enAcm¶ay m2.2 BITRm ¬ m3.0 BIcugTMenr¦ mmd 270= kNVu 73= kNM u 2.20= kNvu 29.1= témøTaMgGs;enHRtUv)anbgðajenAkñúgrUbTI 8>20

7> kugRtaMgkmøaMgkat;TTwgedayebtugKW MPa9.02817.0 =

kugRtaMgkmøaMgkat;TTwgGb,brmaEdlRtUvTb;edayEdkkmøaMgkat;TTwg MPavus 48.09.038.1 =−=

¬ uv nig usv RtUv)anekIneLIgedaypleFob φ/1 kñúgsmIkar 8>28¦



8> eRCIserIsEdkkg 10DB EdlmanEdkBIr 21575.782 mmAv =×=

S ¬caM)ac;¦ mmbvfA

ws

ytv 52325048.0400157

=××

==

maxS ¬sRmab; 2d ¦ mm245= eTA mm120 enAcugTRm

maxS ¬sRmab;Gb,brma vA ¦ mmbfA

w

ytv 71825035.0400157

35.0=

××

==

9> epÞógpÞat;KMlatGtibrma :)2/(d cus fv '33.0≤ MPaMPaf c 48.074.12833.0'33.0 >==

10> karBRgayEdkkg ¬cm¶ayBIcugTMenr¦ EdkkgcMnYnmYymancm¶ay mm50 mm50= EdkkgcMnYndb;mancm¶ay mm120 mm1200= EdkkgcMnYnbImancm¶ay mm175 mm525= EdkkgcMnYnbI;mancm¶ay mm200 mm600= srub mm2375= dUcenHenAsl;cm¶ay mm125 BIépÞénmuxTRm.



8>11> Ggát;rgkarBt;CeRmAeRCA Ggát;rgkarBt;KYrRtUv)anKNnaCaFñwmeRCARbsinebIpleFobén clear span nl ¬Edlvas;BIépÞmuxTl;Kña rbs;TRm rUbTI 8>21¦ elIkm<s;srub h mantémøtUcCag 4 (ACI Code, Section 11.8) . Ggát;KYrrgnUvbnÞúk enAelIépÞEdlQmnwgépÞénTRm EdlGaceFVI[ strut rgkarsgát;GacbegáIteLIgenAcenøaHbnÞúk nigTRm ¬rUbTI 8>22¦. RbsinebIbnÞúkGnuvtþenA)at b¤épÞxagrbs;FñwmeRCA smIkarKNnakmøaMgkat;TTwgsRmab;FñwmFm μta Edl)an[BIxagmuxKYrRtUv)aneRbI. Ca]TahrN_ FñwmeRCAKWCaFñwmElVgxøIEdlRTbnþúkF¶n;/ CBa¢aMgbBaÄreRkam bnÞúkTMnajEpndI (gravity load), shear wall, nigkRmalxNÐrgnUvbnÞúkedk. niymn½yrbs;Ggát;rgkarBt;eRCAk¾RtUv)anbgðajenAkñúg ACI Code, Section 10.7.1. vabgðajfa Ggát;rgkarBt;EdlmanpleFob 4/ <hln nigtMbn;rgbnÞúkcMcMNucsßitenAcm¶ayBIrdgénkm<s;rbs;Ggát;BI épÞénTRmRtUv)ancat;TukCaGgát;rgkarBt;eRCA. FñwmEbbenHKYrRtUv)anKNnaedayKitnUvkarBRgay nonlinear



énkugRtaMg nigkarPøat;xag (lateral buckling) rUbTI 8>22 a.

rUbTI 8>22 a bgðajBIkarBRgaykugRtaMgeGLasÞic enARtg;muxkat;kNþalElVgénFñwmeRCA nigrUbTI

8>22 b bgðajBIExSekagkugRtaMgemenAkñúgFñwmeRCAEdlrgbnÞúkenAépÞxagelI (top-load deep beam). ExS Cab;bgðajBI karBRgaykugRtaMgTaj ÉExSdac;²bgðajBIkarBRgaykugRtaMgsgát;. eRkambnÞúkF¶n; sñameRbH bBaÄreRTtekItmanenAkñgebtugkúñgTisedAEkgnwgkugRtaMgTajem ehIyesÞIrEtRsbeTAnwgExSKnøgdac; ¬rUbTI 8>22 c ¦. dUcenH eKRtUvkarTaMgEdkedk nigEdkbBaÄredIm,ITb;nwgkugRtaMgem. elIsBIenH EdkrgkarBt; edaykarTaj (tensile flexural reinforcement) RtUv)andak;enARbEhlmYyPaKR)aMenA)atrbs;FñwmtamKnøg kugRtaMgTaj ¬rUbTI 8>22b ¦. CaTUeTA karviPaKFñwmeRCAmanlkçN³s μúKsμaj nigGacGnuvtþedayeRbIKMrU truss b¤edIm,ITTYl)anlT§plkan;EtsuRkiteKeRbIviFI finite element b¤viFIRsedogKña. edIm,IgayRsYlkñúgkarKNna kmøaMgkat;TTwgénFñwmeRCA eKGacGnuvtþtamCMhanEdl)anerobrab;xageRkam³

1> muxkat;eRKaHfñak; (critical section) ³ RbsinebImuxkat;eRKaHfñak;sRmab;KNnakmøaMgkat;TTwg enAkñúgFñwmeRCAEdlRTbnÞúkbBaÄrGnuvtþenAépÞxagelIrbs;Fñwm sßitenAcm¶ay X BIépÞénTRm enaHcM gay X GacRtUv)ankMNt;dUcxageRkam ¬rUbTI 8>23¦³

a. sRmab;FñwmeRCAEdlRTbnÞúkBRgayesμ I nlX 15.0= / Edl =nl clear span . b. sRmab;bnÞúkcMcMNuc 11 5.0 aX = ¬TRmxageqVg¦ b¤ 22 5.0 aX = ¬TRmxagsþaM¦ rUbTI

8>23/ Edl 1a nig 2a esμ Inwg shear span Ek,rTRmnImYy². Shear span

Cacm¶ayBIbnÞúkcMcMNuceTAépÞénTRm. enAkñúgRKb;krNITaMgGs; cm¶ay X / 1X nig 2X dac;xatminRtUvFMCagkm<s;RbsiT§PaB d .





2> ersIusþg;kmøaMgkat;TTwgGtibrma nVφ ³ ersIusþg;kmøaMgkat;TTwgGtibrma nVφ sRmab;Ggát;rgkar

Bt;eRCAminKYrmantémøFMCagtémøxageRkam ¬ 75.0=φ ¦³ sRmab; 2<

dln / dbfV wcn '67.0φφ = ¬*>#@ a ¦

sRmab; 52 ≤≤dln / dbf

dlV wcn

n '10055.0 ⎟⎠⎞

⎜⎝⎛ += φφ ¬*>#@ a ¦

b¤yk dbfV wcn '83.0φφ = ¬*>## ¦ krNITaMgBIr manEcgenAkñúg ACI Code, Section 11.8.3. RbsinebI nu VV φ> enaHeKRtUvdMeLIg muxkat;ebtug.

3> a. ersIusþg;kmøaMgkat;TTwgrbs;ebtug cV ³ ersIusþg;kmøaMgkat;Fm μta (nominal shear strength) cV rbs;ebtugGacRtUv)anKNnadUcxageRkam³

dbfV wcc '17.0= ¬*>#$ ¦ cV enHRsedogKñanwgersIusþg;kmøaMgkat;TTwgebtugsRmab;FñwmFmμta dUcenAkñúgEpñkxagmuxénem

eronenH. b. mü:agvijeTot eKGaceRbIsmIkarmYyepSgeTotEdlmanTak;Tgnwgm:Um:g;emKuN nigkmøaMgkat;

TTwgemKuNenAmuxkat;eRKaHfñak; db

MdVf

dVMV w

u

uwc

u

uc ⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−= ρ2.17'16.05.25.3 ¬*>#% ¦



b:uEnþ cV minKYrelIsBI dbf wc'5.0 témø ( )dVM uu /5.25.3 − minKYrFMCag 5.2 nigminKYrtUcCag 1. témøén uM nig uV RtUv)anykenARtg;muxkat;KNnaeRKaHfñak;. ersIusþg;kmøaMgkat;FMénsmIkar ¬*>#$ ¦ RtUv)aneRbICamYyKMnitfa sñameRbHEdltUcesÞIrEtemIlmineXIjGacekItmanenAkñúgFñwmeRCA nigGacGueRKaH)an. sñameRbHGaccab;epþIm ekItmanenARbEhlmYyPaKbIénbnÞúkemKuN.

4> EdkkmøaMgkat;TTwg³ enAeBlkmøaMgkat;TTwgemKuN cu VV φ> eKRtUvdak;EdkkmøaMgkat;TTwg Edlcat;Tukfa )( scu VVV +=φ b¤ φφ /)( cus VVV −= . CMhanénkarKNnamandUcxageRkam³

a. kMNt; sV ³ kmøaMgTb;edayEdkkmøaMgkat;TTwg sV RtUv)ankMNt;BIsmIkarxageRkam³ dfdl

SAdl

SAV y

n

h

vhn

v

vs ⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+⎟⎠⎞

⎜⎝⎛ +

=12

/1112

/1 ¬*>#^ ¦

Edl =vA RkLaépÞsrubénEdkkmøaMgkat;TTwgbBaÄrEdlmanKMlat vS ehIyEkgeTAnwgEdk emrgkarTajedaykarBt;énépÞxagTaMgBIrrbs;Fñwm =vhA RkLaépÞsrubénEdkkmøaMgkat;TTwgedkEdlmanKMlat hS RsbnwgEdkemrgkar

TajedaykarBt;énépÞxagTaMgBIrrbs;Fñwm b. KMlatEdkkmøaMgkat;TTwgKW³

KMlatQrGtibrma mmdSv 3005≤≤

KMlatedkGtibrma mmdSh 3005≤≤

c. EdkkmøaMgkat;TTwgGb,brma³ RkLaépÞEdkkmøaMgkat;TTwgbBaÄrKW vwv SbA 0025.0= . RkLaépÞEdkkmøaMgkat;TTwgedkKW hwvh SbA 0015.0= .

d. EdkkmøaMgkat;TTwgRtUvkarenARtg;muxkat;eRKaHfñak;KYrRtUv)anlatsn§wgeBjRbEvg nigkm<s; rbs;FñwmeRCA.

e. sRmab;FñwmeRCACab; EdkkmøaMgkat;TTwgdUcKñaKYrRtUv)aneRbIenARKb;ElVg RbsinebIElVgTaMgenaH manRbEvges μ IKñaCamYybnÞúkRsedogKña.

5> EdkrgkarBt;énFñwmeRCA³ dMeNIrRbRBwtþeTAénkarBt;rbs;FñwmeRCAKWmanlkçN³sμúKs μaj nigTam TarkarviPaKkugRtaMg nigbMErbMrYlrageFobtamlkçN³ nonlinear tamkm<s;rbs;Fñwm. sRmab;kar KNnadMbUg viFId¾sRmYlxageRkamGacRtUv)aneRbI³

)(yfAM ysn φφ = Edl =y édXñas; ( )2/ad −= . edaysartémø ( )2/ad − mankarBI)akkñgkarKNna/ éd



Xñas; y GacRtUv)anKNnaRbEhlykes μ Inwg h6.0 sRmab; 1/ =hln nigmantémø esμ Inwg h8.0 sRmab; 2/ =hln . viFanéRtzan (Linear interpolation) GacRtUv)an eRbIedIm,IKNna y enAeBl hln / ERbRbYlcenøaH 0.1 nig 0.2 . dUcenH³

y

us yf

MAφ

= ¬*>#&¦

témøén sA minGactUcCagEdkrgkarBt;Gb,brmaEdlRtUvkarsRmab;FñwmFm μtaEdlnwg[enAeBl bnÞab; edaysnμt; hd 9.0= .

sA ¬Gb,brma¦ dbf

dbf

fw

yw

y

c 38.1'25.0≥= ¬*>#*¦

GgÁTIBIrlub enAeBlEdl MPaf c 30' < . cMNaMfa yf nig cf ' KitCa MPa . EdkrgkarTajedaykarBt; (flexural tension reinforcement) KYrdak;enA 4/h eTA 5/h én

Fñwm nigKYrmanKMlatRKb;RKan;tambeNþay)attMbn;Taj. EdkrgkarTajKYrEtf<k;eTAkñúgTRm [)anl¥.

sRmab;karviPaK nigkarKNnaEdlmanlkçN³suRkwt nigsRmab;FñwmeRCACab; viFI nonlinear Edl manlkçN³hμt;ct;GacRtUv)aneRbIedIm,IbrimaNd¾RtwmRtUv nigkarBRgayénEdkrgkarTaj.

]TahrN_5³ FñwmeRCATRmsamBaØmanElVgRbEvg m2.4 man clear span RbEvg mln 6.3= km<s;srub mh 5.2= nigTTwg mmb 4.0= . FñwmeRCARTedaybnÞúkeFVIkarefBRgayesμ I mkN /600 ¬rYmbBa©ÚlbnÞúkpÞal;

xøÜn¦ nigbnÞúkGefr mkN /320 enAelIEpñkxagelIénFñwm. KNnasrésEdkrgkarBt; nigEdkkmøaMgkat;TTwg sRmab;FñwmenH edayeRbI MPaf c 28' = nig MPaf y 400= ¬rUbTI8>24¦. dMeNaHRsay³

1> KNnasRmab;EdkTb;nwgm:Um:g; mkNWWW LDu /12323206.16002.16.12.1 =×+×=+=

mkNLWM uu .56.2716

82.41232

8

22=

×==

44.15.26.3==

hln kMNt;édXñas;/ y . sRmab; 1/ =hln / dy 6.0= nigsRmab; 2/ =hln / dy 8.0= dUcenHsRmab;

44.1/ =hln / dy 688.0= ¬eday interpolation ¦ m55.15.29.0688.0 =××= ¬edaysnμt; hd 9.0= ¦

26

486840015509.0

1056.2716 mmyf

MAy

us =

××⋅

==φ



edaysar MPaf c 30' < sA ¬Gb,brma¦ 231052250400

40038.138.1 mmdb

f wy

=×==

dUcenH 24868mmAs = lb;. eRbI 2510DB ¬ 24909mm ¦EdlmanR)aMedImenAépÞmYy² edayBRgay kñúgkm<s; mmh 5005/ = EdlCatMbn;TajénFñwm. KMlatrbs;Edk mm1005/500 == . EdkTaMgenH KYrbgáb;cUleTAkñúgTRm[)anl¥.

2> KNnasRmab;kmøaMgkat;TTwg k> KNna uV nig uM enAcm¶ay dlx n == 15.0 BImuxépÞénTRm mmln 25.254.06.315.015.0 <=×=

KNna kNVu 3.155254.0123226.31232 =×−×=

mkNM u .9.1017254.0123254.06.31232

2=×−××=

29.025.23.1552

9.1017=

×=

dVM

u

u

x> KNna cV ³ ( ) 5.2775.229.05.25.35.25.3 >=−=−

dVM

u

u

dUcenH eRbI 5.2 . enAkñúgkrNIenH KNna dVM uu / edIm,IeRbIkñúgkarKNna cV ³ )/(5.25.35.2 dVM uu−=

4.0=dV

M

u

u b¤ 5.2=dM

V

u

u

00545.02250400

4909=

×==

dbA

w

swρ

( )[ ] kNVc 2.24321022504005.200545.02.172816.05.2 3 =××××+= − kNdbfV wcc 2.23812250400285.0'5.0 =××=≤

dUcenH kNVc 2.2381= lb;. kNVc 9.1785=φ K> KNna φφ /)( cus VVV −= edaysar kNkNVc 3.15529.1785 >=φ enaH 0=sV

dUcenHeKRtUvkarEdkkmøaMgkat;TTwgGb,brma. X> KNnaEdkkmøaMgkat;TTwg³ edaysnμt;eRbIEdk 12DB sRmab;dak;enAépÞsgçagTaMgtamTisedAedk nigTisedAQrenaH 22 226

4122 mmAA vhv =×==

π



KMlatGtibrmaGnuBaØatrbs;EdkQr nigEdkedk mmmmdSS vhv 300450

52250

5>==== yk mmSS nhv 300==

EdkQrGb,brma vA ¬Gb,brma¦= 22 2263003004000025.0 mmmm >=×× bBa©úHKMlatEdkkgbBaÄr mmSv 226

0025.0400226

=×

= EdkedkGb,brma vhA ¬Gb,brma¦= 22 2261803004000015.0 mmmm <=×× dUcenH eRbI 200@12DB sRmab;TisbBaÄr nig 300@12DB sRmab;Tisedk

3> RbsinebIeyIgeRbI dbfV wcc '17.0= enaH kNVc 6.8091022504002817.0 3 =×××= − nig kNkNVc 3.15522.607 <=φ . dUcenH eKRtUvkarEdkkmøaMgkat;TTwg.

kNVs 1.126075.0

2.6073.1552=

−=

edaysnμt;eRbIEdk 12DB sRmab;dak;enAépÞsgçagTaMgtamTisedAedk nigTisedAQrenaH 22 226

4122 mmAA vhv =×==

π edaysnμt;faKMlatrbs;EdkTaMgBIrTisedAesμ Inwg SSS hv == nig 6.125.2/6.3/ ==dln dfdl

SAdl

SAV y

n

h

vhn

v

vs ⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+⎟⎠⎞

⎜⎝⎛ +

=12

/1112

/1

225040012

6.11122612

6.112261260100 ×⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

+⎟⎠⎞

⎜⎝⎛ +

=SS

mmS 161= yk mmS 150= EdltUcCag vS ¬Gtibrma¦ nig hS ¬Gtibrma¦. eRbI mmS 150= sM rab;TaMgKMlatedk nigKMlatQr.

vA ¬Gb,brma¦= 22 2261501504000025.0 mmmm <=×× vhA ¬Gb,brma¦= 22 226901504000015.0 mmmm <=××

dUcenH eRbI mmDB 150@12 enAelIépÞTaMgBIrTaMgTisedAedk nigTisedAQr. sMNaj;EdkpSarGac RtUv)aneRbIedIm,ICMnYskarBRgayEdkEdlCadMeNaHRsaymYyEdlmanlkçN³snSMsMécCag. kar BRgayEdkenAkñúgmuxkat;ebtugRtUv)anbgðajenAkñúgrUbTI 8>24.



]TahrN_6³ FñwmeRCA strut and tie

FñwmeRCATRmsamBaØEdlman clear span m6.3= km<s;srub m8.1= nigTTwg mm450= . FñwmenHRT ssrkaerEdlmanRCug mm450= enAkNþalElVgEdlRTnUvbnÞúkefr kN1335= nigbnÞúkGefr kN1070= . KNnaFñwmenHedayeRbIviFI strut and tie. eK[ MPaf c 28' = nig MPaf y 400= ¬rUbTI8>25¦.



dMeNaHRsay³ 1> KNnabnÞúkemKuN ¬rUbTI 8>25¦

Tm¶n;Fñwm kN1.912545.08.15.4 =×××= edaysarTm¶n;pÞal;rbs;FñwmmantémøtUcebIeFobCamYybnÞúkcMcMNucenAkNþalElVg dUcenHbEnßmvaeTA kñúgbnÞúkGefrcMcMNucEdlmanGMeBIenAkNþalElVg

( ) kNLDPu 32.342310706.11.9113352.16.12.1 =×++=+= kNRR BA 66.1711==

2> epÞógpÞat;faetIFñwmenHeRCAtamkarEcgrbs; ACI Code, Section 11.8: clear span mln 6.3= nig mh 8.1= ehIy 42/ <=dln dUcenH FñwmenHCaFñwmeRCA.

3> KNnaersIusþg;kmøaMgkat;TTwgGtibrmaénmuxkat;Fñwm³ yk uV enARtg; kNRA A 66.1771== nigsnμt;yk mhd 62.18.19.09.0 =×==

kNdbfV wcn 1.27431016204502883.0'83.0 3 =×××== − un VkNV >=×= 3.20571.274375.0φ ¬OK¦

4> eRCIserIsKMrU truss eRCIserIsKMrU truss RtIekaN. snμt;facMNuc node eFVIGMeBIsßitenAG½kSTRm nigenAcm¶ay mm150 BI EKm)at b¤EKmkMBUlFñwm ¬rUbTI8>26¦. KMrU strut and tie pÁúMeLIgedayGgát; tie AB mYynigGgát; strut BIr AD nig DB . dUcKña Rbtikm μenARtg;cMNuc A nigcMNuc B nigbnÞúk uP Rtg;cMNuc D tMNagCa strut bBaÄr. RbEvg strut Ggát;RTUg mAD 52.2025.25.1 22 =+= yk θ CamMurvagGgát; strut nigGgát; tie enaH

7407.0025.25.1tan ==θ enaH oo 265.36 >=θ ¬OK¦

5> KNnakmøaMgenAkñúgGgát; truss ³ kmøaMgsgát;enAkñúgGgát; strut kNFFAD BDAD 6.2875

5.152.266.1711 ====

kmøaMgTajenAkñgGgát; tie kNFAB AB 231152.2025.26.2875 ===

6> KNnaersIusþg;RbsiT§PaB cef . snμt;EdkTb; (confining reinforcement) RtUv)andak;edIm,IkarBar kmøaMgbMEbk (splitting force). Ggát; strut AD nig DB tMNag[Ggát;rgkarsgát;ragdb (bottle-

shape compression member) dUcenH 75.0=sβ .



MPaff csce 85.172875.085.0'85.0 =××== β Ggát; strut bBaÄrenAcMNuc A / B nig D manmuxkat;es μ I (uniform section) dUcenH 0.1=sβ

MPaff csce 8.2328185.0'85.0 =××== β tMbn;cMNuc (nodal zone) D mankmøaMg CCC −− dUcenH 0.1=sβ . ersIusþg;RbsiT§PaBenA nodal

zone D KW MPaff csce 8.2328185.0'85.0 =××== β

edaysarEtGgát; strut AD nig DB P¢ab;eTAcMNucepSgeTot enaH MPafce 85.17= lb;elI nodal

zone TaMgGs;.

7> KNna nodal zone

k> KNna nodal zone enAcMNuc A ³ snμt;fakmøaMgén nodal zone mankugRtaMgdUcKñaKW MPa85.17 ehIyépÞEkgeTAnwgkmøaMgEdlRtUvKña

un FF ≥φ b¤ ucsce FAf ≥φ Edl 75.0=φ sRmab; strut, tie nig node.



RbEvgénépÞedk ab ¬rUbTI8>27 a¦ esμ Inwg mmbfF ceu 284)45085.1775.0/(1066.1711)/( 3 =××⋅=φ

BIFrNImaRt RbEvg mmac 38366.1711

2311284 == dUcKña RbEvg mmbc 477

66.17116.2875284 ==

TIRbCMuTm¶n;rbs; nodal zone sßitenA mm5.1912/383 = BI)aténFñwm ¬eyIg)ansnμt; mm150 ¦ x> KNna nodal zone enAcMNuc D ¬rUbTI8>27 b¦³ RbEvgénépÞedk ( ) mmde 56845085.1775.0/1032.3423 3 =××⋅= RbEvgén mmefdf 477

32.34236.2875568 ===

RbEvgrbs; mmfg 383)2

568(477 22 =−= dUcenH TIRbCMuTm¶n;én nodal zone sßitenA mm1283/383 = BIépÞxagelIrbs;Fñwm¬eyIg)ansn μt;

mm150 ¦ 8> KNnaEdkQr nigEdkedk³

k> EdkQr³ mMurvagEdkQr nigGgát; strut KW o5.53 BIrUbTI 8>27 a. eRbIEdk 16DB EdlmanKMlat mm300 / 22 402

4162 mmAs =×=

π ¬eCIgBIr¦/ 804.05.53sin =o 0024.0804.0)300450/(402sin)/( =××=issi SbA γ

x> Edkedk³ mMurvagEdkedk nigGgát; strut KW o5.36 BIrUbTI 8>27 a. eRbIEdk 16DB EdlmanKMlat mm300 / 22 402

4162 mmAs =×=

π ¬eCIgBIr¦/ 595.05.36sin =o 0018.0595.0)300450/(402sin)/( =××=issi SbA γ

K> issi SbA γsin)/( ¬srub¦ 003.00042.00018.00024.0 >=+= ¬OK¦ 9> KNnaGgát; tie edk AB ³

k> KNna sA ³ ysu fAF φ= ( ) 23 770340075.0/102311 mmAs =×⋅=

eRbI 3012DB ¬ 28482mmAs = ¦ dak;CabICYrdUcbgðajkñúgrUbTI 8>27 c. x> KNnaRbEvgf<k; (anchorage length)³ RbEvgf<k;RtUv)anvas;BIcMNuccab;BI nodal zone

¬rUbTI8>28¦. xo /1905.36tan =



mmx 257= RbEvgTMBk;Edlman 35225142257 −++= ¬kRmas;ebtugkarBarEdk¦ mm589= RbEvgTMBk;caM)ac;sRmab;Edk 30DB KW mmmm 5891425305.47 >=× dUcenHeRbITMBk; o90 cgP¢ab;CamYyEdkssr

( ) cbyedh fdfl '/02.0 λψ= 0.1== λψ e 30=bd

( ) mmmmldh 58954428/3040024.0 <=×=



]TahrN_7³ eKmanFñwmTRmsamBaØmYyEdlmanRbEvg m6 ¬ clear span ¦ rgnUvbnÞúkBRgayefr

mkN /5.47 nigbnÞúkBRgayGefr mkN /25 . FñwmenHmanmuxkat; cmb 35= nig cmd 55= . FñwmenHBRgwg edayEdk 254DB BRgaymYyCYr. cUrkMNt;nUvmuxkat;caM)ac;sRmab;kmøaMgkat;TTwg. sm μtikm μ³

MPaf c 28' = nig MPaf yt 280= .



dMeNaHRsay³ k> bnÞúkemKuN ¬bnÞúkKNna¦

mkNLD /97256.15.472.16.12.1 =×+×=+ x> kmøaMgkat;TTwgKNnaenARtg;muxxagssr

kNVu 2912697 =×=

K> kmøaMgkat;TTwgKNnaenAcm¶ay d BIépÞxagssr kNVud 65.237)9755.0(291 =×−=

X> ersIusþg;kmøaMgkat;TTwgEdlTb;edayebtug kNbdfV cc 2.1735503502817.0'17.0 =××==

kNVc 130=φ kNVc 65

21

=φ g> kmøaMgkat;TTwgEdlEdkRtUvTb;

kNVVV cus 5.143

75.0)2.17375.0(65.237=

×−=

−=

φφ

c> cm¶ayBImuxépÞssrmk kNVc 6521

=φ mx 33.23

29165291' =×

−=

q> KNnaEdkkg 1> eRCIserIsEdk 10RB ¬EdkkgmaneCIgBIr¦

22 1575.782 mmmmAv =×=⇒ mmmmm

VdfA

ss

ytv 6005.168105.143

55028015731 <=

×××

==⇒

dUcenHykKMlat mm160 RtYtBinitüKMlatGtibrma mmds 275

2550

22 ===

mmb

fAs ytv 8.376

35028015733

3 =××

==

321 sss << 2> RtYtBinitüKMlatGtibrmaes μ I

4d

kNbdfV cc 1.3365503502833.0'33.01 =×××== kNkNVV cc 2.6721.33622 12 =×==



eday 1cs VV < dUcenHKMlatEdkGtibrmakRmitRtwm mmds 2752max ==

C> kmøaMgkat;TTwgEdlTb;edayEdksRmab;KMlat mmds 2752max ==

kNs

dfA275mm sforV ytv

maxs 9.87275

550280157)(max

=××

===

kNkNVs 94.659.8775.0 =×=φ cm¶ayBImuxTRm eTAdl;EdkkgEdlmanKMlat mms 275max =

mx 98.03291

)94.65130(2911 =×

+−=

dUcenH sRmab; m98.0 BImuxénTRm eRbIEdkkg 10RB KMlat mm160 nigsRmab;EpñkenAsl; eRbIEdkkg Gb,brma ¬KMlatGtibrma¦ Q> karBRgayEdkkg

Edkkg1 manKMlat mms 802=

Edkkg6 manKMlat mmmm 960160 = srub mmmm 98.004.11040 >= Edkkg6 manKMlat mmmm 1620270 = srub mmmm 366.22660 <= nigEdkkgcugeRkay m34.0)66.23( =− srubEdkkgTaMgGs;EdlRtUveRbIsRmab;RbEvgFñwm m6 man 28kg.




kRmalxNÐmYyTis 231 T.Chhay

IX. kRmalxNÐmYyTis

9>1> RbePTkRmalxNÐ eRKOgbgÁúMkRmalxNÐebtugRtUv)ansagsg;eLIgedIm,Ipþl;nUvépÞrabes μ I CaTUeTAmanTisedAedk.

kRmalxNÐGacRTedayCBa¢aMg b¤edayFñwmebtugsrésEdkEdlCaTUeTARtUv)ancak;kñúgeBldMNalKñaCamYy kRmalxNÐ (cast monolithically with the slab) b¤edayFñwmEdk b¤edayssr b¤edaydI. CaTUeTAkRmas; kRmalxNÐman témøtUcebIeRbobeFobCamYynwgRbEvgElVg ¬rUbTI 9>1¦.

kRmalxNÐebtugenAkúñgGaKarGacEbgEckdUcxageRkam³ a. kRmalxNÐmYyTis (one-way slab)³ RbsinebIkRmalxNÐEdlRTedayRCugBIrQmKña enaHvanwgekag

b¤ dabkñúgTisedAEkgnwgRCugénTRm. GMeBIrbs;rcnasm½<n§KWmanEtmYyTis ehIybnÞúkEdlRTeday kRmal xNÐenAkñúgTisedAEdldabtUc. kRmalxNÐRbePTenHRtUv)aneK[eQ μaHfa kRmalxNÐmYy Tis ¬rUb TI 9>1a¦. RbsinebIkRmalxNÐRtUv)anRTedayRCugbYn ehIypleFobRCugEvgelIRCugxøIFM Cag b¤esμ Inwg 2 enaHbnÞúkPaKeRcIn ¬RbEhl %95 b¤eRcInCagenH¦RtUv)anRTenAkñúgTisedAxøI ehIy GMeBImYyTis RtUv)anBicarNasRmab;karGnuvtþn_TaMgGs; ¬rUb TI 9>1b¦. RbsinebIkRmalxNÐRtUv)an eFVIeLIgedayebtugBRgwgedayEdkedayKμanrnæxül; (no void) enaHeK[eQμaHfa kRmalxNÐmYy Tistan; (one-way solid slab) . rUb TI 9>1 c, d nig e bgðajBIbøg;BuH nigkarBRgayEdk.

b. RbB½n§kRmalxNÐrnUtmYyTis (one-way joist floor slab)³ kRmalxNÐRbePTenHeKk¾[eQμaHfa ribbed slab. vapSMeLIgedaykRmalxNÐEdlCaTUeTAmankRmas;BI mm50 eTA mm100 RTeday rnUtebtugGarem: (ribs or joist). CaTUeTArnUtmanragsþÜc nigmanKMlatesμ I²KñaminelIs mm750 . rnUt RtUv)anRTedayFñwmEdlsßitenAelIssr. KMlatrvagrnUtGacbegáIt)anedaykareRbIBum<Edk b¤ Bum<eFVIBI fiberglass rUbTI9>2. enAkñúgkRmalxNÐrnUtxøH KMlatrvagrnUtGacRtUv)anbMeBjeday filler edIm,IeFVI[kRmalxNÐEpñkxageRkamrabes μI.

c. RbB½n§kRmalxNÐBIrTis (two-way floor system)³ enAeBlEdlkRmalxNÐRTedayRCugbYn ehIy pleFobénRCugEvgelIRCugxøItUcCag 2 enaHkRmalnwgdabedaykMeNagDubelITisedATaMgBIr. bnÞúk kRmalxNÐRtUv)anbBa¢ÚnkñúgTisedABIreTAFñwmTaMgbYnEdlB½T§CMuvijkRmalxNÐ ¬eyagtamemeronTI 17¦. RbePTepSgeTotrbs;RbB½n§kRmalxNÐBIrTisman flat plate floor, flat slab nig waffle slab EdlkRmalxNÐTaMgenHnwgBnül;kñúgemeronTI17. kñúgemeronenHeyIgniyayEtBIRbB½n§kRmalxNÐ mYyTis.


T.Chhay 232 One-Way Slab

9>2> karKNnaénkRmalxNÐtan;mYyTis RbsinebIkRmalebtugcak;kñúgkRmas;esμ IedayKμanRbehag eKGacehAva)anfa kRmaltan;. enAkñúg

kRmalxNÐmYyTis (one-way slab) pleFobénRbEvgEvgrbs;kRmalxNÐelIRbEvgsøIrbs;vaFMCag 2. bnÞúkrbs;kRmalesÞIrEtTaMgGs;RtUv)anbBa¢ÚneTATisedAxøI ehIykRmalxNÐGaccat;TukdUcCaFñwm. ceRmok kRmalxNÐÉktþa CaTUeTAmanRbEvg m1 RtUv)ancat;TukCaFñwmctuekaN. FñwmenHmanTTwg m1 CamYynwgkm<s;



es μ InwgkRmas;kRmalxNÐ nigRbEvgElVgesμ Inwgcm¶ayrvagTRm. dUcenHkRmalxNÐmYyTispSMeLIgedayFñwm ctuekaNCaeRcInCab;²Kña ¬rUbTI9>1¦.

RbsinebIkRmalxNÐmanEtmYyElVg ehIyvasßitenAelITRmedayesrI enaHm:Um:g;viC¢manGtibrma M

sRmab;bnÞúkBRgayes μI w KW 8/)( 2wLM = Edl L KWCaRbEvgElVgrvagTRm. RbsinebIkRmalxNÐRtUv)an sagsg;eLIgkñúgeBldMNalKñaCamYy b¤Cab;enAelITRmCaeRcIn enaHm:Um:g;viC¢man nigGviC¢manRtUv)anKNna edaykarviPaKeRKOgbgÁúM (structural analysis) b¤edayviFIemKuNm:Um:g; (moment coefficient) sRmab;Fñwm Cab;. ACI Code, Section 8.3 GnuBaØat[eRbInUvemKuNm:Um:g; nigemKuNkmøaMgkat;enAkñúgkrNIkRmalxNÐ man eRcInElVgesÞIres μ IKña ¬rUbTI 9>3¦. krNIenHGaceRbI)ansRmab;ElVgBIrEdlenACab; b¤enAsgçagEvgCag ElVgEdlenA kNþal b¤ElVgCab;enaHticCag %20 . sRmab;bnÞúkBRgayesμ I bnÞúkGefrÉktþaminKYrFMCagbnÞúk efrÉktþa 3bI eT. RbsinebIlkçxNÐTaMgenHminRtUv)anbMeBjeTenaH eKRtUvkarkarviPaKeRKOgbgÁúM (structural

analysis). enAkñúgkarviPaKeRKOgbgÁúM m:Um:g;Bt;GviC¢manenARtg;G½kSrbs;TRmRtUv)anKNna. témøEdlRtUv BicarNaenAkñúgkarKNnaKWm:Um:g;GviC¢manenABImuxépÞénTRm. edIm,ITTYl)antémøenH eKRtUvdktémøm:Um:g; GtibrmaenAG½kSTRmeday 3/Vb Edl V CakmøaMgkat;TTwgEdl)anBIkarviPaKeRKOgpÁúM nig b KWCaTTwgrbs; TRm.

fM ¬enABImuxépÞénTRm¦ cM= ¬enARtg;G½kSénTRm¦3

Vb− ¬(>!¦



bEnßmBIelIm:Um:g; kmøaMgTajGgát;RTUg nigRbEvgf<k;énEdk KYrEtRtUv)anepÞógpÞat;sRmab;karKNnad¾ RtwmRtUv.

lkçxNÐEdlemKuNm:Um:g;sRmab;FñwmCab; nigkRmalCab;Edl[enAkñúgrUbTI 9>3 KYrRtUv)aneRbIGacRtUv segçbdUcxageRkam³

a. ElVgmanRbEvgesÞIesμ IKña³ ElVgEvg 2.1≤ ¬ElVgxøI¦

b. bnÞúkRtUvBRgayes μ I c. pleFob ¬bnÞúkGefr / bnÞúkefr¦ RtUvtUcCagb¤es μ Inwg 3.

d. sRmab;kRmalxNÐEdlmanElVgtUcCagb¤esμ I m3 m:Um:g;Bt;GviC¢manenABImuxépÞénTRmesμ Inwg 2

121

nulw .

e. sRmab;TRm A EdlminCab; nigmanPaBTMenr enaHemKuNm:Um:g;enARtg;cMnuc A KWes μ IsUnü nigRtg;cMnuc 11

1+=B

f. kmøaMgkat;TTwgenARtg;cMnuc 2/15.1 uulwC = nigenABImuxépÞTRmdéTeTotTaMgGs;esμInwg uulw2

1

g. =uM ¬emKuN¦ 2uulw / Edl =nl clear span.



9>3> EdnkMNt;kñúgkarKNnaEdlGnuelameTAtam ACI CODE

EdnkMNt;xageRkamRtUv)ankMNt;eday ACI Code³ a. ceRmokkRmalxNÐEdlmanTTwg m1 RtUv)ansnμt;.

b. kRmas;Gb,brmaénkRmalxNÐmYyTisEdleRbIEdk MPa400 Gnuelamtam ACI Code, Table 9.5a sRmab;kRmalxNÐtan;mYyTis nigsRmab;kRmalxNÐrnUtmYyTisKYres μ InwgtémødUcxageRkam³ - sRmab;TRmsamBaØ³ kRmalxNÐtan; (solid slab)/ 20/Lh = ¬kRmalxNÐrnUt (ribbed slab),

16/Lh = ¦

- sRmab;kRmalxNÐEdlCab;mçag³ kRmalxNÐtan;/ 24/Lh = ¬kRmalxNÐrnUt , 5.18/Lh = ¦

- sRmab;kRmalxNÐEdlCab;sgçag³ kRmalxNÐtan; / 28/Lh = ¬kRmalxNÐrnUt , 21/Lh = ¦

- sRmab;kRmalxNÐ cantilever: kRmalxNÐtan; / 10/Lh = ¬kRmalxNÐrnUt , 8/Lh = ¦

- sRmab; yf xusBI MPa400 enaHtémøTaMgGs;xagelIRtUvKuNnwg yf3105.14.0 −⋅+ Edl yf Kit Ca MPa . kRmas;Gb,brmaenHRtUv)aneRbITal;EtkarKNnaPaBdabbgðajfakRmas;tUcCagenHGac eRbIedayK μanplb:HBal;Rtlb;mkvij.

c. eKRtUvepÞógpÞat;PaBdabenAeBlTRmkRmalxNÐEdlP¢ab;eTAnwgsMNg;TMngCargeRKaHfñak;xøaMgeday PaBdabFM. PaBdabkMNt;RtUv)ankMNt;eday ACI Code, Table 9.5b .

d. eKcUlcitþeRCIserIskRmas;kRmalxNÐedaytMeLIg b¤bnßymþg mm10 .

e. eKRtUvepÞógpÞat;kmøaMgkat;TTwg ebIeTaHbIvaminmantémøFMk¾eday.

f. kRmas;ebtugkarBarEdk (concrete cover) enAkñúgkRmalxNÐebtugminRtUvtUcCag mm20 sRmab;épÞkRmalxNÐEdlRbQmnwgkarswk b¤b:HpÞal;nwgdI. kñúgkrNIenH 2/20 bdmmhd −−= eyagtamrUbTI 9>1 d .

g. sRmab;eRKagkRmalxNÐEdlmankRmas;esμ I enaHbrimaNEdkGb,brmaenAkñúgTisedArbs;kRmalxNÐ minRtUv tUcCagbrimaNEdktRmUvkarsRmab;karrYmmaD nigTb;nwgsItuNðPaB (shrinkage and

temperature reinforcement) eT (ACI Code, Section 7.12).

h. EdkemminRtUvmanKMlatFMCagkRmas;kRmalxNÐbIdg h3 b¤FMCag mm450 eLIy (ACI Code,

Section 7.6.5).



i. eKRtUveRbIRbB½n§EdkRtg;TaMgenAEpñkxagelI nigEpñkxageRkamrbs;kRmalxNÐCab;. eBlxøHeKk¾Gac eRbIRbB½n§EdkcRmuH ¬EdkRtg; nigEdkBt;¦pgEdr.

j. bEnßmBIelIEdkem eKk¾RtUvdak;EdkEdlEkgnwgEdkemEdr. EdkbEnßmenHeKehAfa Edkrg (secondary, distribution) EdkrYmmaD b¤EdksItuNðPaB (shrinkage or temperature

reinforcement).

9>4> EdksItuNðPaB nigEdkrYmmaD CaTUeTAebtugrYmmaDenAeBlEdlTwkkMe)arsIum:g;t¾rwg ehIyeK)anKitTunCamunnUvbrimaNBitR)akdén

karrYmmaD. RbsinebIkRmalxNÐRtUv)aneKdak;[cl½tedayesrIenAelITRmrbs;va enaHvanwgrYjedIm,ITTYlnUv karrYmmaD. b:uEnþkRmalxNÐ b¤Ggát;epSgeTotRtUv)anP¢ab;y:agrwgeTAnwgGgát;déTeToténeRKOgbgÁúM EdlbegáIt nUvkRmiténkarTb;y:agBitR)akdenAcug. CalT§pleKTTYl)ankugRtaMgTajEdleKsÁal;faCakugRtaMgrYm maD. karfycuHnUvkugRtMgEdlekItBIsItuNðPaB nigkugRtaMgEdlekItBIkarrYmmaD)aneFVI[ekItmansñameRbH b:unsréssk; (hairline crack). srésEdkEdkdak;enAkñúgkRmalxNÐKWedIm,ITb;Tl;nwgkarrYjxøI nigkarral dalénsñameRbH. edaysarEtebtugrYmmaD srésEdkrgnUvkarsgát;.

EdksRmab;karkugRtaMgrYmmaD nigkugRtaMgsItuNðPaBEdlEkgnwgEdkem RtUvdak;enAkñúgkRmalxNÐ EdlEdkemRtUv)andak;EtmYyTis. ACI Code, Section 7.12.2 kMNt;nUvGRtaEdkGb,brmadUcxageRkam³

- sRmab;kRmalxNÐEdleRbIEdk MPa280 b¤ MPa350 enaH %2.0=ρ - sRmab;kRmalxNÐEdleRbIEdk MPa400 b¤EdkpSar b¤EdksMNaj;pSar enaH %18.0=ρ K μankrNIEdlEdkRtUv)andak;manKMlatFMCag 5dgkRmas;kRmalxNÐ b¤FMCag mm450 eT. sRmab;EdkrYmmaD nigEdksItuNðPaB kRmas;ebtugTaMgmUl h EdlRbQmnwgkarrYmmaDRtUveRbIedIm,I

KNnaRkLaépÞEdk. ]TahrN_ RbsinebIkRmalxNÐmankRmas;srub mmh 150= nig MPaf y 400= enaH RkLaépÞEdkEdlRtUvkarsRmab;TTwgkRmalxNÐ m1 KW 22700018.01501000 mmAs =××= . KMlatEdk S GacKNnadUcxageRkam³

s

bA

AS

1000= ¬(>@¦

Edl =bA RkLaépÞEdkeRCIserIs =sA RkLaépÞEdkKNna ]TahrN_ RbsinebIeKeRbIEdk 10DB ¬ 25.78 mmAb = ¦ enaH mmS 290270/5.781000 =×=

yk mm250 . RbsinebIeKeRCIserIsEdk 12DB ¬ 2113mmAb = ¦ enaH mmS 418270/1131000 =×=



yk mm400 . EdkenHmantYnaTICaEdkrgEdlRtUv)andak;EkgnwgEdkemEdlRtUv)anKNnaedaykarviPaK edaykarBt; (flexural analysis).

9>5> lMGitsrésEdk enAkñúgkRmalxNÐmYyTisCab; RkLaépÞEdkemRtUv)anKNnaBIRKb;eRKaHfñak;TaMgGs; TaMgenAkNþalElVg

nigenATRm. kareRCIserIssrésEdk niglMGitsrésEdkGaRs½yeTAnwgRkLaépÞEdk KMlatRtUvkar nigRbEvg TMBk;. eKmanRbB½n§rayEdkBIrRbePT.

enAkñúgRbB½n§EdkRtg; ¬rUbTI9>4¦ EdkRtg;RtUv)aneRbIsRmab;dak;enAEpñkxagelI nigEpñkxageRkaménRKb; kRmalxNÐTaMgGs;. karcMNayelIfvikar nigeBlevlasRmab;plitEdkRtg; RtUvkarticCagkñúgkarplitEdk Bt; dUcenHRbB½n§EdkRtg;RtUv)anTUlMTUlayCagenAkñúgsMNg;.

enAkñúgRbB½n§EdkBt; b¤ trussed EdkRtg; nigEdkBt;RtUv)andak;qøas;KñaenAkñgkRmalxNÐ. TItaMgBt; RtUv)anepÞógpÞat;sRmab;karBt; kmøaMgkat;TTwg nigtRmUvkarRbEvgf<k;. sRmab;bnÞúkFm μtaenAkñúgsMNg; bøg;lMGitsrésEdksRmab;ElVgxag nigElVgkNþalénkRmalxNÐtan;mYyTisRtUv)anbgðajenAkñúgrUbTI 9>4.



9>6> karEbgEckbnÞúkBIkRmalxNÐmYyTiseTAFñwmTRm enAkñúgRbB½n§kRmalxNÐmYyTis bnÞúkBIkRmalxNÐRtUv)anbBa¢ÚneTAFñwmTRmtamcugEvgénkRmalxNÐ.

Fñwm bBa¢ÚnbnÞúkrbs;vaeTAssrTRm.

BIrUbTI 9>5 eyIgeXIjfa Fñwm 2B RTbnÞúkBIkRmalxNÐEk,rBIr. edaycat;TukCaFñwmRbEvg m1 bnÞúkbBa¢Ún

eTAFñwmes μ InwgRkLaépÞénceRmokTTwg m1 nigbeNþay S KuNnwgGaMgtg;sIuetbnÞúkEdlmanGMeBIelIkRmal xNÐ.

bnÞúkenHbegáItCabnÞúkBRgayesμ IenAelIFñwm SUU SB ⋅=

bnÞúkBRgayesμ IenAelIFñwmxag 1B esμ InwgBak;kNþalbnÞúkenAelIFñwm 2B edaysarEtvaRTkRmalxNÐEt mçag.

bnÞúkenAelIssr 4C es μ InwgRbtikmμBIFñwm 2B Ek,rBIr bnÞúkenAelIssr LSULUC SB ==4



bnÞúkenAelIssr 3C es μ InwgBak;kNþalbnÞúkenAelIssr 4C edaysarEtvaRTkRmalxNÐEtmçag. dUcKñacM eBaHbnÞúkenAelIssr 2C nig 1C KW³

bnÞúkenAelIssr == SLUC S 22 bnÞúkenAelIssr 3C bnÞúkenAelIssr

221SLUC S=

BIkarviPaKenH eyIgeXIjfassrnImYy²RTbnÞúkBIkRmalxNÐEdlenACMuvijssrenaH edayKitrhUtdl; G½kSénkRmalxNÐEk,r ¬ 2/L tamTisEvg nig 2/S tamTisxøI¦.

karBRgaybnÞúkBIkRmalxNÐBIrTiseTAFñwmTRm nigssrnwgBnül;enAkñúgemeronTI17.

]TahrN_TI1³ KNnaersIusþg;m:Um:g;KNnarbs;kRmalxNÐEdlmankm<s;srub mmh 175= nigBRgwgeday Edk 20DB EdlmanKMlat mmS 175= . eRbI MPaf c 20' = nig MPaf y 400= . dMeNaHRsay³

1> KNnakm<s;RbsiTæPaB d ³

220 bd

mmhd −−= ¬emIlrUb9>1 d¦ mmmmd 145

22020175 =−−=

2> KNna sA mFümEdlpþl;sRmab;TTwgkRmalxNÐ m1 . RkLaépÞénEdk 20DB KW 2314mmAb = mmmAs /1794

1753141000 2=

×=

3> eRbobeFobPaKryEdkEdleRbICamYynwg maxρ nig minρ . sRmab; MPaf c 20' = nig MPaf y 400= enaH 01374.0max =ρ nig 00333.0min =ρ .

ρ ¬eRbIR)as;¦ 0128.0)1401000/(1794 =×= EdlRKb;RKan; ¬ 9.0=φ ¦. 4> KNna )2/( adfAM ysn −= φφ

mmbffAa cys 2.42)10002085.0/(4001794)'85.0/( =×××== ( ) mkNM n .79.762/2.4214040017949.0 =−×××=φ

]TahrN_TI2³ kMNt;bnÞúkGefrBRgayesμ IGnuBaØatEdlGacGnuvtþenAelIkRmalxNÐén]TahrN_TI1 RbsinebI ElVgkRmalxNÐmanRbEvg m9.4 sßitenAcenøaHTRmsamBaØ nigRTnUvbnÞúkefrBRgayes μ I ¬K μanbBa©ÚlbnÞúkpÞal; xøÜn¦ 2/8.4 mkN . dMeNaHRsay³

1> ersIusþg;m:Um:g;KNnaénkRmalxNÐKW mkN.79.76 elIkRmalxNÐTTwg m1



8)9.4(

879.76

22uu

nuWLW

MM ==== φ bnÞúkBRgayesμ IemKuNKW 2/6.25 mkNWu =

2> LDWu 6.12.1 += 2/2.9251175.08.4 mkND =××+=

2/1.9 mkNL =

]TahrN_TI3³ KNnakRmalxNÐTRmsamBaØRbEvg m6.3 edIm,IRTbnÞúkefrBRgayesμ I ¬minrab;bBa©ÚlbnÞúk pÞal;xøÜn¦ 2/75.5 mkN nigbnÞúkGefrBRgayes μ I 2/8.4 mkN . eRbI MPaf c 20' = / MPaf y 400= nigkar kMNt;rbs; ACI Code. dMeNaHRsay³

1> snμt;kRmas;kRmalxNÐ. sRmab; MPaf y 400= kRmas;Gb,brmaedIm,IRKb;RKgPaBdabKW 20/L mm180= . snμt;kRmas;srub mmh 175= nigsnμt; mmd 150= ¬RtUvepÞógpÞat;enAeBleRkay¦.

2> KNnabnÞúkemKuN³ bnÞúkkRmalxNÐ 2/4.425175.0 mkN=×= 2/86.198.46.1)75.54.4(2.16.12.1 mkNLDWu =×++×=+=

sRmab;kRmalxNÐTTwg m1 / 8/2LWM uu = mkNM u .2.32

86.386.19 2

=×

= 3> KNna sA ³ sRmab; mkNM u .2.32= / mb 1= nig md 15.0= / MPabdMR uu 43.1/ 2 == /

01374.00042.0 max =<= ρρ / 9.0=φ . 263015010000042.0 mmbdAs =××== ρ

eRCIserIsEdk 12DB ¬ 2113mmAs = ¦/ nig mmS 179630/1131000 =×= epÞógpÞat; d BitR)akd/ mmd 149620175 =−−= GacTTYlyk)an. dUcenH mmS 175= nig 2645mmAs =

4> epÞógpÞat;ersIusþg;m:Um:g;énmuxkat;cugeRkay mm

bffA

ac

ys 2.1510002085.0

400645'85.0

=××

×==

mkNMmkNadfAM uysn .2.32.332

2.151504006459.02

=>=⎟⎠⎞

⎜⎝⎛ −××=⎟

⎠⎞

⎜⎝⎛ −= φφ

5> KNnaEdkrgEdlEkgnwgEdkem. sRmab; MPaf y 400= 0018.0min =ρ



231517510000018.0 mmAsh =××= eRCIserIsEdk 12DB / 2113mmAb = / mmS 7.358315/1131000 =×= dUcenHeRbI mmDB 350@12 sMeab;Edkrg.

6> epÞógpÞat;kmøaMgkat;TTwgcaM)ac;³ uV enAcm¶ay d BITRmKW kN8.32)15.08.1(86.19 =− kNbdfV cc 5.851015010002017.075.0'17.0 3 =××××== −φφ

kNVkNV uc 8.3275.4221

=>=φ dUcenHmuxkat;RKb;RKan;. 7> muxkat;cugeRkay mmh 175= / Edkem mmDB 175@12 nigEdkrg mmDB 350@12 .

]TahrN_TI4³ muxkat;kRmalxNÐtan;mYyTisCab;RtUv)anbgðajkñúgrUbTI 9>6. kRmalxNÐenHRTedayFñwm EdlmanRbEvg m2.7 . bnÞúkGefrmanGMeBIelIkRmalxNÐ)anmkBIbnÞúkpÞal;xøÜnbUknwg 2/7.3 mkN ehIy bnÞúkGefrKW 2/2.6 mkN cenøaHTRmsamBaØ. KNnakRmalxNÐCab; nigKUrnUvbøg;lMGitsrésEdk. eK[

MPaf c 20' = / MPaf y 280= . dMeNaHRsay³

1> kRmas;Gb,brmaénkRmalxNÐTI1KW 30/L edaysarcugmçagCab; nigcugmçageTotGt;Cab;. cm¶ayrvagG½kSFñwmGaccat;TukCaElVg mL 6.3= . sRmab; MPaf y 280= kRmas;srubGb,brma mmL 120

303600

30==

kRmas;srubGb,brmasRmab;ElVgkNþal mmL 10335

360035

== snμt;kRmas;rbs;kRmalxNÐesμ IKñaRKb;ElVg mmh 125= EdlFMCag mm120 . dUcenH eKmincaM)ac; epÞógpÞat;PaBdab.

2> KNnabnÞúk nigm:Um:g;enAelIceRmokÉktþa bnÞúkGefr=bnÞúkpÞal;xøÜn 7.3+ = 2/8.67.325125.0 mkN=+× bnÞúkemKuN 2/1.182.66.18.62.16.12.1 mkNLDU =×+×=+= RbEvg clear span KW m35.3 . m:Um:g;caM)ac;sRmab;ElVgTImYyenAelITRmEdlmanElVgCab;esI μnwg

10/2UL ( ) mkNUM u .3.20

1035.3 2

== 3> snμt; %4.1=ρ enaH MPaRu 12.3= témøenHtUcCag 0169.0max =ρ nigFMCag 005.0min =ρ

¬ 9.0=φ ¦



mmbR

Md

u

u 81100012.3103.20 6

=×⋅

== 21134811000014.0 mmbdAs =××== ρ

eRCIserIs 16DB kRmas;srub mmd 10920

216

=++= eRbIkRmas;kRmalxNÐ mm125 dUckarsnμt;xagelI km<s; d EdleRbIBitR)akd mm97820125 =−−=

4> m:Um:g; nigsrésEdkRtUvkarenARtg;muxkat;déTeTot edayeRbI mmd 97= mandUcxageRkam³ TItaMg emKuNm:Um:g; uM ).( mkN 2/ bdMR uu = )(MPa ρ (%) sA )( 2mm Edk nigKMlat

A 241− 8.46 tUc 0.00500 485 DB12@200

B 141+ 14.51 1.54 0.00646 627 DB16@300

C 101− 20.31 2.16 0.00928 900 DB16@200

D 111− 18.47 1.96 0.00836 811 DB16@200

E 161+ 12.70 1.35 0.00561 545 DB16@200

karBRgaysrésEdkRtUv)anbgðajenAkñúgrUbTI 9>7. 5> kmøaMgkat;TTwgekItmanenAkRmalxNÐxageRkAénTRmTI2/ muxkat; C 6> uV ¬Rtg; C ¦ kNULn 95.36

255.31.1815.12/15.1 =

××==

7> 3.55109710002017.075.0'17.0 3 =××××== bdfV cc φφ lT§plenHGacTTYlyk)an. cMNaMfa kardak;srésEdkkmøaMgkat;TTwgGb,brmaenAeBlEdl cu VV φ2

1> minRtUv)anGnuvtþsRmab;kRmalxNÐeT ¬ ACI Code, Section 11.5.5¦.

]TahrN_TI5³ kMNt;bnÞúkemKuNBRgayesμ IenAelIFñwmkNþalEdlRTkRmalxNÐén]TahrN_TI 4. dUcKña KNnabnÞúkcMG½kSenAelIssrkNþal eyagtambøg;TUeTAénrUbTI9>5.



dMeNaHRsay³ 1> bnÞúkemKuNBRgayes μ IkñúgmYyEm:RtRbEvgenAelIFñwmkNþalesμInwgbnÞúkemKuNBRgayes μ IenAlIkRmal

xNÐKuNnwg S EdlCaRCugxIørbs;kRmalxNÐ. dUcenH U ¬Fñwm¦=U ¬kRmalxNÐ¦ S× = mkN /8.688.31.18 =×

bnÞúkrbs;FñwmKYrRtUv)anKitbBa©Úl. RbEvgrbs;FñwmKW m2.7 kMNt;km<s;srub mLh 288.08.0

202.78.0

20=×=×= yk mm300

kRmas;kRmalxNÐKW mm125 dUcenHkm<s;énRTnugrbs;FñwmKW mm175125300 =− bnÞúkemKuNénRTnugFñwm mkN /3.12.12525.0175.0 =×××= bnÞúkBRgayesμ IsrubelIFñwm mkN /1.703.18.68 =+=

2> bnÞúkenAleIFñwmkNþal mkNPu /72.5042.71.70 =×=

9>7> RbB½n§kRmalxNÐrnUtmYyTis (One-Way joist Floor System) RbB½n§kRmalxNÐrnUtmYyTispSMeLIgedaykRmalxNÐRbehag (hollow slab) CamYykm<s;srubFMCag

kRmas;rbs;kRmalxNÐtan;mYyTis. kRmalxNÐenHmanlkçN³snSMsMécsRmab;GKarEdlmanbnÞúktUc nig manElVgEvg dUcCa salaeron mnÞIreBTü nigsNæaKar. bnÞúkenAkñúgtMbn;TajK μan\TæiBldUcenH tMbn;enHRtUv )anTuk[RbehagrvagrnUt b¤RtUv)anbMeBjCamYysSmÖar³EdlmanTm¶n;Rsal edIm,Ikat;bnßyTm¶n;pÞal;rbs; kRmalxNÐ.

viFIsaRsþkñúgkarKNna nigtRmUvkarénkRmalxNÐrnUt (ribbed slab) GnuvtþdUckarKNnaFñwmmuxkat;ctu ekaN nigFñwmmuxkat;GkSret EdlmanenAkñúgemeronTI3. cMnucxageRkamRtUv)anGnuvtþsRmab;KNnakRmal xNÐrnUtmYyTis.

1 rnUt (rib) manragsþÜcxageRkam nigmanKMlatdUc²KñaRbEhl mm400 eTA mm750 . Rbehag RtUv)anbegáItrUbragedayeRbIBum<EdlmanTTwg mm500 nigCeRmA mm150 eTA mm500 GaRs½y eTAelItRmUvkarénkarKNna. kMeNInbTdæanrbs;km<s;KWmþg mm50 .

2 rnUtminRtUvmanTTwgtUcCag mm100 nigminRtUvmanCeRmAFMCagTTwg 5.3 dg. KMlat clear

spacing rvagrnUtminRtUvFMCag mm750 (ACI Code, Section 8.11). 3 ersIusþg;kmøaMgkat;TTwgEdlpþl;edayebtugsRmab;rnUtGacykes μ Inwg %10 FMCagersIusþg;kmøaMg

kat;TTwgEdlpþl;edayebtugsRmab;Fñwm. mUlehtucMbgKWbNþalmkBIGnþrkm μrvagkRmalxNÐ nigrnUtEdlmanKMlatCit²Kña (ACI Code, Section 8.11.8).



4 CaTUeTAkRmalxNÐenABIelIrnUtmankRmas;BI mm50 eTA mm100 nigmanEdkGb,brma ¬EdkrYm maD¦. kRmas;enHminRtUvtUcCag 12/1 én clear span rvagrnUt b¤ mm50 (ACI Code, Section

8.11.6). 5 emKuN ACI sRmab;KNnam:Um:g;enAkñúgkRmalxNÐCab; GacRtUv)aneRbIsRmab;KNnakRmalxNÐ

rnUtCab;. 6 eKmanEdnkMNt;bEnßmmYycMnYn EdlRtUv)ansegçbdUcxageRkam³

- TTwgGb,brmarbs;rnUtKW mYyPaKbIénkm<s;srub b¤ mm100 edayykmYyNaEdlFMCag. - EdkrgenAkñúgkRmalxNÐenAkñúgTisedAEkgnwgrnUtminKYrtUcCagbrimaNEdkrYmmaD b¤tUcCag

5/1 énRkLaépÞEdkemenAkñúgrnUt. - EdkrgEdlRsbnwgrnUtKYrdak;enAkñúgkRmalxNÐ ehIyKMlatrbs;vaminRtUvmancm¶ayFMCag

Bak;kNþalénKMlatrvagrnUt. - RbsinebIbnÞúkGefrenAelIkRmalxNÐrnUttUcCag 2/3 mkN ehIyRbEvgrbs;rnUtFMCag m5

enaHrnUtTTwgrg (secondary transverse rib) RtUv)andak;enAkNþalElVg ¬TisedArbs;vaKW EkgnwgTisedArbs;rnUtem¦ nigBRgwgedayEdkEdlmanbrimaNesμ InwgbrimaNEdkenAkñúgrnUt em. EdkxagelIrbs;vaminRtUvtUcCagBak;kNþalEdkemenAkñúgtMbn;Taj. rnUtrgmannaTI BRgwgkRmalxNÐ (floor stiffener) .

- RbsinebIbnÞúkGefrFMCag 2/3 mkN ehIyrnUtemmanRbEvgERbRbYlcenøaHBI m4 eTA m7 eK RtUvdak;rnUtrgmYydUcbgðajxagelI. RbsinebIrnUtemmanRbEvgFMCag m7 y:agehacNas; rnUtrgBIrRtUv)andak;CamYynwgsrésEdkdUckarENnaMxagelI.

]TahrN_TI6³ kMNt;kRmalxNÐrnUtmYyTisenAxagkñúgCamYynwgTinñn½yxageRkam³ RbEvgrnUt m6 ¬TRm samBaØ¦ bnÞúkefr ¬edaymin)anbBa©ÚlbnÞúkpÞal;¦ 2/75.0 mkN bnÞúkGefr 2/1.4 mkN / MPaf c 28' = nig

MPaf y 400= . dMeNaHRsay³

1> KNnakRmalxNÐ³ snμt;kRmas;kRmalxNÐxagelIesμ Inwg mm50 EdlP¢ab;CamYynwgrnUtEdlman clear span mm500 . sSmÖar³edIm,IbMeBj (filler) minRtUv)aneRbI. bnÞúkpÞal;rbs;kRmalxNÐKW

25050.0 × 2/25.1 mkN= . bnÞúkefrsrub 2/.275.025.1 mkND =+=

2/91.46.122.16.12.1 mkNLDU =×+×=+=



12

2ULM u = ¬kRmalxNÐRtUv)ancak;Cab;CamYynwgrnUt¦

mkNM u .19.012

5.09 2=

×=

edaycat;Tukm:Um:g;enAkñúgkRmalxNÐRtUvRTedayebtugsuTæ enaHersIusþg;TajedaykarBt;GnuBaØatrbs;ebtugKW ct ff '415.0= CamYynwgemKuNkat;bnßyersIu sþg; 55.0=φ / MPaft 2.228415.0 == . ersIusþg;TajrgkarBt; tfI

Mc φ== 46

331042.10

12501000

12mmbhI ⋅=

×==

mmhc 252==

mkNMmkNcIfM ut .19.0.5.010

251042.102.255.0 6

6=>=⋅

⋅××== −φ ¬muxkat;RKb;RKan;¦

EdkrYmmaD 2905010000018.0 mmAs =××=

Edk 10DB manKMlat mm300 RtUv)andak;EkgnwgTisedArbs;rnUt. sMNaj;EdkpSar (welded

wire fabric) manlkçN³snSMsMécsRmab;krNIbrimaNEdktic. eRbIEdk 10DB manKMlat mm300 sRmab;dak;RsbnwgTisedArnUt edayEdkmYyedImRtUv)andak;enA BIelIrnUtnImYy² nigEdkmYyeTotRtUv)andak;enAcenøaHkNþalrnUtBIr.

2> KNnam:Um:g;enAkñúgrnYt km<s;Gb,brma mL 3.0

206

20===

km<s;srubrbs;rnUtnigkRmalxNÐKW mm30050250 =+ snμt;TTwgrnUtEpñkxageRkamKW mm100 nigEpñkxagelI ¬nIv:U)atkRmalxNÐ¦KW mm150 rUbTI9>8. TTwgmFümrbs;rnUtKW mm125 cMNaMfa kMeNInénTTwgrbs;rnUtedayeRbIBum<cl½tEdlmanpleFob 12/1 ¬edk 1 nigQr 12¦ Tm¶n;rnUt= mkN /78.02525.0125.0 =×× rnUtRTnUvbnÞúkmkBIkRmalxNÐEdlmanTTwg mm600 bUknwgbnÞúkpÞal;rbs;va

mkNU /35.678.02.16.09 =×+×= mkNULM u .6.28

8635.6

8

22=

×==

3> KNnarnUt³ km<s;srubrbs;rnUtKW mm300 . snμt;eRbIEdk 16DB nigkRmas;ebtugkarBarEdk mm20



km<s;RbsiTæPaB mmd 272820300 =−−= BinitüemIlersIusþg;énsøab ¬snμt;muxkat; tension-controlled section/ 9.0=φ ¦

nMφ ¬søab¦ ⎟⎠⎞

⎜⎝⎛ −=

2tdCφ Edl btfC c'85.0=

( ) mkNM u .7.158102

50272506002885.09.0 6 =⋅⎟⎠⎞

⎜⎝⎛ −×××= −

ersIusþg;m:Um:g;ebs;søabFMCagm:Um:g;Gnuvtþn_ dUcenHrnUtmannaTICamuxkat;ctuekaNEkgEdlmanTTwg mmb 600= nigkm<s;énbøúkrgkarsgát;smmUl a KWtUcCagkRmas;kRmalxNÐ mm50 .

)'7.1

(2 bf

fAdfAadfAM

c

ysysysn −=⎟

⎠⎞

⎜⎝⎛ −= φφφ

⎟⎠⎞

⎜⎝⎛

×××

−×=⋅600287.1

4002724009.0106.28 6 s

sA

A 2297mmAs =

mmmma 5032.86002885.0

400297<=

×××

= eRbIEdk 162DB sRmab;rnUtmYy ( )2402mm

22min 2972.1122721250033.00033.0 mmmmdbA ws <=××==

BinitüemIl 019.0018.0

272600297

max =<=×

= ρρ EdlCamuxkat; tension-controlled section/ 9.0=φ .

4> KNnakmøaMgkat;TTwgenAkñúgrnUt³ ersIusþg;kmøaMgkat;TTwgGnuBaØaténRTnugrnUtKW kNdbfV wcc 2.25102721252817.01.175.0'17.0)1.1( 3 =××××××=×= −φφ

kmøaMgkat;TTwgemKuNenAcm¶ay d BITRmKW ( ) kNVkNV cu 2.253.17272.0335.6 =<=−×= φ

dUcenHEdkkgGb,brmaRtUv)aneRbI ehIykrNIenHEdk 12DB RtUv)anbEnßmenAkñúgkRmalxNÐEpñk xagelIedIm,ITb;Edkkg. vaCakarRbesIreBsinebIeKbEnßmrnUtrgmYyenAkNþalElVgEkgnwgrnUtem ehIymanbrimaNEdkdUcKñanwgrnUtem edIm,IeFVI[kRmalxNÐmanlkçN³rwgmaM.




T.Chhay 248 Axial Loaded Column

X. ssrrgkmøaMgcMG½kS

10>1> esckþIepþIm ssrCaeRKOgbgÁúMd¾sMxan;sRmab;RTnUvbnÞúksgát;cMG½kS ehIymanpleFobssrelIRCugxagEdltUc

CageK FMCag 3. sRmab;sMNg;ebtugGarem: Fñwm kRmal nigssrRtUv)ancak;kñúgeBlEtmYy (monolithic)

EdleFVI[manm:Um:g;xøH manGMeBIelIssredaysarkarTb;enAxagcug. elIsBIenHeTot ssrsRmab;GaKar eRcInCan; kartRmg;ssrtamTisQr minGaceFVIeTA)an\tex©aHenaHeT EdlbegáIt[mankmøaMgcakp©iteday eFobeTA nwgG½kSssr. kmøaMgcakp©itbegáIt[manm:Um:g;elIssr. dUcenH ssrEdlrgnUvbnÞúktamG½kSsuT§min GacekItmanenAkñúgsMNg;ebtugGarem:eT. EteKGacsnμt;fa ssrrgkmøaMgcMG½kS kalNavamancg¶aycakp©it e tUc EdlmantémøRbEhl h1.0 . h CaCeRmAsrubrbs;ssr nig e Cacg¶aycakp©itBIG½kSssr. edayeb tugmanersIusþg;sgát;x<s; ehIyvaCasmÖar³Edlmantémøminéfø dUcenHvaRtUv)aneKeRbIedIm,IKNnasRmab;eRKOg bgÁúMrgkmøaMgsgát; edaymanlkçN³esdækic©x<s;.

10>2> RbePTssr ssrRtUv)anEbgEckedayQrelIeKalkarN_epSg²dUcxageRkam³

i. QrelIeKalkarN_bnÞúk ssrcat;cMNat;fñak;dUcxageRkam³ + ssrrgbnÞúkcMG½kS EdlbnÞúkRtUv)ansn μt;manGMeBIenAcMG½kSénmuxkat;ssr + ssrrgbnÞúkcakp©it EdlbnÞúkmanGMeBIenAcg¶ay e BIG½kSénmuxkat;ssr. cg¶ay e GacsßitenA

tamG½kS x b¤ G½kS y EdlbegáIt)anCam:Um:g;tamG½kS x b¤ G½kS y . + ssrrgbnÞúkcakp©itBIrTis EdlbnÞúkRtUv)anGnuvtþenAcMNucNamYyénmuxkat;ssr ehIyEdl

begáIt)anCam:Um:g;tamG½kS x nigG½kS y . ii. QrelIeKalkarN_RbEvgssrcat;cMNat;fñak;dUcxageRkam³

+ ssrxøI Edlssr)ak;edaykarEbkebtug b¤EdkeFVIkardl;cMnuc yield eRkamlT§PaBRTRTg;bnÞúk eBjrbs;ssr

+ ssrEvg EdlkarPøat; nigPaBrlas;RtUv)anykmkBicarNa dUcenHlT§PaBRTRTg;bnÞúkrbs;ssr RtUv)ankat;bnßyebIeFobnwgssrxøI

iii. QrelIeKalkarN_rUbragénmuxkat; muxkat;ssrGacmanragCa kaer ctuekaNEkg mUl >>>> b¤rUbrag cg;)anNamYy.

iv. QrelIeKalkarN_EdkkgTTwg ssrRtUv)anEbgEckCa³


ssrrgkmøaMgcMG½kS 249 T.Chhay

+ ssrEdlmanEdkkgdac;²BIKña EdlmantYnaTIhMuB½T§EdkbBaÄrem. EdkkgCaTUeTAmanKMlatdUc² KñaeBjmYykm<s;ssr.

+ ssrEdlmanEdkkgvNÐ EdlmantYnaTIhMuB½T§EdkbBaÄrem ehIyCYybegáInPaByWtrbs;ssrmun eBl)ak;. CaTUeTA Edkkg nigEdkkgvNÐ RtUv)aneKeRbIedIm,IkarBarPaBrlas;rbs;ssr kugRtaMgEdk bBaÄrEdlekItBIkarPøat; nigkarpÞúHEbkénebtugkarBarsrésEdk.

v. QrelIeKalkarN_viPaKeRKag ssrCaEpñkmYyéneRKagEdlmanCnÞl;RbqaMgnwgkareRTtcMehog nig CaEpñkmYyéneRKagEdlminmanCnÞl;RbqaMgnwgkareRTtcMehog. cnÞl;Gac)anmkBIkareRbICBa¢aMgeb tugGarem: b¤cnÞl;BIeRKag. sRmab;eRKagmancnÞl; ssrCaeRKOgbgÁMúEdleRbIsRmab;Tb;nwgbnÞúkTMnaj ehIyCBa¢aMgebtugGarem:RtUv)aneKeRbIedIm,ITb;nwgkmøaMgtamTisedk nigbnÞúkxül;. ÉeRKagKμancnÞl; ssrCaeRKOgbgÁúMEdleRbIedIm,ITb;nwgbnÞúkTMnajpg nigbnÞúkxül;pg dUcenHlT§PaBRTRTg;rbs;ssr RtUv)ankat;bnßy.

vi. QrelIeKalkarN_smÖar³ ssrGacCassrebtugGarem: ssrebtugeRbkugRtaMg ssrsmas. ssrebtugGarem:RtUv)aneKeRbICaTUeTAsRmab;sMNg;GKar.



10>3> kareFVIkarrbs;ssrrgbnÞúkcMG½kS enAeBlEdlbnÞúkmanGMeBIcMG½kSénssrxøIebtugGarem: ebtugRtUv)anBicarNa[eFVIkarCalkçN³eGLa

sÞic enAeBlEdlvargnUvkugRtaMgTabEdlmantémøRbEhl cf '31 . RbsinebIbnÞúkEdlmanGMeBIenAelIssrxit

eTArkersIusþg;Gtibrmarbs;va enaHebtugxiteTArkersIusþg;Gtibrma ehIyEdkk¾xiteTArkersIusþg; yield yf . lT§PaBRTRTg;bnÞúkcugeRkaymFümrbs;ssr GacsresrdUcxageRkam³

ystnco fAAfP += '85.0 Edl nA nig stA CaRkLaépÞebtugsuT§ nigRkLaépÞEdk

stgn AAA −= gA Camuxkat;rgGMeBI

kar)ak;rbs;ssr ekIteLIgBIrRbePTepSgKña GaRs½yeTAnwgkareRbIR)as;Edkkg nigEdkkgv½NÐ. sRmab;ssrEdkkg ebtug)ak;edaypÞúHEbkpÞat;ecjeRkA EdkembBaÄr)ak;edayPøat;ecjcenøaHEdkkg dUcenH ssr)ak;ekIteLIgPøam². sRmab;ssrEdkkgv½NÐ)ak;edaymankarbgðajnUvrMhUr EdlekItmannUvkMhUcRTg; RTayEdlGacKit)an munnwgkar)ak;eBjelj.

10>4> lkçxNÐrbs; ACI Code ACI Code )anbgðajnUvlkçxNÐmYycMnYndUcxageRkamkñúgkarKNnaeRKOgbgÁúMrgkarsgát;³ - sRmab;ssrrgkarsgát;cMG½kS k¾dUccakp©it ACI Code )ankMNt;ykemKuNkat;bnßyersIusþg;

65.0=φ sRmab;ssrEdlmanEdkkgdac;² nig 7.0=φ sRmab;ssrEdlmanEdkkgv½NÐ. témøxusKña 05.0 bgðajGMBIPaBsVitrbs;ssrEdlmanEdkkgv½NÐ. emKuNkat;bnßyersIusþg;sRmab;ssrmantémøtUc

CagsRmab;eRKOgbgÁúMrgkarBt; nigkMmøaMgkat;TTwg enHedaysarEtersIusþg;rbs;ssrrgkarsgát;cMG½kSGaRs½y CacMbgeTAnwgersIusþg;rbs;ebtug EdlpÞúyBIeRKOgbgÁúMrgkarBt;EdlTTYl\T§iBlticCagBIersIusþg;ebtug CaBi esskñúgkrNI tension failure section. elIsBIenHeTot rgnUvkarbMEbkFatul,ayebtugeRcInCagkrNIFñwm. ssrRtUvcak;bBaÄrx<s; nigBum<ceg¥ót b:uEnþebtugkñúgFñwmRtUv)ancak;kñúgBum<rak; edk. dUcenHkar)ak;rbs;ssr enAkñúgeRKagRtUv)aneKBicarNaeRcInCagFñwmkRmal.



- PaKryEdkemGb,brma %1 nigGtibrmaKW %8 énmuxkat;ssr. muxkat;EdkGb,brmaRtUv)an dak;sRmab;Tb;nwgkarBt;EdlvaGacekItmaneLIg nigCYykat;bnßy\T§iBl creep nigkarrYmmaDrbs;ebtug eRkamGMeBIénkugRtaMgsgát;. sRmab;karGnuvtþ vaCakarBi)akbMputkñúgkarBRgayEdkEdlmanmuxkat;eRcInCag

%8 eTAkñúgssr BIeRBaHeKRtUvkarKMlatEdksmrmüedIm,I[ebtugeRcotcUlcenøaHEdk. - y:agehacNas;EdkbYnedImRtUv)andak;sRmab;ssrctuekaN nigssrmUlEdlmanEdkkgdac;²

nigEdkR)aMmYyedImsRmab;ssrmUlEdlmanEdkkgv½NÐ. sRmab;muxkat;ssrepSgeTot EdkRtUv)andak;RKb; RCugTaMgGs;. EdkminRtUv)andak;edaymanKMlatFMCag cm15 . kñúgkrNIEdkmanKMlatFMCag cm15 eKRtUv dak;EdkkgbEnßm. RsTab;ebtugkarBarEdkGb,brma mm40 .

- PaKryKitCamaDénEdkkgvNÐelImaDrbs;sñÚlssr sρ RtUv)ankMNt;³

yt

c

c

gs f

fAA ')1(45.0 −=ρ

Edl gA muxkat;ssr cA muxkat;ssrKitRtwmEpñkxageRkAEdkkgv½NÐ ytf ersIusþg;Edkkg



- muxkat;EdkkgvNÐGb,brma mm5.9 nigmanKMlatcenøaH cmcm 5.75.2 → . kartEdkeFVIeLIg edaypSarehIyRbEvgtEdksRmab;fñaMgGMeBA d48 nigFMCag cm30 sRmab;Edkrelag φ72 nigFMCag cm30 .

- Ggát;p©iténEdkkgdac;²Gb,brma mm5.9 RtUv)aneRbIedIm,IrMuB½T§EdkbBaÄrEdlmanGgát;p©ittUcCag mm32 nigsRmab;EdkbBaÄrEdlmanGgát;p©itFMCag mm32 EdkkgRtUvmanGgát;p©it mm12 .

- KMlatEdkkgminRtUvmantémøFMCag

⎪⎩

⎪⎨

⎧

bd16

48min

φ

Edl φ Ggát;p©itEdkkg/ d Ggát;p©itEdkbBaÄr/ b RCugEdlmanTMhMtUcCageKénmuxkat;ssr.

10>5> smIkarsRmab;KNna bnÞúkEdlssrGacRT)anRtUv)ankMNt;edaysmIkar

ystnco fAAfP += '85.0 EtCaTUeTA ssrminEdlrgbnÞúkcMG½kSeT vaEtgEtrgbnÞúkcakp©itbnþic dUcenH ACI Code )anKuNnwg

emKuN 8.0 sRmab;ssrEdlmanEdkkgdac;² nig 85.0 sRmab;ssrEdlmanEdkvNÐ. sRmab;ssrEdlmanEdkkgdac;² bnÞúkemKuNEdlssrGacRT)ankMNt;eday

])('85.0[8.0 yststgcnu fAAAfPP +−== φφ nig 65.0=φ sRmab;ssrEdlmanEdkkgv½NÐ emKuNEdlssrGacRT)ankMNt;eday

])('85.0[85.0 yststgcnu fAAAfPP +−== φφ nig 7.0=φ smIkarxagelITaMgBIrGacsresry:agsegçbdUcxageRkam³

)]'85.0('85.0[ cystgcnu ffAAfkPP −+== φφ Edl 65.0=φ nig 8.0=k sRmab;ssrEdlmanEdkkgdac;² nig 7.0=φ nig 85.0=k sRmab;

ssrEdlmanEdkkgv½NÐ. smIkarxagelIRtUv)aneRbIedIm,IKNnalT§PaBRTRTg;rbs;ssrrgbnÞúkcMG½kS. RbsinebIpleFobEdk

g

stg A

A=ρ enaHsmIkarxagelIkøayeTACa

)]'85.0('85.0[ cygcgnu fffkAPP −+== ρφφ smIkarxagelIenHvij RtUv)aneRbIedIm,IKNnamuxkat;ssr edaysn μt;PaKryEdlenAcenøaH %8%1 → .



10>6> kmøaMgTajcMG½kS ebtugnwgminmansñameRbHeT ebIvargnUvkugRtaMgEdlmantémøTabCagersIusþg;rgkarTajrbs;va kñúg

krNIenH TaMgebtug nigEdkTb;nwgkugRtaMgTaj. b:uEnþenAeBlEdl kmøaMgTajmantémøFMCagersIusþg;rgkar Tajrbs;va ¬RbEhl

101 énersIusþg;rgkarsgát;rbs;ebtug¦ sñameRbH)anekItmanenAelImuxkat;ebtug ehIy

kmøaMgTajTaMgGs; RtUvTb;Tl;edayEdk. bnÞúkFm μtaEdlGgát;TTYl)anKWCaersIusþg;Tajrbs;Edk³ ystn fAT =

ystu fAT φ= 9.0=φ sRmab;karTajcMG½kS

sRmab;Ggát;EdlrgkarTaj ebtugeRbH ehIyr)arEdkrgnUvbnÞúkTajTaMgGs; ebtugmantYnaTICaGñk karBarePøIg nigERcHsIuEdk. sRmab;GagsþúkTwk eKRtUvykcitþTukdak;eTAelIebtug edaymin[vamansñameRbH eRkamGMeBIénkmøaMgTajEdlbNþalmkBIsm<aFTwk. ]TahrN_10>1³ KNnassrxøImuxkat;ctuekaNEdlmanEdkkgdac;² edIm,IRTbnÞúkemKuNcMp©it

kNPu 1765= . edayeRbI MPaf c 30' = / MPaf y 400= / TTwgssr cmb 30= nigPaKryEdk %2=gρ . dMeNaHRsay³ bnÞúkemKuNEdlssrGacssrGacRT)an

)]'85.0('85.0[ cygcgu fffkAP −+= ρφ sRmab;ssrEdlmanEdkkgdac;² 65.0=φ nig 8.0=k

)]'85.0('85.0[85.065.0 cygcgu fffAP −+××=⇒ ρ kMNt;muxkat;ssr

)]'85.0('85.0[8.065.0 cygc

ug fff

PA−+××

=ρ

edaybnÞúkRtUvkarRTnUvbnÞúkcMp©it kNPu 1765= nigssrRtUvmanPaKryEdk %2=gρ 2

3

102887)]3085.0400(02.03085.0[8.065.0

101765 mmAg =×−+×××

×=⇒

eday cmb 30= mma 343

300102887

==⇒ yk 210500035350 mmAcmmma g =⇒== muxkat;Edk 2205710288702.0 mmAs =×= ykEdk 22DB cMnYn 6 edIm 22280mmAs =⇒



RtYtBinitübnÞúkKNnaEdlssrGacRT)an ])('85.0[8.065.0 yststgcu fAAAfP +−×=

⇒ kNkNPu 1765183610]4002280)2280105000(3085.0[8.065.0 3 >=××+−×××= − !OK ykEdkkgmanGgát;p©it mm10 KMlatEdkkg

300300352480

min300

22161048

min1648

min =⎪⎩

⎪⎨

⎧=

⎪⎩

⎪⎨

⎧××

=⎪⎩

⎪⎨

⎧

bdφ

dUcenHeRbIEdkkg 300@10DB .


eRKOgbgÁúMrgkarsgát; nigrgkarBt; 255 T.Chhay

XI. eRKOgbgÁúMrgkarsgát; nigrgkarBt;

11>1> esckþIepþIm eRKOgbgÁúMbBaÄrCaEpñkmYyrbs;eRKagsMNg; EdlrgkmøaMgsgát; nigm:Um:g;. kmøaMgTaMgenH )anBIkmøaMg

xageRkAdUcCa bnÞúkefr bnÞúkGefr nigbnÞúkxül;. kmøaMgRtUv)ankMNt;eday karKNnaedayéd b¤edaykMuBüÚT½r EdlQrelIeKalkarN_sþaTic nigviPaKeRKOgbgÁMú (structural analysis). Ca]TahrN_ sRmab;rUb (1) bgðaj faeRKagQrelITRm hinged BIr EdlrgbnÞúkemKuNBRgayesμ IenAelIGgát; BC. düaRkamm:Um:g;Bt;RtUv)anKUr enAEpñkxagTaj. kMNat;ssr AB nig CD rgnUvkmøaMgsgát; nigm:Um:g;Bt;. pleFobrvagm:Um:g;Bt; nigkmøaMg sgát;RtUv)an[eQ μaHfa cm¶aycakp©it e Edl

n

n

PMe = . e Cacm¶ayBITIRbCMuTm¶n;)aøsÞic(plastic centroid) én

muxkat;eTAcMNucénbnÞúkmanGMeBI. TIRbCMuTm¶n;)aøsÞic (plastic centroid) RtUv)anTTYledaykarkMNt;TItaMg kmøaMgpÁÜbbegáItedaysrésEdk nigebtugedaysnμt;kugRtaMgsgát;sRmab;Edk yf nigkugRtaMgsgát;sRmab; ebtug cf '85.0 . sRmab;muxkat;sIuemRTI TIRbCMuTm¶n;)aøsÞic (plastic centroid) RtYtsIuKñaCamYyTIRbCMuTm¶n;rbs; muxkat;. sRmab;muxkat;minsIuemRTI TIRbCMuTm¶n;)aøsÞic (plastic centroid) RtUv)ankMNt;edayeRbIm:Um:g;eFob nwgG½kS arbitrary axis.

]TahrN_11>1³ kMNt;TIRbCMuTm¶n;)aøsÞic (plastic centroid) énmuxkat;dUcbgðajkñúgrUbTI2. smμtikm μ³


rUbTI1³ eRKagTRm pin BIrCamYynwgdüaRkamm:Um:g;


T.Chhay 256 Members in Compression and Bending

dMeNaHRsay³

!> kugRtaMgsgát;sRmab;ebtugRtUv)ankMNt;yk cf '85.0 =cF kmøaMgkñúgrbs;ebtug gc Af '85.0=

kN4165500350)2885.0( =×××= cF sßitenAelITIRbCMuTm¶n;énmuxkat;ebtug ¬enAcm¶ay mm250 BIG½kS AA − ¦

@> kmøaMgenAkñúgsrésEdk kNfAF yss 2.985400

4284

2

11 =××

×==π

kNfAF yss 6.4924004282

2

22 =××

×==π

#> kMNt;m:Um:g;eFob AA − mmx 85.233

6.4922.9854165)4356.492()652.985()2504165(=

++×+×+×

= dUcenH TIRbCMuTm¶n;)aøsÞic (plastic centroid) RtUvsßitenAelIcm¶ay mm85.233 BIG½kS AA − $> RbsinebI 21 ss AA = ¬muxkat;sIuemRTI¦ dUcenH mmx 250= BIG½kS AA − .

11>2> karsn μt;sRmab;KNnassr GaRs½ytam ACI Code EdnkMNt;sRmab;karKNnassrkMNt;dUcxageRkam³ !> bERmbRmYlrageFob (strain) enAkñúgebtug nigEdk RtUvsmamaRteTAnwgcm¶ayBIG½kSNWt.

rUbTI2³ TIRbCuMTm¶n;)øasÞic (P.C)énmuxkat;



@> RtUvEtbMeBjlkçxNÐ smIkarlMnwgénkmøaMg nigPaBRtUvKñaénbERmbRmYlrageFob (strain

compatibility). #> bERmbRmYlrageFobrbs;ebtugrgkarsgát;EdleRbIR)as;GtibrmaKW 003.0 . $> ersIusþg;rbs;ebtugrgkarTajGacRtUvecal. %> kugRtaMgenAkñúgEdkKW yss fEf ≤= ε . ^> bøúkkugRtaMgGackMNt;manragctuekaNCamYykugRtaMg cf '85.0 BRgayBIRbEvg ca 1β= . Edl c Cacm¶ayBIG½kSNWt nig

⎪⎩

⎪⎨

⎧−

−=

65.0

)7

28'(05.085.085.0

1cfβ sRmab;ebtugEdlmanersIusþg;

MPafMPafMPa

MPaf

c

c

c

56'56'28

28'

>≤<

≤

11>3> düaRkamGnþrkmμrvagbnÞúk nigm:Um:g; (Load-moment interaction diagram) enAeBlEdlbnÞúktamG½kSRtUv)anGnuvtþmkelIssrxøI krNIdUcxageRkamGacekIteLIg edayGaRs½y

eTAnwgTItaMgGnuvtþbnÞúkedayeFobeTAnwg TIRbCMuTm¶n;)aøsÞic (plastic centroid). kmøaMgsgát;tamG½kS oP CakmøaMgsgát;tamG½kSEdlmantémøFMGnuvtþenAelITIRbCMuTm¶n;)aøsÞic (plastic

centroid) 0=e nig 0=nM . kar)ak;rbs;ssr ekIteLIgedayebtugEbk nigEdkeFVIkardl; yielding. vaRtUv)ansMEdgeday oP enAelIExSekag.

!> Maximum nominal axial load maxnP : CakrNIEdlkmøaMgtamG½kSGnuvtþeTAelImuxkat;CamYy cM gaycakp©it eccentricity Gb,rma. tam ACI Code, on PP 80.0max = sRmab;ssrEdkkgdac;² tie

column nig on PP 85.0max = sRmab;ssrEdlmanEdkkgdUcrWus½r spirally reinforced column . kar)ak; ekIteLIgedayebtugEbk nigEdkeFVIkardl; yielding.

@> Compression failure: CakrNIEdlbnÞúktamG½kSFMGnuvtþenAcm¶aycakp©ittUc. bnÞúktamG½kSkñúg krNIenHmantémøERbRbYlBI témøGtibrma maxnn PP = eTAtémøGb,rma bn PP = (balanced load). s r)ak;edayebtugEbkenAEpñkrgkarsgát;CamYYynwgbERmbRmYlrageFob strain 003.0= ÉcMENkkugRtaMg kñúgEdk ¬EpñkrgkarTaj¦ KWtUcCag yield strength ys ff < . kñúgkrNIenH en PP > nig nee < .

#> Balanced condition bP : lkçxNÐenHekItmaneLIgenAeBlEdl bERmbRmYlrageFobrgkarsgát; (compression strain) enAkñúgebtugmantémøesμ I 003.0 ehIybERmbRmYlrageFobrbs;EdkrgkarTajman témø

s

yy E

f=ε . kar)ak;rbs;ebtugekIteLIgdMNalKñanwgEdk yield. m:Um:g;EdlekItedaysarbnÞúkenH



RtUv)aneKehAfa balanced moment bM cm¶aycakp©itRtUv)aneKehAfa balanced eccentricity

b

bb P

Me = .

$> Tension failure: CakrNIekItmanenAxN³Edl bnÞúktamG½kStUc nigcMNakp©itFM ehIyEdlman m:Um:g;FM. muneBl)ak; kugRtaMgTajekItmanenAelIEpñkd¾FMénmuxkat; bNþal[EdkrgkarTaj yield muneBl ebtugEbk. enAeBl)ak; bERmbRmYlrageFobrbs;EdkrgkarTajmantémøFMCagbERmbRmYlrageFob yield

yε ehIybERmbRmYlrageFobenAkñúgebtugesI μ 003.0 . krNIenHekItmanBI Balanced condition eTAdl; pure flexure bn PP < nig eee > .

%> Pure flexure: muxkat;kñúgkrNIenHrgm:Um:g;Bt; nM Edl 0=nP . kar)ak;dUcKñanwg kar)ak;rbs; FñwmrgkarBt;. cMNakp©itRtUv)ansn μt;fa Gnnþ.

rUbTI3 a³ düaRkamGnþrkmμbnÞúk-m:Um:g;



11>4> karpþl;nUvsuvtßiPaB (Safety provisions)

!> emKuNbnÞúksRmab; bnÞúk gravity nigbnÞúkxül; DU 4.1=

rUbTI3 b³ muxkat;ssrEdlbgðajBITItaMgbnÞúk nP sRmab;lkçxNÐbnÞúkepSg²



LDU 6.12.1 += WLDU 8.06.12.1 ++= WLDU 6.10.12.1 ++=

WDU 6.19.0 += bnSMbnÞúkemKuNEdlmantémøsFMCageKRtUv)anykmkeRbIR)as;sRmab;karKNna. @> emKuNkat;bnßyersIusþg; φ eRbIsRmab;KNnassrGaRs½yeTAnwgkrNIxageRkam³ k> enAeBl gcnu AfPP '1.0≥= φ eBlenaH 65.0=φ sRmab;ssrEdkkgdac;² (tie

column) ehIy 7.0=φ sRmab;muxkat;ssrEdlmanEdkkgdUcrWus½r (spirally reinforced column) . krNIenHssrRtUv)anrMBwgfa)ak;edaykarsgát;.

x> muxkat;EdlbERmbRmYlrageFobrgkarTajsuT§ (net tensile strain) tε sRmab;ersIusþg;

Fmμta (nominal strength) enAkñúgEdkrgkarTajeRkAeKbMput KWsißtenAcenøaH 005.0 nig 002.0 (transition

region) φ ERbRbYlCalkçN³bnÞat;cenøaH 9.0 nig 65.0 b¤ ¬ 7.0 ¦. sRmab;muxkat;EdlmanEdkkgdUcrWus½r spiral section

)3

200)(002.0(7.0 −+= tεφ b¤ ⎥⎦

⎤⎢⎣

⎡−+=

35

/12.07.0

tdcφ (11-1)

sRmab;muxkat;epSgeTot

rUbTI4³ témøemKuNφ



)3

250)(002.0(65.0 −+= tεφ b¤ ⎥⎦

⎤⎢⎣

⎡−+=

35

/125.065.0

tdcφ (11-2)

K> enAeBl 0=uP kñúgkrNIrgkarBt;suT§ 9.0=φ sRmab;muxkat; tension-controlled

section nigERbRbYlBI 9.0 nig 65.0 b¤ ¬ 7.0 ¦ enAkñúgtMbn; transition region.

11>5> Balanced condition – muxkat;ctuekaN Balanced condition ekItmanenAkñúgmuxkat;ssrenAeBlEdl bnÞúkEdlGnuvtþmkelImuxkat;ssr

Edlman nominal strength begáItbERmbRmYlrageFobesμ I 003.0 enAkñúgsrésrgkarsgát;rbs;ebtug nigbERmbRmYlrageFobes μ I

s

yy E

f=ε enAkñúgr)arEdkrgkarTajkñúgeBldMNalKña. enHKWCakrNIBiessEdl

G½kSNWt GacRtUv)ankMNt;BI strain diagram edaysÁal;témøFMbMput. enAeBlEdlbnÞúkcakp©itmantémøFMCag bP enaHeKehAmuxkat;enaHfa compression control. pÞúymkvijeKehAfa tension control .

karviPaK balanced column section GacRtUv)anBnül;dUcxageRkam³ !> yk bc Cacm¶ayBIsrésrgkarsgát;q¶aybMputmkG½kSNWt. BI strain diagram

s

y

b

Efd

c

+=

003.0

003.0)balanced( (11-3)

eday MPaEs 200000=

yb f

dC+

=⇒600

600

km<s;bøúkrgkarsgát;smmUl (equivalent compressive block)



df

cay

bb 11 600600 ββ ⎟

⎟⎠

⎞⎜⎜⎝

⎛

+== (11-4)

Edl ⎪⎩

⎪⎨

⎧−

−=

65.0

)7

28'(05.085.085.0

1cfβ sRmab;ebtugEdlmanersIusþg;

MPafMPafMPa

MPaf

c

c

c

56'56'28

28'

>≤<

≤

@> BIsmIkarlMnwg plbUkkmøaMgtamTisedkesIμsUnü 0=+−− TCCP scb

Edl abfC cc '85.0= nig ys fAT = (11-5) )'85.0'(' css ffAC −= ys ff =' enAeBlEdlEdkrgkarsgát;eFVIkardl; yield

ys fc

dcf ≤⎟⎠⎞

⎜⎝⎛ −

='600' pÞúymkvij

yscsscb fAffAabfP −−+=⇒ )'85.0'(''85.0 (11-6) #> cMNakp©it be RtUv)anvas;BI plastic centroid nig 'e RtUv)anvas;BITIRbCMuTm¶n;énEdkrgkarTaj.

"' dee += ¬sRmab;krNIrnH "' dee b += ¦ Edl "d Cacm¶ayBITIRbCMuTm¶n;)øasÞiceTATIRbCMuTm¶n;Edkrgkar Taj. be RtUv)anKNnaedayKitm:Um:g;Rtg; plastic centroid

")"'()"2

( TddddCdadCeP scbb +−−+−−= (11-7) b¤ ")"')('85.0'(')"

2('85.0 dfAdddffAdadabfeP yscscbb +−−−+−−= (11-8)

cMNakp©it balanced eccentricity

b

bb P

Me = (11-9)

sRmab;muxkat;minEmnctuekaN eyIgeRbIviFIsaRsþdUcKñakñúgkarviPaK edayKitRkLaépÞBitR)akdrbs; ebtugrgkarsgát;.

emKuNkat;bnßyersIusþg; φ sRmab; balanced condition CamYy MPaf y 400= RtUv)ansn μt;yk 65.0 b¤ 7.0 . enHedaysar 002.0===

s

yts E

fεε .

]TahrN_11> 2³ kMNt;kmøaMgsgát; balanced compressive force bP rYckMNt; be nig bM sRmab; muxkat;bgðajkñúgrUb. eK[ MPaf c 27' = nig MPaf y 400= .

dMeNaHRsay³ !> sRmab; balanced condition bERmbRmYlrageFobenAkñúgebtugKW 003.0 ehIybERmbRmYlrageFob

enAkñúgEdk 002.0

200000400

==yε



@> TItaMgG½kSNWt mmd

fc

yb 3005006.0

600600

=×=+

=

mmca bb 25530085.01 =×== β @> RtYtBinitü Edkrgkarsgát;/ BI strain diagram

30050300'

003.0' −

=−

=c

dcsε

ys εε >=⇒ 0025.0' dUcenHEdkrgkarsgát; yield

b¤RtYtBinitütam ys fcdcf ≤⎟⎠⎞

⎜⎝⎛ −

="600'

MPaMPaf s 400500300

50300600' >=⎟⎠⎞

⎜⎝⎛ −

=

dUcenH MPaff ys 400' == $> KNnakmøaMgmanGMeBImkelImuxkat;

kNabfC cc 3.20483502552785.0'85.0 =×××== kNfAT yss 2.985400282 =××== π

kNffAC cyss 7.928)2785.0400(28)'85.0(' 2 =×−=−= π %> KNna eP nig be

kNTCCP scb 8.19912.9857.9283.2048 =−+=−+= ")"'()"

2( TddddCdadCePM scbbb +−−+−−==

mkNeM bb .8.7322252.985)22550500(7.928)2252

255500(3.20488.1991 =×+−−+−−== meb 368.0

8.19918.732==⇒

^> sRmab; balanced condition 65.0=φ

rUbTI6³ balanced condition



kNPb 67.12948.199165.0 =×=φ mkNM b .32.4768.73265.0 =×=φ

11>6> muxkat;ssreRkamGMeBIbnÞúkcakp©it (Column sections under eccentric loading)

sRmab;krNIBIr enAeBlEdlmuxkat;ssr)ak;edaykarsgát; b¤karTaj smIkarlMnwgmUldæanBIrGac RtUv)aneRbIsRmab;viPaKssrEdlrgbnÞúkcakp©it.

!> plbUkkmøaMgtamG½kSedk b¤tamG½kSQRtUves μ IsUnü @> plbUkm:Um:g;eFobnwgG½kSNamYyRtUves μ IsUnü eyagtamrUb eKGacsresrsmIkarTaMgBIrxagelIdYcxageRkam !> 0=+−− TCCP scn (11-10) Edl abfC cc '85.0= )'85.0'(' csss ffAC −= ¬RbsinebIEdkrgkarsgát; yield enaH ys ff =' ¦ ss fAT = ¬RbsinebIEdkrgkarTaj yield enaH ys ff = ¦ @> Kitm:Um:g;Rtg;cMNuc sA

0)'()2

(' =−−−− ddCadCeP scn (11-11) Edl "' dee += ¬ "d Cacm¶ayBITIRbCMuTm¶n;)øasÞiceTATIRbCMuTm¶n;rbs;EdkrgkarTaj¦ b¤

2' hdee −+= sRmab;muxkat;ssrEdlmanEdksIuemRTI

⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn (11-12)

Kitm:Um:g;Rtg; cC

rUbTI7³ krNITUeTA muxkat;ctuekaNEkg



0)'2

()2

()2

(' =−−−−⎥⎦⎤

⎢⎣⎡ −− daCadTadeP sn (11-13)

)2

'(

)'2

()2

(

dae

daCadTP

s

n

−+

−+−= (11-14)

RbsinebI ss AA '= ehIy yss fff == ' enaH

22

)'(

2'

)'(ahe

ddfA

dae

ddfAP ysys

n

+−

−=

−+

−= (11-15)

)'(

)22

('

ddf

ahePAA

y

n

ss −

+−== (11-16)

11>7> ersIusþg;rbs;ssrsRmab;kar)ak;edaykarTaj (Strength of columns for tension failure)

enAeBlEdlssrrgbnÞúkcakp©itCamYynwgcMNakp©it e FM enaHeKrMBwgfassrnwg)ak;edaykarTaj. ssr)ak;edayEdkeFIVkardl; yield ehIyebtugEbkenAeBlEdl strain rbs;EdkFMCag )/( syyy Ef=εε . kñúgkrNIenH nominal strength nP nwgmantémøtUcCag bP b¤k¾cMNakp©it nn PMe /= FMCag balanced

eccentricity be . edaysarkñúgkrNIxøHeKmankarBi)akkñúgkarTsSn_TayfavaCamuxkat; tension control b¤ compression control enaHeKGacsnμt;fa tension failure GacekIteLIgenAeBl de > . karsnμt;enHGac eFVIeLIgenAeBleRkay.

smIkarlMnwgTUeTA 0=+−− TCCP scn nig

0)'()2

(' =−−−− ddCadCeP scn GacRtUv)aneRbIR)as;sRmab;KNna nominal strength

rbs;ssr. !> sRmab;kar)ak;edaykarTaj EdkrgkarTaj yield ys ff = . snμt;fakugRtaMgEdkrgkarsgát;

ys ff =' . @> KNna TCCP scn −+= Edl abfC cc '85.0= )'85.0(' cyss ffAC −= ys fAT = #> KNna nP edayKitm:Um:g;Rtg; sA

)'()2

(' ddCadCeP scn −+−=



Edl "' dee += b¤ 2

' hdee −+= enAeBl ss AA '= $> BICMhan @ nig # eyIg)an

⎥⎦⎤

⎢⎣⎡ −+−=−+ )'()

2(

'1 ddCadCe

TCC scsc

vaCasmIkarTIdWeRkTI2 EdlmanGBaØat a . CMnYstémø cC / sC nig T ehIyedaHRsayrk a . %> eRkayBICMnYs cC / sC nig T smIkardWeRkTI2 Gacsresry:agsRmYldUcxageRkam

02 =++ CBaAa Edl bfA c'425.0= )'(2)'('85.0 deAdebfB c −=−= ')'')('85.0'(' efAddeffAC yscss −+−−=

AACBBa

242 −±−

=⇒ RbsinebI 0'85.0' <− cs ff RtUvykvaes μI 0 .

^> CMnYs a eTAkñúgsmIkarCMhan @edIm,ITTYl nP . m:Um:g; nM kMNt;tam ePM nn = &> RtYtBinitüemIlfaetIEdkrgkarsgát; yield dUckarsnμt; b¤Gt;. RbsinebI ys εε ≥' enaH Edkrgkar sgát; yield . pÞúymkvij sss Ef '' ε= . GnuvtþCMhan @ dl;% mþgeTot. [ ] 003.0/)'(' cdcs −=ε /

s

yy E

f=ε nig 1/ βac = .

*> RtYtBinitüfamuxkat;Ca tension control . Tension control enAeBlNa bee > b¤ bn PP < . (> Net tensile strain tε enAkñúgmuxkat; CaFm μtaFMCag limit strain sRmab; compression-controlled

section 002.0 . dUcenHtémøénemKuNkat;bnßyersIusþg; φ ERbRbYlcenøaHBI 65.0 ¬b¤ 70.0 ¦ nig 90.0 . smIkar )

3200)(002.0(7.0 −+= tεφ b¤ ⎥

⎦

⎤⎢⎣

⎡−+=

35

/12.07.0

tdcφ sRmab;muxkat;EdlmanEdkkgdUcrWus½r

spiral section nig )3

250)(002.0(65.0 −+= tεφ b¤ ⎥⎦

⎤⎢⎣

⎡−+=

35

/125.065.0

tdcφ sRmab;muxkat;epSgeTot

RtUv)aneRbIsRmab;KNnarkemKuNkat;bnßyersIusþg; φ . ]TahrN_11>3³ kMNt; nominal compressive strength nP sRmab;muxkat;Edl[dUckñúgrUbxageRkam RbsinebI mme 500= . dMeNaHRsay³ !> eday mme 500= mmd 485=> snμt;famuxkat;)ak;kñúglkçxNÐ tension failure condion controls



¬EdlRtUveFVIkarRtYtBinitüenAeBleRkayeTot¦. Strain rbs;EdkrgkarTaj sε GacFMCag yε dUcenHeyIg ykkugRtaMg yf . edaysnμt;faEdkrgkarsgát; yield ys ff =' EdlRtUvRtYtBinitüenAeBleRkay. @> BIsmIkarlMnwg TCCP scn −+= Edl akNaabfC cc 03.83502785.0'85.0 =××== kNffAC cyss 68.928)2785.0400(

4284)'85.0('

2

=×−=−=π

kNfAT ys 2.985400282 === π 52.5603.82.98568.92803.8 −=−+=⇒ aaPn ¬1¦

#> Kitm:Um:g;Rtg; sA

⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn

edayTIRbCMuTm¶n;)øasÞic plastic centroid sßitenAelITIRbCMuTm¶n;énmuxkat; mmd 210"= . mmdee 710210500"' =+=+=

36.54949.50056.0)65485(68.928)2

485(03.87101 2 ++−=⎥⎦

⎤⎢⎣⎡ −+−= aaaaPn ¬2¦

$> pÁúMsmIkar ¬1¦ nig ¬2¦ eyIg)an 088.60554.20056.0 2 =−+ aa

mma 74.172=⇒ %> kNPn 58.133052.5674.17203.8 =−×=

mkNM n .29.6655.058.1330 =×= ^> RtYtBinitüfa Edkrgkarsgát; yield b¤Gt;

rUbTI8³ ]TahrN_TI3 kar)ak;edaykarTaj Tension failure



mmc 22.20385.074.172

== 002.0

20000040000204.0003.0

22.2036522.203' ==>=

−= ys εε dUcenHEdksgát; yield

RtYtBinitü strain enAkñúgEdkTaj ys εε >=⎟

⎠⎞

⎜⎝⎛ −

= 00416.0003.022.203

22.203485

RbsinebIEdksgát;Gt; yield eRbI sss Ef '' ε= rYceFVIkarKNnaeLIgvij. &> KNna φ ³ eday 00416.0=tε muxkat;sßitenAkñúgtMbn; transition region

( ) 83.03

250002.065.0 =⎟⎠⎞

⎜⎝⎛−+= tεφ

kNPn 38.110458.133083.0 =×=φ mkNM n .19.55229.66583.0 =×=φ

11>8> ersIusþg;rbs;ssrsRmab;kar)ak;edaykarsgát; (Strength of columns for compression failure)

RbsinebIbnÞúkGnuvtþn_sgát; nP FMCagbnÞúk balanced force bP b¤cMNakp©it n

n

PMe = tUcCag be enaH

ssrnwgrMBwgfaRtUv)ak;edaykarsgát;. kñúgkrNI compression controls ehIy strain rbs;ebtugnwgmantémø 003.0 Edl strain rbs;EdkmantémøtUcCag yε . PaKeRcInrbs;muxkat;ssrnwgrgkarsgát;. G½kSNWtxit

eTArkEdkrgkarTaj edaybegáInmuxkat;sgát; dUcenHcm¶ayeTAG½kSNWt bcc > . edaysareKBi)akkñúgkarTsSn_TaynUvmuxkat;ssrfa tension failure b¤ compression failure

eK)ansnμt;fa enAeBl 3

2de < enaHssr)ak;eday compression failure EdlRtUvepÞógpÞat;enAeBleRkay. edIm,IKNna nominal load strength nP eKeRbIeKalkarN_sþaTic. karviPaKmuxkat;ssrsRmab;kar)ak;eday

rUbTI9³ düaRkam strain enAeBl compression controls



karsgát; compression failure eKGaceRbIsmIkar 0=+−− TCCP scn nigsmIkar 0)'()

2(' =−−−− ddCadCeP scn nigdMeNaHRsaymYykñúgcMeNamdMeNaHRsayxageRkam.

11>8>1> dMeNaHRsaysakl,g (Trial solution)

dMeNaHRsayenHRtUv)ansegçbdUcCMhanxageRkam³ !> KNnacm¶ayeTAG½kSNwtsRmab;muxkat; balanced section bc

y

tb f

dc+

=600

600 (11-3)

@> kMNt; nP edayeRbIlkçxNÐlMnwg TCCP scn −+= (11-10)

#> KNna nP edayKitm:Um:g;Rtg;EdkrgkarTaj sA )'()

2(' ddCadCeP scn −+−= (11-11)

Edl "' dee += kñúgkrNITUeTA b¤

2' hdee −+= enAeBl ss AA '=

abfC cc '85.0= )'85.0'(' csss ffAC −= ss fAT = $> edaysn μt;témø bcc > KNna ca 1β= . snμt; ys ff =' %> KNna sf

yt

sss fc

cdEf ≤⎟⎠⎞

⎜⎝⎛ −

== 600ε

^> CMnYstémøEdlrkeXIjeTAkñúgsmIkarCMhan @ nigCMhan # edIm,Irk 1nP nig 2nP . RbsinebI 21 nn PP ≈ eRCIsyktémøtUcCageK b¤mFümPaKén 1nP nig 2nP . EtebI 1nP mantémøxusKñaq¶ayBI 2nP eK

RtUvsnμt; c b¤ a fμ I ehIyeFVIkarKNnaeLIgvijcab;epþImBICMhan $ rhUtdl; 21 nn PP ≈ . ¬eKGacTTYlyk)an ebI 1nP nig 2nP xusKña %1 ¦.

&> epÞógpÞat;fa Edkrgkarsgát; yield edayKNna ( )[ ]cdcs /'003.0' −=ε ehIyeRbobeFobCamYy

s

yy E

f=ε . enAeBlEdl ys εε ≥' Edkrgkarsgát; yield RbsinebImindUcenaHeT sss Ef '' ε= b¤

ys fc

dcf ≤⎟⎠⎞

⎜⎝⎛ −

='600

*> epÞógpÞat;fa bee < b¤ bn PP > sRmab; compression failure.



(> sRmab; compression controlled section CaTUeTA net tensile strain tε enAkñúgmuxkat;tUcCag 002.0 . dUcenH emKuNkat;bnßyersIusþg; 65.0=φ ¬b¤ 70.0 sRmab;ssrEdleRbIEdkkgvNÐ¦.

]TahrN_11>4³ kMNt; nominal compressive strength nP sRmab;muxkat;Edl[RbsinebI mme 254= . dMeNaHRsay³ !> edaysar mmdmme 33.333

32254 =<= . snμt; compression failure. karsnμt;enHRtUvepÞógpÞat;enA

eBleRkay. KNnacm¶ayeTAG½kSNWtsRmab; balanced section bc :

y

tb f

dc+

=600

600 mm300400600500600

=+×

=

@> BIsmIkarlMnwg TCCP scn −+= (11-10)

Edl akNaabfC cc 03.83502785.0'85.0 =×××== kNffAC cyss 68.928)2785.0400(28)'85.0(' 2 =×−=−= π edaysnμt;Edkrgkarsgát; yield ¬karsn μt;enHRtUvepÞógpÞat;enAeBleRkay¦ kNfffAT ssss 46.2282 === π ¬ ys ff < ¦ sn faP 46.268.92803.8 −+= #> Kitm:Um:g;Rtg; sA

⎥⎦⎤

⎢⎣⎡ −+−= )'()

2(

'1 ddCadCe

P scn (11-11)

TIRbCMuTm¶n;)øasÞicsßitenAelITIRbCMuTm¶n;rbs;muxkat; mmd 225"= mmdee 479225254"' =+=+= ( ) 57.8720084.038.8505008.928

250003.8

4791 2 +−=⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= aaaaPn

rUbTI10³ ]TahrN_TI4 Compression controls



$> edaysnμt; mmc 342= EdlmantémøFMCag mmcb 300= mma 7.29034285.0 =×=

CMnYstémø a eTAkñúgsmIkarkñúgCMhanTIBIrxagelIeyIg)an kNPn 78.259857.8727.2900084.07.29038.8 2

1 =+×−×= %> KNna sf BIdüaRkam strain enAeBlEdl mmc 340=

MPafs 19.277600342

342500=

−=

00139.0200000

19.277====

s

sts E

fεε

^> edayCMnYs mma 7.290= nig MPafs 19.277= eTAkñúgsmIkarCMhanTImYyedIm,IKNna 2nP kNPn 11.258119.27746.268.9287.29003.82 =×−+×=

eday 1nP nig 2nP mantémøxusKñamindl; %1 dUcenHeyIgyk kNPn 11.2581= mkNePM nn .6.655254.011.2581 =×==

&> epÞógpÞat;fa Edkrgkarsgát; yield BIdüaRkam strain

002.000256.0003.0342

50342' =>=−

= ys εε

dUcenH Edkrgkarsgát; yield dUckarsnμt;. *> kNPkNP bn 8.199111.2581 =>= ehIy mmemme b 368254 =<= bgðajfavaCamuxkat; compression control dUckarsnμt;. cMNaM³ eKGaceFVIkarsakl,gKNnaedIm,I[ 1nP nig 2nP mantémø kan;Etesμ Ikña. (> KNna φ

mmddt 500== mmc 342= tε ¬enAnIv:UedkrgkarTaj¦ 002.000139.0

342342500003.0 <=

−= enaH 65.0=φ

kNPn 72.167711.258165.0 =×=φ mkNM n .14.4266.65565.0 =×=φ 11>8>2> dMeNaHRsayviPaKcMnYn (Numerical Analysis Solution)

enAeBl compression control karviPaKssrGaceFVIeTA)anedaykat;bnßykarKNnamkRtwmsmIkar dWeRkTI3 EdlmanTRmg; 023 =+++ DCaBaAa rYcedaHRsayrktémø a edayviFIcMnYn numerical method

b¤ a GacTTYl)anBIm:asIunKitelx. BIsmIkarlMnwg TCCP scn −+= sscysc fAffAabf −−+= )'85.0(')'85.0( (11-10)



Kitm:Um:g;Rtg;EdkTaj sA

⎥⎦⎤

⎢⎣⎡ −−+−=⎥⎦

⎤⎢⎣⎡ −+−= )')('85.0(')

2('85.0

'1)'()

2(

'1 ddffAadabf

eddCadC

eP cyscscn (11-11)

BIdüaRkam strain

003.0)(

003.0

1

1

β

βε a

ad

ccdt

s

−=⎟

⎠⎞

⎜⎝⎛ −

=

kugRtaMgenAkñúgEdkTajKW )(600200000 1 ad

aEf ssss −=== βεε

edayCMnYstémø sf eTAkñúgsmIkar (11-10) nigedaHRsaysmIkar (11-10) nig (11-11) eRkayBI sRmYlrYc eyIgTTYl)an

0'600]'600)'')('85.0('[)]'('85.0['85.01

23 =−++−−+−+⎟⎠⎞

⎜⎝⎛ deAaeAddeffAadebfa

cbf

sscyscc β

enHCasmIkardWeRkTI3 EdlmanTRmg; 023 =+++ DCaBaAa Edl

2'85.0 bfA c=

)'('85.0 debfB c −= '600)'')('85.0(' eAddeffAC scys ++−−= deAD s 1'600 β−= enAeBlEdleKKNna)antémø A / B / C nig D enaH a GacRtUv)anKNnaedayviFIsakl,g b¤ TTYl)anedaypÞal;BIm:asIunKitelx. dMeNaHRsaysmIkardWeRkTI3 GacTTYl)anedayeRbIviFI Newton-

Raphson . viFIenHmanRbsiT§PaBkñúgkaredaHRsayrkb¤srbs; ( ) 0=xf . vaTak;Tgnwgbec©keTssamBaØ ehIyeKqab;TTYl)ancemøIyedayeFVItamCMhanxageRkam³ !> [ DCaBaAaaf +++= 23)( nigKNna A / B / C nig D @> KNnaedrIevTImYyén )(af ³ CBaAaaf ++= 23)(' 2 #> edaysnμt;témødMbUg oa KNnatémøbnÞab;

)(')(

1o

oo af

afaa −=

$> edayeRbItémø 1a KNna 2a dUcsmIkarxagelI

)(')(

1

112 af

afaa −=



%> Gnuvtþn_nUvviFIenHrhUtdl;)antémøsuRkitmYy 1−≅ nn aa . kñúgkrNIviPaKssrenAeBl compression

control témø a EtgEtFMCag ba . dUcenH eKcab;epþImCamYy bo aa = ehIyGnuvtþsmIkarxagelIBIrdgedIm,I TTYl)ancemøIy. ]TahrN_11>5³ eFVI]TahrN_TI11>4eLIgvijedayeRbIviFI numerical analysis

dMeNaHRsay³ !> KNna A / B / C nig D nigkMNt; )(af

25.40162

3502785.02

'85.0=

××==

bfA c ( ) 5.1686825004793502785.0)'('85.0 −=−××=−= debfB c

08.734800328

47928600)50500479)(2785.0400(28

'600)'')('85.0('22

=××++−×−=

++−−=

CC

eAddeffAC scys

ππ

4.83300844190350085.047928600'600 21 −=××××−=−= πβ deAD s

4.83300844190308.7348003285.16868225.4016)( 23 −+−= aaaaf

@> KNnaedrIevTI1 08.73480032833736575.12048)(' 2 +−= aaaf #> [ mmaa bo 255== sRmab;muxkat; balanced section mmcb 300= nig mmab 255= 39.295

)255(')255(2551 =−=

ffa

$> nigKNna 2a ³ mm

ffa 4.292

)39.295(')39.295(39.2952 =−=

témørbs; a mantémøRsedognwg a enAkñúg]TahrN_TI3. CMnYstémø a eTAkñúgsmIkar (11-10) b¤ (11-11) eKTTYl)an kNPn 66.2594= 11>8>3> dMeNaHRsayRbEhl (Approximate Solution)

smIkar approximate RtUv)anesñIeLIgeday Whitney edIm,IedaHRsayrk nominal compressive

strength sRmab;ssrxøIenAeBl compression control.

5.0)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n (11-17)



smIkarxagelIenHGaceRbIeTA)ansRmab;EtssrEdlmansrésEdksIuemRTIteRmobEtmYyRsTab; ehIyRsbeTAnwgG½kSénkarBt;. smIkar approximate TI2 RtUv)anesñIeLIgeday Hsu

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+

−−

o

n

bo

bn

MM

PPPP (11-18)

Edl nP = nominal axial strength énmuxkat;ssr bb MP , = nominal load nig nominal moment énmuxkat; balanced section nM = nominal bending moment ePn ⋅=

oP = nominal axial load enAeBl e=0 yststgco fAAAfP +−= )('85.0

gA = gross area énmuxkat; bh= stA = muxkat;EdkbeNþayminEmnkugRtaMgsrub ]TahrN_6³ kMNt; nominal compressive strength nP sRmab;muxkat;Edl[dUckñúg]TahrN_TI4 edaysmIkar ¬!!-!&¦ nig ¬!!-!*¦edayeRbInUvcMNakp©itdUcKña mme 254= rYceRbobeFobcemøIy. dMeNaHRsay³ !> dMeNaHRsaytamsmIkar Whitney k> lkçN³énmuxkat; mmb 350= / mmh 550= / mmd 500= / mmd 50'= / 22463' mmA = nig mmdd 450)'( =− x> GnuvtþsmIkar Whitney

kNPn 15.27455.0

450254

4002463

18.1500

254550327550350

2

=+

×+

+××

××=

kNPn 35.178415.274565.0 =×=φ K> nP EdlKNnaedaysmIkar Whitney CatémøEdlminsnSMsMécenAkñúg]TahrN_enH ehIytémø

kNPn 15.2745= KWFMCagtémøsuRkit kNPn 11.2581= EdlKNnaedaysmIkarsþaTickñúg]TahrN_TI4. @> dMeNaHRsaytamsmIkar Hsu

k> sRmab; balanced condition kNPb 8.1991= nig kNM b 8.732= ¬]TahrN_TI2¦ x> 40024632)24632350550(2785.0)('85.0 ××+×−×××=+−= yststgco fAAAfP kNPo 22.6275=

K> 18.732

02548.199122.6275

8.1991 5.1

=⎟⎠⎞

⎜⎝⎛+

−− nn PP



edayKuNnwg 1000 ehIyedaHRsayrk nP 146500654.023346.0 5.1 =+ nn PP

edaykarsakl,gtémø kNPn 65.2587= EdlmantémøRbEhl kN11.2581 EdlKNnaedaysþa Tic.

11>9> ]TahrN_sRmab;düaRkamGnþrkmμ (Interaction Diagram Example)

enAkñúg]TahrN_TI11>2 bnÞúk balanced load bP , bM nig be RtUv)anKNnasRmab;muxkat;dUckñúgrUb TI6 ¬ mmeb 368= ¦. dUcKña enAkñúg]TahrN_TI3 nigTI4 load capacity sRmab;muxkat;dUcKñaRtUv)anKNna sRmab;krNIenAeBl mme 500= ¬tension failure¦ nigenAeBl mme 254= ¬compression failure¦. témøTaMgenHnwgRtUvbgðajenAkñúgtaragTI1.

edIm,IKUrdüaRkamGnþrkm μrvagbnÞúk nigm:Um:g; témøepSg²én nPφ nig nMφ RtUv)anKNnasRmab;témø e epSg² Edl e ERbRbYlBI 0=e eTA =e Gtibrma sRmab;krNIm:Um:g;Bt;suT§ pure moment enAeBl

0=nP . düaRkamGnþrkm μrvagbnÞúk nigm:Um:g;RtUv)anbgðajkñúgrUbTI11. bnÞÞúk kNPno 90.4078=φ CabnÞúk cMG½kStamRTwsþI enAeBl 0=e . Et ACI Code GnuBaØatbnÞúkGb,brmaRtwmEt kNPno 12.32638.0 =φ Edl

taragTI1³taragKNnasegçb rUbTI11³düaRkamGnþrkmμrvagbnÞúk nigm:Um:g;



RtUvKñanwgcMNakp©wtGb,brma. cMNaMfa sRmab;kar)ak;edaykarsgát; compression failure bee < nig bn PP > ehIysRmab;kar)ak;edaykarTaj (tension failure) bee > nig bn PP < . krNI =e Gtibrma

ssrrgnUv m:Um:g;Bt;suT§dUckrNI Fñwm.

11>10> ssrmuxkat;ctuekaNCamYyEdkxag (Rectangular columns with side bars)

enAkñúgmuxkat;ssrxøH EdkRtUv)aneKdak;BRgaytamRCugTaMgGs;. EdkxagRtUv)andak;tamkm<s;énmux kat;edaybEnßmeTAelIEdkTaj nigEdksgát; sA nig sA' ehIyRtUv)aneKkMNt;[eQ μaH ssA ¬rUbTI12¦. kñúgkrNIenH viFIsaRsþkñúgkarKNnaEdl)anBnül;rYcmkehIyGacRtUv)anGnuvtþ edayKitBicarNabEnßmkar pøas;bþÚr strain tamkm<s;énmuxkat; nigTMnak;TMngkmøaMgenAkñúgEdkxagnImYy²eTAkñúgtMbn;sgát; b¤tMbn;Taj énmuxkat;. kmøaMgTaMgenHRtUv)anbUkbEnßmeTAelI cC sC nig T edIm,IkMNt; nP smIkarmanragdUcxag eRkam³

∑ ∑−+= TCCP scn (11-10a) ]TahrN_TI11> 7 Bnül;BIkarKNnaenH. cMNaMfa RbsinebIEdkxagsßitenAEk,rG½kSNWt ¬rUb12 b¦

strain nigkmøaMg enAkñúgEdkmantémøtUcNas;EdleKGacecal)an. cMENkEdkEdlsßitenAEk,r sA nig sA' man témøFMKYrsm nigCYybegáInlT§PaBRTRTg;bnÞúkénmuxkat;.

]TahrN_11>7³ kMNt;bnÞúk bP m:Um:g; bM nigcMNakp©it be sRmab;muxkat;bgðajkñúgrUbTI13. edayeRbI MPaf c 28' = nig MPaf y 400= .

rUbTI12³ EdkxagenAkñúgmuxkat;ctuekaNEkg



dMeNaHRsay³ muxkat; balanced section RtUv)anKNnadUcKñanwg]TahrN_TI11>2Edr. eK[ == hb mm550 / mmd 485= nig mmd 65'= . 2

2

24.40214325' mmAA ss ===

π ( )325DB / nigEdkxag 326DB ¬ 323DB sRmab;mçag¦.

1> KNnacm¶ayeTAG½kSNWt mmd

fc t

yb 291485

400600600

600600

=⎟⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmca bb 35.24729185.085.0 =×== 2> KNnakmøaMgenAkñúgebtug nigEdk tamry³rUb 13 a . enAtMbn;sgát;

kNabfC cc 81.323755035.2472885.0'85.0 =×××== ( )csss ffAC '85.0'' −=

enAnIv:U mm65− MPaMPa

cdcf s 400466

29165291600'600' 1 >=⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

dUcenH MPaf s 400' = ( ) kNCs 79.15122885.040024.40211 =×−=

enAnIv:U mm170− MPa

cdcf s 48.249

291170291600'600' 2 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

( ) kNCs 3632885.048.2494322

2

2 =×−×=π

enAnIv:U mm275− MPa

cdcf s 99.32

291275291600'600' 3 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

( ) kNCs 78.142885.099.324322

2

3 =×−×=π

enAkñúgtMbn;Taj ¬nIv:U mm380− ¦ 6

4 1053.917003.0291

291380 −⋅=×−

=sε MPafs 5.1831053.917200000 6

4 =⋅×= − kNT 16.295)5.183(

4322

2

1 =×=π

kNT 5.160840024.40212 =×=



3> KNna ∑∑ −+= TCCP scb kNPb 72.3224)5.160816.295()78.1436379.1512(81.3237 =+−+++=

4> KNnam:Um:g;Rtg;TIRbCMuTm¶n;)øasÞic 2105.160810516.29510536321079.1512325.15181.3237 ×+×+×+×+×=bM

mkNMb .54.1214= m

PMe

b

bb 377.0

72.322454.1214

===

5> KNna φ sRmab; balanced section 002.0== yt εε / 65.0=φ kNPn 07.209672.322465.0 =×=φ



niig mkNMb .45.74954.121465.0 =×=φ

]TahrN_11>8³ edaHRsay]TahrN_TI11>7 eLIgvijenAeBlEdl mme 152= . dMeNaHRsay³

1> edaysar mme 152= mmeb 326=< enaHvaCalkçxNÐ)ak;edaykarsgát; (compression failure

condition). snμt; mmc 5.399= ¬edaykarsakl,g¦ nig 85.05.399 ×=a mma 58.339= ¬ rUbTI13 b ¦.

2> KNnakmøaMgenAkñúgebtug nigEdk kNCc 1.444555058.3392885.0 =×××=

dUcKñanwgkrNI balanced MPafs 4001 = nig kNCs 79.15121 = MPafs 68.3442 = nig kNCs 13.5162 = MPafs 98.1863 = nig kNCs 48.2623 =

MPafs 29.294 = nig kNCs 83.84 = MPafs 41.1285 = nig kNT 37.516=

3> KNna ∑ ∑ =−+= kNTCCP scn 96.6228 mkNePM nn .8.94615296.6228 =×=⋅=

4> KNna nP edayKitm:Um:g;Rtg; sA

⎥⎦⎤

⎢⎣⎡ −−+−−+−−+−+−= )3'()2'()'()'()

2(

'1

4321 sddCsddCsddCddCadCe

P sssscn

mmhdee 3622

5504851522

' =−+=−+= mms 105= KMlatrvagEdkxag ¬efr sRmab;]TahrN_enH¦

( ) ( )

( ) ( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

×−−+×−−+

−−+−+⎟⎠⎞

⎜⎝⎛ −

=10536548583.810526548548.262

1056548513.5166548579.15122

58.3394851.44453621

nP

kNPn 6230= 5> KNna φ

mmddt 485== mmc 5.399= tε ¬enAnIv:UEdkTaj¦ ( ) ( ) 00064.05.399/5.39948503.0/03.0 =−=−= ccdt

eday 002.0<tε enaH 65.0=φ kNPn 8.404896.622865.0 =×=φ



mkNM n .42.6158.94665.0 =×=φ cMNaM³ RbsinebIEdkxagminRtUv)anKit enaH

kNPb 1.3142= nP ¬enA mme 152= ¦ kN54.568248.42279.151223.4592 =−+=

RbsinebIeKKitEdkxagenaH bP ekIneLIgRbEhl %6.2 nig nP ekIneLIgRbEhl %6.9 .

11>11> lT§PaBRTbnÞúkrbs;ssrmuxkat;mUl (Load Capacity of Circular Columns)

11>11>1 lkçxNÐ Balanced

témøénbnÞúk balanced load nP nigm:Um:g; balanced moment nM sRmab;muxkat;mUlGacRtUv)ankM Nt;edayeRbIsmIkarlMnwgdUckrNImuxkat;cuekaNpgEdr. srésrEdkenAkñúgmuxkat;rgVg;EdlRtUv)anteRmob eTAtamcm¶ayBIG½kSTIRbCMuTm¶n;)øasÞicERbRbYl KWGaRs½yeTAnwgcMnYnEdkenAkñúgmuxkat;. bBaðacMbgKWrkkm<s; bøúksgát; a nigkugRtaMgenAkñúgsrésEdk. ]TahrN_xageRkamBnül;BIkarviPaKmuxkat;eRkamlkçxNÐ balanced condition. nitiviFIdUcKñaGacRtUv)aneRbIedIm,IviPaKmuxkat;sRmab; tension control b¤ compression

control. ]TahrN_11>9³ kMNt;bnÞúk balanced load nP nig m:Um:g; balanced moment nM sRmab;ssrmuxkat;rgVg; EdkkgvNÐGgát;p©it mm400 CamYynwg 288DB dUcbgðajkñúgrUbTI14. eK[ MPaf c 28' = nig

MPaFy 400= . dMeNaHRsay³

1> edaysarEtEdksIuemRTInwgG½kS AA− Edlkat;tamTIRbCMuTm¶n;rgVg; enaHTIRbCMuTm¶n;)øasÞicsßitenAelI G½kSenaH.

2> kMNt;TItaMgTIRbCMuTm¶n;G½kSNWt mmdt 34.329=

s

yy E

f=ε

yyt

bfd

c+

=+

=600

600003.0

003.0ε

mmcb 6.19734.329400600

600=

+=

mmab 96.167= 3> kMNt;lkçN³rbs;ceRmokrgVg; circular segment ¬rgVg;TI15¦

RkLaépÞceRmokrgVg; ( )ααα cossin2 −= r (-19)



TItaMgTIRbCMuTm¶n; x ¬BITIRbCMuTm¶n; 0¦ ( )

ααααcossin

sin32 3

−=

rx (-20) xrZ −= (-21) ( )arr −=αcos b¤ ⎟

⎠⎞

⎜⎝⎛ −=

ra1cosα (-22)

16.0200

96.1671cos =⎟⎠⎞

⎜⎝⎛ −=α

o79.80=⇒α / 987.0sin =α nig rad41.1=α RkLaépÞceRmokrgVg; ( )987.016.041.12002 ×−=

22.50083 mm=

( ) mmx 39.10216.0987.041.1

987.020032 3

=×−

×⎟⎠⎞

⎜⎝⎛=

mmZ 61.9739.102200 =−= 4> kMNt;kmøaMgsgát; cC

×= cc fC '85.0 RkLaépÞceRmokrgVg; kN11922.500832885.0 =××=

vaeFVIGMeBIenA mm39.102 BITIRbCMuTm¶n;ssr 5> KNna strain, stress nig kmøaMgenAkñúgEdkrgkarTaj nigEdkrgkarsgát;.

kMNt;bERmbRmYlrageFob strain BIdüaRkambERmbRmYlrageFob. sRmab; 1T

002.0== yεε MPaff ys 400== kNT 6.492400

4282

2

1 =×=π

sRmab; 2T 4

3 105.874.13198.55 −⋅== ys εε

MPafs 170200000105.8 43 =×⋅= −

kNT 36.2091704282

2

2 =×=π

sRmab; 1sC 3

1 1093.1003.06.19794.126 −⋅=×=sε

MPafs 3862000001093.1 31 =×⋅= − MPa400<



( ) kNCs 05.4462885.03864

2822

1 =×−=π



sRmab; 2sC

42 1077.7003.0

6.19718.51 −⋅=×=sε

MPafs 4.1552000001077.7 42 =×⋅= −

( ) kNcs 07.1622885.04.1554

2822

2 =×−=π

6> kugRtaMgenAkñúgEdkrgkarsgát;RtUv)ankat;bnßy edIm,IKitenAkñúgebtugEdlCMnYsedayEdk. kmøaMg balanced KW ∑∑ −+= TCCP scb

kNPb 16.1098)36.2096.492()07.16205.446(1192 =+−++= sRmab;muxkat; balanced 002.0=tε nig 65.0=φ

kNPb 8.713=φ 7> Kitm:Um:g;Rtg;TIRbCMuTm¶n;)øasÞic ¬G½kS AA − kat;tamG½kSTIRbCMuTm¶n;¦ sRmab;kmøaMgTaMgGs;

)58.5334.12958.5334.12939.102[ 2121 ×+×+×+×+×== TTCCCePM sscbbb mkNMb .36.263=

mkNMb .18.171=φ mmeb 8.239

16.109836.263

==



11>11>2 ersIusþg;rbs;muxkat;mUlsRmab;kar)ak;edaykarsgát; Strength of circular column for compression failure

muxkat;ssreRkamkmøaMgcMNakp©it GacRtUv)anviPaKtamCMhandUcmuxkat; balanced Edr. vaTTYl )anedaykarsn μt; bCC > b¤ baa > nigKNnakmøaMgenAkñúgebtug nigEdkenATItaMgepSgKñaedIm,IkMNt;

∑ ∑−+= TCCP scn1 . dUcKña nM GacRtUv)anKNnaedayKitm:Um:g;Rtg;TIRbCMuTm¶n;)øasÞic ¬TIRbCuMTm¶n;rbs; muxkat;¦ ehIykMNt;

eMP n

n =2 . RbsinebItémø 1nP nig 2nP minRbhak;RbEhlKñaeTenaH sn μt; C b¤ a fμ I ehIyeFVIkarKNnaeLIgvij ¬emIlcMNucTI8¦. témøxusKñarvag 1nP nig 2nP sßitenArgVg; %1 . muxkat;Ca compression controls enAeBl bee < b¤ bn PP > .

sRmab;]TahrN_ RbsinebIvaTamTarkMNt;ersIusþg;rbs;muxkat;ssrenAkñúg]TahrN_TI9 enAeBlEdl mme 150= nP GacRtUv)anKNnaedayCMhandUcnwg]TahrN_TI 9.

1> eday mme 150= tUcCag mmeb 8.239= lkçxNÐ)ak;edaykarsgát; compression failure

condition ekIteLIg. 2> snμt; mmc 225= ¬edaykarsμan¦ 6.197=> bC nig mma 25.191= 3> KNna mmx 63.89= / mmZ 37.110= RkLaépÞceRmokrgVg; 297.59332 mm= 4> -5> KNnakmøaMg³ kNCc 125.1412= / kNCs 29.4631 = kNCs 73.2282 = / kNT 66.3421 = /

kNT 84.932 = 6> KNna kNTCCP scn 64.16671 =−+= ∑ ∑ 7> Kitm:Um:g;Rtg;G½kSssr ¬TIRbCMuTm¶n;)øasÞic¦³

mkNM n .1.248= mm

eM

P nn 97.16532 == EdlmantémøRbEhl 1nP ¬témøxusKñaRbEhl %1 ¦. dUcenH

kNPn 97.1653= cMNaM³ RbsinebIEdkkgrbs;ssrCaEdkkgvNÐdUcrWus½renaH 70.0=φ . smIkartémøRbEhl approximate equation sRmab;karKNna nP sRmab;muxkat;mUl enAeBl

compression controls RtUv)anesñIeLIgedayelak Whitney

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

+

=

1318.1

67.08.06.9

'

2 s

yst

s

cgn

De

fA

Dhhe

fAP (11-23)

Edl =gA RkLaépÞmuxkat; gross area

=h Ggát;p©itmuxkat;



=sD Ggát;p©itmuxkat;ssrEdlvas;BITIRbCMuTm¶n;EdkmçageTATIRbCMuTm¶n;EdkmçageTot =stA RkLaépÞmuxkat;EdkbBaÄr =e cMNakp©itEdlvas;BITIRbCMuTm¶n;)øasÞic

]TahrN_11>10³ KNnaersIusþg;kmøaMgsgát; nominal nP sRmab;muxkat;sRmab;]TahrN_TI11>9 edayeRbI smIkar Whitney RbsinebIcMNakp©it mme 150=

dMeNaHRsay³ 1> mme 150= tUcCag mmeb 8.239= . tamkarKNnadUceBlmun bgðajfamuxkat;ssrCamuxkat; compression controls. 2> edayeRbIsmIkar Whitney

mmh 400= 222 7.125663400

44mmhAg ===

ππ / mmDs 280120400 =−=

22

49264288 mmAs =

××=π

( )

kNPn 94.17851

2801503

4004926

18.128067.04008.0

1504006.9

287.125663

2

=⎟⎠⎞

⎜⎝⎛ +

××

+

⎥⎥⎦

⎤

⎢⎢⎣

⎡+

×+×

××

×=

3> mkNePM nn .89.26715.094.1785 =×== témø nP enAeBlenHFMCagtémø kNPn 97.1653= EdlKNnaenAeBlmunedaysþaTic.

11>11>3 ersIusþg;rbs;muxkat;mUlsRmab;kar)ak;edaykarTaj Strength of circular column for tension failure

kar)ak;edaykarTajsRmab;ssrmUlenAeBlbnÞúkRtUv)anGnuvtþn_enARtg;cMNakp©it bee > b¤ bn PP < . enAkñúgkrNIenH muxkat;ssrGacRtUv)anviPaKtamCMhandUckarviPaKmuxkat; balanced nigdUc

kñúg]TahrN_TI8. karviPaKRtUv)aneFVIeLIgedaysnμt; bCC < b¤ baa < rYcehIyGnuvtþtamCMhanBnül; kñúgkfaxNÐ11>1. cMNaMfa edaysarEtsrésrEdkRtUv)anteRmobedaymancenøaHefrtambrimaRtmuxkat; rgVg; enaHEdkTaj sA Edlpþl;[GacmantémøtUc ehIylT§PaBRTbnÞúkk¾køayCamantémøtUc. dUcenH eK)an ENnaM[eCosvagkareRbIR)as;muxkat;mUlsRmab;krNIkar)ak;edaykarTaj tension failure.



11>12> karviPaK nigkarKNnassredayeRbIdüaRkam Analysis and Design of Column Using Charts karviPaKmuxkat;ssrEdl)anBnül;BIxagedImKWQrelIeKalkarN_sþaTic. sRmab;karviPaK b¤kar

KNnassrCaCMhandMbUg düaRkam b¤taragBiessGacRtUv)aneRbIedIm,IkMNt; nPφ nig nMφ sRmab;muxkat; Edl[ nigkarKNnamuxkat;EdkcaM)ac;sRmab; uP nig uM Edl[. düaRkam nigtaragenHRtUv)ane)aH Bum< pSayedayviTüasßanebtugGaemric American Concrete Institute (ACI) viTüasßanebtugBRgwgedayEdk Concrete Reinforcing Steel Institute (CRSI) nigsmaKmsIum:gt_Br½Eln Porland Cement Association

(PCA). karKNnassrcugeRkayRtUvEteFVIeLIgedayQrelIsmIkarsþaTic edaykarKNnaedayéd b¤eday kmμviFIkMuBüÚTr½. kareRbIdüaRkam ACI RtUv)anbgðajenAkñúg]TahrN_xageRkam. düaRkamRtUv)anbgðajkñúgrUb TI16 nigrUbTI17.Tinñn½yTaMgenHRtUv)ankMnt;sRmab;muxkat;ssrdUcbgðajenARCugxagelIEpñkxagsþaMén tarag.

]TahrN_11³ kMNt;srésrEdkcaM)ac;sRmab;ssr short tied column dUcbgðajenAkñúgrUbTI 18 a

edIm,IRTnUvbnÞúkemKuN kN2150 nigm:Um:g;emKuN mkN.440 . ssrmanTTwg mm350 nigbeNþaysrub mmh 500= . eRbI MPaf c 28' = / MPaf y 400= .

dMeNaHRsay³ 1> cMNakp©it mm

PM

eu

u 65.2042150440

===

yk mmd 44060500 =−= mmh 380120500 =−=γ enaH 76.0

500380

==γ 2> eday de <= 65.204 snμt;famuxkat;)ak;edaykarsgát; (compression-controlled section)

CamYynwg 65.0=φ kNPn 7.3307

65.02150

== nig mkNM n .9.676

65.0440

==

675.050035028

107.3307'

3=

××⋅

==gc

nn Af

PK

276.0500

65.204675.0 =⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

heKR nn











3> BItaragkñúgrUbTI16 sRmab; 7.0=γ / 048.0=ρ dUcKñasRmab; 8.0=γ / 043.0=ρ

eday interpolation sRmab; 76.0=γ / 045.0=ρ 27875350500045.0 mmAs =××=

eRbI 3210DB ( )248.8042 mmAs = / R)aMedImenAtamRCugxøI. eRbIEdkkg mmDB 350@10 ¬rUbTI18 a¦

]TahrN_12³ eRbItaragedIm,IkMNt;bnÞúkersIusþg; nPφ rbs;ssrxøIdUcbgðajkñúgrUbTI 18 b EdlGnuvtþ enAcm¶aycMNakp©it mme 305= . eRbI MPaf c 35' = nig MPaf y 400= .

dMeNaHRsay³ A. lkçN³rbs;muxkat;³ mmH 600= / mmh 480120600 =−=γ ¬cm¶ayrvagEdlTaj

nigEdk sgát;¦. 8.0600480

==γ ehIy 03.03506004

3282

=×

××

=

π

ρ B. eday de < / snμt;vaCa compression-controlled section.

yk 002.0=tε / 0.1=y

sff ehIy 65.0=φ BItaragkñúgrUbTI 17 eKTTYl)an

3506003536.0

××== n

nP

K dUcenH kNPn 2646=



C. EpÞógpÞat;karsnμt;sRmab;muxkat; compression controlled³ sRmab; 36.0=nK

183.0==heKR nn

BIdüaRkameyIgTTYl)an 03.0019.0 <=ρ / dUcenH kNPn 2646> ¬edIm,I)an 03.0=ρ ¦ D. karsakl,gelIkTI2³ yk 0015.0=tε / MPafs 3002000000015.0 =×=

75.0400300

==y

sff 03.0=ρ 43.0=nK

kNPn 5.31603506003543.0 =×××= E. EpÞógpÞat;karsnμt;³ sRmab; 43.0=nK / 219.0==

heKR nn

BItarag 03.0=ρ dUcGVIEdl[ dUcenH kNPn 5.3160=

kNPn 3.20545.316065.0 =×=φ nig mkNM n .6.626=φ tamkarviPaK kNPn 2027=φ ¬mantémøRbEhlKñanwgkarKNnaedayeRbItarag¦.

11>13> karKNnassreRkambnÞúkcakp©it (Design of Columns Under Eccentric Loading)

karKNnassrmanlkçN³sμ úKsμajCagkarviPaKssr edaysarEtbnÞúkxageRkA uP nigm:Um:g; uM Casm μtikmμ ehIyeKRtUvkarkMNt;nUvGBaØatCaeRcIndUcCa b / h / sA / sA' CamYynwgkarkMNt;rbs; ACI

Code. vaCakarGnuvtþTUeTA edaysnμt;dMbUgnUvmuxkat;ssr ehIykMNt;brimaNmuxkat;EdkRtUvkar. Rbsin ebIGñkKNnaRtUvkardUrmuxkat;EdkKNna enaHmuxkat;ssrk¾RtUv)anEkERbeTAtamenaHEdr. ]TahrN_xag eRkambgðajBIkarKNnassr. 11>13>1 KNnassrsRmab;kar)ak;edaykarsgát; (Design of Column for Compression Failure)

sRmab; compression failure eKniymeRbI ss AA '= sRmab;muxkat;ctuekaN. cMNakp©it u

uP

Me = .

edayQrenAelItémørbs; e eKman2krNIRtUv)anbegáIteLIg 1> enAeBlEdl mme 100≤ krNIcMNakp©itGb,brmaGacekItman EdlGaceKNnaedayeRbIrUbmnþ

( )[ ]cystgcnu ffAAfKPP '85.0'85.0 −+== φφ Edl 65.0=φ nig 80.0=K sRmab;ssrEdl manEdkkgdac;² nig 70.0=φ nig 85.0=K sRmab;ssrEdlmanEdkvNÐ ¬sUmemIl]TahrN_kñúg emeronssrrgkmøaMgcMG½kS¦. sRmab;krNIepSgBIenH GñkKNnaGacGnuvtþtamkrNITI2. krNIbnÞúk



enHRbRBwtþeTAsRmab;ssrGKarCan;eRkaménGKareRcInCan; Edlm:Um:g; uM )anmkBIRbB½n§mYyCan; nig uP )anmkBIbnÞúkRKb;Can;EdlmanGMeBIenABIelIva.

2> tMbn; compression failure KWtMbn;EdlsßitenAcenøaHG½kSQreTAbnÞat; balanced load dUcbgðaj kñúgrUbTI 3 nigrUbTI11. kñúgkrNIenH muxkat; bh GacRtUv)ansnμt; ehIybnÞab;mkmuxkat;EdkRtUv)an KNnasRmab; uP nig uM Edl[. CMhanénkarKNnaRtUv)ansegçbdUcxageRkam³

k> sn μt;muxkat;kaer b¤ctuekaN bh rYckMNt; d / 'd nig u

uPMe =

x> edaysn μt; ss AA '= KNna sA' BIsmIkar 5.0

)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n edayeRbI

TMhMmuxkat;Edl)ansnμt; nig 65.0=φ sRmab;ssrEdleRbIEdkkgFm μta. yk ss AA '= rYceRCIserIsmuxkat;RKb;RKan;. kMNt;muxkat;BitR)akdEdleRbIsRmab; sA nig sA' . mü:ag vijeToteKGaceRbIdüaRkam ACI. K> epÞógpÞat;fa %8'%1 ≤

+=≤

bhAA ss

gρ . RbsinebI gρ mantémøtUc kat;bnßymuxkat; snμt; b:uEnþBRgIkmuxkat;RbsinebIeKcg;)anmuxkat;EdktUc. X> epÞógpÞat;PaBRKb;RKan;rbs;muxkat;cugeRkayedayKNna nPφ BIsmIkarsþaTic dUcBnül; kñúg]TahrN_xagedIm. un PP ≥φ . g> kMNt;EdkkgcaM)ac;.

rUbmnþRbhak;RbEhl approximate formula y:agsamBaØ sRmab;kMNt;muxkat;ssrdMbUg bh b¤PaK ryEdksrub total steel retio gρ KW

2bhKP cn = b¤ 2bhKPP cnu φφ == (11-24) Edl cK mantémødUcbgðajkñúgtaragTI2 nigbgðajkñúgrUbTI19 sRmab;Edk MPaf y 400= nig ss AA '= . xñatrbs; cK KW 3/ mkN . taragTI2 témørbs; cK ¬ MPaf y 400= ¦

cK ( )%gρ )28(' MPaf c )35(' MPaf c )42(' MPaf c 1% 24817 30246 35286 4% 37574 43003 48044 8% 54675 60103 65144



témø cK RtUv)anbgðajkñúgtaragTI2 CatémøRbhak;RbEhl niggayRsYleRbIedaysar cK ekIneLIg mþg 5429 sRmab;karekIneLIgrbs; cf ' mþg 7 . sRmab;muxkat;dUcKña enAeBlEdlcMNakp©it

u

uPMe = ekIn

eLIg nP fycuH dUcenH cK fycuH. dUcenH témø cK sMEdgbnÞúk nP enAelIdüaRkamGnþrkmμcenøaH noP8.0 nig bP dUcbgðajkñúgrUbTI 3 nigTI 11.

Linear interpolation GacRtUv)aneRbI. ]TahrN_ 5.46124=cK sRmab; %6=gρ nig MPaf c 28' = . CMhankñúgkarKNnamuxkat;ssrGacRtUv)ansegçbdUcxageRkam³

1> snμt;muxkat;dMbUgsRmab;muxkat;ssr bh 2> KNna ( )2bh

PK uc

φ=

3> kMNt; gρ BItaragTI 2 sRmab; cf ' Edl[ 4> kMNt;

2'

bhAA g

ssρ

== rYceRCIserIsEdkbBaÄr nigEdkkg. 5> kMNt; nPφ énmuxkat;cugeRkaytamsmIkarsþaTic ¬dMeNaHRsayCak;lak;¦. témøén nPφ KYrEt

mantémøFMCagb¤es μ I uP . RbsinebImindUecñaHeT EktRmUv bh b¤ gρ . mü:agvijeTot RbsinebIeKcg;)anPaKryEdksrubCak;lak; ]TahrN_ %6=gρ bnÞab;mkGnuvtþdUc

xageRkam³

24000

29000

34000

39000

44000

49000

54000

59000

64000

69000

1 2 3 4 5 6 7 8ρ g (%)

K c ( kN/m3)

f'c=28MPaf'c=35MPaf'c=42MPa

rUbTI19 témø cK nig gρ



1> snμt; gρ dUcEdlTamTar nigbnÞab;mkKNna u

uPMe =

2> edayQrelI cf ' nig gρ Edl[/ kMNt; cK BItaragTI2 3> KNna

c

uKPbhφ

=2 bnÞab;mkeRCIserIs b nig h . GnuvtþCMhan 4 nig 5 eLIgvij.

eKKYrEtepÞógpÞat;fa %8%1 ≤≤ gρ . dUcKña epÞógpÞat;fa c Edl)anmkBIkarKNnatamsþaTicmantémøFMCag

y

tb f

dc+

=600

600 sRmab; compression failure .

]TahrN_13³ kMNt;muxkat;EdkTaj nigmuxkat;Edksgát;sRmab;ssrEdleRbIEdkkgFm μtamanmuxkat;

600400× edIm,IRTbnÞúk kNPu 3470= nig mkNM u .530= . edayeRbI kNf c 28' = nig MPaf y 400= . dMeNaHRsay³

1> KNna mmPMe

u

u 74.1523470530

=== . eyIgman mmh 600= yk mmd 550= nig mmd 50'=

edaysar mmde 67.36632

=< snμt;fa compression failure. 2> snμt; ss AA '= . kMNt;témødMbUgrbs; sA' tamrUbmnþ

5.0)'(

'

18.13'

2 +−

++

=

dde

fA

dhebhfP ysc

n (11-17)

sRmab; kNPP un 5.5338

65.03470

===φ

ss AmmA == 28.4271' eRbIEdk 32DB 6=⇒ n edIm

25.4825326 mmDB = sRmab; sA nig sA' ¬rUbTI 20¦



3> %4600400

5.48252=

××

=gρ EdlvaRtUvEttUcCag 08.0 nigFMCag 01.0 4> epÞógpÞat;muxkat;edaysmIkarsþaTictamCMhanénkarKNnakñúg]TahrN_TI4 eKTTYl)an mma 18.430= / mmc 09.506= / kNCc 32.4095= kNCs 35.1815)2885.0400(5.4825 =×−= MPa

ccdfs 06.52

09.50609.506550600600 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

kNfAT ss 21.25106.525.4825 =×== kNkNTCCP scn 5.53385.5659 >=−+=

cMNaMfa RbsinebI un PP <φ cUrdMeLIg sA nig sA' rYceFVIkarKNnaeLIgvij. 5> epÞógpÞat; nP edayeRbIsmIkar ⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= )'(

2'1 ddCadCe

P scn Edl 2

' hdee −+=

eyIgTTYl)an kNPn 5659= 6> sRmab;muxkat; balanced section

mmdf

c ty

b 3305501000600

600600

==⎟⎟⎠

⎞⎜⎜⎝

⎛

+=

edaysarEt mmcmmc b 33009.506 =>= vaCakrNI compression failure dUckarsn μt;. 7> edayeRbIEdkkgmanGgát;p©it mm10

KMlatEdkkg

400400512480

min400

32161048

min1648

min =⎪⎩

⎪⎨

⎧=

⎪⎩

⎪⎨

⎧××

=⎪⎩

⎪⎨

⎧

bdφ

dUcenHeRbIEdkkg 400@10DB . ]TahrN_14³ eFVI]TahrN_TI13 eLIgvijedayeRbIsmIkar ¬11-24¦ dMeNaHRsay³ 1> muxkat;ssrEdl[ 600400× 2> kMNt; cK BIsmIkar ¬11-24¦ 3> 322 37073

6.04.065.03470

mkN

bhPK u

c =××

==φ

4> BItaragTI 2 b¤rUbTI19 sRmab; 337073mmkNKc = MPaf c 28' = eday interpolation

eyIgTTYl)an %88.3248173757414)2481737073(1 =

−−

−+=gρ



5> KNna ( )( ) 246562/6004000388.02/' mmbhAA ss ==== ρ eRbIEdk 32DB 6=⇒ n edIm

6> 25.4825326 mmDB = 7> kMNt; uPφ edayeFVItamCMhan 4-7 sRmab;]TahrN_TI13. kNPkNP nn 5.53385659 =>=

dUcenHmuxkat;EdkRKb;RKan; 8> RbsinebImuxkat;minRKb;RKan; b¤ nn PP <φ tMeLIgmuxkat; sA nig sA' rYceFVIkarepÞógpÞat;eLIgvij

edIm,ITTYl)antémøEk,r. ]TahrN_15³ KNnamuxkat;ssrctuekaNEkgedIm,IRTbnÞúk kNPu 3150= nig mkNM u .630=

CamYynwgPaKryEdksrub gρ RbEhl %4 . eRbI MPaf c 28' = / MPaf y 400= nig mmb 450= . dMeNaHRsay³ 1> KNna m

PMe

u

u 2.03150630

=== . snμt; compression failure ( 65.0=φ ) ¬RtUvepÞógpÞat;enA

eBleRkay¦ ehIy ss AA '= 2> sRmab; %4=ρ nig MPaf c 28' = enaH 37574=cK ¬taragTI2¦ 3> KNna 2bh BIsmIkar (-24): 2bhKP cu φ= b¤ ( )( ) 245.03757465.03150 h= dUcenH

mh 535.0= dUcenHyk mmh 550= . KNna ( ) 24950

255045004.0' mmAA ss =

×== . eRCIserIs 365DB

)4.5089( 2mmAs = dUcbgðajkñúgrUbTI 21. eRbIEdkkg 450@12DB . 4> epÞógpÞat; muxkat;cugeRkayedaykarviPaK RsedogKñanwg]TahrN_TI4 eyIgTTYl)an

mma 8.327= / mmc 65.385= / kNabfC cc 7.3510'85.0 == / MPaf s 400' = / kNffAC cyss 6.1914)'85.0(' =−= / MPa

ccdfs 79.146600 =⎟⎠⎞

⎜⎝⎛ −

= / nig kNT 747=

dUcenH kNTCCP scn 3.4678=−+= ehIy kNkNPP nu 31503041 <==φ edaysarmuxkat;minRKb;RKan; eyIgRtUvdMeLIgmuxkat;Edk b¤muxkat;ebtug rYceFVIkarepÞógpÞat;eLIg vij. ¬yk mmh 600= ¦ rUbTI21.

5> sRmab;muxkat; balanced section mmcmmdc tb 32.436318

400600600

=<=⎟⎠⎞

⎜⎝⎛

+= ¬ mmd 530= ¦

dUcenH vaCa compression failure dUckarsn μt;.



11>13>2 KNnassrsRmab;kar)ak;edaykarTaj (Design of Column for tension Failure)

kar)ak;edaykarTaj (tension failure) ekItmanenAeBl un PP < b¤k¾cMNakp©it bee > dUckarBnül; enAkñúgEpñkTI7. kñúgkarKNnassr uP nig uM RtUv)an[ ehIyvaTamTarnUvkarkMNt;muxkat;ssr nigmux kat;Edk. vaGacRtUv)ansn μt; ¬dUckarENnaM¦ favaCa tension control enAeBlNa

⎩⎨⎧

≥<

>mmhmmh

PM

u

u

600600600530

sMrab; sMrab;

. kñúgkrNIenH muxkat;ssrGacRtUv)ansnμt; ehIybnÞab;mk sA nig

sA' RtUv)ankMNt;. düaRkam ACI GacRtUv)aneRbIedIm,IKNna gρ sRmab;muxkat;Edl[CamYynwg sA = sA' . cMNaMfa φ ERbRbYlcenøaH )7.0(65.0 nig 9.0 dUckarBnül;kñúgEpñkTI 4.

enAeBl tension controls EdkTaj yields b:uEnþEdksgát;Gac yields nigmin yields. karsnμt;dMbUg ys ff =' nig ss AA '= . smIkar (-16) ¬kñúgEpñkTI 6¦ GacRtUv)aneRbIedIm,IKNnatémødMbUgrbs; sA nig

sA' .

( )'22'

ddf

ahePAA

y

n

ss −

⎟⎠⎞

⎜⎝⎛ +−

== (11-16)

edaysar a minRtUv)andwgenAeLIy sn μt; da 4.0= nig nu PP φ= bnÞab;mk

)'()2.05.0('

ddfdhePAA

y

uss −

+−==

φ (11-25)

muxkat;ssrcugeRkayKYrRtUv)anepÞógpÞat;edaysmIkarsþaTicedIm,Ibgðajfa un PP ≥φ . ]TahrN_ TI16 Bnül;BIviFIsaRsþkñúgkarKNnaenH.



enAeBlbnÞúk uP mantémøtUcNas;ebIeRbobeFobCamYynwgm:Um:g; uM TMhMrbs;muxkat;GacRtUv)ankM Nt;edayeRbIEt uM EtmYy)anehIy edaysnμt;fa 0=uP . muxkat;cugeRkayKYrRtUv)anepÞógpÞat;eday smIkarsþaTic. krNIenHekIteLIgsRmab;eRKagGKarmYyCan; b¤BIrCan; EdlGKarenaHRtUv)aneKeRbIsRmab;eFVI CasaltaMgBiBN’ b¤k¾GKarTaMgLayNaEdlmanlkçN³dUcKñaenaH. sRmab;krNIenH sA' GacRtUv)ansnμt; [mantémøtUcCag sA . karKNnay:aglMGitsRmab;saltaMgBiBN’km<s;mYyCan;Edlmansnøak;BIrRtUv)anBnül; enAkñúgCMBUkTI 16

FñwmCab; nigeRKag. ]TahrN_16³ kMNt;srésrEdkcaM)ac;sRmab;ssrragctuekaNEkg 560400× EdlmanEdkkg

FmμtaRTbnÞúk kNPu 1140= nig mkNM u .850= . eRbI MPaf c 28' = nig MPaf y 400=

dMeNaHRsay³

1> KNna mPM

eu

u 7456.01140850

=== . yk mmd 50060560 =−= . edaysar

mmmmP

M

u

u 5306.745 >= b¤edaysar de > snμt;fassrenH)ak;edaykrNI tension failure

enaH 9.0=φ ¬RtUvepÞógpÞat;enAeBleRkay¦. 2> snμt; ss AA '= nig ys ff =' nigeRbIsmIkar (-25) edIm,IkMnt; sA nig sA' . eday kNPu 1140= /

mme 6.745= / mmh 560= / mmd 500= / nig mmd 60'= ( )

( )2

3

71.4070605004009.0

5002.05605.06.745101140' mmAA ss =−×

×+×−⋅==



eRbI 325DB ( )224.4021 mm sRmab; sA nig sA' . ¬rUbTI22¦ 3> epÞógpÞat; ( ) 0359.0

56040024.40212

=×

=gρ EdltUcCag 08.0 nigFMCag 01.0 .

4> epÞógpÞat;kareRCIserIsmuxkat;edaysmIkarsþaTic EdlkarKNnaRsedogKñanwg]TahrN_TI3

a. kMNt;témørbs; a edayeRbIsmIkarTUeTA 02 =++ CBaAa CamYynwg mmhdee 6.965

2' =−+= / 4760'425.0 == bfA c / ( ) 4432512'2 =−= deAB /

( )( ) 758040793''''85.0' −=−+−−= efAddeffAC yscys . eKTTYl)an mma 62.147= nig mmac 67.17385.0/ == .

b. epÞógpÞat; sf ' ³ MPac

dcf s 71.39267.173

6067.173600'600' =⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

c. KNna a eLIgvij ( )( ) 3.773454123'''''85.0'' −=−+−−= efAddeffAC sscss

eKTTYl)an mma 25.150= nig mmc 77.176=

d. epÞógpÞat; sf ' ³ MPac

dcf s 34.39677.176

6077.176600'600' =⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=

KNna kNCc 38.143040025.1502885.0 =×××=

kNffAC csss 07.1498)2885.034.396(24.4021)'85.0'(' =×−=−=

kNfAT ys 5.160840024.4021 =×==

e. kNTCCP scn 95.1319=−+=

5> KNna φ ³ 0055.0003.0 =⎟⎠⎞

⎜⎝⎛ −

=c

cdttε edaysarEt 005.00055.0 >=tε enaH 9.0=φ

6> kNkNPn 114095.118795.13199.0 >=×=φ muxkat;RKb;RKan;

11>14> karBt;tamBIrTis (Biaxial Bending)

karviPaK nigkarKNnassreRkamGMeBIbnÞúkcakp©itEdl)anBiPakSaknøgmk CakrNIkarBt;mYyTis. enHmann½yfa nP GnuvtþenAelIG½kS y ¬rUbTI23¦ begáIt)anbnSMénkmøaMgcMG½kS nP nigm:Um:g;Bt;CMuvijG½kS x es μ Inwg ynnx ePM = b¤ nP GnuvtþenAelIG½kS x ¬rUbTI24¦ CamYynwgcMNakp©it xe begáIt)anbnSMénkmøaMgcM G½kS nP nigm:Um:g;Bt; xnny ePM = .



RbsinebIbnÞúk nP GnuvtþenAkEnøgNamYyEdlmancm¶ay ye BIG½kS x nigcm¶ay xe BIG½kS y enAeBl

enaHmuxkat;ssrnwgrgnUvbnSMbnÞúkEdlman bnÞúkcMp©it nP m:Um:g;Bt;CMuvijG½kS x KW ynnx ePM = nigm:Um:g;Bt; CMuvijG½kS y KW xnny ePM = ¬rUbTI25¦.kñúgkrNIenHmuxkat;ssrrgnUvkarBt;tamBIrTis. vaminEmngay RsYleTenAeBlEdleKeRbIeKalkarN_sþaTicedIm,IviPaK nigKNnamuxkat;ssrsRmab;krNIenH. G½kSNwtsßit enAelIRCugEdlkat;G½kS x nigG½kS y ehIyeKRtUvkarkarKNnad¾EvgedIm,IkMNt;TItaMgrbs;G½kSNWtbERm bRmYlrageFob strain RkLaépÞebtugrgkarsgát; nigkmøaMgkñúgrYmTaMgcMNucEdlvaGnuvtþ. dUcenH eKcaM)ac; RtUvbegáItnUvdMeNaHRsayd¾mansamBaØmYyedIm,IKNnanUvlT§PaBRTRTg;rbs;ssrbnÞúkcMp©it nigm:Um:g;Bt; BIrTis. rUbmnþ Edl)anbegáIteLIgsRmab;ssrrgm:Um:g;BIrTis Tak;TgeTAnwgersIusþg;rbs;vaTb;nwgkarBt;CMuvij G½kSemnImYy².

rUbTI26 bgðajBIExSekagGnþrGMeBIbnÞúk-m:Um:g;kñúglMh ¬3TMhM¦ sRmab;ersIusþg;m:Um:g;BirTisrbs;ssr rgkmøaMgcMG½kS. es‘rIénExSekagGnþrGMeBIbnÞúk-m:Um:g;mYyTis EdlmankaMKUsBIG½kS nP )anbegáItCaépÞénExS ekag GnþrGMeBIbnÞúk-m:Um:g;BIrTis. ExSekag oxM bgðajnUvExSekagGnþrGMeBIsRmab;m:Umg;mYyTisCMuvijG½kS x nigExSekag oyM bgðajnUvExSekagGnþrGMeBIsRmab;m:Umg;mYyTisCMuvijG½kS y . bøg;enARtg;bnÞúkcMG½kSefr nP bgðajBIExSvNÐénm:Um:g;Bt; nM CMuvijG½kSepSg².

ssrEdlmanmuxkat;epSg²RtUv)aneRbIR)as;edIm,ITb;Tl;nwgbnÞúkcMG½kS nigmU:m:g;Bt;BIrTis. muxkat; ssrmUl kaer b¤ctuekaNEkgGacRtUv)aneKeRbIR)as;CamYynwglT§PaBTb;nwgm:Um:g;CMuvijG½kS x nigG½kS y Edl mantémøesμ IKña b¤mines μ IKña.





11>15> ssrmUlCamYynwgkarrayEdkes μ IeRkamm:Um:g;Bt;BIrTis Circular Columns With Uniform reinforcement Under Biaxial Bending ssrmUlCamYynwgkarrayEdkEdlmanlkçN³ÉksNæan manlT§PaBTb;nwgm:Um:g;dUcKñaRKb;Tis. Rb

sinssrmUlRbQmnwgm:Um:g;BIrTisCMuvijG½kS x nigG½kS y enaHm:Um:g;mYyTissmmUl uM GacRtUv)anKNna edayeRbIsmIkarxageRkam³

( ) ( ) ePMMM uuyuxu ⋅=+= 22 (11-26)

nig ( ) ( )u

uyx P

Meee =+= 22 (11-27)

Edl yuux ePM = m:Um:g;emKuNCMuvijG½kS x xuuy ePM = m:Um:g;emKuNCMuvijG½kS y

ePM uu = m:Um:g;emKuNmYyTissmmUlénmuxkat;EdlekIteday uxM nig uyM sRmab;ssrmUl eKcaM)ac;eRbIEdky:agtic6edIm ehIyEdkTaMgenaHRtUv)anBRgayes μ IenAkñúgmuxkat;

enaH. ]TahrN_17³ ssrmUl kMNt;lT§PaBRTbnÞúk nP rbs;ssrragmUlEdlmanGgát;p©it mm500 CamYyEdk 3210DB enAeBl

Edl mmex 100= nig mmey 150= . eRbI MPaf c 28' = nig MPaf y 400= . dMeNaHRsay³ 1> KNnacMNakp©itEdlsmmUleTAnwgkareFVIGMeBItammYyTisedayeRbIrUbmnþ (11-27)

mmeee yx 28.180150100 2222 =+=+=

2> kMNt;lT§PaBRTbnÞúkrbs;ssredayQrelIcMNakp©it mme 28.180= . edaHRsaydUc]TahrN_ TI 9 eKTTYl)an³

mmd 7.430= mma 75.250= mmc 295= ¬edaysakl,g¦

kNCc 49.2345= kNCs 35.1188=∑ kNT 09.662=∑ kNTCCP scn 75.2871∑ ∑ =−+=

3> sRmab;lkçxNÐ balanced condition

mmdc tb 42.2587.4301000600

400600600

==+

=

bcmmc >= 295 EdlCakrNI)ak;edaykarsgát; (compression failure)



11>16> ssrmuxkat;kaer nigctuekaNeRkamm:Um:g;Bt;BIrTis (Square and Rectangular Columns under Biaxial Bending)

11>16>1> viFI; Bresler Reciprocal Method

ssrkaer b¤ctuekaNrgnUvm:Um:g;Bt;CMuvijG½kSemrbs;vamantémømines μ IKña RtUvkarbrimaNEdkxusKña sRmab;TisedAmYy². viFIsaRsþRbEhlsRmab;viPaKmuxkat;EbbenHRtUv)anbegáIteLIgedayelak Boris

Bresler ehIyRtUv)aneK[eQ μaHfa viFI Bresler Reciprocal Method. tamry³viFIenH lT§PaBRTbnÞúkrbs; ssreRkamGMeBIm:Um:g;Bt;2TisGacRtUv)anKNnaedayeRbIsmIkarxageRkam³

uouyuxu PPPP1111

−+= (11-28)

b¤ nonynxn PPPP1111

−+= (11-29)

Edl uP = lT§PaBRTbnÞúkemKuNeRkamGMeBIm:Um:g;BIrTis uxP = lT§PaBRTbnÞúkemKuNtamG½kSmYyenAeBlbnÞúkeFVIGMeBIenAcMNakp©it ye nig 0=xe uyP = lT§PaBRTbnÞúkemKuNtamG½kSmYyenAeBlbnÞúkeFVIGMeBIenAcMNakp©it xe nig 0=ye uoP = bnÞúkcMp©itemKuNenAeBlEdl 0== xy ee

φu

nP

P = φux

nxP

P = φuy

nyP

P = φuo

noP

P =

lT§PaBRTbnÞúktamTismYy nxP / nyP / noP GacRtUv)anKNnaedayeRbIsmIkarnigviFIsaRsþEdl)an ENnaMBIxagmuxkñúgemeronenH. bnÞab;mk vaRtUv)anCMnYseTAkñúgsmIkarTI (-29) edIm,IKNna nP .

smIkar Bresler mann½ysRmab;RKb;krNITaMgGs;enAeBlNaEdl non PP 10.0≥ . enAeBlEdl non PP 10.0< kmøaMgtamG½kSGacRtUvecal ehIymuxkat;GacRtUv)anKNna dUcGgát;rgnUvm:Um:g;Bt;BIrTissuT§

edayeRbIsmIkarxageRkam³ 0.1≤+

y

uy

x

uxMM

MM (11-30)

b¤ 0.1≤+oy

ny

ox

nxMM

MM (11-31)

Edl yuux ePM = = m:Um:g;KNnaCMuvijG½kS x xuuy ePM = = m:Um:g;KNnaCMuvijG½kS y xM nig yM = lT§PaBTb;m:Um:g;CMuvijG½kS x nigG½kS y

φ

uxnx

MM =

φuy

nyM

M = φ

xox

MM =

φy

oyM

M =



smIkar Bresler minRtUv)anENnaM[eRbIenAeBlEdlmuxkat;rgnUvbnÞúkTajtamG½kSeT. 11>16>2> viFIExSvNÐbnÞúk Bresler (Bresler Load Contour Method)

sRmab;viFIenH épÞ)ak; failure surface Edl)anbgðajenAkñúgrUbTI 26 RtUv)ankat;edaybøg;éntémøefr nP pþl;nUvtémøénmU:m:g; nxM nig nyM . CaTUeTA rUbmnþsRmab;viFIenHKW³

0.121

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛αα

oy

ny

ox

nx

MM

MM ` (11-32)

elak Bresler )anbgðajfa niTsSnþ α GacmantémødUcKñasRmab;tYTaMgBIrénsmIkarenH ( )21 αα = . mü:agvijeTot Kat;)anbBa¢ak;fatémø α ERbRbYlcenøaH 15.1 nig 55.1 ehIyvaGacRtUv)ansnμt;esμ I 50.1 sRmab;ssrmuxkat;ctuekaNEkg. sRmab;muxkat;kaer α ERbRbYlBI 5.1 eTA 2 ehIytémømFüm 75.1=α RtUv)aneKeRbIsRmab;karKNnaGnuvtþn_. enAeBlEdsrésEdkRtUv)anBRgaymanlkçN³dUcKñasRmab;muxTaMg bYnrbs;ssrkaer enaHeKGacsnμt;yk 5.1=α .

0.15.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛

oy

ny

ox

nx

MM

MM (11-33)

bTdæanGg;eKøs British Code )ansnμt; 1.67 1.33; 1.0;=α nig 0.2 enAeBlEdlpleFob uo

u

PP1.1

es μ Inwg 0.6 0.4; 0.2; nig 8.0 erogKña.

11>17> viFIExSvNÐbnÞúk Parme (Parme Load Contour Method)

viFIExSvNÐbnÞúk load contour methode EdlesñIeLIgeday smaKmn_sIum:gt¾Br½ELn Porland

Cement Association (PCA) CaviFImYyEdlbegáIteLIgedayeRbIviFIExSvNÐ½bnÞúk Bresler. enAkñúgviFIenH Edl eKGac ehAmü:ageTotfa Parme load contour methode cMNuc B enAelIExSvNÐbnÞúk ¬énbøg;edkenARtg;bnÞúk efr nP dUcbgðajenAkñúgrUbTI 26¦ RtUv)ankMNt;y:agdUcenHfa pleFobénlT§PaBTb;m:Um:g;BIrTis nxM nig

nyM es μ I nwgpleFobénlT§PaBTb;m:Um:g;mYyTis oxM nig oyM .

oy

ox

ny

nx

MM

MM

= b¤ β==oy

ny

ox

nx

MM

MM

témø β EdlmanenAkñúgrUbTI 27 bgðajnUvEpñkefrEdllT§PaBTb;m:Um:g;tamTisnImYy²GacRtUv)an GnuBaØati[GnuvtþmkelImuxkat;ssrkñúgeBldMNalKña.



sRmab;karKNnaGnuvtþn_ ExSvNÐbnÞúk load contour Edl)anbgðajenAkñúgrUbTI27 GacRtUveRbIedIm,I

KNnaedaykarRbhak;RbEhledayeRbIbnÞat;Rtg; AB nig BC . CRmal (slope) rbs;bnÞat; AB KW ββ /)1( − nigCRmal (slope) rbs;bnÞat; BC KW )1/( ββ − . dUcenHenAeBl

ox

nx

oy

ny

MM

MM

> enaH 11=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+

ββ

ox

nx

oy

ny

MM

MM (11-34)

ehIyenAeBl ox

nx

oy

ny

MM

MM

< enaH 11=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+

ββ

oy

ny

ox

nx

MM

MM (11-35)

témøBitR)akdrbs; β GaRs½yeTAnwgpleFob o

n

PP sMPar³ niglkçN³énmuxkat;. sRmab;ssrEdl

RTnUvbnÞúkRsal β nwgERbRbYlBI 55.0 eTA 7.0 . témømFüm 65.0=β GacRtUv)aneRbIsRmab;karKNna. enAeBlEdlsrésEdkRtUv)anBRgaymanlkçN³dUcKñaRKb;épÞTaMgbYnrbs;muxkat;ctuekaN enaHpl

eFob oy

ox

MM mantémøRbhak;RbEhlnwg

hb Edl b nig h CaTTwg nigkm<s;srubrbs;muxkat;ctuekaNerogKña.

edayCMnYspleFobenHeTAkñúgsmIkarTI (-34) nig (-35) eKTTYl)an

oynxny MhbMM ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎠⎞

⎜⎝⎛+

ββ1 (11-36)

oxnynx MbhMM ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛ −⎟⎠⎞

⎜⎝⎛+

ββ1 (11-37)

sRmab; 65.0=β nig 5.1=bh



nxnyoy MMM 36.0+≈ (11-38)

nynxox MMM 8.0+≈ (11-39) BIkarbgðajenH eyIgeXIjfasmIkarsμúKsμajEdlmanlkçN³pÞal;sRmab;KNnassreRkambnÞúkcM G½kS nigm:Um:g;BIrTisminGaceFVIeTA)aneLIy. dUcenHGñkKNnaKYrmanbTBiesaFn_RKb;RKan;edIm,Is μannUvmuxkat; dMbUgedayeRbInUvtémø nP / nxM nig nyM CamYynigsmIkarsRmab;mYyTis nigbnÞab;mkepÞógpÞat;PaBRKb;RKan; rbs;muxkat;edayeRbIsmIkarsRmab;m:Um:g;BIrTis b¤edayeRbIkMuBüÚT½r.

]TahrN_18³ ssrxøIEdleRbIEdkkgFmμtamanmuxkat; 600400× CamYynwg 328DB BRgaydUc bgðajkñúgrUbTI 28. kMNt;bnÞúkKNna design load nPφ enAelImuxkat; RbsinebIvaeFVIGMeBIenA mmex 205= nig mmey 305= . eRbI MPaf c 35' = / MPaf y 400= nig smIkar Bresler Reciprocal equation.

dMeNaHRsay³ 1> kMNt;lT§PaBRTbnÞúkmYyTis nxP tamG½kS x enAeBl mmey 305= . kñúgkrNIenH mmb 400= nig

mmh 600= / mmd 540= / mmd 60'= nig 274.2412' mmAA ss == . dMeNaHRsayGaceFVIeTAtamCMhandUckñúg]TahrN_TI 2 nigTI4sRmab;lkçxNÐmuxkat; balanced

condition nigmuxkat; compression-control condition. a. sRmab; balanced condition

mmdf

cy

b 324540400600

600600

600=⎟

⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmab 2.2593248.0 =×= ¬ 8.01 =β enAeBl MPaf c 35' = ¦ kNabfC cc 48.3084'85.0 ==

MPaf s 89.488324

60324600' =⎟⎠⎞

⎜⎝⎛ −

= dUcenH MPaff ys 400' ==

kNffAC cyss 32.893)'85.0(' =−= kNfAT ys 1.965== kNTCCP scbx 7.3012=−+=

kNPP bxbx 25.19587.301265.065.0 =×==φ ¬ 65.0=φ sRmab; 002.0=tε ¦ b. sRmab; mmdmmey 540305 =<= / snμt;famuxkat;sßitkñúglkçxNÐ compression failure

ehIy GnuvtþtamCMhankñúg]TahrN_TI4 edIm,ITTYl)an mma 69.265= nig mmac 1.332

8.0== mmcb 324=> . dUcenH muxkat;Camuxkat; compression control.

epÞógpÞat; ys fMPa

cdcf >=⎟⎠⎞

⎜⎝⎛ −

= 60.491'600' dUcenH eyIgyk MPaff ys 400' ==



epÞógpÞat; ys fMPac

cdf <=⎟⎠⎞

⎜⎝⎛ −

= 59.375600

KNnakmøaMg kNabfC cc 71.3161'85.0 == kNffAC cyss 32.893)'85.0(' =−= kNfAT ss 2.906=⋅= bxscnx PkNTCCP >=−+= 83.3148 dUcenHvaCakrNI compression

failure dUckarsnñidæan. 002.000188.0003.0 <=⋅⎟

⎠⎞

⎜⎝⎛ −

=c

cdtε 65.0=⇒φ

kNPnx 74.2046=φ c. Kitm:Um:g;Rtg; sA edayeRbIsmIkar (-11)

mmd 240"= mme 545'= ( ) kNddCadC

eP scnx 80.3148'

2'1

=⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −=

2> kMNt;lT§PaBRTbnÞúkmYyTis nyP tamG½kS y enAeBl mmex 205= . kñúgkrNIenH mmh 400= nig mmb 600= / mmd 340= / mmd 60'= nig 274.2412' mmAA ss == .

dMeNaHRsaynwgeFVIeLIgedayeRbIsmIkarsþaTic dUcesckþIBnül;kñúgCMhanxagelI. a. sRmab; balanced condition

mmdf

cy

b 204340400600

600600

600=⎟

⎠⎞

⎜⎝⎛

+=⎟

⎟⎠

⎞⎜⎜⎝

⎛

+=

mmab 2.1632048.0 =×= ¬ 8.01 =β enAeBl MPaf c 35' = ¦ kNabfC cc 12.2913'85.0 ==

MPaf s 5.423204

60204600' =⎟⎠⎞

⎜⎝⎛ −

= dUcenH MPaff ys 400' ==

kNffAC cyss 32.893)'85.0(' =−= kNfAT ys 1.965== kNTCCP scby 34.2841=−+=

kNPP byby 9.184634.284165.065.0 =×==φ ¬ 65.0=φ sRmab; 002.0=tε ¦ b. sRmab; mmdmmex 340205 =<= / snμt;famuxkat;sßitkñúglkçxNÐ compression failure

ehIyGnuvtþtamCMhankñúg]TahrN_TI4 edIm,ITTYl)an mma 166= nig mmac 5.2078.0==

mmcb 204=> . dUcenH muxkat;Camuxkat; compression control. epÞógpÞat; ys fMPa

cdcf >=⎟⎠⎞

⎜⎝⎛ −

= 5.426'600' dUcenH eyIgyk MPaff ys 400' ==



epÞógpÞat; ys fMPac

cdf <=⎟⎠⎞

⎜⎝⎛ −

= 383600

KNnakmøaMg kNabfC cc 3.2963'85.0 == kNffAC cyss 32.893)'85.0(' =−= kNfAT ss 22.924=⋅= byscny PkNTCCP >=−+= 4.2932 dUcenHvaCakrNI compression

failure dUckarsnñidæan. 002.00019.0003.0 <=⋅⎟

⎠⎞

⎜⎝⎛ −

=c

cdtε 65.0=⇒φ

kNPny 1.1906=φ c. Kitm:Um:g;Rtg; sA edayeRbIsmIkar (-11)

mmd 140"= mme 345'= ( ) kNddCadC

eP scny 5.2932'

2'1

=⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −=

3> kMNt;bnÞúkcMp©it noP tamRTwsþI )'85.0('85.0 cystgcno ffAAfP −+=

( ) ( ) kN2.95223585.040064346004003585.0 =×−+×××= kNPno 4.6189=φ

4> edayeRbIsmIkar Bresler (11-28) nigKuNCamYy 1000 eyIg)an 8516.0

4.61891000

1.19061000

74.204610001000

=−+=uP

kNPu 3.1174= nig kNPP un 6.1806

65.0==

cMNaM³ 1> smIkarRbEhl approximate equation b¤taragExSekag ACI GacRtUv)aneRbIedIm,IkMNt; nxP nig

nyP . edaysarEtsmIkar Bresler pþl;cUvdMeNaHRsayEdlmantémøRbhak;RbEhl enaHeKKYr EteRbIviFIsaRsþkñúgkaredaHRsayEdlmanlkçN³suRkitdUcEdl)anGnuvtþkñúg]TahrN_xagelIenH edIm,IkMNt; nxP nig nyP . dMeNaHRsayRbhak;RbEhlCaeRcIn pþl;nUvlT§plminsuRkit. eKGac rk)annUvkm μviFIkMuBÚüT½rEdlQrelIeKalkarN_smIkarsþaTic ehIyeKGaceRbIvaedIm,IepÞógpÞat;nUv lT§plrbs;eyIg.



2> enAkñúg]TahrN_TI 18 xagelI RkLaépÞEdkenARKb;RCugRtUv)aneRbIBIrdg edaymþgeRbIedIm,I

KNna nxP nigmþgeToteRbIedIm,IKNna nyP . dMeNaHRsayEdlmanlkçN³snSMsMéc KweRbIEdk EdlsßitenARCugEtBak;kNþalsRmab;TismYy² Edl 25.1608' mmAA ss == enaHvanwgkat;bnßy témørbs; nxP nig nyP .

]TahrN_19³ kMNt;bnÞúkKNna nominal design load nP sRmab;ssrmuxkat;dUc]TahrN_TI18 edayeRbIviFIExSvNÐbnÞúk Parme. emIlrUbTI29. dMeNaHRsay³ 1> snμt; 65.0=β . lT§PaBRTbnÞúktammYyTissRmab;TisedA x nig y RtUv)anKNnaenA

kñúg]TahrN_TI18. 2> kNPux 74.2046= kNPuy 1.1906= kNPnx 83.3148= kNPny 4.2932= lT§PaBTb;m:Um:g;rbs;muxkat;CMuvijG½kS x mkNePM ynxox .4.960305.083.3148 =×== lT§PaBTb;m:Um:g;rbs;muxkat;CMuvijG½kS x mkNePM xnyoy .14.601205.04.2932 =×== 3> eday nP Ca nominal design load enaH nominal design moment enAelImuxkat;CMuvijG½kS x KW



nynnx PePM 305.0== ehIy nominal design moment enAelImuxkat;CMuvijG½kS y KW

nxnny PePM 205.0== 4> RtYtBinitü >

oy

ny

MM

ox

nx

MM

4.960305.0

14.601250.0 nn PP

> b¤ nn PP 44 1017.31041.3 −− ⋅>⋅ dUcenHeRbIsmIkar (-34)

5> 165.0

65.014.960

305.014.601

250.0=⎟

⎠⎞

⎜⎝⎛ −

+ nn PP

eyIgTTYl)an kNPn 125.1953= kNPP nu 5.1269==φ ( )65.0=φ eyIgeXIjfa uP EdlKNnaedaysmIkar Parm FMCag uP EdlKNnaedaysmIkar Bresler

RbEhl %8 .



11>18> smIkarépÞ)ak; (Equation of failure surface)

smIkarTUeTAsRmab;viPaK nigKNnassrebtugxøIEdkkgFmμtamuxkat;ctuekaNEkgRtUv)anesñIeLIg edayelak Hsu. smIkarRtUv)ansnμt;tMNag[épÞ)ak; failure surface nigdüaRkamGnþrkmμ interaction

diagram rbs;ssrEdlrgnUvm:Um:g;BIrTis nigbnÞúkcMG½kS dUcbgðajkñúgrUbTI26. bnÞúkcMG½kSGacCakmøaMgsgát; b¤kmøaMgTaj.

0.15.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

by

ny

bx

nx

bo

bn

MM

MM

PPPP (11-40)

Edl =nP ersIusþg;Tb;kmøaMgtamG½kS nominal axial strength ¬viC¢manenAeBlrgkarsgát; nigGviC¢ manenAeBlrgkarTaj¦ sRmab;cMNakp©itEdl[.

=oP bnÞúktamG½kS nominal axial load ¬viC¢manenAeBlrgkarsgát; nigGviC¢manenAeBlrgkar Taj¦ sRmab;cMNakp©itsUnü.

=bP bnÞúksgát;tamG½kS nominal axial compressive load enAkñúglkçxNÐ balanced strain. =nynx MM , m:Um:g;Bt; nominal bending moment CMuvijG½kS x nig y erogKña. =bybx MM , m:Um:g;Bt; nominal balanced bending moment CMuvijG½kS x nig y erogKña enAlkçxNÐ

balanced strain condition. edIm,IeRbIsmIkar (11-40) RKb;tYTaMgGs;RtUvmansBaØaviC¢man. témørbs; oP KW

yststgco fAAAfP +−= )('85.0 (11-41) bnÞúk nominal balanced load, bP / nigm:Um:g; nominal balanced moment, bbb ePM = Edl)an[

enAkñúgsmIkar (11-6) nig (11-7) erogKña sRmab;muxkat;CamYynwgEdkrgEtkarTaj nigsgát;b:ueNÑaH. sRmab;muxkat;epSgeTot témøenHGacTTYl)anedayeRbIeKalkarN_smIkarsþaTic.

cMNaMfa smIkarépÞ)ak; failure surface k¾GaceRbIsRmab;m:Um:g;mYyTisEdlbgðajenA kñúgdüaRkam Gnþrkmμ (interaction diagram) pgEdr. kñúgkrNIenH GgÁTIbInwgRtUvlb;ecalenAeBl 0=xe nigGgÁTIBIrRtUv )anlb;ecalenAeBl 0=ye .

enAeBl 0=xe ¬manEtm:Um:g;Bt;CMuvijG½kS x ¦

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

bx

nx

bo

bn

MM

PPPP (11-42)

¬vaCasmIkar (11-18) EdlmanBIxagedIm¦ enAeBl 0=ye ¬manEtm:Um:g;Bt;CMuvijG½kS y ¦

0.15.1

=⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−−

by

ny

bo

bn

MM

PPPP (11-43)



Gnuvtþn_smIkar (11-42) eTAkñúg]TahrN_TI 2 nigTI 4. kNPb 8.1991= mkNM bx .8.732= mmey 254= nig kNPo 23.6275)4008

428()8

428350550(2785.0

22

=×××

+××

−×××=ππ

18.732

254.08.199123.6275

8.1991 5.1

=⎟⎠⎞

⎜⎝⎛+

−− nn PP

23.627502764.0 5.1 =+ nn PP kNPn 5.2603= EdlvamantémøRbEhlnwg nP EdlKNnaedaykarviPaK.

]TahrN_20³ kMNt;bnÞúkKNna nominal design load nP sRmab;ssrmuxkat;dUc]TahrN_TI18 edayeRbIsmIkarépÞ)ak; (equation of failure surface). dMeNaHRsay³ 1> KNna yststgco fAAAfP +−= )('85.0

kNPo 18.95224004328)8

432400600(3585.0

22

=+−××=ππ

2> KNna bP nig bM edayeRbIsmIkar (11-8) nig (11-9) tamG½kS x nig y erogKña A. tamG½kS x mmdt 540=

mmf

dcy

tbx 324

400600540600

600600

=+×

=+

=

mmabx 2.2593248.0 =×= MPa

cdcf s 89.488'600' =⎟⎠⎞

⎜⎝⎛ −

= MPaf s 400' =

mmd x 240" = 274.2412' mmAA ss == yscysbxcbx fAffAbafP −−+= )'85.0(''85.0

kN7.301240074.2412)3585.0400(74.24124002.2593585.0 =×−×−+×××= xysxcysx

bxbxcbx dfAdddffAdadbafM ")"')('85.0('"

2'85.0 +−−−+⎟

⎠⎞

⎜⎝⎛ −−=

mkN.28.973= B. tamG½kS y mmdt 340= mmd y 140" = 274.2412' mmAA ss ==

mmf

dcy

tby 204

400600340600

600600

=+×

=+

=

mmaby 2.1632048.0 =×= MPa

cdcf s 53.423'600' =⎟⎠⎞

⎜⎝⎛ −

= MPaf s 400' =



kNPby 34.284140074.2412)3585.0400(74.24216002.1633585.0 =×−×−+×××=

yysycysyby

bycby dfAdddffAda

dhafM ")"')('85.0('"2

'85.0 +−−−+⎟⎟⎠

⎞⎜⎜⎝

⎛−−=

mkN.09.605= 3> KNnabnÞúk nominal balanced load bbP sRmab;m:Um:g;BirTis

672.0305205tan ====

yn

xn

nx

ny

ePeP

MM

α o9.33=α

α−Δ

=−

ob

obybx PPP

9090 oo

bo

P9.339090

34.28417.3012−Δ

=−

kNPb 8.106=Δ kNPPP bbybb 14.29488.10634.2841 =+=Δ+=

4> KNna nP BismIkarépÞ)ak; failure surface³ 0.1

09.605205.0

28.973305.0

14.294818.952214.2948 5.15.1

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

−− nnn PPP

18.95220775.0 5.1 =+ nn PP edaykarsakl,g eyIgTTYl)an kNPn 3.2094= . edaysar bbn PP < vaCakrNI)ak;eday karTaj tension failure sRmab;karBt;BIrTis. dUcenHeyIgyk kNPo 18.9522−= edIm,IrkSaGgÁ TImYyviC¢man.

0.109.605

205.028.973

305.014.294818.9522

14.2948 5.15.1

=⎟⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛+⎟

⎠⎞

⎜⎝⎛

−−− nnn PPP

18.9522147.0 5.1 −=− nn PP kNPn 5.1811= nig kNPu 5.1177=

cMNaM³ ersIusþg;RTbnÞúk nPφ rbs;ssrmuxkat;ctueekaNEdl)anKNnaedayeRbIsmIkar Bresler

reciplocal equation (11-18) viFI Parme method (11-19) nigviFI Hsu method (11-20) edIm,I TTYl)an kNPn 3.1174=φ / kN5.1269 nig kN5.1177 erogKña. eyIgeXIjfa viFI Parme

method pþl;nUvtémøFMCageKsRmab;]TahrN_enH.


ssrEvg 315 T.Chhay

XII. ssrEvg

12>1> esckþIepþIm sRmab;karKNnassrxøIEdl)anBnül;enAkñúgBIremeronxagedIm )ansnμt;fa karPøat; (buckling) kar

rYjxøIeGLasÞic (elastic shortening) nigm:Um:g;TIBIr (secondary moment) EdlbNþalmkBIPaBdabtamTTwg (lateral deflection) man\T§iBlCaGb,brmaeTAelIersIusþg;cugeRkay (ultimate strength) rbs;ssr dUcenH ktþaTaMgenH minRtUv)anrab;bBa©ÚleTAkñúgdMeNIrkarénkarKNnaeT. b:uEnþ sRmab;ssrEvg ktþaTaMgGs;enHRtUv EtykmkBicarNa. RbEvgbEnßmnwgbNþal[mankarkat;bnßyersIusþg;rbs;ssr edayERbRbYlCamYynwg km<s;RbsiT§PaB nigTTwgrbs;muxkat; pleFobrlas; (slenderness ratio) niglkçxNÐcugssr.

ssrEdlman slenderness ratio FMnwgkat;bnßylT§PaBRTRTg;rbs;ssry:agxøaMg Et slenderness

ratio tUcmann½yfassrxøI ehIykarkat;bnßyersIusþg;GacnwgminKYr[cab;GarmμN_. pleFobrlas; (slenderness ratio) KWCapleFobrvagkm<s;ssr l CamYynwgkaMniclPaB radius of gyration r Edl

AIr /2 = kñúgenaH I Cam:Um:g;niclPaBénmuxkat; moment of inertia of the section nig A CaRkLaépÞ muxkat;.

sRmab;muxkat;ctuekaNEdlmanTTwg b nigkm<s; h ¬rUbTI 1¦ 12/3bhIx = nig bhA = dUcenH hrx 288.0= ¬b¤edaytémøRbEhl hrx 3.0= ¦. dUcKña 12/3hbI y = nig bry 288.0= ¬b¤ bry 3.0= ¦.

sRmab;ssrmUlCamYynwgGgát;p©it D enaH 64/4DII yx π== nig 4/2DA π= dUcenH Drr yx 25.0== . CaTUeTA ssrGacRtUv)anBicarNa dUcteTA³ 1> EvgCamYynwg slenderness ratio FM RtUvkarRbB½n§BRgwg b¤ shear wall.

2> EvgCamYynwg slenderness ratio l μmEdlbgá[mankarkat;bnßyersIusþg;ssr enaHRbB½n§BRgwg GacnwgminRtUvkar Etkarkat;bnßyersIusþg;RtUvEtBicarNa.

3> xøIEdl slenderness ratio tUcEdlbNþal[mankarkat;bnßyersuIsþg;sþÜcesþIg. kmøaMgkat;Gac RtUv)anecal dUcerobrab;BIemeronmun.

12>2> RbEvgssrRbsiT§PaB (Effective Column Length) uKl

pleFobrlas; (slenderness ratio) rl / GacRtUv)anKNnay:agsuRkitenAeBlEdlRbEvgRbsiT§PaB rbs;ssr ¬ uKl ¦ RtUv)aneRbI. RbEvgRbsiT§PaBenHGnuKmn_eTAnwgBIrktþaFM²³

1> RbEvgKμanTRm (unsupported length) ul sMEdgnUvkm<s;minKitTRmrbs;ssrrvagBIrkRmal xNÐ. vaRtUv)anvas;Ca clear distance rvagkRmalxNÐ Fñwm


T.Chhay 316 Slender Column

b¤GgÁeRKOgbgÁúMEdlpþl;nUvTRmxagdl;ssr. enAkñúgRbB½n§kRmalxNÐ flat slab CamYynwg column capital km<s; unsupported height rbs; ssrRtUv)anvas;BIépÞxagelIrbs;kRmalxNÐ xageRkameTA)atrbs; column capital. RbsinebI ssrRtUv)anRTCamYyFñwmEdlmankm<s;x<s; tamTismYyCagtamTismYyeTot enaH ul KYrEtKNnatamTisTaMgBIr ¬tamTis x nig y ¦ énmuxkat;ssr. lT§plEdlFMCagRtUv)anBicarNakñúgkarKNna.

2> emKuNRbEvgRbsiT§PaB K bgðajnUvpleFobéncm¶ayrvagcMNucénm:Um:g;sUnüenAkñúgssr nig km<s;KñanTRmrbs;ssrkñúgTisedAmYy. ]TahrN_ RbsinebIRbEvgKμanTRm (unsupported

height) rbs;ssr TRmsnøak; (hinged) enAcugsgçag ¬Edlkareyalxag (sidesway) RtUv)an Tb;¦ KW ul nigcMNucm:Um:g;sUnüenAcug nigKl;ssr EdlenAcugTRmRtIekaN (hinged) enaHemKuN

uu llK /= KWesμ Inwg 1. RbsinebIssr manTRmbgáb; (fixed) enAcugsgçag ehIykareyalxag

(sidesway) RtUv)anTb; cMNucrbt; ¬cMNucm:Um:g;sUnü¦ sßitenA 4/ul BIcugTRm. dUcenH =K

5.0/5.0 =uu ll ¬rUbTI2¦ edIm,IKNnatémød¾RtwmRtUvrbs; K krNI cMbgBIrRtUv)anBicarNa. - enAeBleRKagbgÁúMEdlpÁúMeLIgedayFñwm nigssrRtUv)anBRgwgedayCBa¢aMg shear wall

RbB½n§BRgwgrwg (rigid bracing) b¤TRmxagEdl)anmkBIeRKagbgÁúMenACab;nwgva. cugrbs; ssrnwgsßitenATItaMgdEdl EdlkarrMkilxagrbs;tMNRtUv)ankarBar. CaTUeTAsRmab; eRKagBRgwg témørbs; K KWtUcCag b¤es μ Inwg 1. ACI code, section 10.12 esñI[eRbI

1=K . - enAeBleRKagbgÁúMminRtUv)anBRgwg vanwgGaRs½yeTAnwgPaBrwgRkaj (stiffness) rbs;Fñwm

nigssr edIm,ITb;nwgPaBdabxag. edaysarkarrMkilrbs;tMNminRtUv)ankarBar eRKag egakeTAtamTisrbs;bnÞúkxag. témørbs; K sRmab;ssr nigeRKagRtUv)an[enAkñúg rUbTI2 edayBicarNakrNITaMgBIr KWenAeBlkareyalxag sidesway RtUv)ankarBar nig minRtUv)ankarBar.

12>3> emKuNRbEvgRbsiT§PaB (Effective Length Factor) K

RbEvgRbsiT§PaBrbs;ssrGacRtUv)anKNnaedayeRbIdüaRkam alignment chart kñúgrUbTI3. edIm,Irk emKuNRbEvgRbsiT§PaB K dMbUgeKcaM)ac;RtUvKNnarkemKuNTb; restraint factor Aψ nig Bψ enAxagcugnig Kl;ssrerogKña Edl


ssrEvg 317 T.Chhay

∑∑= Fwmrbs;

ssrrbs;

lEIlEI c

//

ψ (12-1)

Edl =cl RbEvgKitBIG½kSeTAG½kSéntMNrbs;eRKag =l RbEvgElVgKitBIG½kSeTAG½kSéntMNrbs;eRKag ¬TaMgBIrsßitenAkñúgbøg;Bt;¦. emKuN ψ enAxagcugKYrEtrYmbBa©ÚlTaMgssr nigFñwmEdlCYbKñaenARtg;

tMN. sRmab;TRmsnøak; hinged end ψ KWGnnþ nigGacsnμt;es μ I 10. sRmab;TRmbgáb; fixed end ψ KWsUnü nigGacsnμt;es μ I 1. témøsnμt;TaMgenHGaceRbI)anedaysarEtenAkñúgeRKagbgÁúMebtugGarem:K μansnøak;K μankkit l¥\tex©aH b¤TRmbgát;l¥\tex©aHenaHEdr.

dMeNIrkarrk K KWKNna Aψ sRmab;cugssr nig Bψ sRmab;Kl;ssr. dak; Aψ nig Bψ eTAkñúgdüa Rkam alignment chart énrUbTI3 rYcP¢ab;cMNucTaMgBIredaykat;ExSkNþal EdlbgðajBItémø K . düaRkam BIrEdlmanlkçN³RsedogKñaRtUv)anbgðaj mYysRmab;eRKagBRgwg Edlkareyalxag (sidesway) RtUv)an karBar nigmYyeTotsRmab;eRKagFm μta Edlkareyalxag (sidesway) minRtUv)ankarBar. karbegáItdüaRkam enHKWQrelIkarsnμt;fa³

- eRKagbgÁúMpÁúMeLIgedayeRKagctuekaNsIuemRTI - m:Um:g;Bt;Fñwm)anEckmkssredayTak;TgnwgPaBrwgRkajrbs;va - ssrTaMgGs;TTYlnUvbnÞúkFMenAeBlCamYyKña

edIm,ICMnYsnUvkareRbIdüaRkam alignment chart EdlbgðajkñúgrUbTI3 ACI Code Commentary )an esñInUvsmIkarsRmYldUcxageRkamsRmab;KNnaemKuNRbEvgRbsiT§PaB K .



1> sRmab;Ggát;rgkarsgát;EdlmankarBRgwg témørbs; K GacRtUv)anyktémøtUcCageKkñúg cMeNamsmIkarTaMgBIrxageRkam

)(05.07.0 BAK ψψ ++= (12-2) min05.085.0 ψ+=K (12-3)

Edl Aψ nig Bψ Catémørbs; ψ enAcugsgçagrbs;ssr nig minψ CatémøtUcbMputéntémøTaMgBIr. 2> sRmab;Ggát;rgkarsgát;EdlK μankarBRgwgEtRtUv)anTb;enAcugsgçag témørbs; K Gacsnμt;dUc

xageRkam sRmab; 2<mψ / m

mK ψψ+

−= 1

2020 (12-4)

sRmab; 2≥mψ / mK ψ+= 19.0 (12-5)

Edl mψ CatémømFümrbs; ψ enAcugsgçagGgát;rgkarsgát;. 3> sRmab;Ggát;rgkarsgát;K μankarBRgwgmanTRmsnøak; hinged enAcugmçag enaH K GacRtUv)an

snμt;dUcxageRkam ψ3.02 +=K (12-6)

Edl ψ CatémøenAcugEdlmankarTb;.

]TahrN_ 1³ edayeRbInUvsmIkarxagedIm cUrkMNt;emKuNRbEvgRbsiT§PaB K sRmab;Ggát;rgkarsgát;enA kñúgeRKagCamYynwglkçxNÐxageRkam³

1> eRKagRtUv)anBRgwgedIm,ITb;nwgkareyalxag (sidesway) ehIy 0.2=Aψ nig 0.3=Bψ enAcug xagelI nigxageRkamrbs;Ggát;.

2> eRKagminRtUv)anBRgwgedIm,ITb;nwgkareyalxag (sidesway) eT ehIy 0.2=Aψ nig 0.3=Bψ . ¬Ggát;RtUv)anbgáb;enAcugsgçag¦.

3> eRKagminRtUv)anBRgwgedIm,ITb;nwgkareyalxag (sidesway) eT ehIy 0.0=Aψ ¬TRmsnøak;¦ nig 0.3=Bψ .

dMeNaHRsay³ 1> BIsmIkar (-2) nig (-3)

0.195.0)32(05.07.01 <=++=K 0.195.0)2(05.085.02 <=+=K

eRCIserIsyknUvtémøtUcCageKkñúgcMeNam 1K nig 2K . kñúgkrNIenH 95.0=K .


ssrEvg 319 T.Chhay



2> témømFümrbs; 5.22/)32( =+=mψ . eday 2>mψ eRbIsmIkar (12-5)

684.15.219.0 =+=K 3> BIsmIkar (12-6)

9.2)3(3.02 =+=K


ssrEvg 321 T.Chhay

12>4> PaBrwgRkajrbs;Ggát; (Member Stiffness) EI

PaBrwgRkajrbs;Ggát;eRKages μ InwgplKuNrvagm:UDuleGLasÞic E CamYynwgm:Um:g;niclPaBénmuxkat; I . témøén E nig I sRmab;ebtugGarem:GacRtUv)anKNnadUcxageRkam³

1> m:UDuleGLasÞicrbs;ebtugRtUv)anBnül;kñúgemeronTI2. bTdæan ACI Code [smIkarxag eRkam cc fwE '043.0 5.1= b¤ cc fE '4780=

sRmab;ebtugTm¶n;Fm μta. cMENkÉm:UDuleGLasÞicrbs;EdkKW MPaEs5101.2 ⋅= .

2> sRmab;Ggát;ebtugGarem: m:Um:g;niclPaB I ERbRbYltambeNþayrbs;Ggát; GaRs½yeTAnwgkRmit eRbH nigPaBryEdkEdl)aneRbIR)as;.

edIm,IkMNt;nUvemKuN ψ EI RtUvEt)ankMNt;sRmab;Fñwm nigssr. dUcenH EI GacRtUv)ankM Nt;dUcxageRkam ¬ACI Code, section 10.11.1¦³

sRmab;Fñwm gII 35.0= sRmab;ssr gII 70.0= sRmab;CBa¢aMg¬K μaneRbH¦ gII 70.0= sRmab;CBa¢aMg¬maneRbH¦ gII 35.0= sRmab;kRmalxNÐ (flat plate nig flat slab) gII 25.0= Edl gI Cam:Um:g;niclPaBsRmab;muxkat;ebtugeBjeFobG½kSkat;tamTIRbCMuTm¶n; edayecal

Edk. 3> RkLaépÞmuxkat; gAA = ¬RkLaépÞmuxkat;eBj gross-sectional area¦ 4> m:Um:g;niclPaBKYrEtRtUv)anEckeday ( )dβ+1 enAeBlEdlbnÞúkxagefr (sustained lateral load)

manGMeBIelIeRKagbgÁúM b¤sRmab;epÞógpÞat;sßirPaB stability check Edl

load axial factored totalload axial sustained factored maximum

=dβ

12>5> EdnkMNt;sRmab;pleFobrlas; (Limitation of The Slenderness Ratio) rKlu /

12>5>1> eRKagGt;eyal (Nonsway Frames)

bTdæan ACI Code, section 10.12 ENnaMnUvEdnkMNt;xagRkamrvagssrxøI nigssrEvgenAkñúgeRKag BRgwg ¬Gt;eyal nonsway¦³ 1> \T§iBlrbs;PaBrlas; slenderness GacRtUv)anecal ehIyssrGacRtUv)anKNnaedayKitCassrxøI

enAeBlEdl³



2

11234M

Mr

Klu −≤ (12-7)

Edl 1M nig 2M Cam:Um:g;emKuNenAcugssr ehIy 12 MM > .

2> pleFob

2

1

MM RtUvcat;Tukfa viC¢manRbsinebIGgát;RtUv)anenAkñúgkMeNageTal single curvature

nigGviC¢mansRmab;kMeNagDub double curvature dUcbgðajkñúgrUbTI4. 3> tY )/1234( 21 MM− KYrminRtUvFMCag 40. 4> RbsinebIm:Um:g;ssremKuN (factored column moment) esμ IsUnü b¤ min/ ePMe uu <= témørbs;

2M KYrEtRtUv)anKNnaedayeRbIcMNakp©itGb,brma³ )03.024.15(min he += (12-8)

)03.024.15(2 hPM u += (12-9)

Edl 2M Cam:Um:g;Gb,brma. m:Um:g; 2M KYrEtRtUv)anBicarNaedayeFobnwgG½kSnImYy²rbs;ssrdac; edayELkBIKña. témø K GacRtUv)ansn μt;esμ Inwg 0.1 sRmab;eRKagBRgwg braced frame elIkElgEt vaRtUv)anKNnaedayQrelIkarviPaK EI .


ssrEvg 323 T.Chhay

12>5>2> eRKageyal (sway Frames)

enAkñúgGgát;rgkarsgát;minBRgwgTb;nwgkareyalxag sidesway \T§iBlrbs;pleFobrlas; slenderness ratio GacecalenABlEdl

22<r

Klu (ACI Code, section 10.13) (12-10)

12>5>3> pleFobrlas;FM (High slenderness ratio)

enAeBlEdlGgát;rgkarmYydac;edayELkenAkñúgeRKagmanpleFobrlas; slenderness ratio

100/ >rKlu viFIm:Um:g; magnifier (moment magnifier method) rbs; ACI Code minGacRtUv)aneRbI ehIykarviPaK rigorous dWeRkTIBIr rigorous second-order RtUv)aneRbICMnYsvij. Etmuxkat;GacRtUv)an dMeLIgedIm,Ikat;bnßypleFob rKlu / . tMé;l 100 bgðajBIkarBiesaFCak;EsþgcMNat;fñak;x<s; (ACI

Code, section 10.10.5) .

12>6> viFIKNnabEnßmm:Umg; (Moment-Magnifier Design Method)

12>6>1> esckþIepþIm (Introduction) CMhandMbUgkñúgkarKNnam:Um:g;enAkñúgssrEvgKWkMNt;faetIeRKagEdlKNna CaeRKakBRgwg b¤min

BRgwgTb;nwg sidesway . RbsinebImanGgÁBRgwgxag dUcCa shear walls nig shear trusses b¤ssrmanPaBrwg RkajTTwg lateral stiffness efr enaHPaBdabTTwg lateral deflection mantémøtUc ehIy\T§iBlrbs;vaeTAelI ersIusþg;ssrk¾tUcEdr. eKGacsnμt;faeRKagbgÁúMenAkñúgmYyCan;²RtUv)anBRgwgRbsinebI

05.0≤Δ

= ∑cus

oulV

PQ (-11)

Edl ∑ uP nig usV CabnÞúkbBaÄrsrub nigkmøaMgkat; erogKña ehIy oΔ PaBdabeFobdWeRkTImYy (first-

order relative deflection) rvagkMBUl nig)atrbs;Can;EdlbNþalmkBI usV . RbEvg cl CaRbEvgrbs;Ggát;rg karsgát;enAkñúgeRKagbgÁúM edayvas;BIG½kSeTAG½kSrbs;tMNrenAkñúgeRKag.

CaTUeTA Ggát;rgkarsgát;GacrgnUgPaBdabTTwg lateral deflection EdlbNþalmkBIm:Um:g;TIBIr (secondary moment). RbsinebIm:Um:g;TIBIr 'M RtUv)anbEnßmeTAelIm:Um:g;EdlGnuvtþelIssr aM enaHm:Um:g; cugeRkayKW 'MMM a += . viFIRbEhl (approximate method) sRmab;kMNt;m:Um:g;cugeRkay M KWCakar KuNm:Um:g; aM edayemKuNEdleKehAfa emKuNbEnßmm:Um:g; (magnifying moment factor) ehIyemKuNenH RtUvEt FMCagb¤esμ Inwg 0.1 . b¤ aMM δ=max nig 0.1≥δ . m:Um:g; aM RtUv)anTTYlBIkarviPaKeRKageGLasÞic



eday eRbIbnÞúkemKuN ehIyvaCam:Um:g;GtibrmaEdlmanGMeBIenAcugssr b¤enAkñúgssr RbsinebIbnÞúkxagman vtþman.

RbsinebI\T§iBl Δ−P RtUv)anykmkBicarNa vanwgcaM)ac;RtUvEteRbIkarviPaKdWeRkTIBIr edIm,IKitBI TMnak;TMng nonlinear relationship rvagbnÞúk PaBdabTTwg nigm:Um:g;. eKGaceRbIkm μviFIkMuBüÚTr½edIm,IedaHRsay va. bTdæan ACI Code GnuBaØati[eRbIkarviPaKssrdWeRkTImYy b¤dWeRkTIBIr. karviPaKssrdWeRkTIBIr RtUv)an tRmUv[eRbIenAeBlEdl 100/ >rKlu . viFIKNnam:Um:g;bEnßmrbs; ACI Code CaviFIsRmYlsRmab;KNna emKuNbnÞúkbEnßmTaMgeRKagBRgwg nigeRKagminBRgwg.

12>6>2> m:Um:g;bEnßmenAkñúgeRKagGt;eyal (Magnified Moments in Nonsway Frames)

\T§iBlrbs;pleFobrlas; slenderness ratio rKlu / enAkñúgGgát;rgkarsgát;éneRKagBRgwgGac RtUv)anecalRbsinebI 21 /1234/ MMrKlu −≤ dUcbgðajenAkñúgEpñk 5>1 . RbsinebI >rKlu /

21 /1234 MM− enaH\T§iBlPaBrlas;RtUv)anBicarNa. dMeNIrkarkMNt;emKuNbEnßm nsδ enAkñúgeRKagmin eyalGacRtUv)ansegçbdUcxageRkam (ACI Code, section 10.12)³

1> kNt;faeRKagCaeRKagBRgwgTb;nwg sidesway b¤Gt; rYckMNt;RbEvgKμanTRm ul nigemKuNRbEvg RbsiT§PaB K ¬ K RtUv)ansnμt;[es μ I 0.1 ¦

2> KNnaPaBrwgRkajrbs;Ggát; EI edayeRbIsmIkar

d

sesgc IEIEEI

β++

=1

2.0 (12-12)

b¤smIkarEdlsRmYlCag

d

gcIEEI

β+=

14.0 (12-13)

gcIEEI 25.0= ¬sRmab; 6.0=dβ ¦ (-1214)

Edl cc fE '4780= MPaEs

5101.2 ⋅= =gI m:Um:g;niclPaBénmuxkat;ebtugtamG½kSNamYyEdleyIgBicarNaedayecal sA =seI m:Um:g;nicalPaBénmuxkat;EdkeFobG½kSTIRbCMuTm¶n;rbs;muxkat;ebtug

load axial factored maximumload sustained axial factored maximum

=dβ)(sustained

6.12.12.1

LDD+

=

cMNaMfa³ dβ xagelICapleFobEdlFøab;KNnam:Um:g;bEnßmenAkñúgssrEdlbNþalmkBIbnÞúk sustained .


ssrEvg 325 T.Chhay

smIkar (-13) nig (-14) manlkçN³suRkitticCagsmIkar (-12) . elIsBIenH smIkar (12-14)

TTYl)anedaysnμt; 6.0=dβ CMnYskñúgsmIkar (-13) . 3> kMNt;bnÞúk Euler buckling/ cP ³

( )22

uc

KlEIP π

= (12-15)

eRbItémørbs; EI / K nig ul dUcKNnaBICMhan 1> nigCMhan 2>. 4> KNnatémøénemKuN mC edIm,IeRbIenAkñúgsmIkarénemKuNm:Um:g;bEnßm moment-magnifier

factor. sRmab;Ggát;BRgwgedayK μanbnÞúkxag transverse load 4.04.06.0

2

1 ≥+=M

MCm (12-16)

Edl 21 / MM viC¢manRbsinebIssrRtUv)anBt;kñúgkMeNageTal. sRmab;Ggát;CamYybnÞúkxag enA cenøaHTRm mC KYrRtUv)anykes μ Inwg 0.1 .

5> KNnaemKuNm:Um:g;bEnßm nsδ 0.1

)75.0/(1≥

−=

cu

mns PP

Cδ (12-17)

Edl uP CabnÞúkemKuN nig cP nig mC RtUv)anKNnaBIxagelI. 6> KNnaGgát;rgkarsgát;edayeRbIbnÞúkemKuNtamG½kS uP BIkarviPaKeRKagd¾RtwmRtUv nigm:Um:g;

bEnßm magnified moment cM EdlKNnadYcxageRkam³ 2MM nsc δ= (12-18)

Edl 2M Cam:Um:g;emKuNEdlFMCagEdlekItBIbnÞúk EdllT§plmineyal. sRmab;eRKagBRgwg Tb;nwg sidesway emKuNeyalKW 0=sδ . enAkñúgeRKagGt;eyal nonsway frame PaBdab TTwgRtUv)anrMBwg[tUcCagb¤es μ Inwg 1500/H Edl H Cakm<s;srubrbs;eRKag.

12>6>3> m:Um:g;bEnßmenAkñúgeRKageyal (Magnified Moments in sway Frames)

\T§iBlrbs;PaBrlas;GacRtUv)anecalenAkúñgeRKageyal sway frame ¬KμanBRgwg unbraced¦ enAeBlEdl 22/ <rKlu . karKNnaemKuNbEnßm magnification factored sδ sRmab;eRKageyal ¬Kμan BRgwg¦ RtUv)ansegçbdUcxageRkam (ACI Code, Section 10.13)³

1> kMNt;faeRKagCaeRKagKμanBRgwgTb;nwg sidesway b¤Gt; rYckMNt;RbEvgKμanTRm ul nigemKuN RbEvgRbsiT§PaB K EdlGacTTYlBIsmIkar (12-4) (12-5) nig (12-6) b¤düaRkamrUbTI3.



2-4> KNna EI / cP nig mC dUc[kñúgsmIkar (12-12) dl; (12-16). cMNaMfa dβ ¬edIm,IKNna EI ¦ KW CapleFobrvagkmøaMgkat;TTwgefremKuNGtibrma maximum factored sustained shear tamCan; nigkmøaMgkat;TTwgemKuNsrubenAkñúgCan;enaH.

5> KNnaemKuNm:Um:g;bEnßm moment-magnifier factor/ sδ ³ 0.1

)75.0/(11

≥−

=∑ ∑ cu

s PPδ (12-19)

Edl 5.2≤sδ nig ∑ uP CaplbUkbnÞúkbBaÄrTaMgGs;enAkñúgmYyCan; nig ∑ cP CaplbUk bnÞúksRmab;ssrEdlTb;nwgkareyal sway enAkñúgmYyCan;. dUcKña³

scu

sss M

PPMM ≥

−=

∑ ∑ )75.0/(12δ (12-20)

Edl sM Cam:Um:g;emKuNxagcugbNþalmkBIbnÞúkEdlbegáItkareyalEdlTTYlyk)an. 6> KNnam:Um:g;cugbEnßm 1M nig 2M enAxagcugGgát;rgkarsgát;EtÉg dUcxageRkam³

ssns MMM 111 δ+= (12-21)

ssns MMM 222 δ+= (12-22)

Edl nsM1 nig nsM 2 Cam:Um:g;EdlTTYlBIlkçxNÐGt;eyal b:uEnþ sM1 nig sM 2 Cam:Um:g;Edl TTYl)anBIlkçxNÐeyal. RbsinebI 12 MM > BIkarviPaKeRKag enaHkarKNnam:Um:g;bEnßmKW³

ssnsc MMM 22 δ+= (12-23) m:Um:g;cug 1M nig 2M enAkñúgsmIkar (-21) (-22) nig (-23) manm:Um:g;Gt;eyal bUknigm:Um:g; eyalbEnßm CamYynwglkçxNÐEdl

gcu

uAfPr

l'/

35< (12-24)

enAkñúgkrNIenH Ggát;rgkarsgát;KYrEtRtUv)anKNnasRmab;bnÞúkemKuNtamG½kS uP nig cM . b:uEnþkñúgkrNIEdl

gcu

uAfPr

l'/

35> (12-25)

Ggát;rgkarsgát;KYrEtRtUv)anKNnasRmab; uP nigm:Um:g;Gt;eyalbEnßm 2Mnsδ bUkCamYy nwgm:Um:g;eyalbEnßm 2Msδ CamYynwgm:Um:g;KNna ssnsnsc MMM 22 δδ += . krNIenHGac ekItmansRmab;ssrEvg slender column CamYynwgbnÞúktamG½kSFM enAeBlEdlm:Um:g;Gtibrma ekItmanenAcenøaHcugssr nigminenAxagcug.

bTdæan ACI Code, section 10.13.4 GnuBaØatnUvviFIepSgeTotsRmab;karKNna ssMδ én smIkar (12-20) edayeRbIsnÞsSn_sißrPaB stability index Q Edl[kñúgsmIkar (12-11) Edl

5.1≤sδ ³


ssrEvg 327 T.Chhay

ss

ss MQ

MM ≥−

=1

δ (-26)

]TahrN_ 2³ muxkat;ssrdUcbgðajkñúgrUbTI5 RTbnÞúktamG½kS kNPD 605= nigm:Um:g; mkNM D .157= EdlbNþalmkBIbnÞúkefr nigbnÞúktamGk½S kNPL 490= nigm:Um:g; mkNM L .126= EdlbNþalmkBIbnÞúk cl½t. ssrCaEpñkrbs;eRKagBRgwg nigmankMeNageTaltamG½kSem. RbEvgK μanTRmrbs;ssrKW mlc 8.5= ehIym:Um:g;enAcugTaMgsgçagrbs;ssrmantémøsμ IKña. epÞógpÞat;muxkat;ssredayeRbI MPaf c 28' = nig

MPaf y 400= .

dMeNaHRsay³

1> KNnabnÞúkcugeRkay ultimate load³ kNPPP LDu 15104906.16052.16.12.1 =×+×=+=

mkNMMM LDu .3901266.11572.16.12.1 =×+×=+= mm

PMe

u

u 3.2581510390

===

2> RtYtBinitüemIlfaetIssrEvgb¤xøI. edaysareRKagRtUv)anBRgwg sn μt; 0.1=K mmhr 1655503.03.0 =×== nig mlu 8.5=

15.351655800

==r

Klu sRmab;ssrBRgwg RbsinebI 21 /1234/ MMrKlu −≤ \T§iBlénPaBrlas;GacRtUv)anecal. edaysarssrekagedaykMeNageTal enaH 21 / MM viC¢man. dUcenH



22123412342

1 =−=−MM

edaysar 2215.35/ >=rKlu enaH\T§iBlénPaBrlas;RtUv)anBicarNa. 3> KNna EI BIsmIkar (-12)³

A. KNna cE MPafE cc 4.25293284780'4780 ===

MPaEs5101.2 ⋅=

B. m:Um:g;niclPaBKW ( ) 46

3

106.485212550350 mmIg ⋅== 2

2

24634284' mmAA ss ===

π 46

2

107.2272

12055024632 mmIse ⋅=⎟⎠⎞

⎜⎝⎛ −

×=

pleFobm:Um:g;GefrKW 48.0

15106052.1

=×

=dβ C. PaBrwgRkajKW

d

sesgc IEIEEI

β++

=1

2.0

212656

.109.4848.01

107.227101.2106.48524.252932.0 mmN⋅=+

⋅×⋅+⋅××=

4> KNna cP

( )kN

KlEIPu

c 72.14346)5800(109.48

2

122

2

2

=⋅

==ππ

5> KNna mC BIsmIkar (-16)³ 4.04.06.0

2

1 ≥+=MMCm

( ) 0.114.06.0 =+= 6> KNnaemKuNm:Um:g;bEnßmBIsmIkar (12-17)³

16.1]72.1434675.0/(1510[1

1)75.0/(1

=×−

=−

=cu

mns PP

Cδ

7> KNnam:Um:g;KNna design moment nigbnÞúkKNna design load edaysnμt; 65.0=φ kNPn 2323

65.01510

== mkNM n .600

65.0390

== KNna mkNM c .69660016.1 =×=


ssrEvg 329 T.Chhay

KNnacMNakp©it mme 3002323696

== 8> kMNt;ersIusþg; nominal load strength énmuxkat;edayeRbI mme 300= edayeRbIsmIkar (11-4)³

sn faP 46.258.92633.8 −+= (I) mmhdee 515

2550490300

2' =−+=−+=

( )⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= 6049058.926

249033.8

5151 aaPn

65.773101.893.7 23 +⋅−= − aa (II) BIsmIkar (I) nig (II) eyIgTTYl)an mma 267= / MPafs 338= nig kNPn 2.2319= . edaysarEtersIusþg;bnÞúk load strength kNPn 2.2319= nigbnÞúktRmUvkar required load

kNPn 2323= mantémøRbhak;RbEhlKña enaHmuxkat;RtUv)ancat;TukfaRKb;RKan;. RbsinebI muxkat;minRKb;RKan; RtUvdMeLIgmuxkat;Edk.

9> epÞógpÞat;témøsn μt; φ mma 267= mmc 12.314= mmdt 490=

002.000168.0003.0 <=⎟⎠⎞

⎜⎝⎛ −

=c

cdttε

dUcenH 65.0=φ

]TahrN_ 3³ epÞógpÞat;PaBRKb;RKan;rbs;ssrkñúg]TahrN_TI2 RbsinebIRbEvgKμanTRm (unsupported

length) mlu 3= . kMNt;bnÞúk nominal load GtibrmaenAelIssr. dMeNaHRsay³

1> bnÞúkEdlGnuvtþKW kNPn 2323= nig mkNM n .600= 2> epÞógpÞat;PaBEvgxøIrbs;ssr³ mlu 3= / mmr 1655503.0 =×= nig 0.1=K ¬eRKagRtUv)anBRgwg

Tb;nwgkareyalxag sidesway ¦. 2.18

1653000

==r

Klu epÞógpÞat; bbu MMrKl 21 /1234/ −=

( ) 2211234 =− eday 222.18 <=

rKlu

enaH \T§iBlénPaBrlas;Gacecal)an.



3> kMnt;lT§PaBRTbnÞúk nominal load ebs;ssrxøI dUcBnül;enAkñúg]TahrN_TI4 énemeronTI11 ¬eRKOgbgÁúMrgkarsgát; nigkarBt;;¦. eyIgTTYl)an kNPn 9.2574= ¬sRmab; mme 3.258= ¦ EdlFMCagbnÞúkcaM)ac; kNPn 2323= .

]TahrN_ 4³ epÞógpÞat;PaBRKb;RKan;rbs;ssrkñúg]TahrN_TI2 RbsinebIeRKagminRtUv)anBRgwgTb;nwgeyal xag sidesway emKuNbgáb;cug end-restraint factor KW 8.0=Aψ nig 2=Bψ ehIyRbEvgK μanTRm unsupported length KW mmlu 4850= . dMeNaHRsay³

1> kMNt;témø K BIdüaRkam alignment chart rUbTI3 sRmab;eRKagminBRgwg. P¢ab;témø 8.0=Aψ nig 2=Bψ kat;ExS K Rtg; 4.1=K .

15.41165

48504.1=

×=

rKlu

2> sRmab;eRKagK μanBRgwg RbsinebI 22/ ≤rKlu ssrGacRtUv)anKNnadUcssrxøI. edaysarEttémø 2215.41/ >=rKlu eKRtUvEtKitBI\T§iBlénPaBrlas;.

3> KNnaemKuNm:Um:g;bEnßm nsδ eK[ 1=mC / 4.1=K / 212 .109.48 mNEI ⋅= ¬BI]TahrN_TI2¦ nig

( ) ( )kN

KlEIPu

c 1.1046848504.1

109.482

122

2

2=

×

⋅×==ππ

24.1

1.1046875.015101

1

75.01

=⎟⎠⎞

⎜⎝⎛

×−

=

⎟⎟⎠

⎞⎜⎜⎝

⎛×

−=

c

u

mns

PP

Cδ

4> BI]TahrN_TI2 kNPu 1510= nig mkNMu .390= b¤ kNPn 2323= nig mkNM n .600= m:Um:g;KNna mkNM c .74460024.1 =×= dUcenH

mmPMen

nns 3.3202323744

===δ

5> epÞógpÞat;PaBRKb;RKan;rbs;ssrxøIsRmab; kNPn 2323= / mkNM c .744= nig mme 3.320= . viFIsaRsþkñúgkaredaHRsayRtUv)anBnül;kñúg]TahrN_TI4 én emeronTI 11 ¬eRKOgbgÁúMrgkarsgát; nigkarBt;¦.

6> BI]TahrN_TI4 én emeronTI11 ¬eRKOgbgÁúMrgkarsgát; nigkarBt;¦ eyIg)an sn faP 46.258.92633.8 −+=

mmhdee 3.5352

5504903.3202

' =−+=−+=


ssrEvg 331 T.Chhay

( )⎥⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= 6049058.926

249033.8

3.5351 aaPn

31.74400778.0625.7 2 +−= aa eyIgTTYl)an mma 86.259= dUcenH mmc 7.305= nig kNPn 2200= . lT§PaBRTbnÞúkrbs;ssr kNPn 2200= tUc CagbnÞúkEdlRtUvRT kNPn 2323= . dUcenHmuxkat;minRKb;RKan;.

7> begáInmuxkat;EdkBI 284DB eTA 304DB ehIyeFVIkarKNnaepÞógpÞat;eLIgvij enaHeyIg TTYl)an kNPn 2335= / 002.0<tε nig 65.0=φ .

]TahrN_ 5³ KNnassrkaer:xagkñúgsRmab;Can;TImYyénGKarkariyal½y8Can;. km<s; clear height énCan; TImYyKW m9.4 nigkm<s;sRmab;Can;d¾éTeTotKW m4.3 . GKarenHman 24RbGb; ¬rUbTI6¦ ehIyssrminRtUv )anBRgwgTb;nwgkareyalxag sidesway. bnÞúkEdlGnuvtþmkelIssrxagkñúgCan;TImYy bNþalmkBITMnaj EpndI nigxül;dUcxageRkam³ bnÞúkefrtamG½kS kN1690= bnÞúkGefertamG½kS kN623= bnÞúkxül;tamG½kS kN0= m:Um:g;bnÞúkefr mkN.4.43= ¬xagelI¦ mkN.2.73 ¬xageRkam¦ m:Um:g;bnÞúkGefr mkN.1.27= ¬xagelI¦ mkN.8.48 ¬xageRkam¦

m:Um:g;bnÞúkxül; mkN.8.67= ¬xagelI¦ mkN.8.67 ¬xageRkam¦ lEI / sRmab;Fñwm mmkN.1040 6⋅=

eRbI MPaf c 35' = / MPaf y 400= nigtRmUvkarrbs;bTdæan ACI Code. snμt;fa bnÞúkEdlman GMeBIelIssrxageRkAes μ I 3/2 énssrxagkñúg ehIybnÞúkEdlmanGMeBIelIssrRtg;RCuges μI 3/1 énssrxag kñúg ehIy 55.0=dβ .



dMeNaHRsay³ 1> KNnabnÞúkemKuNedayeRbIkarpSMbnÞúk. sRmab;bnÞúkTMnajEpndI³

kNLDPu 8.30246236.116902.16.12.1 =×+×=+= mkNMMMM LDnsu .92.1658.486.12.732.16.12.12 =×+×=+==

sRmab;bnÞúkTMnajEpndI nigbnÞúkxül; kNWLDPu 5.233906235.016902.1)6.15.02.1( =+×+×=++=

mkNMMMM LDnsuns .92.1658.486.12.732.16.12.12 =×+×=+== mkNMMM wsus .48.1088.676.16.12 =×===

bnSMbnÞúkepSgeTotEdlminsMxan; kNWDPu 152106.116909.06.19.0 =×+×=+=

mkNMM D .84.872.732.19.02 =×== mkNMM ws .48.1088.676.16.12 =×==

mmP

MPMe

u

ns

u

u 85.548.3024

92.1652 ====

mmmmhe 85.5404.2946003.024.15)03.024.15(min <=×+=+= 2> eRCIserIsmuxkat;dMbUgrbs;ssredayEp¥kelIbnSMbnÞúkTMnajEpndIedayeRbItaragb¤düaRkam.

eRCIserIsmuxkat;ssr 460460× CamYynwgEdk 32DB cMnYn4edIm ¬rUbTI7¦.

3> epÞógpÞat; rKlu /

484

103.3712

460 mmI g ⋅== MPaEc 9.28278= sRmab;ssr gII 7.0= sRmab;ssrEdlmankm<s; m9.4


ssrEvg 333 T.Chhay

mmNlEI

c.101.15

49009.28278103.377.0 9

8⋅=

×⋅×=

sRmab;ssrEdlmankm<s; m4.3 mmN

lEI

c.107.21

34009.28278103.377.0 9

8⋅=

×⋅×=

sRmab;Fñwm mmNlEI bg .1040/ 9⋅= / gII 35.0= nig mmNlEI b .1014104035.0/ 99 ⋅=⋅×=

( )( ) 3.1

1014210)7.211.15(

//)()( 9

9=

⋅×⋅+

===∑∑

b

clEIlEIbottomtop ψψ

BItarag alignment chart 4.1=K sRmab;eRKagK μanBRgwg nig 8.0=K sRmab;eRKag BRgwg.

7.494603.0

49004.1=

××

=r

Klu EdlFMCag 22 nigtUcCag 100. dUcenH eKRtUvBicarNaBI slenderness ratio.

4> epÞógpÞat; 5.35)4603.0/(4900/ =×=rlu 8.54

)46046035/(302480035

'/35

=××

=gcu AfP

(-24)

edaysarEt 8.54/ <rlu m:Um:g; nonsway moment mincaM)ac;bEnßm. 5> KNna cP

MPaEc 9.28278= MPaEs5101.2 ⋅=

484

103.3712

460 mmI g ⋅== 4622

10932

3404324 mmIse ⋅=⎟

⎠⎞

⎜⎝⎛=

π

55.0=dβ

d

sesgc IEIEEI

β++

=1

2.0

212658

.102.2655.01

1093101.2103.379.282782.0 mmNEI ⋅=+

⋅×⋅+⋅××=

edIm,IKNna sδ / 0=dβ enaH 212 .63.40102.2655.1 mmNEI =⋅×= kN

KlEIPu

c 86.16827)49008.0(

102.26)( 2

122

2

2=

×⋅×

==ππ ¬BRgwg¦

kNKl

EIPu

c 15.8521)49004.1(

1063.40)( 2

122

2

2=

×⋅×

==ππ ¬K μanBRgwg¦

sRmab;mYyCan;enAkñúgGKar eKmanssrxagkñúg 14 ssrxageRkA 18 nigssrkac;RCug 4 . kNPu 3.63946)5.2339

31(4)5.2339

32(18)5.2339(14 =×+×+=∑



kNPc 244273)15.852132(22)15.8521(14 =×+=∑

54.1)

24427375.03.63946(1

1=

×−

=sδ

EdlFMCag 1 nigtUcCag 5.2 smIkar (-19) mkNMMM ssnsc .33348.10854.192.16522 =×+=+= δ

6> bnÞúkKNnaKW kNPu 5.2339= nig mkNM c .333= mme 34.142

5.2339333

==

emmhe <=×+=+= 04.2946003.024.15)03.024.15(min tamkarviPaK sRmab; mme 34.142= nig 25.1608 mmA = ¬ 65.0=φ ¦ lT§PaBRTbnÞúkrbs; ssrmuxkat; 460460× KW kNPn 1.2348=φ nig mkNM n .2.334=φ dUcenHmuxkat;KWRKb;RKan;. ¬dMeNaHRsaymanlkçN³RsedogKñaeTAnwg]TahrN_TI4 kñúg emeroneRKOgbgÁúMrgkarsgát; nigkarBt;. témø mma 86.242= /

mmc 57.303= / MPafs 6.190= / MPaf s 400' = / kNPb 8.1676=φ nig mmeb 218= ¦.

002.000095.057.303

57.303400003.0 <=−

=tε / 65.0=φ


eCIgtag 335 T.Chhay

XIII. eCIgtag FOOTINGS

13>1> esckþIepþIm (Introduction)

eCIgtagebtugGarem:CaGgát;éneRKOgbgÁúMEdlRtUv)aneRbIedIm,IRTssr nigCBa¢aMg nigmannaTI bBa¢Ún ehIynigBRgaybnÞúkrbs;vaeTAdI. karKNnaKWQrelIkarsnμt;faeCIgtagmanlkçN³rwg dUcenH bERmbRmYlsm<aFdIEdlenABIeRkameCIgtammanlkçN³CabnÞat; (linear). eKTTYl)ansm<aFdIman lkçN³esμIenAeBlEdlbnÞúkssrRtYtsIuKñaCamYynwgTIRbCMuTm¶n;rbs;eCIgtag. ebIeTaHbICakarsnμt;enH Gac TTYlyk)ansRmab;eCIgtagrwg Etkarsnμt;enHkøayeTACaminsUvsuRkitenAeBlEdleCIgtagkøay eTACamanlkçN³Tn; (flexible) xøaMg. karKNnad¾RtwmRtUvrbs;eCIgtagtRmUv[³

- minRtUvFMCaglT§PaBRTRTg;bnÞúkrbs;dI. - RtUveCosvagsRmutFM sRmutDIepr:g;Esül (differential settlement) b¤mMurgVil. - RtUvmanemKuNsuvtßiPaBRKb;RKan;Tb;nwgkarrGil (sliding) nig¼b¤ karRkLab; (overturning).

RbePTeCIgtagEdlmanlkçN³TUeTAbMputenAkñúgsMNg;RtUv)aneRbIKW single footing nig wall

footing ¬rUbTI13>1 nig 13>2¦. enAeBlEdlbnÞúkssrRtUv)anbBa¢ÚneTAdIedayeCIgtag enaHdIrg karsgát;. brimaNénsRmutGaRs½ynwgktþaCaeRcIn dUcCa RbePTdI GaMgtg;sIuetbnÞúk CeRmABIeRkamnIv:U dI RbePTeCIgtag. RbsinebIrcnasm<½n§EtmYymaneCIgtagxusKña enaHvanwgmansRmutxusKña ehIykug RtaMgfμ InwgekItmanenAkñúgeRKOgbgÁúM. sRmutDIepr:g;EsülFMnwgbgá[Ggát;enAkñúgsMNg;EdlminEmnCa eRKOgbgÁúMrgeRKaHfñak; b¤EpñkxøHEdlrgplb:HBal;Gac)ak;.

CaTUeTA bnÞúkbBaÄrRtUv)andak;enAcMTIRbCMuTm¶n;rbs;eCIgtag. RbsinebIkmøaMgGnuvtþn_pÁÜbmin RtYtsIunwgTIRbCMuTm¶n;rbs;eCIgtag enaHm:Um:g;Bt;ekItman. kñúgkrNIenH sm<aFenABIeRkameCIgtagmçag FMCag sm<aFenABIeRkameCIgtagmçageTot.

RbsinebIlT§PaBRTRTg;bnÞúkrbs;dIxusKñaenAeRkameCIgtagepSgKña enaHsRmutDIepr:g;Esülnwg ekItman ¬]TahrN_ RbsinebIeCIgtagénGKarxøHQrelIdI ÉxøHeTotQrelIfμ¦. enAkñúgkrNIEbbenH eKKYreFVIkarEcksMNg;enHCaBIrEpñkedaytMN edIm,IGnuBaØat[vaRsutedayÉkraCüBIKña.

CeRmAeCIgtagBIeRkamnIv:UdIKWCaktþad¾sMxan;kñugkarKNnaeCIgtag. CeRmAKYrRtUv)ankMNt;BIkar BiesaFdI Edl)anpþl;nUvB½t’mand¾KYr[TukcitþBIlT§PaBRTRTg;rbs;dId¾mansuvtßiPaBeTAtamRsTab;dI


T.Chhay 336 Footings

epSgKñaBIeRkamnIv:UdI. r)aykarN_BIkarBiesaFdIkMNt;nUvlT§PaBRTRTg;GnuBaØatedIm,IeRbIkñúgkarKNna. enAtMbn;RtCak;EdlmanFøak;RBil (frost action) GacnwgekIneLIg b¤fycuH. dUcenHeKcaM)ac;RtUvdak; eCIgtagBIeRkam freezing depth edIm,IeCosvagkarmanclna.

13>2> RbePTeCIgtag (Types of Footings)

eKmaneCIgtagCaeRcInRbePTEdleRbIsRmab;RTssr b¤CBa¢aMg. eCIgtagEdleKeRbICaTUeTAman dUcxageRkam³

- Wall footings RtUv)aneRbIedIm,IRT structural wall EdlRTbnÞúkBIkRmalxNÐ b¤edIm,IRT nonstructural walls. vamanTTwgkMNt; nigmanRbEvgCab;KñaenABIeRkamCBa¢aMg ¬rUbTI13>1¦. Wall

footings GacmankRmas;EtmYy Gacmanfñak; b¤GacmanCRmal.


eCIgtag 337 T.Chhay

- Isolated, b¤ single footings RtUv)aneRbIedIm,IRTssreTal ¬rUbTI13>2¦. vaGacmanragkaer ctuekaNEkg b¤rgVg;. mþgeTot eCIgtagmankRmas;esμ I manfñak; b¤manCRmal. vaCaRbePTeCIgtag EdlmanlkçN³snSMsMécbMput nigvaRtUv)aneRbIenAeBlssrmanKMlatq¶ay. RbePTEdleKcUlcitþ eRbICageKKWmanragkaer b¤ctuekaNEkgCamYykRmas;es μ I.

- Combined footing ¬rUbTI13>3¦CaTUeTARTssrBIr b¤ssrbIEdlminenACYrEtmYy. ragrbs; eCIgtagkñúgbøg;GacCactuekaNEkg b¤ctuekaNBñay GaRs½ynwgbnÞúkssr. Combined footings

RtUv)aneRbIenAeBlssrBIrenACitKñaEdleCIgtag single footings minGaceRbI)an b¤enAeBlssrmYy sßitenAelI b¤enAEk,r property line.



- Cantilever or strap footings ¬rUbTI13>4¦ rYmmaneCIgtag single footings BIrP¢ab;edayFñwm mYy b¤ strap mYy nigRTssreTalBIr. vaRtUv)aneRbIenAeBlEdleCIgtagmYyRTssrcakp©it ehIy eCIgtagmYysßitenAEk,rmancm¶ayKMlattUc. RbePTeCIgtagenHCMnYs combined footings nigeBlxøH manlkçN³snSMsMécCag.

- Continuous footings ¬rUbTI13>5¦ RTnUvssrmYyCYrEdlmancMnYncab;BIbIeLIg. vamanTTwg kMNt; nigCab;KñaBIeRkamssrTaMgGs;.


eCIgtag 339 T.Chhay

- Raft b¤ mat foundations ¬rUbTI13>6¦ pSMeLIgedayeCIgtagmYy CaTUeTARtUv)andak;enABI eRkamtYGKarTaMgmUl nigRTssrGKar. vaRtUv)aneRbIenAeBl

a. lT§PaBRTRTg;rbs;dItUc

b. bnÞúkssrFM c. Single footings minGaceRbI d. Piles minRtUv)aneRbI e. sRmutDIepr:g;EsülRtUv)ankat;bnßytamry³RbB½n§RKwHTaMgmUl

- Pile caps ¬rUbTI13>7¦ CakRmalx½NÐRkas;EdlRtUv)aneRbIedIm,IcgP¢ab;RkumssrRKwHCamYy Kña nigedIm,IRT nigbBa¢ÚlbnÞúkssreTAssrRKwH.

13>3> karBRgaysm<aFdI (Distribution of soil pressure)

rUbTI 13>8 bgðajBIeCIgtagEdlRTssreTal. enAeBlbnÞúkssr P RtUv)andak;enABIelITI RbCMuTm¶n;eCIgtag enaHsm<aFesμ IRtuv)ansn μt;ekItmanenAelIépÞdIBIeRkamépÞeCIgtag. b:uEnþkarBit kar BRgaysm<aFdIBitR)akdminesμ IeT vaGaRs½ynwgktþaCaeRcIn CaBiessGaRs½ynwgFatupSMrbs;dI (composition of the soil) nigkRmitTn;rlas; (degree of flexibility) rbs;eCIgtag.



]TahrN_ karBRgaysm<aFenAelIdIEdlK μanPaBs¥it (cohesionless soil) b¤dIxSac;enABIxag eRkameCIgtagrwg (rigid footing) RtUv)anbgðajenAkñúgrUbTI 13>9. sm<aFmantémøGtibrmaenABIxag eRkamG½kSeCIgtag ehIyfycuHenAxagcugeCIgtag. dIEdlK μanPaBs¥it)ancl½tecjBIcugéneCIgtag begáIt[mankarkat;bnßysm<aF b:uEnþsm<aFekIneLIgenAmþúMG½kSedIm,IbMeBjlkçxNÐlMnwg. RbsinebI eCIgtagsßitenABIelIdIs¥it (cohesive soil) dUcCadI\dæ sm<aFenABIxageRkamcugeCIgtagFMCagenARtg; G½kSrbs;eCIgtag ¬rUbTI 13>10¦. dI\dæEk,rcugRKwHmanPaBs¥itxøaMgCamYynwgdI\dæenAEk,rEdlB½T§CMu vijeCIgtag begáIt)anCakarBRgaysm<aFmines μI.

CaTUeTAsm<aFdIRTRTg;GnuBaØat aq RtUv)ankMNt;ecjBIkarBiesaFn_dI. sm<aFdIRTRTg;GnuBaØat enHERbRbYleTAtamRbePTdI BItémøx<s;bMputsRmab;RsTab;fμ (rocky bed) eTAtémøTabbMputsRmab;Rs Tab;dIl,b; (silty soil). ]TahrN_ aq sRmab; sedimentary rock es μ I 2/1450 mkN / sRmab; compacted gravel es μ I 2/400 mkN / sRmab; well-graded compacted sand es μ I 2/300 mkN / nig sRmab; silty-gravel es μ I 2/150 mkN .


eCIgtag 341 T.Chhay

eyagtamrUbTI 13>8 enAeBlEdlbnÞúk P manGMeBI EpñkéneCIgtagBIeRkamssrrkklnwg RsutcuHeRkam. eCIgtagnwgyknUvTRmg;ExSRtg;esμ I EdlbegáItCasm<aFbukeLIgelIvijedIm,ITb;Epñkén eCIgtag. EpñknImYy²mannaTICa cantilever nigRtUv)anKNnasRmab;TaMgm:Um:g;Bt; nigkmøaMgkat;TTwg. karKNnaeCIgtagnwgRtUv)anBnül;y:aglMGitenAeBleRkay.

13>4> karBicarNakñúgkarKNna (Design Consideration)

eCIgtagRtUv)anKNnaedImI,RTbnÞúkssr nigbBa¢ÚnbnÞúkssreTAdIy:agsuvtßiPaB. viFIsaRsþkñúg karKNnaRtUvEtykersIusþg;caM)ac;xageRkammkBicarNa³

- RkLaépÞeCIgtagQrelIlT§PaBRTRTg;dIGnuBaØat - kmøaMgkat;mYyTis one-way shear - kmøaMgkat;BIrTis two-way shear b¤kmøaMgpug punching shear - m:Um:g;Bt; nigbrimaNEdkRtUvkar - lT§PaBRTRTg;rbs;ssrenA)atrbs;va nigEdk dowel caM)ac; - RbEvgf<k;rbs;Edk - sRmutDIepr:g;Esül

ersIusþg;caM)ac;TaMgenHnwgRtUvBnül;enAkñúgEpñkxageRkam.

13>4>1> TMhMeCIgtag (size of Footing) RkLaépÞeCIgtagGacRtUv)anKNnaBIbnÞúkxageRkABitR)akd ¬m:Um:g; nigbnÞúkK μanemKuN¦Edl

minFMCaglT§PaBRTRTg;rbs;dI. CaTUeTA sRmab;bnÞúkQr RkLaépÞeCIgtag

aq pressure, soil allowableweight)-self (including load service total

= ¬!#>!¦

b¤ aq

totalPArea )(=

Edl bnÞúkeFVIkarsrubCabnÞúkKNnaKμanemKuN. enAeBlEdlRkLaépÞRtUv)ankMNt;sm<aFdI emKuNRtUv)anTTYledayEckbnÞúkemKuN LDPu 6.12.1 += eday®kLaépÞeCIgtag. kareFVIEbb enHedIm,IKNnaeCIgtagtamviFIKNnaersIusþg; (strength design method) .



footing of areau

uP

q = ¬!#>@¦

sm<aFdIGnuBaØat aq RtUv)anTTYlBIkarBiesaFdI nigQrelIlkçxNÐbnÞúkeFVIkar (service load) .

13>4>2> kmøaMgkat;mYyTis ¬kmøaMgkat;Fñwm¦ 1uV One-Way Shear (Beam Shear) sRmab;eCIgtagCamYynwgkmøaMgBt;mYyTis muxkat;eRKaHfñak;sßitenAcm¶ay d BIépÞmuxrbs;

ssr. kmøaMgTajGgát;RTUgenAmuxkat; mm − kñúgrUbTI13>11 GacRtUv)anBinitüemIldUcGVIEdl)aneFVI sRmab;Fñwm. kmøaMgkat;TTwgGnuBaØatenAkñúgkrNIenHes μ Inwg³

bdfV cc '122 φφ = ¬ 75.0=φ ¦ ¬!#>#¦

Edl =b TTwgrbs;muxkat; mm − . kmøaMgkat;TTwgemKuNenAmuxkat; mm − GacRtUv)an KNnadUcxageRkam³

⎟⎠⎞

⎜⎝⎛ −−= dCLbqV uu 221 ¬!#>$¦

RbsinebIEdkkmøaMgkat;TTwgminRtUv)aneRbI enaH d GacRtUv)anKNna edaysnμt; cu VV φ= ³

bfV

dc

u

'212 1

φ= ¬!#>%¦


eCIgtag 343 T.Chhay

13>4>3> kmøaMgkat;BIrTis ¬kmøaMgpug¦ 1uV Two-Way Shear (Punching Shear) kmøaMgkat;BIrTisCargVas;énkmøaMgTajGgát;RTUgEdlbNþalmkBI\T§iBlénbnÞúkssrenAelI

eCIgtag. sñameRbHeRTt GacekIteLIgenAkñúgeCIgtagenAcm¶ay 2/d BImuxépÞssrenARKb;RCug. eCIg tagnwg)ak;enAeBlEdlssrBüayamTMluHEpñkéneCIgtag ¬rUbTI13>12¦.

ACI Code, Section 11.12.2 GnuBaØatersIusþg;kmøaMgkat;TTwg cV enAkñúgeCIgtagEdlKμanEdk kmøaMgkat;TTwgsRmab;GMeBIkmøaMgkat;BIrTis es μ InwgtémøtUcCageKbMputén

dbfV occ '124

1 = ¬!#>^¦

12'422

dbfV oc

c ⎟⎟⎠

⎞⎜⎜⎝

⎛+=β

¬!#>&¦

12'

23dbf

bd

V oc

o

sc ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

α ¬!#>*¦

Edl =β pleFobRCugEvgelIRCugxøIrbs;ssr =ob brimaRténmuxkat;eRKaHfñak;EdlenAcm¶ay 2/d BIRkLaépÞbnÞúk ¬muxkat;ssr¦ emIlrUbTI 13>12 =d km<s;RbsiT§PaBrbs;eCIgtag

sRmab;témø 1cV nig 2cV eyIgeXIjfa 1cV lub ¬tUcCag 2cV ¦ enARKb;eBlEdl 2≤β b:uEnþ 2cV lub ¬tUcCag 1cV ¦ enARKb;eBlEdl 2>β . enHbgðaj[eXIjfakmøaMgkat;TTwgGnuBaØat cV

RtUv)ankat;bnßysRmab;eCIgtagEvgxøaMg. bERmbRmYlsm<aFdIBitR)akdtambeNþayRCugEvgCamYynwg karekIneLIgén β . sRmab;rUbragdéTeToteRkABIctuekaN β KWCapleFobrvagTMhMEvgCageKbMputén RkLaépÞbnÞúkRbsiT§PaBkñúgTisedAEvg elITTwgFMCageKbMputkñúgTisedAxøI ¬EkgnwgTisedAEvg¦. sRmab;smIkar ¬!#>*¦ sα RtUv)ansnμt;es μ I 40 sRmab;ssrenAkNþal/ esμ I30 sRmab;ssr enAxag nigesμ I 20 sRmab;ssrenARCug. ersIusþg;kmøaMgkat;TTwgrbs;ebtug 3cV bgðajBI\T§iBlén kMeNIn ob elI d . sRmab;pleFobx<s;én dbo / enaH 3cV nwglub.



QrelItémøTaMgbIxagelIrbs; cV km<s;RbsiT§PaB d EdlcaM)ac;sRmab;kmøaMgkat;BIrTisKW)an mkBItémøEdlFMCageKkñúgcMeNamrUbmnþxageRkam ¬ 75.0=φ ³

oc

u

bfV

d'

3 21

φ= ¬Edl 2≤β ¦ ¬!#>(¦

b¤ oc

u

bf

Vd

'42

12 21

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

βφ

¬Edl 2>β ¦ ¬!#>!0¦

oc

o

s

u

bfb

dV

d'2

12 22

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=α

φ ¬!#>!!¦

kmøaMgkat;TTwgBIrTis 2uV nigkm<s;RbsiT§PaB d caM)ac; ¬RbsinebIEdkkmøaMgkat;TTwgminRtUv )aneRbI¦GacRtUv)anKNnadUcxageRkam ¬eyagtamrUbTI 13>12¦³

a. snμt; d b. kMNt; ob ³ )(4 dcbo += sRmab;ssrkaer EdlRCugesμ I c .


eCIgtag 345 T.Chhay

)(2)(2 21 dcdcbo +++= sRmab;ssrctuekaN EdlmanRCuges μInwg 1c nig 2c

c. kmøaMgkat;TTwg 2uV eFVIGMeBIenAelImuxkat;EdlmanbeNþay )(4 dcbo += b¤ 1(2 cbo = )(2) 2 dcd +++ nigkm<s; d . muxkat;enHrgnUvkmøaMgbBaÄrcuHeRkam uP nigkmøaMg

bBaÄreLIgelI uq ¬smIkar !#>@¦. dUcenH 2

2 )( dcqPV uuu +−= sRmab;ssrkaer ¬!#>!@a¦ ))(( 212 dcdcqPV uuu ++−= sRmab;ssrctuekaNEkg ¬!#>!@b¦

d. kMNt; d FMbMput ¬én 1d nig 2d ¦. RbsinebI d EdlrkeXIjminmantémøEk,rtémø d Edl)ansn μt; eFVIkarsnμt;nigedaHRsayeLIgvij.

13>4>4> ersIusþg;Bt; nigEdkeCIgtag (Flexural Strength and Footing Reinforcement)

muxkat;eRKaHfñak;sRmab;m:Um:g;Bt;ekItmanenABImuxépÞssr ¬muxkat; nn − / rUbTI 13>13¦. eKRtUvBinitüemIlm:Um:g;Bt;enAelITisnImYy²rbs;eCIgtag nigdak;brimaNEdkRKb;RKan;. sRmab;eCIg tagkaer nigssrkaer m:Um:g;Bt;mantémøes μ IKñaTaMgBIrTis. edIm,IkMNt;muxkat;EdkcaM)ac; eKRtUveRbI km<s;rbs;eCIgtagTaMgBIrTis. edaysarEtEdkenAkñúgTismYysßitenAelIEdkenAkñúgTismYyeTot km<s;RbsiT§PaB d ERbRbYleTAtamGgát;p©itrbs;EdleRbI. témømFümrbs; d GacRtUv)anykmk eRbI. témøsRmab;karGnuvtþ d RtUv)ansnμt;esμ I mmh 110− .

CaerOy² km<s;RbsiT§PaBrbs;eCIgtagRtUv)anRKb;RKgedaykmøaMgkat;TTwg EdlcaM)ac; RtUvkarkm<s;eCIgtagFMCagkm<s;eCIgtagEdlRtUvkaredaym:Um:g;Bt;. EdkBRgwgkñúgTisedAnImYy²Gac RtUv)anKNnaenAkñúgkrNIGgát;rgkarBt;dUcxageRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

bffA

dfAMc

ysysu '7.1

φ ¬!#>!#¦

mü:ageTot PaKryEdk ρ GacRtUv)ankMNt;dUcxageRkam ¬smIkar $>@¦

( ) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

c

u

y

cf

Rf

f'85.0

211

'85.0φ

ρ ¬!#>!$¦

Edl 2/ bdMR uu = . enAeBlEdl uR RtUv)ankMNt; ρ k¾RtUv)anTTYlBIsmIkar !#>!$. tRmUvkarpleFobEdkGb,brmaenAkñúgGgát;rgkarBt;KWes μ Inwg yf/4.1 enAeBl

MPaf c 31' < niges μ Inwg yc ff 4/' enAeBl MPaf c 31' ≥ . b:uEnþ ACI Code, Section 10.5



bgðajfasRmab;kRmalxNÐEdlmankRmas;esμ IRkLaépÞGb,brma nigKMlatGtibrmaénEdkenAkñúgTis edAénkarBt;KYrRtUvkarEdkrYmmaD nigEdksItuNðPaB. tRmUvkarEdkGb,brmaelIkeRkayenHmantémø tUcehIypleFobEdkGb,brmaEdlmantémøFMCagRtUv)anesñIeLIg EtvaminKYrFMCag yf/4.1 .

EdkenAkñúgeCIgtagmYyTis nigeCIgtagBIrTisRtUvEtBRgayeBjTTwgeCIgtag. kñúgkrNI

eCIgtagctuekaNBIrTis ACI Code, Section 15.4.4 kMNt;faenAkñúgTisedAEvg EpñkénEdksrub lsγ RtUv)anEbgEckes μ IenAelITTwgrbs;eCIgtag. enAkñúgTisedAxøI PaKryBitR)akdrbs;EdksrubenAkñúgTis edAenHRtUvEt)andak;esμ IenAkñúg bandwidth esμ InwgRbEvgénRCugxøIéneCIgtagGaRs½ynwg

12+

=β

γ s ¬!#>!%¦


eCIgtag 347 T.Chhay

Edl footing of sideshort footing of side long

=β ¬!#>!^¦

Bandwidth RtUvEtsßitenAkNþalénG½kSrbs;ssr ¬rUbTI13>14¦. EdkEdlenAsl;enA kñúgTisedAxøIRtUvEtBRgayes μ IBIxageRkA Bandwidth . PaKryEdkenAsl;enHminKYrticCagEdkrYmmaD nigEdksItuNðPaB.

enAeBlEdlssreRKOgbgÁúMGMBIEdk b¤ssr\dæRtUv)aneRbI enaHmuxkat;eRKaHfñak;sRmab; m:Um:g;Bt;enAkñúgeCIgtagRtUv)anykenAcenøaHBak;kNþal nigEKmCBa¢aMg\dæ nigcenøaHBak;kNþalépÞ ssr nigEKmén steel base plate (ACI Code, Section 15.4.2).

13>4>5> lT§PaBRTRTg;rbs;ssrenARtg;)at (Bearing Capacity of Column at Base)

bnÞúkmkBIssrmanGMeBIelIeCIgtagenAKl;rbs;ssr EdlmanRkLaépÞesI μnwgRkLaépÞmux kat;ssr. kmøaMgsgát;RtUv)anbBa¢ÚnmkssredaypÞal;eday bearing enAelIebtug. kmøaMgEdlman GMeBIenAelIebtugenARtg;Kl;énssrminRtUvelIslT§PaBRTRTg;rbs;ebtugEdlkMNt;eday ACI Code,

Section 10.17 ³ lT§PaBRTRTg; )'85.0( 11 AfN cφ= ¬!#>!&¦ Edl 65.0=φ nig =1A RkLaépÞ bearing énssr.

témøénlT§PaBRTRTg;Edl[ edaysmIkar 13.17 GacRtUv)anKuNedayemKuN 0.2/ 12 ≤AA sRmab; bearing enAelIeCIgtagenA eBlépÞEdlRTFMCagRkLaépÞbnÞúkenARKb;RCug. 2A enATIenHCa RkLaépÞénEpñkéneCIgtagEdlrUb FrNImaRtdUcKña ehIyRtYtsIuKñaCamYynwgRkLaépÞbnÞúk ¬rUbTI 13>15¦. edaysarEt 12 AA > enaH emKuN 12 / AA nwgFMCagmYy EdlbgðajfalT§PaBRTRTg; GnuBaØatekIneLIgedaysarTRmxagénRkLaépÞeCIgtagEdlB½T§CMuvijKl;ssr. lT§PaBRTRTg;kMEN modified bearing strength KW³

( )11

212 '85.02)'85.0( Af

AA

AfN cc φφ ≤= ¬!#>!*¦

RbsinebIbnÞúkemKuN uP FMCag 1N b¤ 2N EdkRtUv)andak;edIm,IbBa¢ÚnkmøaMgelIs. eKGac TTYlva)anedaydak;Edk dowel b¤EdkssrRtUv)andak;bgðÜscUleTAkñúgeCIgtag. kmøaMgelIsKW

1NPP uex −= ehIyRkLaépÞrbs;Edk dowel KW 1005.0)/( AfPA yexsd ≥= Edl 1A CaRkLaépÞ rbs;muxkat;ssr. y:agehacNas;EdkbYnedImRtUv)aneRbIbYnedImenARCugTaMgbYnrbs;ssr.



RbsinebIkmøaMgemKuNtUcCag 1N b¤ 2N enaHeKdak;EdkGb,brma. ACI Code, Section

15.8.2 bgðajfaRkLaépÞEdkGb,brmarbs;Edk dowel y:agehacNas;es μ Inwg gA005.0 ¬nigminRtUv ticCagbYnedIm¦ Edl gA CaRkLaépÞeBj (gross section) rbs;muxkat;ssr. EdkGb,brmak¾RtUv)an eRbIEdrenAeBlEdlkmøaMgemKuNFMCag 1N b¤ 2N . Edk dowel RtUv)andak;enARCugTaMgbYnrbs;ssr ehIybgðÜscUleTATaMgkñúgssr nigTaMgkñúgeCIgtag. Ggát;p©itEdk dowel minKYrFMCagEdkbBaÄrenAkñúg ssr mm4 . tRmUvkarenHcaM)ac;edIm,IFanakareFVIkard¾l¥rvagssr nigeCIgtag. Edkb®Ba¢Üsrbs;Edk dowel RtUv)anBinitüemIledIm,IkMNt;nUvkarbBa¢Únd¾l¥énkmøaMgsgát;eTAkñúgeCIgtag.


eCIgtag 349 T.Chhay

13>4>6> RbEvgEdkRCYs (Development Length of the Reinforcing bars) muxkat;eRKaHfñak;sRmab;RtYtBinitüRbEvgEdkbgáb;dUcKñasRmab;m:Um:g;Bt;.

RbEvgbgáb;sRmab; Edksgát;RtUv)an[enAkñúgemeronTI7³

c

bydc

f

dfl

'

24.0=

b:uEnþvaenHminRtUvtUcCag yb fd044.0 cm20≥ . sRmab;témøepSgeToteyag tamemeronTI7. 13>4>7> sRmutDIepr:g;Esül ¬karKNnaeCIgtagkñúglkçxNÐlMnwg¦

Differential Settlement (Balanced Footing Design) CaTUeTAeCIgtagRTnUvbnÞúkdUcxageRkam³

- bnÞúkefrEdl)anmkBIeRKagxageRkam (substructure) nigeRKagxagelI (superstructure) .

- bnÞúkGefrEdlGnuvtþmkelI - Tm¶n;rbs;smÖar³EdleRbIsRmab;cak;bMeBj - bnÞúkxül;

eCIgtagnImYy²enAkñúgGKarRtUv)anKNnaedIm,IRTbnÞúkGtibrmaEdlGacekItmanenAelIssr Edl)anBIkarbnSMbnÞúkd¾eRKaHfñak;bMput edayeRbIsm<aFRTRTg;rbs;dIGnuBaØat.

bnÞúkefr nigRbEhlCabnÞúkGefrmYyEpñktUc ¬EdleKehAfa bnÞúkGefrFm μta (usual live

load)¦ GacGnuvtþCab;Gt;dac;mkelIeRKagsMNg;. bnÞúkGefrEdlenAsl;epSgeTot GacekItmanyUr² mþg ehIymanGMeBImkelIeRKagsMNg;EpñkxøHEtb:ueNÑaH EdlbNþal[manbnÞúkepSg²KñaenAelIssr. dUcenH sm<aFdIenABIeRkameCIgtagepSgKña nwgERbRbYlGaRs½ynwgbnÞúkenAelIssr ehIysRmutDIepr:g; EsülnwgekItmanenABIeRkameCIgtagepSgKñaénsMNg;EtmYy. edaysarsRmutedayEpñk (partial

settlement) minGaceCosput enaHbBaðabEgVr[sRmutDIepr:g;Esülrbs;sMNg;CagGt;»n[)an. brimaNénsRmutDIepr:g;EsülGaRs½ynwgPaBxusKñaénkRmitENnrbs;dI/ kRmas;smÖar³EdlGacsgát; )anenABIeRkamnIv:UeCIgtag nigPaBrwgRkajén combined footing nigsMNg;xagelI. sRmutDIepr:g; EsülFMFIV[ebtugeRbH nigeFVI[xUcxatdl;kargarbegðIy (cladding or finishing) CBa¢aMgxNÐ nigBi dan.



sRmutDIepr:g;EsülGacsMEdgedaykarrmUlrbs;eRKag (angular distortion of structure). Bjerrum bgðajfakarEdkkMNt;eRKaHfñak;rbs;karrmYlsRmab;lkçxNÐxøHERbRbYlcenøaHBI 600/1 eTA

150/1 GaRs½ynwgkarxUcxatEdlnwgekItmanenAelIrcnasm<½n§. sRmab;karGnuvtþn_ eKGacsnμt;fasm<aFdIeRkambnÞúkefrmantémøesμ IKñasRmab;RKb;eCIgtag

dUcenH vaeFVI[manbnÞúkes μI. bnÞúkefr ¬b¤bnÞúkFmμta¦ GacRtUv)ansnμt;es μ InwgplbUkrvagbnÞúkGefr nig PaKryénbnÞúkGefrEdlekItmanCaerOy²enAelIeRKagsMNg;. K μankrNIEdllT§PaBRTRTg;dIGnuBaØat FMCagbnÞúkefrbUknwgbnÞúkGefrGnuBaØatsRmab;eCIgtagnImYy²eT. ]TahrN_TI13>4 Bnül;BIviFIsaRsþ sRmab;KNnaRkLaépÞeCIgtagEdlykmkKitBicarNaBI\T§iBlrbs;sRmutDIepr:g;Esül. 13>5> eCIgtagebtugsuT§ (Plain Concrete Footings)

eCIgtagebtugsuT§GacRtUv)aneRbIedIm,IRTCBa¢aMg\dæ b¤bnÞúkRsal nigbBa¢ÚlbnÞúkTaMgenaHeTAdI Edlva. ACI Code GnuBaØat[eRbIeCIgtagebtugsuT§enAelIdI RbsinkugRtaMgKNnaminRtUvFMCagkrNI xageRkam³

- kugRtaMgrgkarBt;GtibrmasRmab;karTajRtUvEttUcCagb¤esμ Inwg 12/'5 cfφ ¬Edl 55.0=φ ¦

- kugRtaMgGtibrmaenAkñúgkmøaMgkat;TTWgmYyTis (beam action)RtUvtUcCagb¤es μ Inwg 9/'cfφ ¬Edl 55.0=φ ¦

- kugRtaMgGtibrmaenAkñúgGMeBIBIrTisKW

cc ff '1266.2'

92

91 φφ

β≤⎟⎟

⎠

⎞⎜⎜⎝

⎛+ ¬Edl 55.0=φ ¦

- ersIusþg;kmøaMgsgát;GtibrmaminKYrFMCagkarkMNt;rbs;lT§PaBRTRTg;ebtugGnuBaØat. cf ' énebtugsuT§minKYrtUcCag MPa17 .

- kRmas;Gb,brmarbs;eCIgtagebtugsuT§minKYrtUcCag cm20 . - muxkat;eRKaHfñak;sRmab;m:Um:g;Bt;KWsßitenAépÞrbs;ssr b¤CBa¢aMg. - muxkat;eRKaHfñaksRmab;GMeBIénkmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwgBIrTisKWsßitenAcm¶ay

d nig 2/d BIépÞénssr b¤CBa¢aMg erogKña. eTaHbICaeCIgtagebtugsuT§minRtUvkarEdkk¾eday k¾vaCakarEdlRbesIkñúgkardak;srésEdkrYmmaDsRmab;TisTaMgBIrrbs;eCIgtag.


eCIgtag 351 T.Chhay

- kugRtaMgEdlbNþalBIbnÞúkemKuNRtUv)anKNnaedaysnμt;BRgayCaragbnÞat;enAkñúgebtug. - km<s;RbsiT§PaB d RtUv)anKitfaesμ Inwgkm<s;srubdk[ mm75 . - sRmab;karBt; nigkmøaMgkat;mYyTis eRbImuxkat;eBj bh b:uEnþsRmab;kmøaMgkat;BIrTis eRbI

hbo edIm,IKNna cVφ .

]TahrN_ 13>1³ KNnaeCIgtagebtugBRgwgedayEdkedIm,IRTCBa¢aMgebtugEdlmanTTwg cm50 Edl RTbnÞúkefr mkN /5.379 EdlrYmbBa©ÚlbnÞúkpÞal;rbs;CBa¢aMg nigRTnUvbnÞúkGefr mkN /292 . )at rbs;eCIgtagsßitenACeRmA m8.1 BInIv:UdI. eK[ MPaf c 28' = / MPaf y 400= nigsm<aFdIGnuBaØat

2/24024.0 mkNMPa = . dMeNaHRsay³

1> KNnasm<aFdIRbsiT§PaB. snμt;km<s;srubrbs;eCIgtagKW cm50 . Tm¶n;rbs;eCIgtagKW 2/5.12255.0 mkN=× . edaysnμt;Tm¶n;maDrbs;dIes μ Inwg 3/16 mkN

enaHTm¶n;dIbMeBjBIelIeCIgtagKW 2/8.20)5.08.1(16 mkN=−× . bnÞúkCBa¢aMgEdlbgáb;enAkñúgdIKW m1/)5.08.1(5.025 −×× 2/25.16 mkN= . bnÞúkCBa¢aMgebtugbgát;kñúgdIKitCadI 2/4.101/)5.08.1(5.016 mkNm =−×× . sm<aFdIRbsiT§PaBenA)atrbs;eCIgtagKW

2/85.2004.1025.168.205.12240 mkN=+−−− . 2> KNnaTTwgrbs;eCIgtagsRmab;CBa¢aMgRbEvg m1

TTwgrbs;eCIgtag = bnÞúksrub ¼ sm<aFdIRbsiT§PaB

pressure soil effectiveloal totalfooting ofwidth =

m34.385.2002925.379

=+

= yk m4.3

3> sm<aFdIsuT§= bnÞúkemKuN ¼ TTwgeCIgtag ¬sRmab;RbEvg m1 ¦ mkNLDPu /6.9222926.15.3792.16.12.1 =×+×=+=

sm<aFdIsuT§ æ (net upward pressure) = 2/4.2714.36.922 mkNqu ==



4> epÞógpÞat;km<s;snμt;sRmab;tRmUvkarkmøaMgkat;TTwg. kRmas;karBarEdksRmab;eCIgtagKW mm75 ehIysnμt;eRbIEdk 25DB enaH mmd 4131275500 =−−= .

muxkat;eRKaHfñak;sRmab;kmøaMg kat;TTwgmYyTisKWsßitenAcm¶ay d BIépÞénBa¢aMg³ kNcdBqV uu 28.010

2500413

234004.271

226 =⎟

⎠⎞

⎜⎝⎛ −−=⎟

⎠⎞

⎜⎝⎛ −−= −

kmøaMgkat;TTwgmYyTisGnuBaØat= 9.02817.0 = d EdlRtUvkar mm

bfV

c

u 41519.075.0

280'17.0

=××

==φ

km<s;srubKW mm5021275415 =++ b¤ mm500 . d Cak;EsþgKW mm4131275500 =−− ¬dUckarsnμt;¦. cMNaMfa eKnwgRtUvkarkarsakl,gmYycMnYnedIm,Isnμt; nigKNnatémø d [mantémøEk,r.

5> KNnam:Um:g;Bt; nigEdk. muxkat;eRKaHfñak;KWsßitenAépÞénCBa¢aMg³

mkNcBqM uu .3.28525.0

24.3

24.271

2221 22

=⎟⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛ −=

MPabdM

R uu 67.1

4131000103.285

2

6

2=

×

⋅==

sRmab; MPaRu 67.1= / MPaf c 28' = nig MPaf y 400= enaHPaKryEdk

( ) 0048.02885.09.0

67.1211400

2885.0'85.0

211

'85.0=⎥

⎦

⎤⎢⎣

⎡

×××

−−×

=⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

c

u

y

cf

Rf

fφ

ρ

PaKryEdkGb,brmasRmab;Ggát;rgkarBt; 0035.0

4004.14.1

min ===yf

ρ

PaKryEdkrYmmaDKW %18.0 ¬sRmab; MPaf y 400= ¦. dUcenHeRbI 0048.0=ρ dUcEdl)an KNna

mmmAs /4.198241310000048.0 2=××= eRbIEdk 25DB EdlmanKMlat mm225 ¬ 22182mmAs = ¦

6> RtYtBinitüRbEvgEdkbgáb;sRmab;Edk 25DB mmdl bd 1200254848 =×== ¬eyagtamemeronTI 7¦

Edl[ mmcBld 137575

2500

2340075

22=−−=−−=


eCIgtag 353 T.Chhay

7> KNnaEdkrgkñúgTisedAbeNþayeCIgtag³ mmmAs /90050010000018.0 2=××= eRbIEdk 16DB KMlat mm200 ¬ 21005mmAs = ¦. bøg;lMGitRtUv)anbgðajenAkñúgrUbTI 13>16.

]TahrN_ 13>2³ KNnaeCIgtag single footing edIm,IRTssrebtugeRbIEdkkgFm μtasßitenAxagkñúg EdleRbI 288DB . ssrenHRTnUvbnÞúktamG½kSGefrK μanemKuN kN1090 nigbnÞúkcMG½kSefrK μanemKuN

kN890 . )atrbs;eCIgtagsßitenACeRmA mm1200 BInIv:UdI ehIysm<aFdIGnuBaØatKW 2/240 mkN . eK[ MPaf c 28' = / MPaf y 400= . dMeNaHRsay³

1> KNnasm<aFdIRbsiT§PaB. snμt;kRmas;srubrbs;eCIgtag mm600 . Tm¶n;eCIgtagKW 256.0 × 2/15 mkN= . bnÞúkdIenABIelIeCIgtag ¬snμt;Tm¶n;maDrbs;dIes μ Inwg 3/16 mkN ¦ KW 166.0 × 2/6.9 mkN=

sm<aFdIRbsiT§PaBKW = 2/4.2156.915240 mkN=−−=

2> KNnaRkLaépÞrbs;eCIgtag bnÞúkeFVIkar kNLD 19808901090 =+=+= RkLaépÞeCIgtag 22.9

4.2151980 m==



RCugrbs;eCIgtagKW m03.3= dUcenHeRbI m3= ¬rUbTI 13>17¦

3> sm<aFdIsuT§= bnÞúkemKuN ¼ RkLaépÞeCIgtag kNLDPu 27328906.110902.16.12.1 =×+×=+=

sm<aFdIsuT§ æ (net upward pressure) = 2/6.30333

2732 mkNqu =×

= 4> epÞógpÞat;km<s;snμt;EdlbNþalmkBIkmøaMgkat;TTwgBIrTis. RbsinebIeKGt;eRbIEdkkmøaMgkat;

TTwg enaHkmøaMgkat;TTwgBIrTiskMNt;km<s;caM)ac;rbs;eCIgtag. sRmab;km<s;eCIgtagsrub snμt; mm600 KNna d eTAG½kSTIRbCMuTm¶n;énEdkRsTab;xagelIedIm,Idak;enAkñúgeCIgtagTaMg BIrTis. eRbIEdk 15DB sRmab;KNna d .

mmd 4883775600 =−−= ¬vaCakarRbesIrEdlsnμt; 112−= hd ¦

( ) ( ) mmdcbo 375248845044 =+=+= mmdc 938488450 =+=+

( ) ( ) kNdcqPV uuu 9.2464488.0450.06.3032732 222 =+−=+−=

1d caM)ac; oc

u

bfV

'3 2

φ= mm6.496

37522875.024649003

=××

×= ¬ 1=β smIkar !#>(¦

2d caM)ac; oc

o

s

u

bfb

dV

'2

12 2

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=α

φ mm8.275

37522823752

4884075.0

246490012=

×⎟⎠⎞

⎜⎝⎛ +

××

=

¬ 40=sα sRmab;ssrenAkNþal¦ edaysar dd >1 snμt; dUcenHeyIgRtUveFVIkarKNnasak l,grhUtdl; 1d nig d mantémøRbEhlKña. eRkayBIkarKNnamkeyIgTTYl)an

mmh 610= / mmd 498= / mmd 5.4951 = . dUcenH km<s;snμt;elIkeRkay mmh 610= RKb;RKan;.

5> RtYtBinitükm<s;EdlbNþaledaysarGMeBIkmøaMgkat;mYyTis³ muxkat;eRKaHfñak;enAcm¶ay d BI épÞssr cm¶ayBIcugeCIgtag mmdcL 777

22=⎟

⎠⎞

⎜⎝⎛ −−=

kNVu 7.7073777.06.3031 =××= km<s;caM)ac;sRmab;kmøaMgkat;TTwgmYyTisKW


eCIgtag 355 T.Chhay

mmmmbf

Vd

c

u 49835030002817.075.0

707700'17.075.0

1 <=××

=×

=

6> KNnaEdk nigm:Um:g;Bt;. muxkat;eRKaHsßitenAépÞssr. cm¶ayBIcugeCIgtagKW mmcL 12752251500

22=−=⎟

⎠⎞

⎜⎝⎛ −

mkNbcLqM uu .3.7403275.16.30321

2221 2

2=××=⎟

⎠⎞

⎜⎝⎛ −=

MPabdM

R uu 995.0

4983000103.740

2

6

2=

×

⋅==

BIsmIkar !#>!$ eyIg)an 0028.0=ρ 22.418349830000028.0 mmbdAs =××== ρ

sA Gb,brma ¬EdkrYmmaD¦ 22 2.41832.268949830000018.0 mmmm <=××= sA Gb,brma ¬EdkrgkarBt;¦ 22.493049830000033.0 mm=××=

dUcenH eyIgyk 22.4930 mmAs = . eRbI 2213DB ¬ 27.4941 mmAs = ¦ KMlat rbs;EdkKW mms 5.23712/)1503000( =−= enAkñúgTiwedATaMgBIr.

7> RtYtBinitükugRtaMgRT (bearing stress) a. ersIusþg;RT (bearing strength) 1N enA)atrbs;ssr ¬ 2

1 450450 mmA ×= ¦KW kNAfN c 7.3132104504502885.065.0)'85.0( 3

11 =×××××== −φ b. ersIusþg;RT (bearing strength) 2N enAépÞxagelIrbs;eCIgtag ¬ 2

2 33 mA ×= ¦ KW

11

212 2N

AA

NN ≤= 2

2 9000000mmA = 21 202500mmA =

267.6202500

9000000>=

dUcenH kNNN 4.62652 12 == . edaysar 12732 NkNPu <= enaHkugRtaMgRTKWRKb; RKan;. RkLaépÞGb,brmaénEdk dowel caM)ac;KW 450450005.0005.0 1 ××=A

25.1012 mm= . cMnYnEdkGb,brmaKW 4 dUcenHeRbIEdk 25DB dak;enARCugTaMgbYnrbs; ssr.

c. RbEvgbgáb;rbs;Edk dowel enAkñúgkmøaMgsgát;³ mm

f

fdl

c

ybdc 5.453

284002524.0

'

24.0=

××==



dcl Gb,brma mmmmfd yb 200440044.0 >== . dUcenHeRbIEdk dowel 25DB 4edIm RbEvg mm455 dak;kñúgssrnigeCIgtag. cMNaMfa mmdldc 498=< RKb;RKan;.

8> RbEvgbgáb;rbs;EdkemenAkñúgeCIgtagsRmab; 22DB KW mmld 10562248 =×= ¬eyagtamem eronTI 7¦. RbEvgbgáb;BitR)akdenAkñúgeCIgtagKW

752251500752/2/ −−=−−= cLld mm1200= . bøg;lMGitrbs;eCIgtagRtUv)anbgðajenAkñúgrUbTI 13>17.

]TahrN_ 13>3³ KNnaeCIgtagragctuekaNsRmab;ssrén]TahrN_TI13>2 RbsinebIRCugmYy rbs;eCIgtagRtUv)ankMNt;esμ I m6.2 .


eCIgtag 357 T.Chhay

dMeNaHRsay³ 1> viFIsaRsþKNnasRmab;eCIgtagctuekaNmanlkçN³RsedogKñanwgkarKNnaeCIgtagkaer

eday KitBicarNaGMeBIrbs;kmøaMgmkelIeCIgtagtmaTisnImYy²dac;edayELkBIKña. 2> BI]TahrN_mun RkLaépÞcaM)ac;rbs;eCIgtagKW 22.9 m

beNþayeCIgtag m54.36.22.9==

dUcenHyk m6.3 ¬rUbTI 13>18¦. TMhMeCIgtagKW 26.36.2 m× 3> kNPu 2732= . dUcenH sm<aFdIsuT§ æ (net upward pressure) KW

2/9.2916.36.2

2732 mkNqu =×

= 4> RtYtBinitükm<s;EdlbNþalBIkmøaMgkat;TTwgmYyTis. muxkat;eRKaHfñak;sßitenAcm¶ay d BIépÞ

rbs;ssr. sRmab;TisedAEvg bqdcLV uu ×⎟

⎠⎞

⎜⎝⎛ −−=

221

kN4.8176.29.291498.0245.0

26.3

=××⎟⎠⎞

⎜⎝⎛ −−= kmøaMgkat;TTwgenHlb;

sRmab;TisedAxøI kNVu 3.6061 = ¬mineRKaHfñak;¦ d caM)ac; mm

bfV

c

u 47526002875.0104.8176

'6 3

1 =×⋅×

==φ

d EdleRbI mmmm 475498 >= 5> RtYtBinitüGMeBIkmøaMgkat;TTwgBIrTis ¬kmøaMgkat;pug (punching shear)¦. muxkat;eRKaHfñak;

enAcm¶ay 2/d BIépÞssrTaMgbYnRCug. ( ) mmbo 37924984504 =+=

( ) mmdc 948498450 =+=+ 238.1

6.26.3

<==β eRbI 3/' dbfV ocu φ=

kNdcqPV uuu 7.2469948.09.2912732)( 222 =×−=+−=

mmbf

Vd

oc

u 49237922875.0

24697003'

3 21 =

××

×==

φ

mmd 5.2712 =



6> KNnaEdkenAkñúgTisedAEvg. muxkat;eRKaHfñak;enAnwgépÞénTRm. cm¶ayBIcugéneCIgtagKW mmcL 1575

2450

23600

22=−=−

mkNM u .3.9416.2575.19.29121 2 =××=

MPabdM

R uu 46.1

498.06.2103.941

2

3

2=

×

⋅==

−

GnuvtþtamsmIkar !#>!$ eyIgTTYl)an 0042.0=ρ 22.543849826000042.0 mmAs =××= sA Gb,brma ¬EdkrYmmaD¦ 2285561026000018.0 mm=××=

sA Gb,brma ¬EdkrgkarBt;¦ 2427349826000033.0 mm=××= eRbI 22.5438 mmAs = . eRCIserIs 2810DB ¬ 25.6157 mmAs = ¦ KMlatEdkKW

( ) mmS 2729/1502600 =−= 7> KNnaEdkenAkñúgTisedAxøI. cm¶ayBIépÞssreTAcugeCIgtagKW

mm10752

4502

2600=−

mkNM u .2.6076.3075.19.29121 2 =××=

MPabdM

R uu 68.0

498.06.3102.607

2

3

2=

×

⋅==

−

GnuvtþeTAkñúgsmIkar !#>!$ eK)an 0019.0=ρ 2340649836000019.0 mmAs =××=

sA Gb,brma ¬EdkrYmmaD¦ 2395361036000018.0 mm=××= sA Gb,brma ¬EdkrgkarBt;¦ 2591649836000033.0 mm=××=

témørbs; sA EdlRtUveRbIRtUvEtFMCagb¤es μI 23953mm . eRbI 2018DB ¬ 25655mmAs = ¦ 84.0

16.26.32

12

=+

=+

=β

γ s

cMnYnEdkenAkñúgceRmokRbEvg m6.2 KW 1584.018 =× edIm. cMnYnEdkenAsl;sRmab;RCugmçag² KW ( ) 22/1518 =− edIm. dUcenHdak;Edk 2015DB enAkñúgceRmokRbEvg m6.2 ehIydak; 202DB ¬ 2628mmAs = ¦ enAelIRbEvg m5.0 enAelIRCugnImYy²sgçagceRmok m6.2 . cMnYnEdksrubKW 19 edIm. enAkñúg]TahrN_enH


eCIgtag 359 T.Chhay

EdkRtUv)anBRgayedayKMlatesμ I²Kña elIRbEvg m6.3 / ( ) mmS 19218/1503600 =−= . bøg;lMGitsrésrEdkRtUv)anbgðajenAkñúg rUbTI !#>!*.

8> RtYtBinitükugRtaMgRTenA)atssr dUcEdl)anBnül;enAkñúg]TahrN_mun. eRbIEdk dowel 25DB cMnYn 4 edIm.

9> RbEvgbgáb;rbs;Edkem mmld 960= sRmab; 20DB nig mmld 1344= sRmab; 28DB . dl Edldak; ¬TisEvg¦ mm150075

2450

23600

=⎟⎠⎞

⎜⎝⎛ −−=

dl Edldak; ¬TisxøI¦ mm1000=

]TahrN_ 13>4³ KNnaRkLaépÞeCIgtagcaM)ac;sRmab;sRmutesμ IKña ¬karKNnaeCIgtagEdlman lMnwg (balanced footing design)¦ RbsinebIbnÞúkGefrFm μta (usual live load) esμ I %20 sRmab;



RKb;eCIgtagTaMgGs;. eCIgtagrgnUvbnÞúkefr nigbnÞúkGefrdUcbgðajenAkñúgtaragxageRkam. sm<aF dIsuT§GnuBaØat (allowable net soil pressure) esμ I 2/287 mkN .

elxeCIgtag 1 2 3 4 5

bnÞúkefr kN535 kN800 kN620 kN845 kN935

bnÞúkGefr kN670 kN980 kN890 kN755 kN1070

dMeNaHRsay³

1> kMNt;eCIgtagEdlmanpleFobbnÞúkGefrelIbnÞúkefrFMCageK. enAkñúg]TahrN_enH eCIgtag elx 3 manpleFob 44.1 FMCagpleFobdéT.

2> KNnabnÞúkFmμtasRmab;RKb;eCIgtagTaMgGs;. bnÞúkFm μtaKWCabnÞúkefr nigEpñkénbnÞúkGefr EdlmanGMeBIrCaTUeTAenAelIeRKagsMNg;. enAkñúg]TahrN_enH bnÞúkFmμta ).(2.0. LLLD += témøénbnÞúkFmμtaRtUv)anbgðajenAkñúgtaragxageRkam.

3> kMNt;RkLaépÞrbs;eCIgtagEdlmanpleFob LDLL ./. RkLaépÞeCIgtagelx 3 226.5

287890620

pressure soil allowable.. mLLLD

=+

=+

=

sm<aFdIFmμtaeRkameCIgtagelx 3 KW 2/7.151

26.5798

footing of Areaload Usual mkN==

4> KNnaRkLaépÞcaM)ac;sRmab;eCIgtagnImYy²edayEckbnÞúkFmμtarbs;vaedaysm<aFdIenAeRkam eCIgtagelx 3. RkLaépÞrbs;vaRtUvbgðajenAkñúgtaragxageRkam. ]TahrN_ eCIgtagelx 1 RkLaépÞcaM)ac;rbs;vaesμ I 241.47.151/669 m= .

5> KNnasm<aFdIGtibrmaeRkameCIgtagnImYy² 2

max /287 mkNarea

LDq ≤+

= ¬sm<aFdIGnuBaØat¦


eCIgtag 361 T.Chhay

elxeCIgtag 1 2 3 4 5

load Liveload Dead 25.1 225.1 44.1 89.0 14.1

bnÞúkFmμta ).(2.0. LLLD += )(kN 669 996 798 996 1149 RkLaépÞcaM)ac;

151.7load Usual

= )( 2m 41.4 57.6 26.5 57.6 57.7 sm<aFdIGtibrma

areaLD +

= )/( 2mkN 2.273 9.270 87.2 5.243 9.264 ]TahrN_ 13>5³ KNnaeCIgtagebtugsuT§edIm,IRTCBa¢aMgebtugEdlmankRmas; mm400 . bnÞúkEdl manGMeBIelICBa¢aMgrYmmanbnÞúkefr mkN /5.233 ¬rYmbBa©ÚlbnÞúkpÞal;rbs;CBa¢aMgrYc¦ nigbnÞúkGefr

mkN /146 . )atrbs;eCIgtagsßitenACeRmA mm1200 BInIv:UdI. eK[ MPaf c 20' = nigsm<aFdI GnuBaØat 2/240 mkN . dMeNaHRsay³

1> KNnasm<aFdIRbsiT§PaB. sn μt;km<s;srubeCIgtagKW mm710 Tm¶n;rbs;eCIgtag 2/172471.0 mkN=×= edaysnμt;Tm¶n;maDdIes μ I 3/16 mkN enaHTm¶n;rbs;dIenAelIeCIgtages μ I 16)71.02.1( ×−

2/84.7 mkN= . sm<aFdIRbsiT§PaBKW 2/16.21584.717240 mkN=−− .

2> KNnaTTwgeCIgtagsRmab;CBa¢aMgRbEvg m1 ¬ mb 1= ¦

pressure soil effectiveload totalfooting ofwidth =

m76.116.2151465.233

=+

= yk m8.1 ¬rUbTI 13>19¦

3> mkNLDU /8.5131466.15.2332.16.12.1 =×+×=+= sm<aFdIsuT§ (net upward pressure) esμ I 2/4.2858.1/8.513 mkNqu ==

4> RtYtBinitükugRtaMgBt;. muxkat;eRKaHfñak;KWsßitenAépÞCBa¢aMg. sRmab;RbEvg m1 énCBa¢aMg nigeCIgtag

mkNcLqM uu .9.6924.0

28.14.285

21

2221 22

=⎟⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛ −=



kMNt;km<s;RbsiT§PaB d esμ I mm63575710 =− edaysnμt;fa)at mm75 K μanRbsiT§PaB. 410

331013.2

126351000

12mmbdI g ⋅=

×==

kugRtaMgTajedaykarBt;KW MPaI

cMf ur 04.1

2635

1013.2109.69

10

6=⎟

⎠⎞

⎜⎝⎛

⋅

⋅==

kugRtaMgTajedaykarBt;GnuBaØatKW MPaf c 02.12055.0415.0'415.0 =×=φ ¬Ek,r¦ 5> RtYtBinitükugRtaMgkmøaMgkat;TTwg³ muxkat;eRKaHfñak;sßitenAcm¶ay mmd 635= BIépÞCBa¢aMg

kNdcLqV uu 55.18635.024.0

28.14.285

22=⎟

⎠⎞

⎜⎝⎛ −−=⎟

⎠⎞

⎜⎝⎛ −−=

kNbdf

V cc 5.173

91063510002055.0

9' 3

=×××

==−

φφ dUcenH muxkat;manlkçN³RKb;RKan;. vaCakarRbesIrEdleRbIbrimaNEdkGb,brmasRmab;TaMg BIrTis.

13>6> Combined Footings

enAeBlEdlssrmanTItaMgsßitenAEk,rRBM enaHEpñkéneCIgtag single footing GaclycUl eTAkñúgRBMGñkCitxag. edIm,IeCosvagsßanPaBEbbenH eKGacdak;ssrenAelIRCugEKméneCIgtagbegáIt )anCabnÞúkcakp©it. eKminGaceRbIdMeNaHRsayenHsRmab;lkçxNÐxøH nigeBlxøHvaCadMeNaHRsay


eCIgtag 363 T.Chhay

EdlminsnSMsMéc. karKNnad¾l¥GacTTYledalbBa©ÚleCIgtagCamYynwgeCIgtagssrxagkñúgEdlsßit enACitCageK begáIt)anCa combined footing . TIRbCMuTm¶n;rbs; combined footing RtYtsIuKñaCamYy nwgkmøaMgpÁÜbénssrTaMgBIr. krNIepSgeTot Edl combined footing caM)ac;RtUv)aneRbIKWenAeBlEdldImanlkçN³exSay ehIyeCIgtagssrmYyKgelIeCIgtagenAEk,r. ragrbs;eCIgtag combined footing GacCactuekaN Ekg b¤ctuekaNBñay ¬rUbTI 13>20¦. enAeBlEdlbnÞúkssrxagenAEk,rRBMmantémøFMCagbnÞúkssr kñúg eCIgtagmanragctuekaNBñayGacRtUv)aneRbIedIm,IrkSaTIRbCMuTm¶n;eCIgtagenAelIExSCamYynwgbnÞúk pÁÜbénssrTaMgBIr. CaTUeTA eKcUlcitþeRbIeCIgtagragctuekaNEkg.

beNþay nigTTwgrbs;eCIgtagRtUv)aneRCIserIsedaykMeNInmþg mm75 EdlGacbNþal[ sm<aFBRgayesμ IenAeRkameCIgtagERbRbYltUc. sRmab;sm<aFBRgayesμ IeLIgelI (uniform upward

pressure) eCIgtagnwgdabdUcbgðajenAkñúgrUbTI 13>21. ACI Code, Section 15.10 min)anpþl;nUvviFI KNnalMGitsRmab; combined footing eT. CaTUeTA karKNnaQrelIkarviPaKeRKOgbgÁúM (structural

analysis). viFId¾samBaØénkarKNnaKWcat;TukeCIgtagdUcFñwmenAkñúgTisedAEvg EdlRTnUvsm<aFBRgayes μ I

eLIgelI (uniform upward pressure) uq . sRmab;TisedATTwg eKsnμt;fabnÞúkssrRtUv)anBRgay eBjTTwgenABIeRkamssrEdlesμ InwgTTwgssrbUknwg d énRCugnImYy². mü:agvijeTot bnÞúkssrman GMeBIelIFñwmenAeRkamssrCamYynwgeCIgtagEdlmanTTWgGtibrma dc 2+ nigbeNþayesμ InwgRCugxøI rbs;eCIgtag ¬rUbTI 13>22¦. eKk¾GaceRbITTwgEdlmantémøtUcCagrhUtdl; dc + .



]TahrN_ 13>6³ KNnaeCIgtag combined footing ragctuekaNEkgedIm,IRTssrBIrdUcbgðajkñúg rUbTI 13>23. ssrxagelx I manmuxkat; mm400400× nigRT ..LD kN800 nig LL. kN535 . ssrxagkñúgelx II manmuxkat; mm500500× nigRTbnÞúk ..LD kN1115 nig LL. kN625 . sm<aF dIGnuBaØatKW 2/240 mkN ehIy)atrbs;eCIgtagsßitenACeRmA m5.1 BInIv:UdI. KNnaeCIgtagedayeRbI

MPaf c 28' = / MPaf y 400= nigviFIKNnaersIusþg; ACI.


eCIgtag 365 T.Chhay

dMeNaHRsay³ 1> kMNt;TItaMgkmøaMgpÁÜbénbnÞúkssr. Kitm:Um:g;CMuvijG½kSénssrxagelx I ³

mx 7.2772)535800()6251115(

4900)6251115(=

+++×+

= BIssr I

cm¶ayBIkmøaMgpÁÜbmkExSRBMKW mm7.33726007.2772 =+ . RbEvgrbs;eCIgtagKW mm4.674527.3372 =× yk mm6750 . kñúgkrNIenHkmøaMgpÁÜbrbs;ssrRtYtsIuKñaCamYy

nwgkmøaMgpÁÜbrbs;sm<aFdIEdlmanGMeBIelIeCIgtag. 2> kMNt;RkLaépÞrbs;eCIgtag. snμt;km<s;eCIgtagsrub mm920 ¬ mmd 805115920 =−= ¦

bnÞúkeFVIkarsrub kN30756251115535800 =+++= ¬Total actual (working)load¦ sm<aFdIfμ I 2/72.2071658.02592.0240 mkN=×−×−= ¬New upward pressure¦ ¬snμt;Tm¶n;maDdI 3/16 mkN ¦ RkLaépÞcaM)ac; 28.14

72.2073075 m== ¬Required area¦

TTwgeCIgtag m19.275.68.14== ¬Width of footing¦

ykTTwgeCIgtagesμ I m2.2 . dUcenHTMhMeCIgtagKW m2.275.6 × ¬RkLaépÞ 285.14 m ¦ 3> kMNt;sm<aFdIemKuN ¬factored soil pressure¦ edayeRbIbnÞúkemKuN³

1uP ¬ssrelx I¦ kN18165356.18002.1 =×+×= 2uP ¬ssrelx II¦ kN23386256.111152.1 =×+×=

sm<aFdIemKuNsuT§KW ( ) 2/73.27985.14/23381816 mkNqu =+= ¬net factored soil

pressure¦ 4> KUrdüaRkamkmøaMgkat;TTwgemKuNsRmab;FñwmEdlmanRbEvg mmL 6750=

EdlenAelIssrBIr nigrgnUvsm<aFdI mkN /4.6152.273.279 =× ¬kñúgRbEvgeCIgtag m1 ¦ uV ¬enAépÞxageRkArbs;ssr I ¦ kN16.246)2.06.0(4.615 =−×= uV ¬enAépÞxagkñúgrbs;ssr I ¦ ( ) kN68.13232.06.04.6151816 =+−= uV ¬enAépÞxageRkArbs;ssr II ¦ kN4.615)25.025.1(4.615 =−×= uV ¬enAépÞxagkñúgrbs;ssr II ¦ kN9.1414)25.025.1(4.6152338 =+×−=

5> KUrdüaRkamm:Um:g;emKuNedayKiteCIgtagCaFñwmEdlman mmL 6750= RTedayssrBIr. sm<aFdIBRgayes μI mkN /4.615



1uM ¬enAépÞxageRkAssr I ¦ mkN.2.4924.04.615

2=×=

2uM ¬enAépÞxagkñúgssr II ¦ mkN.7.3072

14.6152=×=

m:Um:g;GtibrmaekItmanenAkmøaMgkat;TTwgesμ IsUnü uM Gtibrma¬KNnaBIssr I ¦ ( ) ( )26.02.015.2

24.6152.015.21816 ++−+=

mkN.84.1589= uM Gtibrma¬KNnaBIssr II ¦ ( ) ( )225.125.03.2

24.61525.03.22338 ++−+=

mkN.7.1518= m:Um:g;EdlKNnaBIRCugTaMgBIréneCIgtagRtUvmantémøRbhak;RbEhlKña. kñúgkrNIenH eyIgyk

maxuM mkN.84.1589= . bERmbRmYltémørbs;m:Um:g;GaRs½yCacMbgCamYynwgRbEvg nig TTwgrbs;eCIgtag.

6> RtYtBinitükm<s;sRmab;kmøaMgkat;mYyTis. kmøaMgkat;TTwgGtibrmaekItmanenAcm¶ay mmd 805= BIépÞssrxagkñúg II ¬rUbTI 13>23¦.

kNVu 5.919805.04.6159.14141 =×−= mm

bfV

dc

u 5.61928220017.075.0

919500'17.0

1 =×××

==φ

km<s;RbsiT§PaBEdl[KW mmmmd 5.619805 >= dUcenHeCIgtagmanlkçN³RKb;RKan;. 7> RtYtBinitükm<s;sRmab;kmøaMgTTwgBIrTis ¬kmøaMgkat;pug¦. sRmab;ssrxagkñúg

( ) ( ) mmdcbo 522080550044 =+=+= ( ) ( ) mmdc 1305805500 =+=+ kmøaMgkat;TTwg 2uV enAmuxkat; 2/d BIRKb;RCugrbs;ssres μ I

kNdcqPV uuu 6.1861305.173.2792338)( 2222 =×−=+−=

mmmmbf

Vd

oc

u 8056.26952202875.0

18616003'

3 2 <=×

×==

φ

ssrxageRkARtUv)anRtYtBinitünigbgðajfaminmaneRKaHfñak;. 8> RtYtBinitükm<s;sRmab;m:Um:g; nigkMNt;srésEdkcaM)ac;enAkñúgTisEvg

m:Um:g;Bt;Gtibrma mkN.84.1589=


eCIgtag 367 T.Chhay

MPabdM

R uu 115.1

80522001084.1589

2

6

2 =×

⋅==

GnuvtþkñúgsmIkar ¬!#>!$¦ PaKryEdkKW ( )min0033.00032.0 ρρ ≈= 23.584480522000033.0 mmAs =××=

sA Gb,brma ¬rYmmaD¦ 22.364392022000018.0 mm=××= 23.5844 mmAs = lub. eRbI 2810DB ¬ 25.6157 mmAs = ¦

KMlatEdk mm228spacing) of (no. 9

cover) (concrete 1502200=

−=

EdkRtUv)andak;bgðÚtenAcenøaHssrenAEpñkxagelIeCIgtagCamYykRmas;karBarEdk mm75 . dak;EdkGb,brmaenA)atrbs;eCIgtagedIm,ITb;nwgm:Um:g;viC¢man. RtYtBinitüRbEvgbgáb; dl BIépÞ ssr. EdkGb,brmaKW 22.3643 mmAs = . eRbI 258DB ¬ 23927mmAs = ¦. RbEvgEdkbgáb;caM)ac;sRmab;EdkemxagelIKW mmdl bd 1747483.13.1 =××= RtUv)andak; ecjBIcMNucm:Um:g;Gtibrma. RbEvgEdkbgáb;Edldak;enARtg;ssrTaMgBIrKWRKb;RKan;.

9> sRmab;EdkenAkñúgTisedAxøI. karKNnam:Um:g;Bt;enAkñúgTisedAxøI ¬TisedATTwg¦ manlkçN³ dUcKñakñúgkrNI single footing. EdkenAeRkamssrnImYy² RtUv)andak;enAkñúgceRmokTTwg (bandwidth) Edlesμ InwgplbUkTTwgssrnigkm<s;RbsiT§PaB d BIrdg ¬rUbTI !#>@$¦.

a. EdkenABIeRkamssr I³ Bandwidth 805column) of sideexterior (on 040dth)(column wi 400 ++=

mm1605= eRbI m6.1 . sm<aFdIeLIgelIsßitenAkñúgTisedAxøIeRkamssr I KW mkN

Pu /5.8252.2

1816footing ofwidth 1 ==

cm¶ayBIcugTMenreTAépÞssrKW mm9002

4002

2200=−

uM ¬enAépÞénssr I¦ mkN.3.3349.02

5.825 2 ==

MPabdM

R uu 32.0

8051600103.334

2

6

2 =×

⋅==

PaKryEdk ρ tUcCagPaKryEdkGb,brmasRmab;EdkrYmmaD 0018.0 . 2

min 6.264992016000018.0 mmAs =××=



eRbI 256DB ¬ 22.2945 mmAs = ¦ dak;enAkñúg bandwidth RbEvg m6.1 .

b. EdkenABIeRkamssr II³

Bandwidth mm2110805805 500 =++= eRbI mm2100 . sm<aFdIeLIgelIsiT§enAkñúgTisedAxøIeRkamssr II KW


eCIgtag 369 T.Chhay

mkNPu /7.1062

2.22338

footing ofwidth 2 ==

cm¶ayeTAépÞssrKW mm8502

5002

2200=−

uM ¬enAépÞénssr II kñúgTisedAxøI¦ mkN.9.38385.02

7.1062 2 ==

MPabdM

R uu 28.0

8052100109.383

2

6

2 =×

⋅==

PaKryEdk ρ tUcCagPaKryEdkGb,brmasRmab;EdkrYmmaD 0018.0 . 2

min 6.347792021000018.0 mmAs =××= eRbI 258DB ¬ 23927mmAs = ¦ dak;enAkñúg bandwidth RbEvg m1.2 BIeRkamssr II dUcbgðajenAkñúgrUb !#>@# nig !#>@$. RbEvgbgáb;rbs;Edk 25DB enAkñúgTisedAxøI KW m2.1 .



13>7> eCIgtageRkambnÞúkssrcakp©it (Footings under Eccentric Column Loads)

enAeBlEdlssrbBa¢ÚnEtkmøaMgtamG½kS enaHeKGacKNnaeCIgtagEdlmanbnÞúkeFVIGMeBIcMTIRb CMuTm¶n;rbs;eCIgtag EdlbegáIt)anCasm<aFBRgayes μ IeRkameCIgtag. b:uEnþ enAkñúgkrNIxøHssrbBa¢Ún kmøaMgcMG½kS nigm:Um:g;Bt; dUckñúgkrNIeCIgtageRKagbgáb;cug (fixed-end frame). sm<aF q EdlekIt manenAelIdInwgminBRgayes μ I EdlGackMNt;BIsmIkarxageRkam³

0≥±=I

McAPq ¬!#>!(¦

Edl A nig I CaRkLaépÞ nigm:Um:g;niclPaBéneCIgtag erogKña. eKmanlkçxNÐdIxusKñaEdl GaRs½ynwgtémø P nig M / nig sm<aFdIGnuBaØat. lkçxNÐKNnaxusKñaRtUv)anbgðajenAkñúgrUbTI 13> 25 nigRtUv)ansegçbdUcxageRkam³

1> enAeBl 6// LPMe <= sm<aFdImanragctuekaNBñay

2max6BL

MLBP

IMc

APq +=+= ¬!#>@0¦

2min6BL

MLBP

IMc

APq −=−= ¬!#>@!¦

2> enAeBl 6// LPMe == sm<aFdImanragctuekaNEkg

LBP

BLM

LBPq 26

2max =+= ¬!#>@@¦

2min60BL

MLBPq −== b¤ 2

6BL

MLBP

= ¬!#>@#¦

3> enAeBlEdl 6/Le > sm<aFdImanragRtIekaN eLyLx −=

−=

23

BxqP ⎟⎠⎞

⎜⎝⎛=

23

max

)2(34

32

max eLBP

xBPq

−== ¬!#>@$¦

4> enAeBleCIgtagRtUv)anrMkilcm¶ay e BIG½kSénssredIm,IbegáItsm<aFdIBRgayesμ IenA eRkameCIgtag. m:Um:g;GtibrmaekItmanenAmuxkat; nn −

HhMM −= ' nig PMe =


eCIgtag 371 T.Chhay

13>8> eCIgtageRkamm:Um:g;BIrTis (Footings under Biaxial Moment)

enAkñúgkrNIxøH eCIgtagGacrgnUvkmøaMgtamG½kS nigm:Um:g;Bt;BIrTisCMuvijG½kS x nigG½kS y dUc krNIm:asIunsÞÚcEdlbgVilxøÜn)an o360 . enaHeCIgtagRtUv)anKNnasRmab;bnÞúkeRKaHfñak;.

tamrUbTI 13>26 RbsinebIbnÞúkcMG½kS P manGMeBIenAcm¶ay xe BIG½kS y nig ye BIG½kS x . enaH³

yx PeM = nig xy PeM =



sm<aFdIenARCug ! KW y

xy

x

yx

IcM

IcM

APq ++=max

enARCug @ KW y

xy

x

yx

IcM

IcM

APq +−=2

enARCug # KW y

xy

x

yx

IcM

IcM

APq −−=3

enARCug $ KW y

xy

x

yx

IcM

IcM

APq −+=4

cMNaMfa kugRtaMgxageRkAminRtUvFMCagsm<aFRTRTg;rbs;dI nigmü:ageTotdIminGacrgkmøaMg

Taj)aneT Edl 0≥q .

]TahrN_ 13>7³ ssrctuekaNEdlmanmuxkat; mm600300× dUcbgðajkñúg rUbTI 13>27 a rgnUv bnÞúkcMG½kS kNPD 980= nigm:Um:g; mkNM D .244= EdlbNþalBIbnÞúkefr nigbnÞúkcMG½kS

kNPL 734= nigm:Um:g; mkNM L .190= EdlbNþalBIbnÞúkGefr. )atrbs;eCIgtagsßitenACeRmA m5.1 BInIv:UdI ehIysm<aFRTRTg;dIGnuBaØatKW 2/240 mkN . KNnaeCIgtagedayeRbI MPaf c 28' = /

MPaf y 400= .


eCIgtag 373 T.Chhay

dMeNaHRsay³ eCIgtagrgnUvbnÞúkcMG½kS nigm:Um:g; kNP 1714734980 =+= mkNM .434190244 =+= cMNakp©itKW m

PMe 253.0

1714434

=== yk mm250 eKGacKNnaeCIgtagtmaviFIsaRsþBIrKW³ viFIsaRsþTI1³ rMkilG½kSeCIgtagcm¶ay mme 250= BIG½kSssr. kñúgkrNIenH sm<aFdIRtUv)an cat;TukfaBRgayes μIenABIeRkameCIgtag ¬rUbTI 13>27 b¦. viFIsaRsþTI2³ G½kSrbs;eCIgtag nigG½kSrbs;ssrRtYtsIuKña. kñúgkrNIenH sm<aFdImanragCa RtIekaN b¤ctuekaNBñay ¬rUbTI 13>27 c¦ ehIytémøGtibrma nigGb,brmaRtUv)anKNnadUcbgðaj enAkñúgrUbTI 13>27.

karGnuvtþénviFIsaRsþTaMgBIrsRmab;]TahrN_TI 13>7 GacnwgBnül;y:agsegçbdUcxageRkam³ 1> sRmab;viFIsaRsþTI1 sn μt;km<s;eCIgtag mm500 ¬ mmd 420= ¦ nigsnμt;Tm¶n;maDdIesμ I

3/16 mkN sm<aFdIeLIgelIsuT§KW 2/5.211161255.0240 mkN=×−×− RkLaépÞeCIgtag 21.8

5.2111714 m==

snμt;TTwgeCIgtagKW m7.2 enaHeCIgtagmanbeNþay m37.2/1.8 = . dUcenHeyIgeRCIserIs eCIgtagEdlmanTMhM m37.2 × nigssrmanTItaMgcakp©itdUcbgðajkñúgrUbTI 13>27 d. G½kS eCIgtagmancm¶ay mm250 BIG½kSssr.

2> \LÚvviFIsaRsþKNnamanlkçN³RsedogKñanwgkarKNnaeCIgtageTal (single footing). RtYtBinitükm<s;eCIgtagsRmab;GMeBIkmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwgBIrTis. kMNt;m:U m:g;Bt;enAépÞssrsRmab;TisxøI nigTisEvg. edaysarcMNakp©itrbs;eCIgtag muxkat;eRKaH fñak;nwgsßitenAxageqVgénépÞssr dUcbgðajkñúgrUbTI 13>27 d. cm¶ayeTAcugeCIgtagKW

mm1450 kNLDPu 4.23507346.19802.16.12.1 =×+×=+=

2/2.29037.24.2350 mkNqu =

×=



m:Um:g;Gtibrma mkNM u .7.823245.17.22.290

2=××= ¬enAelITTwg m7.2 ¦

enAkñúgTisedAxøI mkNM u .8.62622.132.290

2=××=

BinitüelIgvijkm<s;eCIgtagEdl)ansnμt;RbsinebIcaM)ac; nigeRCIserIsbrimaNEdkcaM)ac;enA kñúgTisTaMgBIrrbs;eCIgtag dUcEdl)anBnül;enAkñúg]TahrN_GMBIeCIgtageTal (single

footing).


eCIgtag 375 T.Chhay

3> sRmab;viFIsaRsþKNnaTI2 KNnaRkLaépÞrbs;eCIgtagtamviFIdUcEdl)anBnül;enAkñúgviFI saRsþTI1 bnÞab;mkKNnasm<aFdIGtibrma nigeRbobeFobvaCamYynwgsm<aFdIGnuBaØatEdleRbI bnÞúkFmμta bnÞúksrub kNP 1714= TMhMrbs;eCIgtag m37.2 ×= edaysarcMNakp©itKW mmLmme 5006/30006/250 ==<= karBRgaysm<aFdIeLIgelI manragCactuekaNBñay. KNnasm<aFdIGtibrma nigGb,brma³

2222max /5.211/8.318

37.24346

37.217146 mkNmkN

BLM

LBPq >=

×

×+

×=+=

eCIgtagKμansuvtßiPaB. sakl,g m48.2 × ¬RkLaépÞ 22.11 m= ¦ 22

22max /5.211/2.21148.2

434648.2

17146 mkNmkNBL

MLBPq <=

×

×+

×=+=

222min /9.94

48.24346

48.217146 mkN

BLM

LBPq =

×

×−

×=−=

5> KNnasm<aFeLIgelIemKuNedayeRbIbnÞúkemKuN bnÞab;mkKNnam:Um:g; nigkmøaMgkat;TTwg dUc Bnül;kñúg]TahrN_mun.

13>9> kRmalxNÐelIdI (Slabs on Ground)

kRmalxNÐebtugEdldak;pÞal;elIdIGacnwgrgnUv³ - bnÞúkBRgayesμ IenAelIépÞrbs;va EdlbegáIt)anCakmøaMgkñúgtUc² - bnÞúkcMcMNuc b¤bnÞúkBRgayminesμ IEdlbegáItm:Um:g;Bt; nigkmøaMgkat;. kugRtaMgkmøaMgTajekIt

eLIg ehIysñameRbHnwgekItmanEpñkxøHrbs;kRmalxNÐ. kugRtaMgTajCaTUeTAekItmanedaybnSMén³

- karrYj (contraction)EdlbNþalmkBIsItuNðPaB nigkarrYmmaD EdlbgçaMgedaykmøaMgkkit rvagkRmalxNÐ nig subgrade begáItCakugRtaMgTaj.

- karxUcragmuxkat;rbs;kRmalxNÐedaykarmYl (warping of the slabe). - lkçxNÐénkardak;bnÞúk - sRmut



tMN contraction joint RtUv)anbegáIteLIgedIm,Ikat;bnßykugRtaMgTajenAkñúgkRmalxNÐ. tMN expansion joint RtUv)andak; sRmab;kRmalxNÐesþIgEdlmankRmas;rhUtdl; mm250 .

kRmalxNÐCan;eRkamdIéneRKagsMNg;GKarsñak;enA GacCaebtugGarem:EdlmankRmas;BI mm100 eTA mm150 EdlBRgwgedaysMNaj;Edk. sRmab;XøaMg kRmalxNÐGacmankRmas;BI mm150 eTA mm300 GaRs½yelIbnÞúkenAelIkRmalxNÐ. kRmalxNÐCan;eRkamdIRtUv)anKNna

edIm,ITb;nwgsm<aFdI eLIgelI nigsm<aFTwk. RbsinebIkRmalxNÐsßitenAelIdIEdlmanlkçN³sßirPaB b¤ENn (incompressible soil) enaHsRmutDIepr:g;EsülRtUv)anecal. kñúgkrNIenH kRmas;kRmal xNÐGacGb,brmaRbsinebIKμanRsTab;TwkeRkamdI. RbsinebIsRmutDIepr:g;EsülFM enaHkRmalxNÐ RtUv)anKNnaCa stiff raft foundation.

13>10> eCIgtagenAelIssrRKwH (Footings on Piles)

enAeBlEdlRsTab;dImanlkçN³Tn;enAkñúgkRmas;d¾Rkas; ehIylT§PaBRTRTg;rbs;vatUc eK nwgminENnaM[dak;eCIgtagedaypÞal;enAelIdIeT. vaCakarRbesIrkñúgkarbBa¢ÚnkmøaMgtamssrRKwHeTA RsTab;d¾eRCAEdlmanlkçN³rwgRKb;RKan;edIm,IRTbnÞúk b¤begáItkmøaMgkkitRKb;RKan;CMuvijépÞxagssr RKwH. ssrRKwHCaeRcInRbePTRtUv)aneRbIsRmab;RKwH. kareRCIserIsssrRKwHGaRs½yelIlkçxNÐdI/ vtþmanRsTab;TwkeRkamdI/ tYrnaTIrbs;ssrRKwH nigfvikar. ssrRKwHGaceFVIBI ebtug Edk b¤eQI. CaTUeTA eCIgtagssrRKwH (pile cap) mansar³sMxan;kñúgkarEbgEckkmøaMgBIssreTAk,al ssrRKwH. eCIgtagssrRKwH (pile cap)RtUvmanTMhMRKb;RKan;edIm,IQrelIssrRKwH. eCIgtagssrRKWH (pile cap) RtUv)anKNnadUcFñwmEdledkenAcenøaHssrRKwH nigRTbnÞúkcMcMNucBIssr. enAeBlEdl ssrRtUv)anRTedayssrRKwHBIr eCIgtagssrRKwHGacRtUv)anKNnadUc truss ebtugGarem:ragRtI ekaN. ACI Code, Section 15.2 bgðajfakarKNnam:Um:g; nigkmøaMgkat;TTwgsRmab;eCIgtagelIssr RKwHRtUv)anQrelIkarsnμt;faRbtikmμmkBIssrRKwHsßitenAcMG½kSssrRKwH. RkLaépÞeCIgtag b¤cMnYn ssrRKwHRtUv)ankMNt;BIbnÞúk nigm:Um:g;K μanemKuN.


eCIgtag 377 T.Chhay

kRmas;ebtugGb,brmasRmab;eCIgtagssrRKwHRtUv)ankMNt;Rtwm mm300 (ACI Code,

Section 15.7) . sRmab;karKNnassrRKwH nigeCIgtagssrRKwHlMGit sUmGanesovePAvisVkmμRKwH (books on foundation engineering) .


T.Chhay 378 Retaining Walls

XIV. CBa¢aMgTb; Retaining Wall


CBa¢aMgTb;CaeRKOgbgÁúMEdlRtUv)aneRbIedIm,Ipþl;lMnwgdl;dI b¤smÖar³epSgeTot nigedIm,IkarBarva BICRmalFmμCatirbs;va. kñúgn½yenH CBa¢aMgTb;rkSadIEdlmankRmitkm<s;xusKñaedayépÞTaMgBIrrbs;va. smÖar³EdlRtUv)anTb;enAnIv:Ux<s;CagGnuvtþkmøaMgeTAelICBa¢aMgTb;EdlGacbNþal[vaRkLab; (overturning) b¤)ak; (failure). CBa¢aMgTb;RtUv)aneRbIenAkñúgsMNg;s<anCa abutment/ enAkñúgsMNg;Ca basement walls/ nigenAkñúg embankments. vak¾RtUv)aneRbIedIm,ITb;sarFaturav dUcCaGagTwk nigGag sewage-treatment tank.

14>2> RbePTCBa¢aMgTb; (Types of Retaining Walls)

CBa¢aMgTb;RtUv)ancat;cMNat;fñak;dUcxageRkam ¬eyagtamrUb 14>1¦³ - Gravity walls CaTUeTArYmmanebtugsuT§ b¤\dæ edayGaRs½yeTAelITm¶n;pÞal;rbs;vaedIm,I

pþl;lMnwgRbqaMgkarrujénsmÖar³EdlRtUvTb;. CBa¢aMgenHmanTMhMFMEdlkugRtaMgTajminekIt manenAkñúgebtug b¤\dæbNþalmkBIkmøaMgrujelICBa¢aMgeT. km<s;sRmab;Gnuvtþkñúg gravity

walls minRtUvFMCag m3 . - Semigravity walls Ca gravity walls Edlman)atFMedIm,Ipþl;lT§PaBlMnwgrbs;CBa¢aMg nig

edIm,IkarBarkarekIteLIgénkugRtaMgTajenAelI)at. brimaNEdkd¾tictYcRtUveRbIenAkñúg)at b¤ enAkñúgCBa¢aMgenAeBlxøH edIm,Ikat;bnßymuxkat;d¾FMrbs;CBa¢aMg.

- Cantilever retaining wall CaCBa¢aMgebtugGarem:EdlCaTUeTARtUv)aneRbIEdlmankm<s;BI m4.2 eTA m6 . vaCaRbePTFmμtabMputéneRKagsMNg;Tb; edaysarlkçN³esdækic© nig

lkçN³samBaØrbs;va. CBa¢aMg cantilever retaining wall CaeRcInRbePTRtUv)anbgðajkñúgrUb 14>1.

- Counterfort retaining walls mankm<s;x<s;Cag m6 begáItm:Um:g;Bt;FMenA)aténCBa¢aMgTb; EdleFVI[karKNnaénCBa¢aMgKμanlkçN³esdækic©. dMeNaHRsaymYyenAkñúgkrNIenHKWkarbEnßmnUvCBa¢aMgTTwg (counterfort)


CBa¢aMgTb; 379 T.Chhay

EdlcgP¢ab;CBa¢aMgeTAnwg)at. Counterfort mannaTICaGgát;rgkarTajEdlRTCBa¢aMgbBaÄr. karKNnaCBa¢aMgenHmanlkçN³esdækic©edaysarEtCBa¢aMgRtUv)anKitCakRmalxNÐCab;Edl manKMlattamTisedkcenøaH counterfort. kRmalxNÐRtUv)anKNnadUckRmalxNÐEdlRTenAelITRmbIRCug ¬rUbTI 14>1 h ¦.

- Buttressed retaining wall manTRmg;RsedogKñanwg nounterfort wall Edr b:uEnþkñúgkrNIenH

CBa¢aMgTTwgmanTItaMgsßitenAmuxmçageTotEdleyIgemIleXIj ehIyCBa¢aMgTTwgenHmannaTICa Ggát;rgkarsgát; ¬rUbTI 14>1 i ¦. CBa¢aMgEbbenHmanlkçN³esdækic©enAeBlEdlvamankm<s; x<s;Cag m6 . vaminmankareBjniymeT edaysarEteKemIleXIjCBa¢aMgTTwg (buttress).



- Bridge abutment CaCBa¢aMgTb;enAEpñkxagelIEdlRtUveRbIedIm,IRTkRmals<an. CBa¢aMgRtUv)an snμt;fabgáb;enAEpñkxageRkamenAnwg)at nigRTedayTRmsamBaØenAEpñkxagelI.

- Basement walls Tb;sm<aFdIBIépÞmçagrbs;CBa¢aMg niglatsn§wgtamTisQrBIkRmalxNÐCan; eRkamdIeTAkRmalxNÐCan;TImYy. CBa¢aMgGacRtUv)ansnμt;bgáb;enA)at nigRTedayTRmsamBaØ b¤Tb;edayEpñk (partially restrained) enAEpñkxagelI.

14>3> kmøaMgenAelICBa¢aMgTb; (Forces on Retaining Walls)

CaTUeTA CBa¢aMgTb;rgnUvbnÞúkTMnajEpndI nigsm<aFdIEdlbNþalmkBIsmÖar³Tb;enAelICBa¢aMg. bnÞúkTMnajEpndIEdlbNþalmkBITm¶n;rbs;smÖar³RtUv)ankMNt;edaykarKNnaedaypÞal; niggay RsYl. GaMgtg;sIuet nigTisedArbs;sm<aFdIenAelICBa¢aMgTb;GaRs½yelIRbePT niglkçN³dIEdlRtUv )anTb; nigktþaepSgeTotEdleKminGacKNna)anRtwmRtUvdUcbnÞúkTMnajEpndIeT. eKGackMNt;sm<aF dImanGMeBIelICBa¢aMgTb;tamRTwsþI nigviFIsaRsþEdlmanBnül;kñúgmuxviC¢aemkanicdI. sßanPaBlMnwgrbs; CBa¢aMgTb; nig\T§iBlénkmøaMgDINamiceTAelICBa¢aMgk¾manEcgkñúgmuxviC¢aenHEdr. dIRtsuH (granular material) dUcCaxSac; manlkçN³emkanicxusBIdIs¥it (cohesive material) dUcCadI\dæ b¤BIbnSMénRbePTdITaMgBIr. eTaHCaGaMgtg;sIuetsm<aFdIenAelICBa¢aMgTb;manlkçN³s μ úKsμaj eK)ansnμt;karBRgaysm<aFdImkelICBa¢aMgTb;manlkçN³CabnÞat;. GaMgtg;sIuetsm<aFekIneLIg smamaRtCamYynwgCeRmA ehIytémørbs;vaCaGnuKmn_eTAnwgkm<s;CBa¢aMg/ Tm¶n;dI nigRbePTdI. GaMg tg;sIuetdI p enACeRmA h BIeRkamépÞdIRtUv)anKNnadUcxageRkam³

Cwhp = ¬!$>!¦ Edl w CaTm¶n;maDdI nig C CaemKuNEdlGaRs½yeTAnwglkçN³rUbrbs;dI. témørbs;emKuN C ERbRbYlBI 35.0 sRmab;dIRtsuH (loose granular soil) dUcCaxSac; eTA 0.1 sRmab;dIs¥it (cohesive

soil) dUcCadI\dæesIm. RbsinebICBa¢aMgTb;RtUv)ansnμt;rwgdac;xat enaHkrNIsm<aFdIenAes¶omnwgekIt eLIg. eRkamsm<aFdI CBa¢aMgGacdab b¤rMkiledaybrimaNtictYcBIdI ehIysm<aFdIskmμnwgekIteLIg dUcbgðajenAkñúgrUbTI 14>2. RbsinebICBa¢aMgrMkileq<aHeTAdI enaHsm<aFdIGkm μnwgekItman. TaMgsm<aF dIskmμ nigsm<aFdIGkm μRtUv)ansnμt;faERbRbYlCabnÞat;CamYynwgCeRmACBa¢aMg ¬rUbTI 14>2¦. sRmab; dIRtsuH (granular) s¶Üt/ Gt;s¥it (noncohesive) RtUv)ansnμt;fasm<aFBRgaymanragCabnÞat; (linear) ÉdIs¥it b¤dIxSac;Eq¥tTwkmanlkçN³epSg KWsm<aFBRgaymanlkçN³minEmnbnÞat; (nonlinear). dUc



enH CaTUeTAeKeRbIdIRtsuHCasmÖar³cak;bMeBjedIm,Ipþl;nUvdüaRkamsm<aFbnÞat; nigmü:ageTotpþl; lT§PaBkñúgkarbgðÚrTwkBICBa¢aMgxageRkay. sRmab;sm<aFbnÞat; GaMgtg;sIuetsm<aFskm μ nigsm<aFGkm μRtUv)anKNnadUcxageRkam³ whCP aa = ¬!$>@¦ whCP pp = ¬!$>#¦ Edl aC nig pC CaemKuNénsm<aFskm μ nigsm<aFGkm μerogKña.

14>4> sm<aFdIGkm μ nigsm<aFdIskm μ (Active and Passive Soil Pressures)

RTwsþId¾samBaØCaeKBIrEdlRtUv)aneRbICaTUeTAkñúgkarKNnasm<aFdIKW Rankine nig Coulomb. a. sRmab;viFIrbs; Rankine CBa¢aMgTb;RtUv)ansnμt;fa yield RKb;RKan;edIm,IbegáItnUvsßanPaBlM

nwg)øasÞic enAkñúgdMudIenAépÞCaBa¢aMg. dIEdlenAes¶ómenArkSakñúgsßanPaBeGLasÞic. RTwsþIenH GnuvtþCacMbgcMeBaHdIK μanPaBs¥it (cohesiveless)/ dIEdlminGacsgát;)an (incompressible)/ dIEdlmanlkçN³sac;mYy (homogeneous) nigminKitnUvkmøaMgkkitrvagdI nigCBa¢aMg. sm<aF dIskmμenACeRmA h manGMeBIelICBa¢aMgTb;edayQrelIRTwsþI Rankine RtUv)ankMNt;dUcxag eRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛+−

==φφ

sin1sin1whwhCP aa ¬!$>$¦



Edl ⎟⎟⎠

⎞⎜⎜⎝

⎛+−

=φφ

sin1sin1

aC

=φ mMukkitkñúgrbs;dI ¬tarag !$>!¦ sm<aFskmμsrub ⎟⎟

⎠

⎞⎜⎜⎝

⎛+−

=φφ

sin1sin1

2

2whH a ¬!$>%¦

tarag !$>! témøén w nig φ RbePTdIcak;bMeBj Tm¶n;maD ¬ 3/ mkg ¦ mMukkitkñúg φ

Soft clay 19201440 − oo 150 − Medium clay 19201600 − oo 3015 − Dry loose silt 19201600 − oo 3027 − Dry dense silt 19201760 − oo 3530 −

Loose sand and gravel 21001600 − oo 4030 − Dense sand and gravel 21001920 − oo 3525 − Dry loose sand, graded 21001840 − oo 3533 − Dry dense sand, graded 21001920 − oo 4642 −

kmøaMgpÁÜb aH GnuvtþGMeBIenAkm<s; 3/h BI)at ¬rUbTI !$>@¦. enAeBlEdldIrgbnÞúkbEnßmeday mMu δ EdlpÁúMCamYyG½kSedk enaH



⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−+

−−=

φδδ

φδδδ

22

22

coscoscos

coscoscoscosaC ¬!$>^¦

whCP aa = nig 2

2whCH aa = kmøaMgpÁÜb aH eFVIGMeBIenAkm<s; 3/h nigeRTtedaymMu δ eTAnwgbnÞat;edk ¬rUbTI 14>3¦. témø

aC EdlsMEdgedaysmIkar !$>^ sRmab;témøepSg²én δ nig φ RtUv)anbgðajenAkñúgtarag !$>@.

tarag !$>@ témørbs; aC φ ¬mMukkitkñúg¦

δ o28 o30 o32 o34 o36 o38 o40 o0 361.0 333.0 307.0 283.0 260.0 238.0 217.0 o10 380.0 350.0 321.0 294.0 270.0 246.0 225.0

o20 461.0 414.0 374.0 338.0 306.0 277.0 250.0

o25 573.0 494.0 434.0 385.0 343.0 307.0 275.0

o30 .0 866.0 574.0 478.0 411.0 358.0 315.0

sm<aFdIGkm μekItmanenAeBlEdlCBa¢aMgTb;rMkil nigsgát;dI. sm<aFdIGkmμenAkm<s; 'h enA elICBa¢aMgTb;CamYynwgdIcak;bMeBjtamTisedkRtUv)ankMNt;dUcxageRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

==φφ

sin1sin1whwhCP pp ¬!$>&¦

Edl a

p CC 1

sin1sin1

=⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=φφ

sm<aFGkmμsrubKW ⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=φφ

sin1sin1

2

2whH p ¬!$>*¦

kmøaMgpÁÜb pH manGMeBIenA 3/'h BI)at ¬rUbTI 14>2¦. enAeBldIrgnUvbnÞúkbEnßmedaymMu

δ eTAnwgbnÞat;edk enaH ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−−

−+=

φδδ

φδδδ

22

22

coscoscos

coscoscoscospC ¬!$>(¦

whCP pp = nig 2

2whCH pp =



pH manGMeBIenA 3/'h ehIyeRTtedaymMu δ eTAnwgbnÞat;edk ¬rUbTI 14>4¦. témø pC Edl sMEdgedaysmIkar !$>( sRmab;témøepSg²én δ nig φ RtUv)anbgðajenAkñúgtarag !$>#. témøén φ nig w ERbRbYleTAtamRbePTdIcak;bMeBj. tamkarENnaM témøFmμtarbs; φ nig w RtUv)an[enAkñúgtarag !$>!.

tarag !$># témørbs; pC φ ¬mMukkitkñúg¦

δ o28 o30 o32 o34 o36 o38 o40 o0 77.2 00.3 25.3 54.3 85.3 20.4 60.4 o10 55.2 78.2 02.3 30.3 60.3 94.3 32.4

o20 92.1 13.2 36.2 61.2 89.2 19.3 53.3

o25 43.1 66.1 90.1 14.2 40.2 68.2 00.3

o30 .0 87.0 31.1 57.1 83.1 10.2 38.2

b. sRmab;RTwsþIrbs; Coulomb/ sm<aFdIskmμRtUv)ansnμt;faCalT§pléndMudI (wedge of soil)

rGilRbqaMgmkelIépÞCBa¢aMgTb;. dUcenHRTwsþI Coulomb KWsMedAeTARTwsþI wedge. enAeBl EdlkmøaMgkkitRtUv)anKitenAkñúgCBa¢aMgTb; eK)ansnμt;faépÞrGilCabøgerobes μ I EtkarBitva



manlkçN³ekagbnþic. kMhusenAkñúgkarsnμt;enHRtUv)anecalenAkñúgkarKNnasm<aFdIskm μ. smIkar Coulomb edIm,IKNnasm<aFdIskmμ nigsm<aFdIGkm μmandUcxageRkam³ sm<aFdIskm μKW whCP aa = Edl ( )

( ) ( ) ( )( ) ( )

22

2

coscossinsin1coscos

cos

⎥⎦

⎤⎢⎣

⎡

−+−+

++

−=

βθβθδφβφβθθ

θφaC ¬!$>!0 a ¦

Edl =φ mMukkitkñúgrbs;dI =θ mMuénépÞsm<aFdImkG½kSQr =β mMukkittambeNþayépÞCBa¢aMg ¬mMurvagdInigebtug¦ =δ mMuénbnÞúkbEnßm (surcharge) eTAG½kSedk sm<aFdIskm μsrubKW

22

2 hPwhCH aaa == enAeBlEdlépÞCBa¢aMgmanlkçN³bBaÄrRtg; enaH o0=θ nigRbsinebI δβ = enaH aC ehIysmIkar ¬!$>!0 a ¦ køayeTACasmIkar ¬!$>^ ¦ rbs; Rankine. sm<aFdIGkm μKW whCP pp = Edl ( )

( ) ( ) ( )( ) ( )

22

2

coscossinsin1coscos

cos

⎥⎦

⎤⎢⎣

⎡

−+++

−−

+=

βθβθδφβφβθθ

θφpC ¬!$>!0 a ¦

témørbs; φ nig w ERbRbYleTAtamRbePTdIcak;bMeBj. tamkarENnaM témøFm μtarbs; φ nig w RtUv)an[ enAkñúgtarag !$>!.

c. enAeBlEdldIEq¥tTwk rn§es<atrbs;dIeBjeTAedayTwk EdlbegáItCasm<aFGIuRdUsþaTic. enAkñúg krNIenHTm¶n;maDdIEdllicTwk (submerged unit weight)RtUv)aneRbI. Tm¶n;maDdIlicTwk Ca Tm¶n;maDdIEdl)andkTm¶n;maDTwk. \T§iBlrbs;sm<aFTwkGIuRdUsþaTicRtUvEtKitenAkñúgkar KNnaCBa¢aMgTb;EdlRbQmnwgRsTab;Twkx<s; nigdIlicTwk. eKGaceRbImMukkitkñúgEdl)an bgðajenAkñúgtarag !$>!.



14>5> \T§iBlénbnÞúkbEnßm (Effect of Surcharge)

bnÞúkepSg²énbnÞúkRtUv)andak;enAelIépÞéndIcak;bMeBjBIxageRkayCBa¢aMgTb;. RbsinebIbnÞúk CabnÞúkBRgayesμ I km<s;smmUlrbs;dI sh RtUv)ansnμt;famanGMeBIeTAelICBa¢aMgedIm,IbegáInsm<aF. sRmab;CBa¢aMgdUcbgðajenAkñúgrUbTI 14>5 sm<aFedkEdlbNþalBIbnÞúkbEnßmmantémøefreBjkm<s; rbs;CBa¢aMgTb;.

ww

h ss = ¬!$>!!¦

Edl =sh km<s;smmUlrbs;dI =sw sm<aFbnÞúkelIs =w Tm¶n;maDdI sm<aFsrubKW ⎟

⎟⎠

⎞⎜⎜⎝

⎛+=+= saaaa hhhwCHHH

2

2

21 ¬!$>!@¦

enAkñúgkrNIbnÞúkBRgayes μIedayEpñkmanGMeBIenAcm¶aymYyBICBa¢aMgTb; enaHvamanEtsm<aFén bnÞúkbEnßmsrubmYyEpñkman\T§iBleTAelICBa¢aMg ¬rUbTI !$>^¦. vaCakarGnuvtþn_TUeTAedaysnμt;fakm<s;RbsiT§PaBénbnÞúkbEnßmKW 'h Edlvas;BIcMnuc B eTA)at rbs;CBa¢aMgTb;. bnÞat; AB pÁúMmMu o45 CamYyG½kSedk. kñúgkrNIbnÞúkkg;LanmanGMeBIenAcm¶aymYyCBa¢aMg bnÞúkRtUv)anBRgayelIépÞkMNt;mYy Edl CaTUeTAkMNt;eday specification EdleKTTYlsÁal;dUcCa AASHTO nig AREA.



14>6> kmøaMgkkitenAelI)atCBa¢aMgTb; (Friction on the Retaining Wall Base)

bgÁúMkmøaMgtamTisedkénkmøaMgTaMgGs;manGMeBIelICBa¢aMgTb;)anrujCBa¢aMgtamTisedAedk. )atCBa¢aMgTb;RtUvEtFMRKb;RKan;edIm,ITb;nwgkarrGilrbs;CBa¢aMg. emKuNkmøaMgkkitEdlRtUv)aneRbIKWCa emKuNkmøaMgkkiténdIenAelICBa¢aMgsRmab; coarse granular soils nigCaersIusþg;kmøaMgkat;TTwgéndI s¥it. emKuNkmøaMgkkit μ EdlGacTTYlyksRmab;RbePTdIepSg²mandUcxageRkam³

- Coarse-grained soils without silt, 55.0=μ - Coarse-grained soils with silt, 45.0=μ - Silt, 35.0=μ - Sound rock, 60.0=μ

kmøaMgkkitsrub F enAelI)atedIm,ITb;nwgkarrGilKW pHRF += μ ¬!$>!#¦

Edl =μ emKuNkmøaMgkkit =R kmøaMgbBaÄrmanGMeBIelI)at =pH kmøaMgTb;Gkm μ emKuNsuvtßiPaBRbqaMgnwgkarrGilKW

emKuNsuvtßiPaB 5.1≥+

==ah

p

ah HHR

HF μ ¬!$>!$¦

Edl ahH CabgÁúMkmøaMgedkénsm<aFskmμ aH . emKuNsuvtßiPaBRbqaMgnwgkarrGilminKYr tUcCag 5.1 RbsinebIkmøaMgTb;Gkmμ pH RtUv)anecal nigminKYrtUcCag 0.2 RbsinebI pH RtUv)an ykmkKitBicarNakñúgkarKNna.



14>7> sßanPaBlMnwgRbqaMgnwgkarRkLab; (Stability against Overturning)

bgÁúMkmøaMgedkénsm<aFskmμ aH nwgeFVI[CBa¢aMgTb;RkLab;eFobcMnuc 0 ¬rUbTI 14>7¦. m:U m:g;eFVI[RkLab; (overturning moment) 3/0 hHM a= . Tm¶n;rbs;ebtug nigdIbegáItCam:Um:g;Edl eFVI[manlMnwg (balancing moment or tightening moment) edIm,ITb;Tl;nwgm:Um:g;eFVI[RkLab;.

m:Um:g;eFVI[manlMnwgsRmab;krNICBa¢aMgdUcbgðajkñúgrUbTI 14>7 KW

∑=++= wxxwxwxwM b 332211 emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW



emKuNsuvtßiPaB 0.2

30

≥== ∑hH

wsMM

a

b ¬!$>!%¦

emKuNsuvtßiPaBenHminRtUvKYrtUcCag 0.2 eT. kmøaMgpÁÜbénkmøaMgTaMgGs;manGMeBIelICBa¢aMgTb; AR RbsBVenA)atCBa¢aMgTb;Rtg;cMnuc C ¬rUb

TI 14>7¦. CaTUeTA cMnuc C minRtYtsIuKñaCamYyG½kSrbs;)atCBa¢aMg dUcenHvabegáIt)anCakmøaMgcakp©it enAelIeCIgtag. vaCakarRbesIredayrkSacMnuc C enAkñúgEpñkkNþalénRbEvgmYyPaKbIén)atCBa¢aMg edIm,IeFVI[)atCBa¢aMgTaMgmUlsßiteRkamsm<aFdI. ¬krNIeCIgtageRkambnÞúkcakp©itRtUv)anBnül;kñúg emeronTI 13¦.

14>8> smamaRténCBa¢aMgTb; (Proportions of Retaining Walls)

karKNnaCBa¢aMgTb;cab;epþImCamYynwgkarmuxkat;sakl,gEdlmanTMhMRbhak;RbEhl. bnÞab;mkmuxkat;snμt;enaHRtUv)anepÞógpÞat;sßanPaBlMnwg nigPaBRKb;RKan;rbs;eRKOgbgÁúM. xageRkam Cac,ab;EdlGaceRbIedIm,IkMNt;xñatRbhak;RbEhlénEpñkepS²rbs;CBa¢aMgTb; cantilever³



a. km<s;rbs;CBa¢aMg³ km<s;srubrbs;CBa¢aMgesμ InwgPaBxusKñaénkRmitkm<s;bUknwg mm900 eTA mm1200 EdlCakarKNnaCeRmAénCRmabTwkkk (frost penetration depth) sRmab;rdæPaK

xageCIgrbs;RbeTsGaemrik. b. kRmas;CBa¢aMg³ GaMgtg;sIueténsm<aFekIneLIgeTAtamCeRmArbs;CBa¢aMg ehIytémøGtibrma

rbs;vasßitenA)atCBa¢aMg. dUcenH m:Um:g;Bt;Gtibrma nigkmøaMgkat;TTwgGtibrmaenAkñúgCBa¢aMg ekItmanenAnwg)atrbs;va. kRmas;CBa¢aMgenA)atRtUv)ankMNt;esμ Inwg 12/1 eTA 10/1 énkm<s; CBa¢aMg h . kRmas;rbs;CBa¢aMgenAkMBUlRtUv)ansnμt; mm200 nig mm300 . edaysarCBa¢aMg Tb;RtUvKNnasRmab;Tb;sm<aFdIskmμ edIm,IeFVI[manPaBdabrbs;CBa¢aMgtUc vaCakarRbesIr edIm,IeFVI[épÞCBa¢aMgmanCRmalGb,brmakñúgkRmit mm25 kñúgkm<s; m1 . sRmab;CBa¢aMgTab Edlmankm<s; m3 eKGacykkRmas;CBa¢aMgefr)at.

c. RbEvgeCIgtag³ karkMNt;dMbUgsRmab;RbEvg)ates μ Inwg 5/2 eTA 3/2 énkm<s;CBa¢aMg h . d. kRmas;rbs;)at³ kRmas;)atxageRkamRtUv)ankMNt;es μIkRmas;CBa¢aMgenA)at Edles μ Inwg 12/1

eTA 10/1 énkm<s;CBa¢aMg. kRmas;Gb,brmaRtUv)ankMNt;RbEhl mm300 . )atCBa¢aMgGac mankRmas;esμ I b¤sþÜcenAcugTaMgsgçag Edlmanm:Um:g;Bt;sUnü. smamaRtrbs;CBa¢aMg cantilever retaining wall RtUv)anbgðajenAkñúgrUbTI 14>8.

14>9> tRmUvkarsRmab;KNna (Design Requirement)

ACI Code, Chapter 14 pþl;nUvviFIsaRsþsRmab;KNnalT§PaBRTRTg;rbs;CBa¢aMg. tRmUvkar cMbgdUcxageRkam³

a. kRmas;Gb,brmaénCBa¢aMgKW 25/1 énkm<s; b¤énRbEvgCBa¢aMg ykmYyNaEdltUcCageK b:uEnþ minRtUvtUcCag mm100 .

b. RkLaépÞGb,brmaénEdkedkenAkñúgCBa¢aMgKW bh0025.0 Edl bh CaRkLaépÞebtugCBa¢aMg. témøenHRtUv)ankat;bnßyRtwm bh002.0 RbsinebIeKeRbIEdk 16DB b¤EdkEdlmanmuxkat; tUcCagenH nigman MPaf y 400≥ . sRmab;EdksMNaj;pSar ¬EdkmUl b¤EdkfñaMgGMeBA¦ Rk LaépÞEdkGb,brmaKW bh002.0 .



c. RkLaépÞGb,brmaénEdkQrKW bh0015.0 b:uEnþvaRtUv)ankat;bnßyRtwm bh0012.0 RbsinebI Edk 16DB b¤EdkEdlmanGgát;p©ittUcCagenHCamYynwg MPaf y 400≥ RtUv)aneRbI. sRmab; EdksMNaj;pSar ¬EdkmUl b¤EdkfñaMgGMeBA¦ brimaNEdkGb,brmaKW bh0012.0 .

d. KMlatGtibrmaénEdkbBaÄr nigEdkedkKWtémøtUcCageKkñúgcMeNam mm450 b¤kRmas;CBa¢aMg bIdg.

e. RbsinkRmas;CBa¢aMgFMCag mm250 enaHEdkbBaÄr nigEdkedkKYrEtdak;BIrRsTab;RsbKñanwg épÞxagkñúg nigxageRkAdUcxageRkam³ sRmab;épÞCBa¢aMgxageRkA y:agtic 2/1 énbrimaNEdk sA ¬b:uEnþminRtUveRcInCag 3/2 sA ¦ KYr mankRmas;karBarEdkGb,brma mm50 b:uEnþminRtUvFMCag 3/1 énkRmas;CBa¢aMg. enHeday sar épÞCBa¢aMgxageRkARbQmnwglkçxNÐGakasFatuepSgKña nigbERmbRmYlsItuNðPaB. sRmab;épÞCBa¢aMgxagkñúg EdktRmUvkarenAkñúgTisedAnImYy²KYrmankRmas;karBarEdkGb,brma

mm20 b:uEnþminRtUvFMCag 3/1 énkRmas;CBa¢aMg. EdkGb,brmaenAkñúgeCIgtagCBa¢aMg eyagtam ACI Code, Section 10.5.3 KWfaEdktRmUvkar sRmaab;EdkrYmmaD nigEdksItuNðPaB Edlfa bh0018.0 enAeBl MPaf y 400= nig

bh0020.0 enAeBl MPaf y 280= b¤ MPaf y 350= . edaysarbrimaNEdkGb,brma mantémøtUceBk enAkñúgkarGnuvtþeKRtUvdMeLIgvadl;brimaNEdkGb,brma sA sRmab;karBt;³

dbf

dbff

A wy

wy

cs

4.14

'min ≥= nig ¬!$>!^¦

14>10> karbgðÚrTwk (Drainage)

sm<aFdIEdl)anerobrab;BIxagedImmin)anrab;bBa©Úlsm<aFGIuRdUsþaTic. RbsinebITwkRbmUlpþúMenA xageRkayCBa¢aMgTb; sm<aFTwkRtUvEtrab;bBa©ÚlkñúgkarKNna. épÞ b¤RsTab;TwkeRkamdIGacRCabenAkñúg dIcak; nigbegáItkrNIdIlicTwk. edIm,IeCosvagsm<aFGIuRdUsþaTic karbgðÚrTwkKYrRtUvdak;enABIeRkay CBa¢aMg. RbsinebIdIGt;manPaBs¥itbgðÚrTwk)anl¥RtUv)aneRbIsRmab;cak;bMeBj CBa¢aMgGacRtUv)anKNna sRmab;E sm<aFdIsuT§. RbBn§karbgðÚrTwkGacrYmmanmYy b¤bnSMénkarerobrab;xageRkam³

- rn§Rbehag (weep holes) enAkñúgCBa¢aMgTb;manGgát;p©it mm100 b¤FMCagenH nigmanKMlat RbEhl m5.1 enAkNþalG½kSedk nigG½kSQr ¬rUbTI 14>9 a ¦.



- TIbRbehag (perforated pipe) EdlmnaGgát;p©it mm200 dak;tambeNþayénCBa¢aMgB½T§CMu vijedayxSac; b¤f μbMEbk ¬rUbTI 14>9 b ¦.

- labépÞCBa¢aMgxagcak;bMeBjCamYy asphalt edIm,IkarBarkarRCabTwk. - viFIepSgeTotedIm,IbgðÚrTwk

]TahrN_14>1³ muxkat;sakl,grbs;CBa¢aMgTb;ebtugsuT§ semigravity RtUv)anbgðajenAkñúgrUbTI 14>10. CBa¢aMgenHcaM)ac;RtUvkarRtYtBinitüsuvtßiPaBTb;nwgkarRkLab;/ karrGil nigRTRTg;nUvsm<aFBI eRkameCIgtag. eK[³ Tm¶n;maDdIcak;bMeBj 3/6.17 mkN / mMukkitkñúg o35=φ / emKuNkkitrvag ebtug nigdI 5.0=μ / sm<aFdIGnuBaØatKW 2/120 mkN nig MPaf c 20' = . dMeNaHRsay³

1> edayeRbIsmIkar Rankine 271.0

574.01574.01

sin1sin1

=+−

=+−

=φφ

aC

sm<aFGkmμenAEpñkxagmuxKWsRmab;km<s; mm300 EdlCatémøtUcGacecal)an. kNwhCH a

a 262

3.36.17271.02

22=

××==

aH eFVIGMeBIenAcm¶ay mh 1.13/ = BI)at. 2> m:Um:g;eFVI[RkLab; (overturning moment) KW mkNM .6.281.1260 =×= 3> KNnam:Um:g;eFVI[manlMnwg (balancing moment) bM edayKiteFobcMnuc 0 ¬rUbTI 14>10¦³





Tm¶n; )(kN édXñas; )(m m:Um:g; ).( mkN 6.212433.01 =××=w 4.0 64.8

( ) 27243.005.1321

2 =×−××=w 8.0 6.21 52.11246.13.03 =××=w 8.0 22.9

( ) 8.196.173.005.1321

4 =×−××=w 05.1 79.20 84.156.1733.05 =××=w 45.1 23

kNRw 76.95==∑ ∑ == kNMM b 25.83 4> emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW 0.291.26.28/25.83 >= 5> kmøaMgRbqaMgkarrGil kNRF 88.4776.955.0 =×== μ

emKuNsuvtßiPaBTb;nwgkarrGilKW 5.184.126/88.47/ >==aHF 6> KNnasm<aFdIeRkam)at

a. cm¶ayrbs;kmøaMgpÁÜbBIcMnuc 0 m

RMMx b 57.0

76.956.2825.830 =

−=

−=

cMNakp©itKW me 23.057.08.0 =−= . kmøaMgpÁÜb R manGMeBIenAkñúgEpñkkNþalénmYyPaKbIRbEvgeCIgtag nigmancMNakp©it

me 23.0= BIG½kSrbs;)at ¬rUbTI 14>10¦. b. sRmab;eCIgtagRbEvg m1 nigRbEvgeCIgtagRbsiT§PaB m6.1

m:Um:g;niclPaB 43 34.012/6.11 mI =×= / RkLaépÞ 26.1 mA = c. sm<aFdIenAcugTaMgBIrrbs;eCIgtagKW IMcARqq //, 21 ±= .

m:Um:g; M KW mkNeR .2223.076.95 =×=⋅ nig mc 8.0= kNq 6.111

34.08.022

6.176.95

1 =×

+= kNq 1.8

34.08.022

6.176.95

2 =×

−= 7> RtYtBinitükugRtaMgBt;enAkñúgebtugRtg;cMnuc A

a. sm<aFdIRtg;cMnuc A ¬BIFrNImaRt¦KW



( ) kNqA 4.951.86.1116.135.11.8 =−⎟

⎠⎞

⎜⎝⎛+=

b. m:Um:g; AM RtUv)anKNnaenARtg; A bNþalmkBIkugRtaMgctuekaNEkg nigkugRtaMg RtIekaN

mkNM A .32.33225.0

225.02.16

225.04.95 2

=⎟⎠⎞

⎜⎝⎛ ×

×+

×=

c. kugRtaMgBt;enAkñúgebtugKW MPa

IMc 221.010

1025.215.032.3 3

3 =⋅⋅

×= −

−

Edl mhc 15.023.0

2=== nig 433 1025.212/3.01 mI −⋅=×=

d. m:UDuldac;rbs;ebtug (modulus of rupture of concrete) KW MPaMPaf c 221.08.2'623.0 >=

emKuNsuvtßiPaBRbqaMgnwgkareRbHKW 67.12221.08.2

= . dUcenH muxkat;manlkçN³RKb;RKan;. eKmincaM)ac;esñInUvmuxkat;epSgeTotedIm,IRtYtBinitüeT.

]TahrN_14>2³ KNnaCBa¢aMgTb; cantilever edIm,ITb;dIRcaMgkm<s; m5 . enAelIdIEdlTb;manbnÞúk bEnßm 2/25.9 mkN . eK[³ Tm¶n;maDdIcak;bMeBj 3/5.18 mkN / mMukkitkñúg o35=φ / emKuNkkit rvagebtug nigdI 5.0=μ / emKuNkkitrvagRsTab;dI 7.0=μ / lT§PaBRTdIGnuBaØat 2/200 mkN /

MPaf c 20' = nig MPaf y 400= . dMeNaHRsay³

1> kMNt;TMhMrbs;CBa¢aMgTb;edayeRbITMnak;TMngRbhak;RbEhlEdl)anbgðajenAkñúgrUbTI 14>8 a. km<s;CBa¢aMg³ edaybgáb;CBa¢aMgTb; mm900 enaHkm<s;rbs;CBa¢aMgTb; mh 9.59.05 =+= b. kRmas;)at³ sn μt;kRmas;)ates μ I mh 472.09.508.008.0 =×= yk m45.0 . km<s;

rbs;tYCBa¢aMg m45.5 c. RbEvgeCIgtag³ RbEvgeCIgtagERbRbYlcenøaH h4.0 nig h67.0 . edaysn μt;yktémø

mFüm enaHRbEvgeCIgtages μ I mh 127.39.553.053.0 =×= yk m2.3 . RbEvg)atenABI muxtYCBa¢aMgERbRbYlcenøaH h17.0 nig h125.0 . snμt;RbEvg)atxagmuxes μ I

m19.517.0 =× .



d. kRmas;CBa¢aMg³ kRmas;Gtibrmarbs;CBa¢aMgsßitenAKl;EdlERbRbYlcenøaH h08.0 eTA h1.0 . eRCIserIskRmas;CBa¢aMgGtibrmaesμ InwgkRmas;eCIgtagKW m45.0 .

kRmas;Gb,brmarbs;CBa¢aMg sßitenAkMBUlrbs;CBa¢aMg edaykMNt;yk m3.0 . CRmalGb,brmarbs;épÞCBa¢aMgKW mmm /25 . sRmab;CBa¢aMgEdlmankm<s;

m45.5 enaHRbEvgsþÜcesμ Inwg 025.045.5 × m136.0= EdltUcCagRbEvgsþÜcEdlman m15.03.045.0 =− . TMhMrbs;CBa¢aMg Edl)anesñIeLIgRtUv)anbgðajenAkñúg

rUbTI14>11.

2> tamsmIkar Rankine ³

271.0574.01574.01

sin1sin1

=+−

=+−

=φφ

aC

3> emKuNsuvtßiPaBRbqaMgnwgkarRkLab;GacRtUv)ankMNt;dUcxageRkam³



a. KNnakmøaMgK μanemKuNBitR)akdEdlmanGMeBIelICBa¢aMgTb;. dMbUg kMNt;nUvral;kmøaMg EdleFVI[CBa¢aMgRkLab;³

sh ¬EdlbNþalBIbnÞúkelIs¦ mwws 5.0

5.1825.9

===

21 /5.25.05.18271.0 mkNwhCp sa =××==

22 /58.299.55.18271.0 mkNwhCp a =××==

kNH a 75.149.55.22 =×= édXñas; m95.229.5==

kNHa 26.879.558.2921

2 =×= édXñas; m97.139.5==

b. m:Um:g;EdleFVI[RkLab; (overturning moment) KW mkN.4.21597.126.8795.275.14 =×+×

c. m:Um:g;eFVI[manlMnwgEdlRbqaMgnwgkarRkLab; ¬emIlrUbTI 14>12¦

kmøaMg )(kN édXñas; )(m m:Um:g; ).( mkN 875.402545.53.01 =××=w 3.1 14.53

22.102545.515.021

2 =××=w 1.1 24.11 362545.02.33 =××=w 6.1 6.57

44.1765.1845.575.14 =××=w 375.2 419 ∑ == kNRw 5.263 ∑ = mkNM .541

emKuNsuvtßiPaBRbqaMgnwgkarRkLab;KW 251.24.215

541>=

4> KNnasm<aFdIeRkameCIgtag. Kitm:Um:g;eFobcMnuc 0 ¬rUbTI 14>12¦ edIm,IkMNt;TItaMg kmøaMgpÁÜb R énkmøaMgbBaÄr

5.2634.215541 goverturnin balancing −

=−

=−

= ∑ ∑R

MMR

HyMx

mm 066.132.3236.1 =>=

cMNakp©itKW me 364.0236.12/2.3 =−= . kmøaMgpÁÜb R manGMeBIenAkñúgEpñkkNþalén RbEvgmYyPaKbIéneCIgtag nigmancMNakp©it me 476.0= BIG½kSrbs;eCIgtag. sRmab; RbEvgbeNþay m1 rbs;eCIgtag

RkLaépÞ 22.32.31 m=×=



m:Um:g;niclPaB 43

73.2122.31 mI =×=

221 /200/56.138

73.26.1364.05.263

2.35.263 mkNmkN

ICeR

ARq <=

××+=

⋅⋅+=

22 /13.26

73.26.1364.05.263

2.35.263 mkN

ICeR

ARq =

××−=

⋅⋅−=

sm<aFdIKWRKb;RKan;

5> KNnaemKuNsuvtßiPaBRbqaMgnwgkarrGil. emKuNsuvtßiPaBGb,brmaRtUvesμ I 5.1 .

kmøaMgeFVI[rGil kNHH aa 10226.8775.1421 =+=+=



kmøaMgTb;kMu[rGil kNR 75.1265.2535.0 =×== μ emKuNsuvtßiPaBRbqaMgnwgkarrGil 5.124.1

10275.126

<== kmøaMgTb;RbqaMgnwgkarrGilEdlmanmin)anpþl;suvtßiPaBRKb;RKan;RbqaMgnwgkarrGileT. enA kñúgkrNIenH key RtUv)anbegáItedIm,IbegáItsm<aFGkmμFMRKb;RKan;edIm,ITb;nwgkmøaMgd¾FMEdleFVI [rGil. tYnaTIepSgeTotrbs; key KWpþl;nUvRbEvgbgáb;RKb;RKan;sRmab;Edk dowel rbs;tY CBa¢aMg. dUcenH key RtUv)andak;enATItaMgEdlépÞxagmuxrbs;vamancm¶ay mm150 BIépÞxag eRkayrbs;CBa¢aMg ¬rUbTI14>13¦. enAkñúgkarKNnasm<aFGkmμ dIenABIelIeCIgtagEpñkxag muxRtUv)anecalkñúgkm<s; mm300 . dUcenHenAkñúg]TahrN_enHkm<s;dIKItBI)ateCIgtages μ I

mm600 . snμt; key mankm<s; mmt 450= nigTTwg mmb 450= . 69.3

271.011

sin1sin1

===−+

=a

p CC

φφ

( ) ( ) kNthwCH pp 63.3745.06.05.1869.321'

21 22 =+×=+=

\LÚvkarrGilGacnwgekItmanenAelIépÞ AC / CD nig EF ¬rUbTI14>13¦. épÞrGil AC CaépÞrGilrvagRsTab;dInigRsTab;dIEdlmanemKuNkmøaMgkkitkñúg 7.035tantan === oφ . cMENkÉépÞrGil CD nig EF CaépÞrGilrvagebtugnigRsTab;dIEdlmanemKuNkmøaMgkkitkñúg esμ I 5.0 dUcEdl)an[enAkñúgsm μtikmμrbs;]TahrN_. ersIusþg;kmøaMgkkitKW 2211 RRF μμ += .

=1R Rbtikmμén kNAC 4.1503.12

89.9256.138=×⎟

⎠⎞

⎜⎝⎛ +

=

kNRRR 1.1134.1505.26312 =−=−= =2R Rbtikmμén kNCDF 1.1139.1

213.2689.92

=×⎟⎠⎞

⎜⎝⎛ +

=

kNF 83.1611.1135.04.1507.0 =×+×= kmøaMgTb;srubKW kNHF p 5.19963.3783.161 =+=+ emKuNsuvtßiPaBRbqaMgnwgkarrGilKW 5.196.1

1025.199

<= b¤ 5.159.1102

83.161<=

emKuNsuvtßiPaBFMCag 5.1 EdlRtUv)anENnaMenAeBlEdlsm<aFGkm μRbqaMgnwgkarrGilmin RtUv)anKitbBa©Úl.



6> KNnatYCBa¢aMg. karKNnaénGgát;ebtugGarem:GaceFVI)anedayeRbI ACI Code alternative

design method, appendix B and C. a. Edkem (main reinforcement)³ kmøaMgtamTisedkEdlGnuvtþmkelICBa¢aMgRtUv)anKNna

edayeRbIemKuN 6.1 . muxkat;eRKaHfñak;sRmab;m:Um:g;Bt;KWsßitenARtg;)aténCBa¢aMg ¬km<s; mh 45.5= ¦ KNnakmøaMgemKuN

( ) ( ) 21 /01.45.05.18271.06.16.1 mkNwhCP sa =××==

( ) ( ) 22 /72.4345.55.18271.06.16.1 mkNwhCP a =××==

kNH a 85.2145.501.41 =×= édXñas; m725.2245.5

== kNH a 14.11945.572.43

21

2 =×= édXñas; m82.1345.5

==



uM ¬enA)atrbs;CBa¢aMg¦ mkN.4.27682.114.119725.285.21 =×+×= kRmas;srubEdleRbIKW mm450 / mb 1= nig

md 387.0diameter)bar the(halfcover) (concrete45.0 =−−= MPa

bdMR u

u 85.13871000104.276

2

6

2 =×

⋅==

PaKryEdk 0058.0'85.0

211'85.0=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

c

u

y

cf

Rf

fφ

ρ 26.224438710000058.0 mmAs =××=

eRbI 25DB KMlat mm200 ¬ 24.2454 mmAs = ¦. EdkbBaÄrGb,brma sA eyagtam ACI Code, Section 14.3 KW

22 4.245467510004500015.0 mmmmAs <=××= edaysarEtm:Um:g;fycuHtamkm<s;rbs;CBa¢aMg sA KYrRtUv)ankat;bnßyeTAtamm:Um:g;Edl ekItmanenAelICBa¢aMg. CakarGnuvtþn_ eKKYreRbI sA b¤KMlatmYy sRmab;Bak;kNþalCBa¢aMg xageRkam nig sA b¤KMlatmYyepSgeTot sRmab;Bak;kNþalCBa¢aMgxagelI. edIm,IKNna m:Um:g;enAkm<s;Bak;kNþalCBa¢aMg ¬ m725.2 BIkMBUl¦

( ) ( ) 21 /01.45.05.18271.06.16.1 mkNwhCP sa =××==

( ) ( ) 22 /86.21725.25.18271.06.16.1 mkNwhCP a =××==

kNH a 93.10725.201.41 =×= édXñas; m36.12725.2

== kNH a 78.29725.286.21

21

2 =×= édXñas; m91.03725.2

==

uM ¬enAkm<s;Bak;kNþal¦ mkN.96.4191.078.2936.193.10 =×+×= kRmas;srubenAkm<s;Bak;kNþalKW mm375

2450300

=+ / mb 1= nig

md 312.0013.005.0375.0 =−−= MPa

bdMR u

u 43.031210001096.41

2

6

2 =×

⋅==

PaKryEdk 0013.0'85.0

211'85.0=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−−=

c

u

y

cf

Rf

fφ

ρ 26.40531210000013.0 mmAs =××=



22min 6.4055.56237510000015.0 mmmmAs >=××=

eRbIEdk 12DB KMlat mm200 ¬ 25.565 mmAs = ¦. b. EdksItuNðPaB nigEdkrYmmaD³ EdkedkGb,brmaenA)atCBa¢aMgGaRs½ynwg ACI Code,

Section 14.3 KW 2

min 9004501000002.0 mmAs =××= ¬sRmab;mYyPaKbIBI)at¦/ edaysnμt;eRbIEdk 16DB b¤tUcCagenH.

2min 8004001000002.0 mmAs =××=

¬sRmab;BIPaKbIBIkMBUl¦. edaysar épÞxagmuxrbs;CBa¢aMgrgnUvbERmbRmYlsIuNðPaB dUcenH eKeRbI mYyPaKBIreTAmYyPaKbIénEdkedk enAépÞxageRkArbs;CBa¢aMg nigdak;nUv brimaNdUcKñaenAépÞxagkñúg.

24509005.05.0 mmAs =×= eRbIEdk 12DB KMlat mm200 ¬ 25.565 mmAs = ¦enATaMgépÞxagkñúg nigépÞxageRkA rbs;CBa¢aMg. eRbIEdk 12DB KMlat mm300 edIm,IRTEdkedkrYmmaD nigEdksItuNðPaB.

c. Edk dowel sRmab;EdkbBaÄr³ RbEvgf<k;rbs;Edk 25DB eTAkñúgeCIgtagRtUvEtman RbEvg y:agticbMput mm550 . eRbIRbEvgEdkbgáb; mm600 eTAkñúgeCIgtag nig key

BIeRkamtY CBa¢aMg. d. KNnasRmab;kmøaMgkat;TTwg³ muxkat;eRKaHfñak;sRmab;kmøaMgkat;TTwgsßitenAcm¶ay

mmd 387.0= BI)attYCBa¢aMg. enARtg;muxkat;enH cm¶ayBIkMBUlesμ I m063.5387.045.5 =−

( ) ( ) 21 /01.45.05.18271.06.16.1 mkNwhCP sa =××==

( ) ( ) 22 /61.40063.55.18271.06.16.1 mkNwhCP a =××==

kNH a 3.20063.501.41 =×= kNH a 8.102063.561.40

21

2 =×= kNHHH aa 1.12321 =+=

kNkNbdfV cc 1.1237.2201038710002017.075.0'17.0 3 >=⋅×××== −φφ 7> KNnaeCIgtagEpñkxageRkayCBa¢aMg³ emKuNbnÞúk 2.1 RtUv)aneRbIsRmab;KNnam:Um:g;Bt; emKuN

nigkmøaMgkat;TTwgEdlekItBIdIcak;bMeBjnigebtug. cMENkÉemKuNbnÞúk 6.1



RtUv)aneRbIsRmab;bnÞúkbEnßm. sm<aFdIeLIgelIRtUv)anecaledaysarvanwgkat;bnßy\T§iBléndIcak;bMeBj nigebtugeTAelI eCIgtagEpñkxageRkayCBa¢aMg. eyagtamrUbTI 14>12 bnÞúksrubenAelIeCIgtagEpñkxag eRkayrbs;CBa¢aMgKW

( ) kNVu 3.2615.1875.15.06.12575.145.05.1875.145.52.1 =×××+××+××= uM ¬enARtg;épÞCBa¢aMg¦ mkNVu .64.228

275.1

== CaTUeTAmuxkat;eRKaHfñak;sRmab;kmøaMgkat;TTwgsßitenAcm¶ay d BIépÞCBa¢aMgenAeBlEdlkmøaMg RbtikmμbegáItkmøaMgsgát;enAtMbn;xagcugrbs;Ggát;. kñúgkrNIenH muxkat;eRKaHfñak;RtUv)anKit faekItmanenAnwgépÞCBa¢aMg edaysarEtkmøaMgTaj minEmnkmøaMgsgát;ekItmanenAkñúgebtug.

kNVu 3.261= kNkNbdfV cc 3.2614.20210362100020

12275.0'

122 3 <=⋅×××== −φφ

edaysar kNVV uc 3.216=<φ enaHmuxkat;RtUv)andMeLIgedayGRta 4.202/3.261 b¤k¾Edk kmøaMgkat;TTwgRtUv)andak;. d caM)ac; mm467362

4.2023.261

=×= kRmas;eCIgtagsrubcaM)ac; mm5551375467 =++= ykkRmas;eCIgtages μ I mm560 nig mmd 472=

MPaRu 03.147210001064.228

2

6=

×

⋅= 0031.0=ρ

22.1463 mmAs = EdkrYmmaDGb,brma 2100856010000018.0 mmAs =××= EdkrgkarBt;Gb,brma 26.155747210000033.0 mmAs =××= eRbIEdk 20DB manKMlat mm200 ¬ 28.1570 mmAs = ¦. RbEvgEdkbgáb;sRmab;

20DB es μI nwg mmld 11004.1 = . dUcenHEdkRtUv)andak;bgðÜscUleTAkñúgEpñkxagmuxrbs;eCIgtageday RbEvg mm1100 . EdkrYmmaD igEdksItuNðPaBsRmab;TisedAEvgmincaM)ac;RtUv)andak;enAkñúgeCIgtagEpñkxagmux nigEpñkxageRkayrbs;eCIgtageT. b:uEnþCakarGnuvtþn_ eKRtUvdak;brimaNEdkGb,brmaenAkñúg TisedAenH edayeRbI 300@12DB .



8> KNnaeCIgtagEpñkxagmuxCBa¢aMg³ Epñkxagmuxrbs;eCIgtageFVIkardUcCaFñwm cantilever Edl rgnUvsm<aFdIeLIgelICamYynwgbnÞúkemKuN 6.1 edaysarvaekIteLIgCadMbUledaykmøaMgxag. muxkat;eRKaHfñak;sRmab;kmøaMgkat;TTwgsßitenAcm¶ay d BIépÞxagmuxrbs;CBa¢aMg edaysarEt RbtikmμenAkñúgTisedAénkmøaMgkat;TTwgbegáItkmøaMgsgát;enAkñúgEpñkxagmuxrbs;eCIgtag.

eyagtamrUbTI 14>13 Epñkxagmuxrbs;eCIgtagrgnUvsm<aFeLIgelIedaysardI nigsm<aFcuH eRkamedaysarbnÞúkpÞal;rbs;kRmaeCIgtagEpñkxagmux.

( ) kNVu 3.100528.02556.02.1528.02

12056.1386.1 =×−⎟⎠⎞

⎜⎝⎛ +

=

vamantémøtUcCag kNVc 8.263=φ . mkNM u .1.93

212556.02.1

325.01)43.10356.138(1

243.1036.1

22 =

⎥⎥⎦

⎤

⎢⎢⎣

⎡×−⎥⎦

⎤⎢⎣⎡ ×××−+=

MPabdMR u

u 42.04721000101.93

2

6

2 =×

⋅== 00125.0=ρ

2590472100000125.0 mmAs =××= EdkGb,brmasItuNðPaB nigrYmmaD 2100856010000018.0 mmAs =××=

EdkGb,brmargkarBt; 26.155747210000033.0 mmAs =××= eRbIEdk 20DB manKMlat mm200 dUcKñanwgEpñkxagmuxCBa¢aMg. RbEvgEdkbgáb;sRmab;Edk

20DB es μ Inwg mm650 . bgðÜsEdkcUleTAkñúgEpñkxageRkayCBa¢aMgRbEvg mm650 . bøg;srés EdklMGitRtUv)anbgðajenAkñúgrUbTI 14>14.

9> Shear keyway rvagCBa¢aMg nigeCIgtag³ enAkñúgkarsagsg;CBa¢aMgTb; eCIgtagRtUv)ancak;mun bnÞab;mkeTIbEpñkxagelIRtUv)ancak;bnþ. Construction joint RtUv)aneRbIenA)atCBa¢aMg. épÞ tMNRtUv)anykmanragCa keyway dUcbgðajenAkñúgrUbTI 14>15 b¤RtUvTuk[manlkçN³ KeRKIm ¬rUbTI 14>14¦. tMNRtUvmanlT§PaBbBa¢ÚnkmøaMgkat;TTwgBItYCBa¢aMgeTAeCIgtag.

10> enAkñúgkarKNnaenH eKcaM)ac;RtUvdak;RbB½n§bgðÚrTwkBIdIcak;bMeBj[)anRtwmRtUv BIeRBaHsm<aFdI EdleRbIKWsRmab;dIcak;bMeBjEdlbgðÚrTwkecj. Weep holes KYrRtUv)andak;enAkñúgCBa¢aMg Edl manGgát;p©it mm100 manKMlat m5.1 tamTisedAedk nigTisedAbBaÄr.





14>11> CBa¢aMgCan;eRkamdI (Basement Walls)

CBa¢aMgCan;eRkamdIRtUv)aneKsnμt;fasßitenAcenøaHkRmalxNÐCan;eRkamdI nigkRmalxNÐCan; pÞal;dI. eKmanBIrkrNIkñúgkarKNnaCBa¢aMgCan;eRkamdI. TImYy enAeBlEdlCBa¢aMgRtUv)ansg;enABIelIkRmalxNÐCan;eRkamdI CBa¢aMgnwgrgnUvsm<aFdI tamTisedk nigminrgbnÞúkbBaÄreRkABIbnÞúkpÞal;xøÜn. kñúgkrNIenH CBa¢aMgmannaTICa cantilever ehIy brimaNEdkRKb;RKan;KYrRtUv)andak;sRmab;karKNnaCBa¢aMg cantilever. krNIenHGaceCosvag)an eda dMeLIgkRmalxNÐCan;eRkamdI nigkRmalxNÐCan;TImYymunnwgcak;bMeBjdI. TIBIr enAeBlEdlkRmalxNÐCan;TImYy nigkRmalxNÐCan;epSgeTotRtUv)ansg; ehIysMNg; RtUv)andak;bnÞúkeBj enaHCBa¢aMgCan;eRkamdImannaTICaCBa¢aMg propped cantilever EdlrgnUvsm<aFdI k¾dUcCasm<aFbBaÄr. sRmab;mMukkitkñúg o35=φ enaHemKuNsm<aFskmμ 271.0=aC . sm<aFsIedkenAnwg)atKW

whCP aa = . sRmab; 3/6.17 mkNw = nigCBa¢aMgmankm<s;mFüm mh 3= enaH 2/31.1436.17271.0 mkNPa =××= mkNHa /46.21

236.17271.0

2=××= énCBa¢aMg

aH eFVIGMeBIenARtg; mh 13/33/ == BI)at. sm<aFbEnßmRbEhl 2/6.9 mkN RtUv)anKitfa manenAelIdIxageRkayCBa¢aMg enaH

mhs 55.06.176.9==

2/62.255.06.17271.0 mkNwhCP sas =××== ( ) mkNhwhCH sas /86.7362.2 =×== énCBa¢aMg

sH énbnÞúkbEnßmeFVIGMeBIenA mh 5.12/ = BI)at. kñúgkarKNnaelIkmun eK)ansnμt;fadIcak;bMeBjmanlkçN³s¶Üt b:uEnþsRmab;krNIenHeKcaM)ac;

RtUvKitBIsm<aFTwkenABIeRkayCBa¢aMg. sm<aFTwkGtibrmaekItmanenAeBlkm<s;CBa¢aMgTaMgmUlrbs; CBa¢aMgCan;eRkamdIrgnUvsm<aFTwk. 2/30310 mkNPw =×=

mkNwhH w /452

3102

22=== énCBa¢aMg

sm<aFGtibrmaminGacmanvtþmanenABIeRkayCBa¢aMgCab;rhUteT. dUcenH RbsinebIdIesImyUr² mþg enaHeKGacyksm<aFTwkRtwm %50 mkKit.



2/152

302

mkNPw ==

mkNH

H ww /5.22

2' == énCBa¢aMg

wH ' eFVIGMeBIenA mh 13/33/ == BI)at. TwkGacRtUv)ankarBarBIkarRbmUlpþúMRbqaMgnwgCBa¢aMg edayerobcMkarbgðÚrenAEpñkxageRkaménCBa¢aMg.

bEnßmBIelIkarerobcMRbB½n§bgðÚr CBa¢aMgEpñkxageRkARtUvlabfñaMkarBarCMrabTwk (waterproofing

or damp-proofing membrane) . ACI Code, Section 14.5

kMNt;fakRmas;Gb,brmaénCBa¢aMgeRkam dIEpñkxageRkA nigRKwHrbs;vaKW mm190 . CaTUeTA kRmas; Gb,brmarbs;CBa¢aMgRTesμ InwgtémøtUcCageK kñúgcMeNam 25/1 énkm<s; b¤ 25/1 éRbEvgCBa¢aMg b¤

mm100 .

]TahrN_14>3³ kMNt;kRmas; nigbrimaNEdkcaM)ac;sRmab;CBa¢aMgTb;Can;eRkamdIdUcbgðajkñúgrUbTI 14>16. eK[³ Tm¶n;maDdIcak;bMeBj 3/6.17 mkN / mMukkitkñúg o35=φ / MPaf c 20' = nig


1> CBa¢aMgmanElVgtamTisQr nigRtUv)ancat;TukfamanTRmbgáb;enA)at nigTRm propped

enAkMBUl. edaycat;TukRbEvgElVg mL 925.2= dUcbgðajkñúgrUbTI 14>16. sm<aFxag epSg²EdlmanGMeBIelICBa¢aMgkñúgRbEvg m1 mandUcteTA³ sm<aFEdlekItBIsm<aFdI mkNPa /31.14= nig kNHa 46.21= sm<aFEdlekItBIsm<aFTwk mkNPw /15= nig kNH w 5.22= sm<aFEdlekItBIbnÞúkelIs mkNPs /62.2= nig kNH s 86.7=

aH nig wH KWbNþalmkBIbnÞúkBRgayrayRtIekaN b:uEnþ sH )anBIbnÞúkBRgayes μ I. BI rUbTI 14>16 nigedayeRbIemKuNm:Um:g;énFñwm propped EdlrgbnÞúkRtIekaN nigbnÞúk BRgayesμ I CamYynwgemKuNbnÞúk 6.1= (ACI Code, Appendix C)

( )8

6.15.7

6.1 LHLHHM swau ++= ( ) mkN.03.32

8925.286.76.1

5.7925.25.2246.216.1 =××++=



kNRB 78.18925.203.32

286.7

35.2246.216.1 =−⎟

⎠⎞

⎜⎝⎛ +

+=

( ) kNRA 13.6478.1886.75.2246.216.1 =−++= m:Um:g;viC¢manGtibrmaEdlekItmanenAmuxkat;EdlmankmøaMgkat;sUnü

( ) 02925.2

1531.146.162.26.178.182=⎟

⎠⎞

⎜⎝⎛ +

−−=xxVu

mx 291.1= mkNM c .15

3291.1

294.12291.1

262.26.1291.178.18

22 =⎟

⎟⎠

⎞⎜⎜⎝

⎛+−×=

2> edaysnμt; 01.0=ρ enaH MPaRu 3=

mmbR

Mdu

u 10010003

1003.30 6=

×⋅

==

kRmas;srub mm146640100 =++= . eRbIkRmas; mm190 dUcenH mmd 144= MPa

bdMR u

u 45.114410001003.30

2

6

2 =×⋅

==

PaKryEdk 0045.0=ρ nig 264814410000045.0 mmAs =××= sA Gb,brma 228519010000015.00015.0 mmbh =××== sA Gb,brmargkarBt; 22.47514410000033.0 mm=××=

eRbIEdk 16DB manKMlat mm300 ¬ 2670mmAs = ¦ 3> sRmab;m:Um:g;viC¢man mkNM c .15=

MPaRu 72.01441000

10152

6=

×

⋅= 0022.0=ρ

22 6708.31614410000022.0 mmmmAs <=××= eRbIEdk 12DB manKMlat mm250 ¬ 2452mmAs = ¦

4> m:Um:g;sUnüekItmanenAcm¶ay m288.2 BIkMBUl nig m637.0 BI)at. RbEvgRCYsrbs;Edk 16DB KW mm360 ¬tMbn;sgát;¦. dUcenH dak;Edkem 16DB RbEvg mmmm 360637 +

mm997= b¤ mm1000 BI)at rYcbnÞab;mkeRbIEdk 12DB KMlat mm300 enAépÞxageRkA. sRmab;épÞxagkñúg eRbIEdk 12DB KMlat mm250 .



5> brimaNEdkbeNþay³ eRbIPaKryEdkGb,brma 002.0=ρ ¬ACI Code, Section 14.3¦

b¤ 23801901000002.0 mmAs =××= . eRbI 12DB KMlat mm300 enAépÞTaMgsgçag. 6> RbsinebIm:Um:g;Bt;enA)aténCBa¢aMgmantémøFM enaHeKcaM)ac;RtUvkarkRmas;kRmalxNÐ

CBa¢aMgFM ]TahrN_ mm300 b¤FMCagenH. enAkñúgkrNIxøHeKGaceRbI haunch dUcbgðaj kñúgrUbTI 14>17. eKeFVIEbbenHedIm,Ikat;bnßykRmas;CBa¢aMg edaysarEtm:Um:g;RtUv)an KNnaenAelI muxkat;BIelI haunch Etmþg.

7> kRmalxNÐCan;eRkamdIGacmankRmas;FMCagkRmas;CBa¢aMg nigGacRtUv)anBnøÚtecjeRkA hYs épÞCBa¢aMgRbEhl mm250 b¤FMCagenHRbsinebIcaM)ac;.




karKNnasRmab;kmøaMgrmYl 411 T.Chhay

XV. karKNnasRmab;kmøaMgrmYl Design for Torsion


kugRtaMgrmYlekItmanenAkñúgmuxkat;FñwmenAeBlEdlm:Um:g;manGMeBIRsbeTAnwgmuxkat;enaH. m:Um:g;rmYleFVI[Ggát;vil nigmansñameRbHenAelIépÞrbs;va CaTUeTAEtgekItmanenAelImuxkat;mUl. edIm,IbgðajkugRtaMgrmYl eKGnuvtþkmøaMgrmYl T Fñwm cantilever muxkat;mUlEdleFVIBI elastic

homogenous material dUcbgðajkñúgrUbTI 15>1. kmøaMgrmYlnwgeFVI[Fñwmvil. cMNuc B cl½teTA cMNuc 'B enAxagcugrbs;Fñwm b:uEnþcugmçageTotrbs;FñwmRtUv)anbgáb;. mMu θ RtUv)aneKehAfa mMurmYl (angle of twist). bøg; OBAO' nwgdUrrageTACarag ''OBAO . edaysnμt;fa Ggát;enArkSaRbEvgrbs; vadEdl enaH shear strain KW

Lr

LBB θγ ==

' Edl L CaRbEvgrbs;Fñwm nig r CakaMrbs;muxkat;rgVg;.


T.Chhay 412 Design for Torsion

enAkñ μ úgeRKOgbgÁúMebtugGarem: Ggát;nwgrgm:Um:g;rmYlenAeBlGgát;enaHekagenAkñúgbøg;/ RT cantilever slab/ mannaTICa spandrel beam (end beam)/ b¤CaEpñkrbs;CeNþIrvil.

Ggát;eRKOgbgÁúMGacrgnUvEtkmøaMgrmYlsuT§ b¤enAkñúgkrNICaeRcIn vargCamYyKñakñúgeBlEtmYy nUvkmøaMgkat;TTwg nigm:Um:g;Bt;. ]TahrN_TI15>1 bgðajBIkmøaMgepSg²EdlGacGnuvtþmkelImuxkat; epSgKñaénFñwm cantilever.

]TahrN_TI15>1³ KNnakmøaMgEdlmanGMeBIenAmuxkat; !/ @ nig # énFñwm cantilever EdlbgðajenAkñúgrUbTI 15>2. Fñwm rgnUvkmøaMgbBaÄr kNP 671 = / kmøaMgedk kNP 5.532 = EdleFVIGMeBIenAcMNuc C nigbnÞúkedk

kNP 893 = EdlGnuvtþenAcMNuc B nigEkgeTAnwgTisedArbs;kmøaMg 2P .

dMeNaHRsay³ yk =N kmøaMgEkg (normal force)/ =V kmøaMgkat; (shear force)/ =M m:Um:g;Bt; (bending

moment)/ T =m:Um:g;rmYl (torsional moment). kmøaMgTaMgGs;RtUv)anbgðajenAkñúgtaragxageRkam³



muxkat; )(kNN ).( mkNM x ).( mkNM y )(kNVx )(kNVy ).( mkNT ! 0 9.180− 45.144 5.53 67 0 @ 5.53− ¬sgát;¦ 0 45.144 89 67 9.180 # 5.53− ¬sgát;¦ 2.241 85.464 89 67 9.180

RbsinebI 1P / 2P nig 3P CabnÞúkemKuN ¬ LDu PPP 6.12.1 += ¦ enaHral;témøenAkñúgtaragCakmøaMg KNnaemKuN.

15>2> m:Um:g;rmYlenAkñúgFñwm (Torsional Moments in Beams)

dUcbgðajenAkñúgrUbTI 15>1 kmøaMgGacGnuvtþenAelIeRKagsMNg;GKar edayeFVI[manm:Um:g;

rmYl. RbsinebIkmøaMgcMcMNuc P GnuvtþenARtg;cMNuc C enAelIeRKag ABC dUcbgðajenAkñúgrUb 15>3 a vabegáItm:Um:g;rmYl PZT = enAkñúgFñwm AB Rtg;cMNuc D . enAeBl D sßitenAkNþalElVgénFñwm AB enaHm:Um:g;rmYlKNnaenAkñúgkMNat; AD esμ Inwgm:Um:g;rmYlKNnaenAkñúgkMNat; DB b¤esμ Inwg

T21 . RbsinebIkRmal cantilever slab RtUv)anRTedayFñwm AB ¬rUbTI 15>3 b¦ enaHkRmalxNÐ



begáItm:Um:g;rmYlBRgayes μ I tm tambeNþayFñwm AB . m:Um:g;rmYlBRgayesμ IenH KWekItBIbnÞúkenAelI ceRmokTTwkmYyÉktþarbs;kRmalxNÐ. RbsinebI S CaTTwgén cantilever slab nig w CabnÞúkenA elIkRmalxNÐ ¬ 2/ mkN ¦ enaH 2/2wSmt = ¬ mmkN /. ¦énFñwm AB . m:Um:g;rmYlKNnaGtibrma enAkñúgFñwm AB KW 2/LmT t= EdlGnuvtþenARtg;cMNuc A nig B . krNIbnÞúkepSgeTotRtUv)anbgðaj enAkñúgtarag 15>1. CaTUeTA düaRkamm:Um:g;rmYlenAkñúgFñwmmanrag nigmantémødUcKñanwgdüaRkamkmøaMg kat;TTwgsRmab;FñwmEdlrgnUvkmøaMg tm nig T .

15>3> kugRtaMgrmYl (Torsional Moments in Beams)

edayBicarNaelIFñwm cantilever Edlmanmuxkat;mUl ¬rUbTI15>1¦ enAeBlEdlm:Um:g;rmYl T manGMeBIelIFñwm vanwgbegáIt[mankmøaMgkat;TTwg dV EkgeTAnwgkaMrbs;muxkat;. BIlkçxNÐlMnwgm:Um:g; rmYlxageRkARtUv)anTb;edaym:Um:g;rmYlxagkñúgEdlmantémøT esμ IKñaEtTisedApÞúyKña . RbsinebI dV CakmøaMgkat;TTwgeFVIGMeBIelIépÞ dA ¬rUbTI 15>4¦ enaHGaMgtg;sIueténkmøaMgrmYlKW ∫= rdVT edayyk v CakugRtaMgkmøaMgkat;TTwenaH

vdAdV = nig ∫= rvdAT kmøaMgkat;TTwgeGLasÞicGtibrmaekItmanenAépÞxageRkArbs;muxkat;rgVg;Rtg;kaM r CamYynwg

kRmas; dr enaHkmøaMgrmYlGacRtUv)ankMNt;edayKitm:Um:g;eFobnwgcMNuc 0 sRmab;RkLaépÞkg³ ( )vrrdrdT π2=

Edl rdrπ2 CaRkLaépÞkg nigv CakugRtaMgkmøaMgkat;TTwgenAkñúgkg. dUcenH ( ) drrvrrdrT

RR∫∫ ==0

20

22 ππ ¬!%>!¦ sRmab;muxkat;RbehagEdlmankaMxagkñúg 1R /

drrTR

R∫= 1

22π ¬!%>@¦ sRmab;muxkat;tan; edayeRbIsmIkar ¬!%>!¦ nig Rrvv /max=

∫∫ ⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

RRdrrv

Rdr

RrvrT

03

maxmax

02 22 ππ

3max

4

max 242 RvRvR

⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛=

ππ





3max

2RTv

π= ¬!%>#¦

m:Um:g;niclPaBb:UElrénmuxkat;rgVg;KW 2/4RJ π= . dUcenH kugRtaMgkmøaMgkat;GacRtUv)an sresrCaGnuKmn_énm:Um:g;niclPaBb:UElrdUcxageRkam³

JTRv =max ¬!%>$¦

15>4> m:Um:g;rmYlenAkñúgmuxkat;ctuekaN (Torsional Moments in Rectangular Sections)

karKNnakugRtaMgenAkñúgGgát;manmuxkat;minmUlEdlrgbnÞúkrmYlminsamBaØdUckarKNna sRmab;muxkat;mUleT. b:uEnþ lT§plEdlTTYlBIRTwsþIeGLasÞic (theory of elasticity) bgðajfakug RtaMgkmøaMgkat;TTwgGtibrmasRmab;muxkat;ctuekaNEkgGacRtUv)ankMNt;dUcxageRkam³

yxTv 2max

α= ¬!%>%¦

Edl =T kmøaMgrmYlEdlGnuvtþ =x RCugxøIrbs;muxkat;ctuekaN =y RCugEvgrbs;muxkat;ctuekaN

=α emKuNEdlGaRs½ynwgpleFobén xy / témørbs;vaRtUv)an[enAkñúgtarag xageRkam.

xy / 0.1 2.1 5.1 0.2 0.4 10 α 208.0 219.0 231.0 246.0 282.0 312.0



kugRtaMgkmøaMgkat;TTwgGtibrmaekItmanenAtamG½kSénRCugEvg y ¬rUbTI 15>5¦. sRmab;Ggát;EdlekItBIkarpÁúMénmuxkat;ctuekaNEkg dUcCamuxkat;GkSr L / T nig I témø α

GacRtUv)ansnμt;faes μ Inwg 3/1 ehIymuxkat;GacRtUv)anEckecjCamuxkat;ctuekaNCaeRcInEdlman RCugEvg iy nigRCugxøI ix . kugRtaMgkmøaMgkat;TTwgGacRtUv)anKNnaBI

∑=

ii yxTv 2max

3 ¬!%>^¦

Edl ii yx∑ 2 CatémøEdl)anBIplbUkmuxkat;ctuekaNEkgtUc². enAeBlEdl 10/ ≤xy eK GaceRbIsmIkarsRmYlxageRkam³

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛−

=

yx

yx

Tv

63.01

3

2max ¬!%>&¦

15>5> kmøaMgpÁÜbrvagkmøaMgkat; nigkmøaMgrmYl (Combined Shear and Torsion)

enAkñúgkrNIGnuvtþn_CaeRcIn Ggát;eRKOgbgÁúMGacrgnUvTaMgkmøaMgkat; nigkmøaMgrmYlCamYyKña. kugRtaMgkmøaMgkat;GacnwgekItmanenAkñúgmuxkat;CamYynwgkugRtaMgkmøaMgkat;mFüm 1v= enAkñúgTis edAénkmøaMgkat; V ¬rUbTI 15>6 a¦. kmøaMgrmYl T begáItkugRtaMgrmYlenAelIRKb;RCugrbs;muxkat; ctuekaN ABCD ¬ rUbTI 15>6 a¦ CamYynig 23 vv > . karBRgaykugRtaMgcugeRkayRtUv)anTTYlBI karbUkbBa©ÚlnUv\T§iBlénkugRtaMgkmøaMgkat; nigkugRtaMgrmYl edIm,IbegáIttémøGtibrmaesμ I 31 vv + enA



elIRCug CD b:uEnþRCug AB nwgmankugRtaMgcugeRkayes μ I 31 vv − . RCug AD nig BC nwgrgEtkugRtaMg rmYl 2v . muxkat;RtUvd)anKNnasRmab;kugRtaMgGtibrma ( )31 vvv += .

15>6> RTwsþIkarrmYlsRmab;Ggát;ebtug (Torsion Theories for Concrete Members)

eKmanviFICaeRcInsRmab;viPaKGgát;ebtugBRgwgedayEdkEdlrgkarrmYl b¤rgkarrmYl karBt; nigkarkat;kñúgeBlEtmYy. CaTUeTAviFIKNnasMGageTAelIRTwsþIeKalBIrKW³ the skew bending theory nig space truss analogy.

15>6>1> Skew Bending Theory

viFIeKalrbs; skew bending theory EdlENnaMeday Hsu CaviFIEdlsikSakar)ak;énmuxkat; ctuekaNedaykarrmYlEdlekItedaykarBt;eFobG½kSRsbeTAnwgépÞénmuxkat; y FMCag nigeRTteday



mMu o45 eTAnwgG½kSEvgénFñwm ¬rUbTI 15>7¦. QrelIviFIsaRsþenH m:Um:g;rmYlGb,brma nT GacRtUv)an KNnadUcxageRkam³

rn fyxT ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

3

2 ¬!%>*¦

Edl rf KWm:UDuldac;rbs;ebtug. rf RtUv)ansnμt;esμ Inwg 12/'5 cf enAkñúgkrNIenH Edl RtUv)aneRbobeFobCamYy 12/'5.7 cf EdlTTYleday ACI Code sRmab;KNnaPaBdabenAkñúgFñwm.

kmøaMgrmYlTb;edayebtugsMEdgdUcxageRkam³

cc fyxx

T '1 2⎟⎠

⎞⎜⎝

⎛= ¬!%>(¦

nigkmøaMgTb;karrmYledayEdkTb;karrmYlKW

sfAyx

T yts

)( 111α= ¬!%>!0¦ dUcenH scn TTT += Edl nT lT§PaBTb;m:Um:g;rmYl nominal énmuxkat;.

15>6>2> Space Truss Analogy



viFIsaRsþén space truss analogy KWQrelIkarsnμt;falT§PaBTb;Tl;karrmYlrbs;ebtugGar

em:muxkat;ctuekaNRtUv)anKitecjEtBIEdknigebtugEdlB½T§CMuvijEdkb:ueNÑaH. kñúgkrNIenH muxkat; thin-wall RtUv)ansnμt;mannaTICa space truss ¬rUbTI 15>8¦. ceRmokebtugv½NÐeRTtcenøaHsñameRbH Tb;kmøaMgsgát; b:uEnþEdkbeNþayenARCug nigEdkkgTb;nwgkmøaMgTajEdlekItedaym:Um:g;rmYl.

kareFVIkarrbs;FñwmebtugGarem:EdlrgkarrmYlsuT§GacbgðajedayRkaPicénTMnak;TMngrvagkar rmYlnigmMurmYl dUcbgðajenAkñúgrUbTI15>9. eyIgemIleXIjfa munnwgeRbH ebtugTb;nwgkugRtaMgrmYl nigEdkswgEtK μanrgkugRtaMg. eRkayeBleRbH kareFVIkarrbs;FñwmCalkçN³eGLasÞicminGacGnuvtþ)an dUcenHmMurmYlekIteLIgPøam² EdlekIneLIgrhUtdl;lT§PaBTb;Tl;m:Um:g;rmYlekItman. karkMNt;Edl manlkçN³Rbhak;RbEhlénlT§PaBTb;karrmYlsRmab;muxkat;eRbHGacnwgsMEdgdUcxageRkam³

112 yxsfAT st

n ⎟⎠⎞

⎜⎝⎛= ¬!%>!!¦

Edl =tA éneCIgmçagrbs;Edkkg =s KMlatEdkkg

1x nig =1y RbEvgxøI nigRbEvgEvg KitBIG½kSeTAG½kSénEdkkgbiTCit b¤BIEdkenARCug.



smIkarmunecalnUvlT§PaBTb;karrmYlrbs;ebtug. Mitchell nig Collins ENnaMnUvsmIkarxag

eRkamedIm,IKNnamMurmYlkñúgmYyÉktþaRbEvg ψ ³ ( )

⎥⎦

⎤⎢⎣

⎡+⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛=

αεαε

αε

ψsin2tan

tan2d

o

hhl

o

oP

PAP ¬!%>!@¦

Edl =lε bERmbRmYlrageFob (strain) enAkñúgEdkbeNþay (longitudinal reinforcing steel)

=hε bERmbRmYlrageFobenAkñúgEdkkg (hoop steel) =dε bERmbRmYlrageFobebtugGgát;RTUgenARtg;TItaMgénkmøaMgpÁÜbénrMhUrkmøaMgkat;

(shear flow) =hP brimaRtrbs;EdkkgKitRtwmG½kSEdk =α mMuénkmøaMgsgát;Ggát;RTUg ( ) ⎥

⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++=

o

hhdld P

Pεεεε /

=oA RkLaépÞEdlB½T§CMuvijedaykmøaMgkat; b¤ q2/torque= ¬Edl =q rMhUrkmøaMgkat;¦ =oP brimaRténKnøgrMhUrkmøaMgkat; ¬brimaRtrbs; oA ¦ smIkarmMurmYlxagelImanlkçN³RsedogKñanwgsmIkarmMukMeNagkñúgkarBt; ¬rUbTI 15>10¦



d

sc εεφ +== curvature ¬!%>!#¦

Edl cε nig sε CabERmbRmYlrageFobenAkñúgebtug nigEdk erogKña. smIkard¾samBaØRtUv)an bkRsayeday Solanki edIm,IkMNt;lT§PaBTb;nwgkarrmYlsuT§rbs;FñwmebtugGarem: edayQrelI space truss analogy dUcxageRkam³

( )21

2⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎟⎠

⎞⎜⎜⎝

⎛=

∑sfA

PfA

AT hyh

o

sysou ¬!%>!$¦

Edl oA / oP nig s RtUv)anBnül;BIxagelI =∑ sys fA kmøaMg yield énEdkbeNþayTaMgGs; =hyh fA kmøaMg yield énEdkkg ACI Code )anTTYlykRTwsþIenHedIm,IKNnaGgát;eRKOgbgÁúMebtugEdlrgkarrmYl b¤karrmYl

nigkarkat;enAkúñgviFIsaRsþd¾sRmYl.

15>7> ersIusþg;rmYlénGgát;ebtugsuT§ (Torsional Strength of Plain Concrete Members)

Ggát;ebtugrgkarrmYlCaTUeTARtUv)anBRgwgedayEdkTb;nwgkarrmYlBiess. kñúgkrNIEdlkug RtaMgrmYlmantémøtUc nigRtUvkarKNnasRmab;Ggát;ebtugsuT§ kugRtaMgkmøaMgkat; tcv GacRtUv)an kMNt;edayeRbIsmIkar !%>^³



2

'32

ctc

fyx

Tv ≤=∑φ

nigmMurmYlKW yGxTL 3/3=θ / Edl T Cam:Um:g;rmYlEdlGnuvtþmkelImuxkat; ¬tUcCagm:Um:g; rmYlEdleFVI[eRbH¦ nig G KWCam:UDulkmøaMgkat; nigGacRtUv)ansnμt;es μInwg 45.0 dgénm:UDuleG-LasÞicrbs;ebtug cE Edl cfG '2135= . kmøaMgkat;TTwgeFVI[eRbHedaysarkarrmYl (torsional

cracking shear) cv enAkñúgebtugsuT§GacRtUv)ansnμt;es μ I cf '5.0 . dUcenH sRmab;muxkat;ctuekaN ebtugsuT§ cc fyxT '

122φ

= ¬!%>!%¦ nigsRmab;muxkat;EdlpSMeLIgedayctuekaNEkgeRcIn ∑= yxfT cc

2'12φ ¬!%>!^¦

15>8> karrmYlenAkñúgGgát;ebtugBRgwgedayEdk (Torsion in Reinforced Concrete Memebers (ACI Code Procedure))

15>8>1> sBaØaNTUeTA (General) dMeNIrkarKNnasRmab;karrmYlmanlkçN³RsedogKñaeTAnwgkmøaMgkat;TTwgedaykarBt;. enA

eBlEdlm:Um:g;rmYlemKuNGnuvtþenAelImuxkat;FMCaglT§PaBTb;m:Um:g;rmYlkñúgrbs;ebtugGacTb;)an enaHsñameRbHEdlekItedaykarrmYl (torsional crack) ekIteLIg dUcenHEdkTb;karrmYl (torsional

reinforcement) kñúgTRmg;CaEdkkgbiTCit (closed stirrup or hoop reinforcement) RtUv)andak;. bEnßmBIelIEdkkgbiTCit EdkbeNþayk¾RtUv)andak;enAtamRCugrbs;Edkkg nigRtUv)anBRgayy:ag l¥enACMuvijmuxkat;. TaMgEdkkgbiTCit nigEdkbeNþaymansarsMxan;Nas;kñúgkarTb;nwgkmøaMgTaj Ggát;RTUgEdlbNþaymkBIkmøaMgrmYl EdkEtmYyRbePTnwgKμanRbsiT§PaBeTebIKμanEdkmYyRbePT eTot. EdkkgRtUvEtbiTCit edaysarkugRtaMgrmYlekItmanenARKb;RCugrbs;muxkat;.

EdkcaM)ac;sRmab;karrmYlRtUv)anbEnßmelIEdkcaM)ac;sRmab;kmøaMgkat; sRmab;karBt; nig kmøaMgtamG½kS. EdkEdkcaM)ac;sRmab;karrmYlRtUv)andak;edIm,IeFVI[ersIusþg;m:Um:g;rmYlrbs;muxkat;

nTφ FMCagb¤esμ Inwgm:Um:g;rmYlemKuN uT EdlRtUv)anKNnaBIbnÞúkemKuN. un TT ≥φ ¬!%>!&¦



enAeBleKRtUvkarEdkTb;karrmYl ersIusþg;m:Um:g;rmYl nTφ RtUv)anKNnaedaysnμt;kmøaMg rmYl uT TaMgGs; RtUv)anTb;edayEdkkg nigEdkbeNþayCamYynwgersIusþg;Tb;karrmYlrbs;ebtug

0=cT . kñúgeBlCamYyKña ersIusþg;kmøaMgkat;EdlTb;edayebtug cv RtUv)ansnμt;enAdEdledayK μan karERbRbYledaysarvtþmanrbs;ersIusþg;rmYl. 15>8>2> )a:ra:Em:RtFrNImaRténkarrmYl (Torsional Geometric Parameters)



enAkñúg ACI Code, Section 11.6 karKNnasRmab;karrmYlKWQrenAelI space truss analogy

dUcbgðajenAkñúgrUbTI 15>8. eRkayeBlEdlsñameRbHedaykarrmYlekIteLIg karrmYlRtUv)anTb; edayEdkkgbiTCit EdkbeNþay nigersIusþg;kmøaMgsgát;Ggát;RTUgrbs;ebtug. sac;ebtugenAxageRkA EdkkgkøayeTACaK μanRbsiT§PaB nigRtUv)anecalenAkñúgkarKNna. RkLaépÞB½T§CMuvijedayG½kSénEdk kgbiTCitxageRkAbMput RtUv)ankMNt;eday ohA ¬épÞqUtenAkñúgrUbTI 15>11¦. edaysarGgÁdéTeTot RtUv)aneRbIenAkñúgsmIkarKNna vak¾RtUv)anENnaMCadMbUgenATIenHedIm,ICYy[karyl;nUvsmIkarman lkçN³gayRsYl. BIrUbTI 15>11 GgÁEdl[RtUv)ankMNt;dUcxageRkam³

=cpA RkLaépÞmuxkat;ebtugEdlB½T§CMuvijedaybrimaRtxageRkAénmuxkat;ebtug =cpP brimaRténmuxkat;ebtugTaMgmUl cpA =ohA RkLaépÞEdlB½T§CMuvijedayG½kSénEdkrgkarrmYlTTwgbiTCitxageRkAbMput ¬épÞqUtkñúgrUbTI

15>11¦ =oA RkLaépÞEdlB½T§CMuvijedayKnøgrMhUrkmøaMgkat;TTwg nigGacykesμ Inwg ohA85.0 =hP brimaRtebtugrbs;EdkrgkarrmYlTTwgbiTCitxageRkAbMput =θ mMuénkmøaMgsgát;Ggát;RTUgcenøaH o30 eTA o60 ¬b¤Gacykesμ Inwg o45 sRmab;Ggát;ebtugGarem:¦

sRmab;muxkat;GkSr T nig L TTwgRbsiT§PaBénsøabmçag²RtUv)ankMNt;esμ Inwgkm<s;FñwmEdl sßitenABIelI b¤BIeRkamkRmalxNÐ edayykmYyNaEdlFMCag b:uEnþminRtUvFMCag 4 dgkRmas;kRmal xNÐeT ¬ACI Code, Sections 11.6.1 and 13.2.4¦. 15>8>3> m:Um:g;rmYleFVI[eRbH crT (Cracking Torsional Moment crT )

m:Um:g;eFVI[eRbHeRkamm:Um:g;rmYlsuT§ crT GacRtUv)anTajecjedayCMnYsmuxkat;BitR)akd munnwgeRbH CamYynwg thin-walled tube smmUl cpcp PAt /75.0= / CamYynwgRkLaépÞEdlB½T§CMuvij edayG½kSCBa¢aMg 3/20 cpAA = . enAeBlEdl kugRtaMgTajGtibrma ¬kugRtaMgem¦ mantémøesμ I

3/'cf sñameRbHnwgekItman ehIyCaTUeTAm:Um:g;rmYl T esμ Inwg tAT oτ2= ¬!%>!*¦ Edl =τ kugRtaMgkmøaMgkat;edaykarrmYl 3/'cf= sRmab;sñameRbHedaykarrmYl. CMnYs τ eday 3/'cf



ncp

cpccr T

PAf

T =⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

2

3' nig cru TT φ= ¬!%>!(¦

edaysnμt;fam:Um:g;rmYltUcCagb¤esμ Inwg 4/crT nwgmineFVI[mankarkat;bnßyersIusþg;Tb;karBt; b¤Tb;kmøaMgkat;enAkñúgGgát;énrcnasm<½n§ ACI Code, Section 11.6.1 GnuBaØat[ecalnUv\T§iBlm:Um:g; rmYlenAkñúgGgát;ebtugGarem:enAeBlEdlm:Um:g;rmYlemKuN 4/cru TT φ≤ b¤

acp

cpcu T

PAf

T =⎟⎟

⎠

⎞

⎜⎜

⎝

⎛≤

2

12'

φ ¬!%>@0¦

enAeBlEdl uT FMCagtémøenAkñúgsmIkar !%>@0 uT TaMgGs;RtUv)anTb;edayEdkkgbiTCit nigEdkbeNþay. m:Um:g;rmYl uT RtUv)anKNnaBImuxkat;EdlmanTItaMgRtg;cm¶ay d BIépÞénTRm nig

nu TT φ= Edl 75.0=φ .

]TahrN_TI15>1³ sRmab;muxkat;bIEdlbgðajenAkñúgrUbTI 15>12 nigQrelIkarkMNt; ACI Code cUrkMNt;

a. m:Um:g;eFVI[eRbH crTφ b. m:Um:g;rmYlemKuNGtibrma nTφ EdlGacGnuvtþelImuxkat;nImYy²edaymineRbIEdkRTnugTb;kar

rmYl.



snμt; MPaf c 28' = / MPaf y 400= / kRmas;ebtugkarBarEdk mm40 nigeRbIEdkkg 12DB .

dMeNaHRsay³

1> muxkat; ! a. mU:m:g;eFVI[eRbH crTφ GacRtUv)anKNnaBIsmIkar !%>!(

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

cp

cpccr P

AfT

2

3'

φφ

sRmab;muxkat;enH oocp yxA = RkLaépÞmuxkat;TaMgmUl Edl mmxo 400= nig mmyo 610=

2244000610400 mmAcp =×= =cpP brimaRténmuxkat;ebtugTaMgmUl

( ) ( ) mmyx oo 202061040022 =+=+= mkNTcr .39

2020244000

32875.0

2=⎟

⎟⎠

⎞⎜⎜⎝

⎛=φ

b. nTφ GnuBaØatEdlGacGnuvtþedaymineRbIEdkTb;karrmYlRtUv)anKNnaBIsmIkar !%>@0 mkNTT cr

a .75.94

394

===φ

2> muxkat; @ a. dMbUgKNna cpA nig cpP sRmab;muxkat;enH nigGnuvtþsmIkarTI !%>!( edIm,IKNna

crTφ . edaysnμt;søabRtUv)andak;CamYyEdkkgbiTCit enaHsøabRbsiT§PaBEdlRtUveRbIenA RCugmçag²énRTnugesμ Inwg $dgkRmas;søab b¤ ( ) mmhmm w 4004001004 ===

flanges effective of areaarea web +=cpA 22550004001002350500 mmAcp =××+×=

( ) ( ) mmhbPcp 3300500400235022 =+×+=+= mkNTcr .26

3300255000

32875.0

2=⎟

⎟⎠

⎞⎜⎜⎝

⎛=φ



cMNaM³ RbsinebIsøabRtUv)anecal ehIyEdkTb;karrmYlRtUv)andak;EtenAkñúgRTnug enaH

2175000500350 mmAcp =×= ( ) mmPcp 17005003502 =+=

mkNTcr .8.23=φ b. nTφ GnuBaØatEdlGacGnuvtþedaymineRbIEdkTb;karrmYl

mkNTT cra .5.6

426

4===

φ 3> muxkat; 3

a. snμt;søabRtUv)andak;EdkkgbiTCit RbEcgRbsiT§PaBes μ Inwg mmmmhw 6001504370 =×<=

2237500150370520350 mmAcp =×+×= ( ) mmhbPcp 24805203703502)(2 =++=+=

mkNTcr .302480

23750032875.0

2=⎟

⎟⎠

⎞⎜⎜⎝

⎛=φ

cMNaM³ RbsinebIsøabRtUv)anecal enaH 2182000520350 mmAcp =×=

( ) mmPcp 17405203502 =+= mkNTcr .2.25=φ

b. nTφ GnuBaØat mkNTT crn .5.7

430

4===

φφ

15>8>4> m:Um:g;rmYllMnwg nwgm:Um:g;rmYlRtUvKña (Equilibrium Torsion and Compatibility Torsion) kñúgkarviPaKeRKOgbgÁáúMGgát;ebtug kmøaMgepSg²EdlGnuvtþrYmman kmøaMgEkg (normal force)/ m:Um:g;Bt; (bending moment)/ kmøaMgkat; (shear force) nigm:Um:g;rmYl Edl)anBnül;enAkñúg]TahrN_ TI 15>1. karKNnaGgát;ebtugGarem:KWQrelIkar)ak;rbs;Ggát;GMeBIrbs;bnÞúkemKuN. sRmab;Ggát; sþaTicminkMNt; (statically indeterminate member) karEbgEckm:Um:g;mþgeTot (redistribution of

moments) ekItmanmuneBl)ak; dUcenHm:Um:g;KNnaGacnwgRtUv)ankat;bnßy b:uEnþ sRmab;Ggát;sþaTickM



Nt; (statically determinate member) dUcCaFñwmsamBaØ (simple beam) b¤Fñwm cantilever K μankar EbgEckm:Um:g;mþgeTotekIteLIgeT. enAkñúgkarKNnaGgát;Edlrgm:Um:g;rmYl eKmanBIrkrNIEdlGacGnuvtþbnÞab;BIkareRbH.

!> krNIm:Um:g;rmYllMnwg (equilibrium torsion case) ekItmanenAeBlm:Um:g;rmYlEdlRtUvkar sRmab;eRKOgbgÁúMsßitkñúgsßanPaBlMnwg ehIy uT minGacRtUv)ankat;bnßyedaykarEbg EckeLIgvijrbs;m:Um:g;eT dUckrNIFñwmTMrsamBaØ. kñúgkrNIenHEdkTb;rmYlRtUv)andak; edIm,ITb;RKb; uT . rUbTI 15>13 FñwmEdlenAEKmRTkRmalxNÐ cantilever EdlK μankar EbgEckm:Um:g;mþgeTotekItman.

@> krNIm:Um:g;rmYlRtUvKña (compatibility torsion case) ekItmanenAeBlm:Um:g;rmYl uT Gac RtUv)ankat;bnßyedaykarEbgEckkmøaMgkñúgmþgeTotbnÞab;BIeRbH enAeBlEdlPaBRtUvKña énkMhUcRTg;RTay (compatibility of deformation) RtUv)anrkSa enAkñúgGgát;eRKOgbgÁúM. rUbTI 15>14 bgðajBI]TahrN_sRmab;krNIenH EdlFñwmTTwgBIrmanGMeBIelIFñwmEKmbegáIt m:Um:g;rmYl. mMurmYlFMekItman enAeBlsñameRbHedaykarrmYlelcecj Edlpþl;nUvkar bgEckbnÞúkd¾FMenAkñúgeRKOgbgÁúM. vanwgeTAdl;m:Um:g;rmYlEdleFVI[eRbH crT eRkamGMeBI énbnSM karBt; karkat; nigkarrmYl enAeBlEdlkugRtaMgem (principle stress) mantémø RbEhl 3/'cf . enAeBlEdl cru TT > m:Um:g;rmYles μ Inwg crT ¬smIkar !%>!(¦ Edl Gacsnμt;ekItmanenARtg;muxkat;eRKaHfñak;enACitépÞénTRm.

ACI Code kMNt;m:Um:g;rmYlKNnaes μ InwgtémøtUcCageKén uT Edl)anBIbnÞúkemKuN b¤ crTφ BIsmIkar !%>!(.

15>8>5> karkMNt;énersIusþg;m:Um:g;rmYl (Limitation of Tortional Moment Strength) ACI Code,Section 11.6.3 kMNt;TMhMmuxkat;edaysmIkarxageRkamBIr³

!> sRmab;muxkat;tan;

⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛≤⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛c

w

c

oh

hu

w

u fdb

VAPT

dbV '

32

7.1

2

2

2

φ ¬!%>@!¦



@> sRmab;muxkat;Rbehag ⎥

⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛≤⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛c

w

c

oh

hu

w

u fdb

VAPT

dbV '

32

7.1 2 φ ¬!%>@@¦

Edl == 6/' dbfV wcc ersIusþg;kmøaMgkat;sRmab;ebtugTMgn;Fm μta. Ggát;déTeTotRtUv)an kMNt;enAkñúgEpñk 8>2.

karkMNt;enHKWQrelIPaBCak;EsþgEdlfaplbUkénkugRtaMgEdlbNþalBIkmøaMgkat; nigm:Um:g; rmYl ¬GgÁxageqVg¦ minRtUvFMCagkugRtaMgEdleFVI[eRbHbUknwg 3/'2 cf . krNIdUcKñaRtUv)anGnuvtþ edIm,IKNnakmøaMgkat;edayKμanm:Um:g;rmYlenAkñúgemeronTI 8. eKRtUvkarkarkMNt; (limitation) edIm,I kat;bnßysñameRbH nigedIm,IkarBarEbképÞebtugEdlbNþalmkBIkugRtaMgkmøaMgkat;TTwgeRTt nig m:Um:g;rmYleRTt.



15>8>6> muxkat;Rbehag (Hollow Section) bnSMénkugRtaMgkmøaMgkat; nigkugRtaMgm:Um:g;rmYlenAkñúgmuxkat;RbehagRtUv)anbgðajenAkñúgrUb 15>6 EdlkRmas;CBa¢aMgRtUvOansn μt;faefr. enAkñúgmuxkat;RbehagxøH kRmas;CBa¢aMgGacERbRbYlCMuvij brimaRt. sRmab;krNIenH smIkar !%>@@ RtUv)ankMNt;enATItaMgEdlGgÁxageqVgmantémøGtibrma. cM NaMfa enAnwgsøabxagelI nigsøabxageRkam CaTUeTAkugRtaMgkmøaMgkat;RtUv)anecal. CaTUeTA Rbsin ebIkRmas;CBa¢aMgénmuxkat;Rbehag t tUcCag hoh PA / enaHsmIkar !%>@@ køayCa ⎥

⎦

⎤⎢⎣

⎡+⎟⎟⎠

⎞⎜⎜⎝

⎛≤⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟⎠

⎞⎜⎜⎝

⎛c

w

c

oh

hu

w

u fdb

VtA

PTdb

V '32

7.1φ ¬!%>@#¦

(ACI Code, Section 11.6.3). 15>8>7> EdkRTnug (Web Reinforcement)

dUcEdl)anBnül;rYcehIy viFI ACI Code sRmab;KNnaGgát;Edlrgm:Um:g;rmYlKWQrelI space

truss analogy enAkñúgrUbTI 15>8. bnÞab;BIkareRbHedaykarrmYl eKRtUvkarEdkBIrRbePTedIm,ITb;nwg m:Um:g;rmYlEdlGnuvtþ uT KW EdkTTwg (transverse reinforcement) tA enAkñúgTRmg;CaEdkkgbiTCit nig EdkbeNþay (longitudinal reinforcement) lA . ACI Code )anbgðajnUvsmIkarxageRkamedIm,I KNna tA nig lA ³

!> EdkkgbiTCit tA EdlGacKNnadUcxageRkam³

sfAA

T ytton

θcot2= ¬!%>@$¦

Edl φu

nTT = nig 75.0=φ

=tA RkLaépÞéneCIgmYyrbs;EdkkgbiTCit =ytf ersIusþg;yal (yield strength) rbs; tA MPaAt 400≤ =s KMlatEdkkg

oA nig θ RtUv)ankMNt;enAkñúgEpñk 8>2. smIkar !%>@$ GacRtUv)ansresrdUcxageRkam

θcot2 yto

ntfAT

sA

= ¬!%>@%¦

RbsinebI o45=θ enaH 0.1cot =θ nigRbsinebI MPaf yt 400= enaHsmIkar !%>@% køayCa



o

ntA

TsA

800= ¬!%>@^¦

Edl nT KitCa mmN . . KMlatEdkkg s minRtUvFMCagéntémøtUcCageKkñúgcMeNam 8/hP nig mm300 . sRmab;muxkat; RbehagrgkarrmYl cm¶ayEdlvas;BIG½kSénEdkkgeTAépÞxagkñúgrbs;

CBa¢aMgminRtUvtUcCag hoh PA /5.0 . @> EdkbeNþaybEnßm lA EdlcaM)ac;sRmab;karrmYlminKYrtUcCagtémøxageRkam³

θ2cot⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

y

yth

tl f

fP

sAA ¬!%>@&¦

Rbsin o45=θ nig MPaff yyt 400== sRmab;TaMgEdkkg nigEdkbeNþay enaHsmIkar !%>@& køayCa

( )112 yxsAP

sAA t

ht

l +⎟⎠⎞

⎜⎝⎛=⎟

⎠⎞

⎜⎝⎛= ¬!%>@*¦

hP RtUv)ankMNt;enAkñúgEpñk 8>2. cMNaMfa EdkEdlcaM)ac;sRmab;karrmYlKYrRtUv)anbEnßmBI elI EdlEdlcaM)ac;sRmab;kmøaMgkat; m:Um:g;Bt; nigkmøaMgtamG½kSEdleFVIGMeBIrYmKñaCamYykmøaMgrmYl. karkMNt;epSgeTotsRmab;EdkbeNþay lA mandUcxageRkam³

a. Ggát;p©itEdktUcbMputsRmab;EdkbeNþayKW 10DB b¤KMlatEdkkgelI 24 b¤ 24/s edayykmYyNaEdlmantémøtUcCageK.

b. EdkbeNþayKYrRtUv)anBRgayCMuvijbrimaRtrrbs;EdkkgCamYyKMlatGtibrma mm300 .

c. EdkbeNþayKYrEtdak;enAkñúgEdkkg y:agehacNas;k¾dak;EdkenARKb;mMurbs;Edkkg. EdkEdldak;enAnwgmMurbs;EdkkgRtUv)aneKrkeXIjfamanRbsiT§PaBkñúgkarbegáItersIu sþg;m:Um:g;rmYl nigkñúgkarkarBarsñameRbH.

d. EdkTb;m:Um:g;rmYlRtUvdak;enAcm¶ay ( )dbt + BIcMNucEdlRTwsþIRtUvkar Edl tb CaTTwgén Epñkrbs;muxkat;EdlmanEdkkgTb;kmøaMgrmYl.

15>8>8> EdkTb;karrmYlGb,brma (Minimum Torsional Reinforcement) enAkEnøgNaEdlEdkTb;karrmYlGb,brmaRtUvkar EdkTb;karrmYlGb,brmaRtUv)ankMNt;dUc xageRkam (ACI Code, Section 11.6.5) ³



!> EdkkgbiTCitGb,brmasRmab;bnSMénkmøaMgkat;TTwg nigkarrmYl ¬emIlEpñk 8>6¦³

yt

wtv f

sbAA 35.02 ≥+ ¬sRmab; MPaf c 31' < ¦

⎟⎟⎠

⎞⎜⎜⎝

⎛≥+

yt

wctv f

sbfAA '063.02 ¬sRmab; MPaf c 31' ≤ ¦

¬!%>@(¦ Edl =vA RkLaépÞeCIgTaMgBIrrbs;EdkkgEdlkMNt;)anBIkmøaMgkat; =tA RkLaépÞeCIgEtmYyrbs;EdkkgEdlkMNt;BIm:Um:g;rmYl =s KMlatEdkkg =ytf ersIusþg;yal (yield strength) rbs;Edkkg MPa400≤ KMlatEdkkg s minKYrFMCagtémøtUcCagkñúgcMeNam 8/hP nig mm300 . KMlatenHRtUvkar edIm,IRKb;RKgsñameRbH. @> RkLaépÞEdksrubGb,brmarbs;EdkbeNþayTb;karrmYl³

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=

y

yth

t

y

cpcl f

fP

sA

fAf

A'5

min ¬!%>#0¦

Edl sAt / minRtUvyktUcCag ytw fb /173 . lA Gb,brmaenAkñúgsmIkar !%>#0 RtUv)ankMNt;edIm,Ipþl;nUvGRtaGb,brmaénmaDEdkTb; kMmøaMgrmYlelImaDebtug mantémøRbEhl %1 sRmab;ebtugGarem:EdlrgkmøaMgrmYlsuT§.

15>9> segçbviFIsaRsþKNnaeday ACI Code (Summary of ACI Code Procedures)

viFIsaRsþKNnasRmab;bnSMkmøaMgkat;TTwg nigkmøaMgrmYlGacRtUv)ansegçbdUcxageRkam³ !> KNnakmøaMgkat;TTwgemKuN uV nigm:Um:g;rmYlemKuN uT BIkmøaMgEdlGnuvtþmkelIeRKOg

bgÁúM. témøeRKaHfñak;sRmab;kmøaMgkat;TTwg nigkmøaMgrmYlKWsßitenARtg;muxkat;EdlmancM gay d BIépÞrbs;TMr.

@> a. eKRtUvkarEdkkmøaMgkat;TTwgenAeBl 2/cu VV φ> Edl 6/' dbfV wcc = . b. EdkTb;karrmYlRtUvkarenAeBlEdl

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛>

cp

cpcu P

AfT

2

12'

φ ¬!%>@0¦

RbsinebIEdkRTnugRtUvkarGnuvtþviFIsaRsþxageRkam.



#> KNnasRmab;kmøaMgkat;TTwg a. KNnaersIuisþg;kmøaMgkat; nominal Edlpþl;edayebtug cV . kMNt;kmøaMgkat;TTwg

EdlTb;edayEdkRTnug³ scu VVV +=φ b¤

φφ cu

sVV

V−

=

b. eRbobeFob sV Edl)anKNnaCamYynwgtémøGnuBaØatGtibrma 3/'2 dbf wc eyag tam ACI Code. RbsinebI sV tUcbnþkarKNna EtpÞúymkvijtMeLIgTMhMmuxkat;rbs; ebtug.

c. EdkRTnugkmøaMgkat;TTwgRtUv)anKNnadUcxageRkam³

dfsVA

yt

sv =

Edl =vA RkLaépÞéneCIgTaMgBIrrbs;Edkkg =s KMlatEdkkg EdkkmøaMgkat;TTwgkñúgmYyÉktþaRbEvgKW

dfV

sA

yt

sv =

d. RtYtBinitü sAv / Edl)anKNnaCamYynwg sAv / Gb,brma³

⎟⎟⎠

⎞⎜⎜⎝

⎛≥⎟

⎟⎠

⎞⎜⎜⎝

⎛=

yt

w

yt

wc

vfb

fbf

sA 35.0'063.0(min)

vA Gb,brma RtUv)ankMNt;edaybTdæaneRkambnSMénGMeBIrbs;kmøaMgkat;TTwg nigkM laMgrmYlRtUv)an[enAkñúgCMhanTI5

$> KNnasRmab;karrmYl³ a. RtYtBinitüfaetIm:Um:g;rmYlemKuN uT begáItm:Um:g;rmYllMnwg (equilibrium torsion)

b¤m:Um:g;rmYlRtUvKña (compatibility torsion). sRmab; equilibrium torsion eRbI uT . sRmab; compatibility torsion m:Um:g;rmYlKNnaKWtémøtUcCageKén uT BIbnÞúkemKuN nig

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

cp

cpcu P

AfT

2

2 3'

φ ¬!%>!(¦



b. RtYtBinitüfaetITMhMénmuxkat;RKb;RKan;b¤Gt;. vaTTYl)anedayeRbIsmIkar !%>@! sRmab;muxkat;tan; b¤smIkar !%>@@ sRmab;muxkat;Rbehag. RbsinebItémøenAGgÁ xageqVgFM Cag ( )3/'2/ cwc fdbV +φ enaHbegáInmuxkat; pÞúymkvijKNnabnþ. sRmab;muxkat; Rbehag RtYtBinitüfaetIkRmas;CBa¢aMg t tUcCag hoh PA / b¤Gt;. RbsinebIvatUcCageRbI smIkar !%>@# pÞúymkvijeRbIsmIkar !%>@@.

c. kMNt;EdkkgbiTCitcaM)ac;BIsmIkar !%>@%

θcot2 yto

ntfAT

sA

= ¬!%>@%¦

sAt / minRtUvtUcCag ytw fb /173 . ehIy mMu θ Gacsnμt;es μ I o45 / φ/un TT = nig 75.0=φ .

snμt; ( )1185.085.0 yxAA oho == Edl 1x nig 1y CaTTwg nigkm<s;rbs;muxkat;KitBIG½kSeTAG½kSEdkkg ¬emIlrUb TI !%>!!¦. sRmab; o45=θ nig MPaf y 400=

o

ntA

TsA

800= ¬!%>@^¦

KMlatGnuBaØatGtibrma s KWtémøtUcCageKén mm300 b¤ 8/hP . d. kMNt;EdkbeNþaybEnßmBIsmIkar !%>@&³

θ2cot⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

y

yth

tl f

fP

sAA ¬!%>@& a ¦

EtminRtUvtUcCag

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

y

yth

t

y

cpcl f

fP

sA

fAf

A12

'5min ¬!%>@& b ¦

sRmab; o45=θ nig MPaf yt 400= enaH ( ) htl PsAA /= ¬!%>@*¦ EdkbeNþayTb;karrmYlKYrmanGgát;p©ity:agticesμIKMlatEdkkgelI 24 b¤ 24/s b:uEnþ minRtUvtUcCag 10DB . EdkbeNþayRtUvdak;enAkñúgEdkkgbiTCitCamYyKMlatGtibrma esμ I mm300 . y:agehaceKRtUvdak;EdkmYyedImenARKb;mMurbs;Edkkg. CaTUeTAmYy PaKbIén Edk lA RtUv)anbEnßmeTAelIEdkTaj mYyPaKbIenABak;kNþalkm<s;rbs;mux kat; nigmYyPaKbIeTotenAEpñksgát;.

%> kMNt;RkLaépÞsrubénEdkkgbiTCitEdlbNþalBI uV nig uT .



( )yt

wtvvt f

sbAAA 35.02 ≥+= ¬!%>@(¦

eRCIserIsEdkkgbiTCitsmrmüCamYyKMlat s EdlmantémøtUcCageKkñúgcMeNam mm300 nig 8/hP . EdkkgKYrRtUv)andak;enAcm¶ay )( dbt + eRkaycMNucEdlRTwsþIRtUvkar Edl =tb TTwgén muxkat;EdlTb;nwgkmøaMgrmYl.

]TahrN_15>3³ (Equilibrium Torsion) kMNt;brimaNEdkRTnugcaM)ac;sRmab;muxkat;ctuekaNEkgdUcbgðajenAkñúgrUbTI 15>15. muxkat;rgnUvkM laMgkat;emKuN kNVu 5.213= nigkmøaMgrmYllMnwg (equilibrium torsion)

mkNTu .41= enATItaMg Edlmancm¶ay d BIépÞénTMr. eK[ MPaf c 28' = nig MPaf y 400= .

dMeNaHRsay³ CMhanxageRkambgðajBIviFIsaRsþkñúgkarKNna

1> kmøaMgKNnaKW kNVu 5.213= nig mkNTu .41= 2> a. EdkTb;kmøaMgkat;RtUvkarenAeBl 2/cu VV φ> .

( )( ) kNbdfV cc 6.1371052040028675.0'

63 =⋅== −φφ



kNVkNV cu 8.68

25.213 =>=

φ eKRtUvkarEdkTb;kmøaMgkat;. b. eKRtUvkarEdkTb;karrmYlenAeBl

acp

cpcu T

PAf

T =⎟⎟

⎠

⎞

⎜⎜

⎝

⎛>

2

12'

φ

2232000580400 mmyxA oocp =×== ( ) ( ) mmyxP oocp 184052040022 =+== ( ) mkNTa .7.910

1840122320002875.0 6

2=

×= −

mkNmkNTu .7.9.41 >= EdkTb;kmøaMgrmYlRtUvkarcaM)ac;. cMNaMfa RbsinebI uT tUcCag mkN.7.9 enaHEdkTb;kar

rmYlnwgminRtUvkar b:uEnþEdkTb;kmøaMgkat;RtUvkar. 3> KNnakmøaMgkat;TTwg³

a. scu VVV φφ += / kNVs 2.101= b. ( )( ) scs VkNbdfV >=== 8.73352040028

32'

32(max)

c. mmmdf

Vs

A

y

sv /5.0520400102.101 2

3=

×⋅

== ¬eCIgBIr¦

mmms

Av /25.02

2= ¬eCIgmYy¦ 4> KNnasRmab;karrmYl

a. kmøaMgrmYlKNna mkNTu .41= . KNnalkçN³muxkat; edaysn μt;kRmas;ebtugkarBar Edk mm40 nigeRbIEdkkg 12DB ³

( ) mmx 30864024001 =+−= ( ) mmy 48864025801 =+−= CakarGnuvtþn_ eKGacsn μt; mmbx 901 −= nig mmhy 901 −= 2

11 150304488308 mmyxAoh =×== 24.12775885.0 mmAA oho == ( ) ( ) mmyxPh 159248830822 11 =+=+=



o45=θ nig 0.1cot =θ b. RtYtBinitüPaBRKb;RKan;rbs;muxkat;edayeRbIsmIkar !%>@!³

⎥⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛≤⎟

⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛c

w

c

oh

hu

w

u fdb

VAPT

dbV '

32

7.1

2

2

2

φ

kNVc 6.137=φ nig kNVc 5.183=

MPa82.11503047.1

159241000000520400

137600side handLeft2

2

2=⎟

⎠⎞

⎜⎝⎛

×

×+⎟

⎠⎞

⎜⎝⎛

×=−

MPaMPa 82.13.32832

52040018350075.0side handRight >=⎟

⎠⎞

⎜⎝⎛ +

×=−

muxkat;RKb;RKan; c. kMNt;EdkkgbiTCitcaM)ac;EdlbNþalBIkarrmYlBIsmIkar !%>@%³

θcot2 yto

ntfAT

sA

=

mkNTT un .7.54

75.041

===φ

0.1cot =θ 24.127758 mmAo =

mmmsAt /535.0

4004.1277582107.54 2

6=

××⋅

= ¬eCIgmYy¦ d. kMNt;EdkbeNþaybEnßmBIsmIkarTI !%>@&³

θ2cot⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

y

yth

tl f

fP

sAA

535.0=sAt mmPh 1592= MPaff yyt 400== 0.1cot =θ

272.8511592535.0 mmAl =×=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−=

y

yth

t

y

cpcl f

fP

sA

fAf

A12

'5(min)

2232000mmAcp = 535.0=sAt MPaff yyt 400==

( ) ( )( ) 24271592535.040012

232000285(min) mmAl =−×

= 272.851 mmAl = lb;

5> kMNt;RkLaépÞEdkkgsrub a. sRmab;eCIgmYyrbs;Edkkg

sA

sA

sA vtvt

2+=



EdkkgEdlcaM)ac; mmmAvt /785.025.0535.0 2=+= ¬eCIgmYy¦ eRbIEdk 12DB RkLaépÞmuxkat;rbs;EdkkgsRmab;eCIgmYyKW 2113mm mm144

785.0113stirrups of spacing == yk mm140

b. KMlatGtibrma mmPs h 1998

15928

=== b¤ mm300 mYyNaEdltUcCag. KMlatEdleRbIKW mmmm 199140 <

c. sAvt / Gb,brma mmmmmmf

b

yt

w /785.0/35.0400

40035.035.0 22 <=×

==

6> edIm,IrkkarBRgayEdkbeNþay cMNaMfa lA srub 272.851 mm= . eRbImYyPaKbIenAEpñkxag elI b¤ 29.2833/72.851 mm= edIm,IbEnßmenAkñúgEdkrgkarsgát; sA' . eRbImYyPaKbIdak;enA EpñkxageRkam edIm,IbEnßmBIelIEdkrgkarTaj nigEdkmYyPaKbIeTotdak;enAkm<s;Bak; kNþal. a. RkLaépÞEdksrubenAEpñkxagelIesμI 29.5099.283226 mm=+ . eRbI 163DB

¬ 2603mmAs = ¦ b. RkLaépÞEdksrubenAEpñkxageRkamesμ I 27.33629.2838.3078 mm=+ . eRbI 283DB

nig 322DB enARCugmMu ¬ sA srub 28.3455 mm= ¦ lA srubEdleRbI ( ) ( ) 27548.30788.3455226603 mm=−+−=

c. enAkm<s;Bak;kNþal eRbIEdk 122DB ¬ 2226mmAs = ¦ bøg;srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 15>15. KMlatEdkbeNþayesμ Inwg mm230 EdltUcCagKMlatEdkGtibrmaEdlRtUvkar 2300mm . Ggát;p©itEdkkg 12DB Edl

eRbIFMCagGgát;p©itGb,brma 10DB b¤KMlatEdkkgelI 24 ¬ mms 8.524/ = ¦.

]TahrN_15>4³ (Compatibility Torsion) edaHRsay]TahrN_TI 15>3 eLIgvij RbsinebIkmøaMgrmYlemKuNCa compatibility torsion. dMeNaHRsay³ eyagtamdMeNaHRsaykñúg]TahrNITI 15>3

!> kmøaMgKNnaKW kNV u 5.213= nig compatibility torsion mkNTu .41= @> CMhan (a) nig (b) dUcKñaenAkñúg]TahrN_TI 15>3. eKRtUvkarEdkRTnug.



#> CMhan (c) KWdUcKña. $> KNnasRmab;kmøaMgrmYl³

edaysar compatibility torsion mkNTu .41= enaH uT KNnaRtUvtUvCag mkN.41 b¤ crTφ RtUv)an[enAkñúgsmIkar !%>!(

mkNPAf

Tcp

cpccr .7.3810

1840232000

32875.0

3' 6

22

=⋅⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛= −φφ

edaysarEt ucr TT <φ / eRbI mkNTu .7.38= . GnuvtþeLIgvijRKb;CMhanenAkñúg]TahrN_TI 15>3 edayeRbI mkNTu .7.38= edIm,IkMNt;famuxkat;RKb;RKan;.

mmmsAt /5.0 2= ¬eCIgmYy¦

279615925.0 mmAl =×= eRbI (min)852 2

ll AmmA >= %> vtA caM)ac; mmm /75.05.0

25.0 2=+= ¬eCIgmYy¦

mms 6.15075.0

113==

eRbI mm150 . eRCIserIsEdkbeNþay nigEdkkgdUckñúg]TahrN_TI 15>3. ]TahrN_15>5³ (L-section with Equilibrium Torsion) FñwmxagénRbB½n§kRmalxNÐrbs;GKardUcbgðajenAkñúgrUbTI 15>16. muxkat;enAcm¶ay d BIépÞénTRm rg kNVu 235= nig equilibrium torque mkNTu .27= . KNnaEdkRTnugcaM)ac;edayeRbI

MPaf c 28' = nig MPaf y 400= sRmab;RKb;EdkEdleRbIenAkñúgFñwm. dMeNaHRsay³

1> kmøaMgKNnaKW kNVu 235= nig mkNTu .27= 2> a. EdkTb;kmøaMgkat;RtUvkarenAeBl 2/cu VV φ> kNdb

fV w

cc 3.10510455350

62875.0

6' 3 =⋅×== −φ

φ

kNVV cu 65.52

2=>

φ eKRtUvkarEdkkmøaMgkat;TTwg

b. RtYtBinitüfaetIEdkTb;karrmYlRtUvkarb¤Gt;. sn μt;fasøabcUlrYmkñúgkarTb;karrmYl RbEvg



søabRbsiT§PaBKW mmmmhw 6004150380 =×<= . mmxo 350= nig mmyo 530= ( ) ( ) 2242500380150530350 mmAcp =×+×= ( ) mmPcp 25205307302 =+= BIsmIkar !%>@0 mkNTa .7.710

252024250028

1275.0 6

2=⋅⎟

⎟⎠

⎞⎜⎜⎝

⎛= −

au TT > muxkat;RtUvkarEdkTb;karrmYl.

3> KNnaEdkTb;kmøaMgkat;TTwg³ a. scu VVV φφ += sV75.03.105235 += kNVs 173= b. swcs VkNdbfV >== 8.561'

32(max)

c. mmmdf

Vs

A

y

sv /95.0455400

173000 2=×

== ¬eCIgBIr¦

mmms

Av /475.0295.0

22==

4> KNnaEdkTb;karrmYl³ mkNTu .27= a. KNnalkçN³muxkat;edaysnμt; kRmas;ebtugkarBarEdk mm40 nigEdkkg 12DB .

RTnug ( ) mmx 258124023501 =−×−= ( ) mmy 438124025301 =−×−= søab mmx 3801 = ¬EdkkghYscUleTAkñúgRTnug¦ mmy 58921501 =−= ( ) ( ) 213504443825838058 mmAoh =×+×= 24.11478785.0 mmAA oho == ( ) ( ) mmPh 22684382582380582 =+++= o45=θ 0.1cot =θ

b. RtYtBinitüPaBRKb;RKan;rbs;muxkat;edayeRbIsmIkarTI !%>@!³ kNVu 235= / kNVc 3.105=φ / kNVc 4.140= / mkNTu .27=



MPa47.21350447.1

22681027455350

235000side handLeft 2

62=⎟

⎟⎠

⎞⎜⎜⎝

⎛

×

×⋅+⎟

⎠⎞

⎜⎝⎛

×=−

MPa3.32832

45535014040075.0side handRight =⎟

⎠⎞

⎜⎝⎛ +

×=−

muxkat;manlkçN³RKb;RKan; c. kMNt;EdkkgbiTCitedIm,ITb;karrmYl sAt / BIsmIkar !%>@%³ mmm

fAT

sA

yto

nt /392.04004.114787275.0

1027cot2

26

=×××

⋅==

θ ¬eCIgmYy¦

d. KNnaEdkbeNþaybEnßmBIsmIkar !%>@* ¬sRmab; MPaf c 400' = nig 0.1cot =θ ¦ 28892268392.0 mmP

sA

A ht

l =×=⎟⎠⎞

⎜⎝⎛=

minlA ¬BIsmIkar !%>#0¦ KW 2

min 7.44788940012242500285 mmAl =−

××

= karcUlrYmrbs;søabRtUv)anecaledaysarTTYl)anlT§plxusKñatictYc nigtémøBlkm μ ticCag.

5> kMNt;RkLaépÞmuxkat;EdkkgbiTCit a. sRmab;eCIgmYy

sA

sA

sA vtvt

2+=

muxkat;cM)ac; mmmAvt /867.0475.0392.0 2=+= ¬eCIgmYy¦ eRCIserIsEdk 12DB ¬ 2113mmAs = ¦ KMlatEdkkg mm130

867.0113

== eRbI mm125

b. KMlatEdkGtibrma mmPs h 5.2838

22688max === . eRbI mms 125= dUckarKNna.

c. mmmmmmf

bs

A

yt

wvt /867.0/31.0400

35035.035.0 22 <=×

== dUcenHeRbI

125@12DB 6> kMNt;karBRgayrbs;EdkbeNþay. lA srubKW 2889mm . eRbImYyPaKbI b¤

23.2963/889 mm= enAEpñkxagelI EpñkkNþal nigEpñkxageRkam. a. brimaNEdksrubenAEpñkxagelI 26.9243.2963.628 mm=+= eRbI 203DB

¬ 25.942 mmAs = ¦



b. brimaNEdksrubenAEpñkxagelI 23.27593.2962463 mm=+= eRbI 285DB ¬ 28.3078 mmAs = ¦

lA srubEdleRbI ( ) ( ) 293024638.30783.6285.942 mm=−+−= c. eRbIEdk 122DB enABak;kNþalkm<s; ¬ 2226mmAs = ¦. bøg;EdklMGitRtUv)anbgðajenA

kñúgrUbTI 15>16. KMlatEdkbeNþayKW mmmm 300190 < . Ggát;p©itrbs;EdkkgKW mm12 EdlFMCagGgát;p©itEdk 10DB b¤KMlatEdkkgelI 24 ¬ mms 2.524/ = ¦.

bEnßmEdkbeNþay 12DB enARKb;mMurbs;EdkkgenAkñúgRTnugFñwm nigsøabFñwm.




FñwmCab; nigeRKagCab; 445 T.Chhay

XVI. FñwmCab; nigeRKag Continuous Beams and Frames


GKarebtugBRgwgedayEdkpÁúMeLIgedayGgát;eRKOgbgÁúMCaeRcInRbePTdUcCa kRmalxNÐ (slab) Fñwm (beam) ssr (column) nigeCIgtag (footing) . Ggát;eRKOgbgÁúMTaMgenHGacRtUv)ancak;dac;eday ELkBIKña dUcCakRmalebtugcak;eRsc (precast concrete slab) Fñwmcak;eRsc nigssrcak;eRsc eday manbnSl;TuksrésEdkedIm,IP¢ab;KñaBIGgát;eRKOgbgÁúMmYyeTAGgát;eRKOgbgÁúMmYyeTot edim,IeFVI[vakøay Carcnasm<½n§EtmYy (monolithic structure). Ggát;Edlcak;eRscRtUv)anKNnadUcGgát;eRKOgbgÁúMenA elITRmsamBaØ eTaHbICaRbePTénPaBCab;xøHRtUv)anpþl;[enAEpñkcugrbs;va. sRmab;Ggát;Edlman lkçN³EtmYy (monolithic member) PaBCab;énGgát;nImYy²RtUv)anpþl;[ EdleFVI[Ggát;eRKOg bgÁúMRtUv)anviPaKdUcrcnasm<½n§sþaTicminkMNt; (statically indeterminate structure) .

karviPaK nigkarKNnakRmalxNÐmYyTisCab;RtUv)anbgðajenAkñúgemeronTI 9 ehIyemKuNKNna (design coefficient) nigsrésEdklMGitRtUv)anbgðajenAkñúgrUbTI 9>8 nig 9>9. enAkñúgRbB½n§kRmal xNÐ½mYyTis bnÞúkkRmalxNÐRtUv)anbBa¢ÚnmkFñwmTRm dUcbgðajenAkñúgrUb 16>1 a . RbsinebIbnÞúk emKuNenAelIkRmalxNÐKW uw enaHbnÞúkBRgayes μ IenAelIFñwm AB nig BC kñúgmYyÉktþaRbEvgKW

swu bUknwgTm¶n;pÞal;rbs;Fñwm. bnÞúkBRgayesμ IenAelIFñwm DE nig EF KW 2/swu bUknwgTm¶n;pÞal; rbs;Fñwm. bnÞúkenAelIssr B esμ Inwg Lswu b:uEnþbnÞúkenAelIssr E / A nig D KW 2/Lsws /

2/Lsws nig 4/Lsws erogKña. enAkñúgkRmalxNÐBIrTisEdlRTedayFñwmenARCugTaMgbYn bnÞúkkRmalxNÐRtUv)anbBa¢ÚneTAFñwmBI

RkLaépÞcMNuHEdlB½T§edaybnÞat; o45 dUcbgðajenAkñúgrUbTI 16>1 b. EpñkxøHénbnÞúkkRmalxNÐ RtUv)anbBa¢ÚneTAFñwmEvg AB / BC / DE nig EF BIRkLaépÞctuekaNBñay b:uEnþbnÞúkkRmalxNÐEdl enAsl;RtUv)an bBa¢ÚneTAFñwmxøI AD / BE nig CF BIRkLaépÞRtIekaN. sRmab;kRmalxNÐkaer bnÞúk RtUv)anbBa¢ÚneTAFñwm EdlB½T§CMuvijBIRkLaépÞRtIekaN. FñwmenAxagkñúgTTYlbnÞúkBIRCugTaMgBIr b:uEnþFñwm xagrgbnÞúkEtmYyxag b:ueNÑaH. edaysarFñwmTaMgBIrTisRtUv)ancak;ebtugkñúgeBlCamYyKñanwgkRmal xNÐ enaHvaRtUv)anviPaKCa FñwmCab;sþaTicminkMNt; (statically indeterminate continuous beam). FñwmbBa¢ÚnbnÞúkbnþeTAssr. bnÞúkenAelIssr B es μ Inwg Lswu enAeBlEdl bnÞúkenAelIssr E / A


T.Chhay 446 Continuouse Beams and Frames

nig D KW 2/Lsws / 2/Lsws nig 4/Lsws erogKña. RkLaépÞcMNuHsRmab;ssrnImYy²RtUv)anKitBIG½kSrbs;ElVgEdlenA Ek,rRKb;Tis.

16>2> m:Um:g;GtibrmaenAkñúgFñwmCab; (Maximum Moment in Continuous Beams)

16>2> 1> eKalkarN_viPaK (Basic Analysis) CaTUeTA karKNnam:Um:g;Bt; nigkmøaMgkat;TTwgenAkñúgFñwmCab;ebtugGarem:KWQrelIRTwsþIeGLasÞic

(elastic theory). enAeBlmuxkat;ebtugGarem:RtUv)anKNnaedayeRbIviFIKNnaersIusþg; (strength

design method) lT§plEdlTTYl)annwgmineqøIytbCamYynwgkarviPaKeGLasÞic (elastic analysis)

eT. b:uEnþ ACI Code min)anbBa¢ÚllkçxNÐsRmab;karKNna)øasÞic (provision for a plastic design) b¤ karKNnasßanPaBkMNt; (limit state design) éneRKOgbgÁúMCab;ebtugGarem: RKan;EtGnuBaØatkarEbg Eckm:Um:g;eLIgvij (moment redistribution) dUcEdlnwgBnül;enAkñúgemeronenH. 16>2> 2> karGnuvtþkardak;bnÞúk (Loading Application)

m:Um:g;Bt;enARtg;cMNucNamYyenAkñúgFñwmCab; vaminGaRs½yEtnwgbnÞúkEdlmanTItaMgenAelIFñwmdUcKña enaHeT b:uEnþvak¾GaRs½ynwgbnÞúkEdlsßitenAelIFñwmdéTeTotEdr. kñúgkrNIbnÞúkefr RKb;FñwmTaMgGs;RtUv



Etdak;bnÞúkkñúgeBldMNalKña edaysarEtbnÞúkefrmanTItaMg nigtémøkMNt;. kñúgkrNIbnÞúkcl½t b¤ bnÞúkGefrEdlekIteLIgmþgmáal EbbbTénkardak;bnÞúkRtUv)anBicarNay:gNaedIm,IkMNt;m:Um:g;Gti-brmaenATItaMgeRKaHfñak;. ExS\T§iBlGacRtUv)aneRbIedIm,IkMNt;TItaMgrbs;bnÞúkGefredIm,IKNnam:Um:g; Gtibrma nigm:Um:g;Gb,brma. b:uEnþenAkñúgemeronenH k,Ünd¾samBaØEdlQrelIExSekagbnÞúk-PaBdab (load-deflection curve) RtUv)aneRbIedIm,IkMNt;EbbbTénkardak;bnÞúkEdlbegáItm:Um:g;Gtibrma. 16>2> 3> m:Um:g;viC¢manGtibrma nigGb,brmaenAkñúgElVg

Maximum and Minimum Positive Moments within a Span



m:Um:g;Bt;viC¢manGtibrmaenAkñúgFñwmTRmsamBaØEdlrgbnÞúkBRgayesμ I w KWsßitenAkNþalElVg Ca mYynwg

8

2wlM = . RbsinebIcugrbs;vamYy b¤TaMgBIrRtUv)anbnþ karTb;enAcugEdlCab;nwgbegáItm:Um:g; GviC¢manenAelITRm ehIyTItaMgénbnÞúkviC¢manGtibrmaGacpøas;bþÚrbnþicBIkNþalElVg. ragdabénFñwm Cab;sRmab;kardak;bnÞúkEtelIElVgEtmYy RtUv)anbgðajenAkñúgrUbTI 16>2 a . PaBdabcuHeRkambgðaj fam:Um:g;viC¢man ehIyPaBdabeLIgelIbgðajm:Um:g;GviC¢man. RbsinebIRKb;ElVgEdldabcuHeRkamRtUv)an dak;bnÞúk enaHbnÞúknImYy²nwgbegáInm:Um:g;viC¢manenAkñúgElVg AB ¬rUbTI 16>2 d ¦. dUcenHedIm,IKNna m:Um:g;viC¢manGtibrmaenAkñúgElVgNamYy bnÞúkGefrRtUv)andak;enAelIElVgenaH nigenAelIElVgqøas;TaMg sgçag. m:Um:g;bnÞúkGefremKuNEdlKNnadUcBnül;BImunRtUv)anbEnßmBIelIm:Um:g;bnÞúkGefremKuNenA elImuxkat;dUcKñaedIm,ITTYl)anm:Um:g;viC¢manGtibrma.

düaRkamm:Um:g;Bt;Edl)anBIbnÞúkBRgayes μ IenAelIElVg AB RtUv)anbgðajenAkñúgrUbTI 16>2 b. PaBdab nigm:Um:g;Bt;fycuHy:agelOnCamYynwgcm¶ayBIElVg AB EdlrgbnÞúk. dUcenH edIm,IsRmYl karviPaKFñwmCab; m:Um:g;enAkñúgElVgNamYyGacRtUv)anKNnaedayBicarNaEtFñwmEdlrgbnÞúk AB nig FñwmBIreTotEdlenAsgçagva nigsn μt;TRmbgáb;enAcugEdlq¶ayTaMgsgçag ¬rUbTI 16>2 c ¦.

RbsinebIElVgEdlCab;nwgElVg AB RtUv)andak;bnÞúk ExSekagdabRtUv)anbgðajenAkñúgrUb 16>2 e . PabdabenAkñúgElVg AB nwgeLIgelI ehIym:Um:g;GviC¢mannwgRtUv)anbegáItenAkñúgFñwm AB . m:Um:g;GviC¢-manenHnwgRtUv)anbEnßmeTAelIm:Um:g;viC¢manEdl)anBIbnÞúkefredIm,ITTYl)anm:Um:g;Bt;cugeRkay. dUcenH edIm,IKNnam:Um:g;viC¢manGb,brma ¬b¤m:Um:g;GviC¢manGtibrma¦ enAkñúgElVg AB bnÞúkGefrRtUv)andak; enAElVgEk,rnwgElVg AB nigRKb;ElVgqøas;nwgElVgEdlrgbnÞúk ¬rUbTI 16>2 e ¦. 16>2> 4> m:Um:g;GviC¢manGtibrmaenAelITRm (Maximum Negative Moments at Supports)

kñúgkrNIenH eKcaM)ac;kMNt;m:Um:g;GviC¢manGtibrmaenAelITRmNamYy dUcCaTRm A ¬rUbTI 16>3¦. enAeBlEdlElVg AB RtUv)andak;bnÞúk m:Um:g;GviC¢manRtUv)anbegáItenAelITRm A . dUcKña bnÞúkénElVg AF k¾nwgbegáItm:Um:g;GviC¢manenAelI A Edr. dUcenH edIm,IKNnam:Um:g;GviC¢manGtibrmaenAelITRmNa mYy bnÞúkGefrRtUv)andak;enAelIElVgEk,rTaMgBIr nigenAelIRKb;ElVgqøas;TaMgsgçag ¬rUbTI 16>3¦.



enAkñúgkarviPaKeRKOgbgÁúM (structural analysis) énFñwmCab; RbEvgElVgRtUv)anKitBIG½kSeTAG½kS TRmEdlRTedayTRmcugkaMbiT (knife-edge support). enAkñúgkarGnuvtþ TRmRtUv)aneFVIeLIgedayman TMhMRKb;RKan;edIm,ITTYlbnÞúkEdlbBa¢ÚnedayFñwm CaTUeTAm:Um:g;eFVIGMeBIenAnwgépÞénTRm. edIm,IKNna m:Um:g;enAnwgépÞénTRm eKGacdkedaym:Um:g;EdlesI μnwg 3/cVu BIm:Um:g;emKuNenAG½kSrbs;TRm Edl uV KWCakmøaMg kat;TTwgemKuN nig c CaTTwgssr. 16>2> 5> m:Um:g;enAkñúgFñwmCab; (Moments in Continuous Beams)

FñwmCab; nigeRKagCab;GacRtUv)anviPaKedayeRbIviFIRbhak;RbEhl (approximate method) b¤kmμ -viFIkMuBüÚT½r. viFIepSgeTotdUcCa viFIbnÞúk nigbMlas;TI (displacement and force method) énkarviPaK EdlQrelIkarKNnaénm:aRTIsénPaBrwgRkaj nigPaBrlas; (stiffness and flexibility matrices) GacRtUvykmkeRbI. viFI slope deflection nigviFI moment-distibution k¾GacRtUv)aneRbI. viFITaMgenH manBnül;enAkñúgesovePAEdlniyayBIkarviPaKeRKOgbgÁúM (structural analysis) énFñwm nigeRKag. ACI Code, Section 8.3 pþl;nUvemKuNRbhak;RbEhlsRmab;KNnam:Um:g;Bt; nigkmøaMgkat;TTwgenAkñúg Fñwm nigkRmalxNÐCab;. emKuNTaMgenHRtUv)an[enAkñúgemeronTI 9. m:Um:g;EdlTTYl)anBIemKuN ACI nwgmantémøFMCagm:Um:g;EdlTTYl)anBIkarKNnaviPaKbnþic. eKRtUveKarBtamkarkMNt;Edlman EcgenAkñúgkareRbIR)as;emKuNTaMgenaH.

]TahrN_TI 16>1³ RbB½n§kRmalxNÐ-Fñwm Edl)anbgðajenAkñúgrUbTI 16>4 RTnUvbnÞúkGefrBRgayesμ I 2/2.6 mkN nigbnÞúkefrEdlrYmmanbnÞúkpÞal;rbs;kRmalxNÐbUknwg 2/8.3 mkN . edayeRbIemKuNm:Um:g; ACI

KNnaFñwmCab;enAxagkñúg nigKUrmuxkat;lMGit. eK[ MPaf c 28' = / MPaf y 400= / TTWgFñwm mmb 300= / muxkat;ssr mm300300× nigkRmas;kRmalxNÐ mm125 .



dMeNaHRsay³

1> KNnakRmalxNÐ³ kRmalxNÐmannaTICakRmalxNÐmYyTis edaysarpleFobRCugEvgelI RCugxøIFMCag 2 . karKNnaénRbePTkRmalxNÐCab;RtUv)anBnül;enAkñúg]TahrN_TI 9>4.

2> bnÞúkenAelIkRmalxNÐ³ bnÞúkefr 2/925.68.325125.0load Dead mkN=+×= bnÞúkGefr 2/2.6load Live mkN= bnÞúkemKuN 2/23.182.66.1925.62.1)( load Ultimate mkNwu =×+×=

bnÞúúúkenAelIFñwm³ Fñwmxagkñúg ABC RTbnÞúkkRmalxNÐTaMgsgçag CamYynwgTTwgkRmalxNÐsrub m6.3 bnÞúkemKuNenAelIFñwm

( ) webbeam ofweight -self2.123.186.3beamon load Factored +×= km<s;rbs;FñwmGacRtUv)ankMNt;edayeRbIemKuNénkRmas;FñwmGb,brmadUcEdl)anbgðajenA kñúgtarag]bsm<½n§ B.6. sRmab; MPaf y 420= km<s;FñwmGb,brmarbs;FñwmTI1 AB KW



5.18/L m389.018/2.7 == . snμt;km<s;Fñwmsrub mm550 km<s;RTnugFñwmKW mm425125550 =− . dUcenHbnÞúkemKuNenAelIFñwm ABCD KW

( ) mkNwu /45.69253.0425.02.123.186.3 =××+×= yk mkNwu /5.69= 3> m:Um:g;enAkñúgFñwm ABC ³ emKuNm:Um:g;RtUv)anbgðajenAkñúgrUbTI 9>8. FñwmCab;Kñaman 5 ElVg

ehIysIuemRTIKñaeFobG½kSkNþalRtg;cMNuc D . dUcenH eKcaM)ac;KNnaEtFñwmBak;kNþal ABCD BIeRBaHFñwmBak;kNþaleTotnwgmanTMhMehIynwgbrimaNEdkdUcKña. edaysarElVg AB nig BC minesμ IKñaEtmanpleFob 2.7/9.7 mantémøtUcCag 2.1 enaHemKuNm:Um:g; ACI

GacGnuvtþ)ansRmab;FñwmenH. elIsBIenHRbEvg clear span mFümEdlenAEk,rRtUv)aneRbI edIm,IKNnam:Um:g;GviC¢manenAelITRm.

m:Um:g;enAmuxkat;eRKaHfñak;RtUv)anKNnadUcxageRkam ¬rUbTI 16>4¦ 2tcoefficien nuu lwM ×=

TItaMg ! @ # $ % ^

emKuNm:Um:g; 161

− 141

+ 101

− 161

+ 111

− 161

+

uM ¬ mkN. ¦ 8.206− 35.236 3.365− 9.250 9.364− 9.250 4> kMNt;TMhMFñwm nigsrésEdk a. m:Um:g;GviC¢GtibrmaKW mkN.3.365− . edayeRbI 016.0max =ρ enaH MPaRu 5= / 9.0=φ

mmbR

Mdu

u 5.4933005

103.365 6=

×⋅

==

sRmab;EdkmYyRsTab; km<s;FñwmsrubKW mm5.553605.493 =+ yk mm600 d EdleRbIR)as;BitR)akdKW mm54060600 =− 22592540300016.0 mmAs =××= eRbI 304DB ¬mYyRsTab;¦



cMNaMfa³ km<s;FñwmEdleRbIenATIenHKW mm600 EdlFMCagkm<s;Fwñmsnμt;Edles μ Inwg mm550 edIm,IkMNt;Tm¶n;rbs;Fñwm. edaysarbnÞúkbEnßmmantémøtUcGacecal)an eKmincaM)ac;eFVIkar KNnaeLIgvijeT.

b. muxkat;enATRmeFVIGMeBICamuxkat;ctuekaNEkgCamYyEdkTajenAkñúgsøab. EdkcaM)ac;enAkñúgTRm mandUcxageRkam³ TItaMg ! # %

).( mkNM u 8.206− 3.365− 9.364− )(MPaRu 36.2 17.4 17.4

(%)ρ 74.0 39.1 39.1 )( 2mmAs 1199 2252 2252

cMnYnEdk 30DB 2 4 4 c. sRmab;muxkat;GkSr T enAkNþalElVg mkNM u .9.250= . sRmab; mma 25=

nigTTwgsøab mb f 8.1= ( )

26

2.13215.125404009.0

109.250

2

mmadf

MAy

us =

−×⋅

=⎟⎠⎞

⎜⎝⎛ −

=φ

RtYtBinitü a ³ mmbf

fAa

c

ys 34.1218002885.04002.1321

'85.0=

×××

==

CamYy mma 34.12= eKTTYl)an 25.1305 mmAs = . dUcenHeRbIEdk 253DB ¬ 26.1472 mmAs = ¦ sRmab;RKb;muxkat;kNþalElVgTaMgGs;. bøg;EdklMGitRtUv)anbgðaj enAkñúgrUbTI 16>5.

5> KNnaFñwmsRmab;kmøaMgkat;TTwg dUcEdl)anBnül;enAkñúgemeronTI 8. 6> RtYtBinitüPaBdab nigsñameRbH dUcEdl)anBnül;enAkñúgemeronTI 9.



16>3> eRKagsMNg;GKar (Building Frames)

eRKagGKarKWCaRbB½n§eRKOgbgÁúMbITMhM ¬kñúglMh¦ (three-dimensional structural system) EdlpÁúM eLIgeday Ggát;Rtg;²Edlsagsg;CamYyKña (built monolithically) nigmantMNrwg. eRKagGacman mYyElVg nigmankm<s;mYyCan; dUcCa portal frame nig gable frame dUcbgðajenAkñúgrUbTI 16>6 a b¤ GacpSM eLIgedayeRcInElVg nigeRcInCan; dUcbgðajenAkñúgrUbTI 16>6 b. RKb;Ggát;rbs;eRKagRtUv)an cat;Tuk faCab;sRmab;TisTaMgbI ehIyssrcUlrYmCamYynwgFñwmedIm,ITb;bnÞúkxageRkA. eRkABIkarkat; bnßym:Um:g; edaysarPaBCab; eRKagGKarcg;)ankarBRgaybnÞúkkan;Etes μ Ikan;Etl¥. \T§iBlénbnÞúk xag dUcCabnÞúkxül; nigbnÞúkrBa¢ÜydI RtUv)anBRgayenAelIeRKagTaMgmUl edIm,IbegáInsuvtßiPaBrbs;va. sRmab;karKNna viFIRbhak;RbEhl (approximate method) GacRtUv)aneRbIedaysnμt;RbB½n§eRKag BIrTMhM ¬kñúgbøg;¦. eRKagEdlrgnUvRbB½n§bnÞúkGacRtUv)anviPaKedayviFIeRKagsmmUl (equivalent frame method). enAkñúgviFIenH karviPaKtamCan;KWRtUveFVIeLIgedaysnμt;facugssrEdlenAq¶ayBIelI nigBIeRkamnIv:U kRmalxNÐRtUv)anbgáb; ¬rUbTI 16>7¦. CaTUeTA karviPaKRtUv)aneFVIeLIgedayeRbIviFIEbgEckm:Um:g; (moment-distribution method).



enAkñúgkar TMhMkRmal (panel) cm¶aycenøaHssr/ cMnYnCan; nigkm<s;énCan;nImYy²RtUv)ansÁal;BI eRBaHBYkvaRtUv)anpþl;[edaykarKNnasßabtükmμ ehIyRbB½n§brikçaRtUv)anKitrYcCaeRsc. TMhMssr nigTMhMFñwmRtUv)aneFVIkar)a:n;sμanCamun ehIypleFobPaBrwgRkajrbs;vaEdlQrelImuxkat;ebtug RtUv)aneRbI. enAeBlm:Um:g;RtUv)ankMNt; eKRtUvRtYtBinitümuxkat;Edl)ansnμt;BImun nigeFVIkarEktRmUv RbsinebIcaM)ac;. karviPaKEdlmanlkçN³suRkitCagGaceFVIeLIgedayeRbIkm μviFIkMuBüÚT½rEdlRtUv)an ENnaMsRmab;karviPaK eRKOgsþaTicminkMNt;EdlmanGBaØateRcIn. viFIénkarviPaKRtUv)anBN’naenAkñúg esovePACaeRcInEdlniyayBIkarviPaKeRKOgbgÁúM.



16>4> Portal Frames

Portal frames pSMeLIgedayFñwmebtugGarem:EdlrwgRtUv)ancak;CamYynigTRmssrrbs;va. tMN rvagFñwm nigssrRtUv)anBicarNabgáb;rwgCamYynwgplbUkm:Um:g;enARtg;tMNes μ IsUnü. Portal frames RtUv)aneRbIenAkñúgsMNg;salEdlmanElVgFM (large-span halls)/erag (sheds)/ s<an nigs<ankat; RClgPñM (viaducts). Ggát;EpñkxagelIrbs;eRKagGacedk (portal frames) b¤eRTt (gable frames) ¬rUb TI 16>8¦. eCIgeRkamrbs;eRKagGacCaTRmbgáb; b¤TRmsnøak;. Portal frames sþaTicminkMNt;GacRtUv)anviPaKedayviFIEbgEckm:Um:g; b¤viFIdéTeTotEdleRbI edIm,IviPaKeRKagsþaTicminkMNt;. Ggát;rbs;eRKagRtUv)anKNnasRmab;m:Um:g; kmøaMgkat;TTwg nigkmøaMg Ekg b:uEnþeCIgtagRtUv)anKNnaedIm,IRTkmøaMgEdlmanGMeBIenA)atssr. Fñwm nigssrrbs;eRKagGacmanTMhMes μI b¤ERbRbYl dUcbgðajenAkñúgrUbTI 16>8. kmøaMgenAkñúg portal frames EdlmanmYyElVgehIymanmuxkat;esμ IGacRtUv)anKNnadUcxageRkam³ 16>4> 1> cugsnøak;BIr (Two Hinged Ends) kmøaMgenAkñúgGgát;rbs; portal frames Edlmancugsnøak;BIrGacRtUv)anKNnaedayeRbIsmIkar xageRkam ¬rUbTI 16>9¦³ sRmab;krNIbnÞúkBRgayes μ IenAelIGgát; BC / yk ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

223

Edl 1I nig =2I m:Um:g;niclPaBrbs;ssr nigFñwm h nig =L km<s; nigRbEvgElVgrbs;eRKag m:Um:g;Bt;enAtMN B nig C KW

KwLMM CB 4

2−==

m:Um:g;viC¢manGtibrmaenAkNþalElVg BMwLBC +=8

2

kmøaMgRbtikmμtamTisedkenARtg;cMNuc A KW DBA HhMH == / kmøaMgRbtikmμtamTisQrenARtg;cMNuc A KW DA VwLV == 2/ sRmab;bnÞúkBRgayes μ IenAelIEtBak;kNþalFñwm BC ¬rUbTI 16>9 b¦



K

wLMM CB 8

2−==

h

MHH BDA ==

8/3wLVA = nig 8/wLVD =

16>4> 2> cugbgáb;BIr (Two Fixed Ends) kmøaMgenAkñúgGgát;rbs; portal frames Edlmancugbgáb;BIrGacRtUv)anKNnaedayeRbIsmIkar xageRkam ¬rUbTI 16>10¦³ sRmab;krNIbnÞúkBRgayes μ IenAelIGgát; BC / yk ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

21 2

K

wLMM CB 4

2−==



2

BDA

MMM ==

BMwLM +=8

)midspan(2

2

3 ADA

MHH == nig 2

wLVV DA == sRmab;bnÞúkBRgayes μ IenAelIEtBak;kNþalFñwm BC ⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

Lh

IIK

1

22 61

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

21

2

81

31

8 KKwLM A ⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

21

2

81

32

8 KKwLM B

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

21

2

81

32

8 KKwLM C ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

21

2

81

31

8 KKwLM D

hK

wLHH DA1

2 18

×==

DA VwLV −=2

nig ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

2411

8 KwLVD



16>5> eRKagTUeTA (General Frames)



rUbragcMbgrbs;eRKagKWtMNrwg EdlP¢ab;FñwmdMbUledk b¤eRTteTAnwgGgát;eRKOgbgÁúMEdlRTva. PaBCab;rvagGgát;nwgEbgEckm:Um:g;Bt;EdlmanCab;CamYynwgRbB½n§bnÞúkeTAGGát;eRKOgbgÁúMepSgeTot eTAtampleFobénPaBrwgRkajrbs;va. eRKagGacRtUv)ancat;cMNat;fñak;dUcxageRkam³

- eRKagsþaTickMNt; (statically determinate frame) ¬rUbTI 16>11 a¦ - eRKagsþaTicminkMNt; (statically indeterminate frame) ¬rUbTI 16>12¦ - eRKagsþaTicminkMNt; CamYynwgGgát;cMNg (statically indeterminate frame with tie) ¬rUbTI

16>13¦



16>6> karKNnasnøak;rbs;eRKag (Design of Frame Hinges)

RbePTd¾sMxan;énsnøak;EdleRbIenAkñúgeRKagebtugKW Mesnager hinges, Considère hinges

nig lead hinges. 16>6>1> Mesnager hinges

CaTUeTA kmøaMgEdlmanGMeBIenAelIsnøak;KWkmøaMgedk H nigkmøaMgbBaÄr P . kmøaMgpÁÜbén kmøaMgTaMgBIr R RtUv)anbBa¢ÚneTAeCIgtagtamry³EdkExVg A nig B dUcEdl)anbgðajenAkñúgrUbTI 16>14. PaBeRTtrbs;r)ar A nig B eTAnwgG½kSedkERbRbYlBI o30 eTA o60 CamYynwgcm¶ay Gb,brma a ¬Edlvas;BIEpñkeRkameKrbs;eRKagssr¦ esμ Inwg D8 Edl D CaGgát;p©itrbs;Edk eRTt. cenøaH y rvageRKagssr nigEpñkxagelIrbs;eCIgtagERbRbYlcenøaHBI mm25 eTA '3.1 h Edl

'h Ca TTwgrbs;muxkat;ebtugenAnIv:Usnøak;. km<s;cenøaHsRmab;karGnuvtþn_ERbRbYlBI mm50 eTA mm100 . karvilrbs;cugeRKagRtUv)aneFVIeLIgedaysnøak; ehIyCaTUeTAcenøaHRtUv)anbMeBjeday

bituminous cork nigsmÖar³EdlmanlkçN³bt;EbnRsedogKña. Bitumen karBar cork kMu[xUceday sarkarb:HCamYydI. EdkExVg A nig B rgnUvkugRtaMgsgát;EdlminRtUvFMCag 3/1 énersIusþg;yal (yield strength) rbs;Edk yf eRkambnÞúkeFVIkar (service load) b¤ yf55.0 eRkambnÞúkemKuN



(factored load). kugRtaMgtUcRtUv)ansn μt;edaysarkarvilenAsnøak;cg;Bt;Edk nigegáItkugRtaMgBt;TI BIr (secondary flexural stresses). CaTUeTA eKcaM)ac;RtUvrkSakugRtaMgsgát;[tUclμmRbesIrCagKNna kugRtaMgTIBIr. RkLaépÞEdk A nig B RtUv)anKNnadUcxageRkam³

RkLaépÞmuxkat;Edk A ³ y

s fRA55.0

11 = ¬!^>!¦

RkLaépÞmuxkat;Edk B ³ y

s fRA55.0

22 = ¬!^>@¦

Edl 1R nig 2R CabgÁúMénkmøaMgpÁÜb R enAkñúgTisedAénEdkeRTt A nig B edayeRbIbnÞúkem KuN. CaTUeTA bgÁúMkmøaMg 1R nig 2R RtUv)anTTYledaysmIkarsþaTicxageRkam³

θθ sinsin 12 RRH =+ nig θsin12

HRR −= ¬!^># a¦ dUcKña ( ) uPRR =+ θcos21 dUcenH ⎥⎦

⎤⎢⎣⎡ −−=−=

θθθ sincoscos 121HRPRPR uu

⎥⎦⎤

⎢⎣⎡ +=

θθ sincos21

1HPR u ¬!^># b¦

Edksnøak;eRTtbBa¢ÚnkmøaMgrbs;vatamry³cMNgenAtamRbEvgEdkbgáb;eTAkñúgssreRKag nig eCIgtag. dUcenH EdkeRTtbeBa©jkmøaMgFak;ecjeRkA EdlRtUvTb;edayEdkcMNg. EdkcMNgRtUv)an dak;elIcm¶ay Da 8= ¬Ggát;p©itEdkEdlFMCageKkñúgcMeNam A nig B ¦ TaMgenAkñúgssr nigeCIg tag. kmøaMgFak;ecj (bursting force) GacRtUv)ankMNt;dUcxageRkam³

dHaPF u85.0

tan2

+= θ ¬!^>$¦ RbsinebIkarcUlrYmrbs;ebtugRtUv)anecal enaHRkLaépÞmuxkat;rbs;EdkcMNg stA EdlcaM)ac; Tb;kmøaMg F KW³

yyst f

FfFA

85.0==

φ ¬!^>%¦

kugRtaMgenAkñúgEdkcMNgk¾GacRtUv)ankMNt;dUcxageRkam³

yst

u

s fAab

dHaP

f 85.0)tie(005.0

85.0tan

2)tie( ≤+

+=

θ ¬!^>^¦

Edl =stA RkLépÞmuxkat;Edkkgkñúgcm¶ay Da 8= =d km<s;RbsiT§PaBrbs;muxkat;ssr



=b TTwgrbs;muxkat;ssr snøak;RbePTenHRtUv)aneRbIsRmab;kmøaMgl μm nigRtUv)ankMNt;edaycMnYnEdkeRTtGtibrma EdlGacRtUv)andak;enAkñúgTTwgssr.

16>6>2> Considère hinges PaBxusKñarvag Considère hinges nig Mesnager hinges KWfakmøaMgEkg uP RtUv)ansnμt;fa vaRtUv)anbBa¢ÚneTAeCIgtagedaykUnssrEdkkgv½NÐ (spirally reinforced short columns) mYyb¤eRcIn Edldak;bBa©ÚleTAkñúgeCIgtag b:uEnþkmøaMgedk H RtUv)ansnμt;Tb;edayEdkeRTt A nig B ¬rUbTI !^>%¦. lT§PaBRTbnÞúkrbs;kUnssrEdkkgvNÐ½GacRtUv)ankMNt;edayeRbIsmIkar !^>& edayecalem KuN 85.0 sRmab;cMNakp©itGb,brma. ( )[ ]yststgcnu fAAAfPP +−== '85.070.0φ ¬!^>&¦



Edl gA CaRkLaépÞmuxkat;rbs;muxkat;snøak;ebtug b¤ 'bh / nig stA CaRkLaépÞmuxkat;Edk beNþayenAkñúgEdkkgv½NÐ. EdkcMNgRtUv)andak;enAkñúgssrrhUtdl;cm¶ayEdles μ InwgRCugEvgrbs; muxkat;ssr h .

16>6>3> Lead hinges

eBlxøH Lead hinges RtUv)aneRbIenAkñúgeRKagssrebtugGarem:. enAkñúgsnøak;RbePTenH CaTU eTA lead plate EdlmankRmas;BI mm20 eTA mm25 RtUv)anebIedIm,IbBa¢ÚnkmøaMgtamG½kS uP eTAeCIg tag. kmøaMgedk H RtUv)anTb;edayEdkbBaÄrEdldak;enARtg;G½kSrbs;ssr nigRtUv)andak;bBa©Úl eTAkñúgssr ¬rUbTI 16>16¦. enARtg;)atrbs;ssr kmøaMgEkg uP minRtUvFMCagersIusþg;Tb; ( )1'85.0 Af cφ ¬EdlkMNt;eday ACI Code, Section 10.15¦ Edl 65.0=φ nig '1 bhA = . RkLa

épÞmuxkat;EdkbBaÄrKW ys fHA 6.0/= Edl =H kmøaMgedkemKuN.



]TahrN_16>2³ salmYymanTMhM m122.25 × RtUv)anRKbedaykRmalebtugGarem:EdlRTeday portal frame Edl mansnøak;enATRm. Portal frame manKMlatBIG½kSeTAG½kS m6.3 ¬rUbTI 16>17¦. km<s;eRKagKW

m5.4 ehIyK μanssrenAkñúgsaleT. bnÞúkefrenAelIkRmalxNÐKW)anBIbnÞúkpÞal;bUknwg 2/6.3 mkN Edl)anmkBIkargarbegðIyrbs;dMbUl. bnÞúk efrenAelIkRmalxNÐKW 2/4 mkN . KNnaeRKagenA xagkñúgeday eRbI MPaf c 28' = nig MPaf y 400= sRmab;eRKag ehIymuxkat;ssrmanTTwg

mmb 400= . dMeNaHRsay³ karKNnaeRKageménGKarrYmmandUcxageRkam³

- KNnakRmalxNÐmYyTis - viPaK Portal frame - KNnaFñwmeRKagEdlbNþalmkBIm:Um:g; - KNnaFñwmeRKagEdlbNþalmkBIkmøaMgkat; - KNnassr - KNnasnøak; - KNnaeCIgtag



1> kRmalxNÐmYyTis³ kRmas;Gb,brmarbs;kRmalxNÐTI1KW 30/L edaysarcugmçagCab;

nigcugmçageTotminCab; ¬tarag B.6 enAkñúg]bsm<½n§ B¦. km<s;Gb,brma mm120

303600

== karKNnakRmalxNÐGnuvtþtamCMhanEdlmanenAkñúg]TahrN_9>5.

2> viPaK Portal frame enAxagkñúg³ a. bnÞúkenAelIkRmalxNÐKW

bnÞúkefrenAelIkRmalxNÐ 2/6.62512.06.3 mkN=×+= bnÞúkemKuNenAelIkRmalxNÐ 2/32.140.46.16.62.1 mkN=×+×=

b. kMNt;bnÞúkenAelIeRKag³ eRKagxagkñúgRTbnÞúkBIkRmalxNÐ m6.3 bEnßmBIelIbnÞúkpÞal;rbs; FñwmeRKag. sn μt;km<s;rbs;FñwmKW

mmL 50024/1200024/ == . edayeRbIkm<s;BIeRkam kRmalxNÐ mm400 enaHkm<s;srubrbs;FñwmKW mm520 . bnÞúkefrBIbnÞúkpÞal;rbs;Fñwm mkN /4254.0 2 =×= bnÞúkemKuNsrubenAelIeRKag mkN /352.5642.16.332.14 =×+×=



dUcenH mkNwu /5.56= c. kMNt;m:Um:g;niclPaBénmuxkat;Fñwm nigmuxkat;ssr. FñwmeFVIkarCalkçN³muxkat;GkSr T .

TTwgRbsiT§PaBrbs;kRmalxNÐEdleFVIskmμPaBCamYynwgFñwmKWCatémøtUcCageKén 4/1 én RbEvgElVg m34/12 == / mbh ws 32.24.012.01616 =+×=+ nig m6.3 . yk

mb 32.2= . TIRbCMuTm¶n;énmuxkat;BIsrésxagelIeKKW mmy 89.154

4004001202320320400400601202320

=×+×

××+××=

⎟⎟⎠

⎞⎜⎜⎝

⎛×++⎟

⎠⎞

⎜⎝⎛ ××+×= 22

423 11.165400

1240089.941202320120

122320)(beamIb

46109336 mm⋅= vaCakarGnuvtþTUeTAedayKitm:Um:g;niclPaBRbhak;RbEhlrbs;FñwmGkSr T esμ Inwg 2 dg énm:Um:g;niclPaBrbs;muxkat;ctuekaNEkgEdlmankm<s;srubCaplbUkrvagkm<s;RTnugFñwm nigkRmas;kRmalxNÐ³

463

10937412

5204002)beam( mmIb ⋅=×

×= sRmab;Fñwmxag m:Um:g;niclPaBRbhak;RbEhlKW 12/5.1 3bhI ×= . snμt;muxkat;ssresμ I mm500400× ¬EdlmanTTwgdUcTTwgFñwm¦

463

10416712

500400)column( mmIc ⋅=×

= d. KNnaemKuN K

68.4104167

450012000

1093742323 6

6=⎟

⎟⎠

⎞⎜⎜⎝

⎛

⋅+

⋅+=⎟⎟

⎠

⎞⎜⎜⎝

⎛×+=

c

bIh

LIK

tamrUbTI 16>17 nigsRmab;bnÞúkBRgayesμ I mkNwu /5.56= enAelIGgát; BC mkN

KLwMM u

CB .6.43468.44125.56

4

22−=

××

−=−== m:Um:g;viC¢manGtibrmaenAkNþalElVg BC es μ Inwg

mkNMLw Bu /4.5826.4348

125.568

22=−

×=+

kmøaMgRbtikmμedkenARtg;cMNuc A KW³ kN

hMHH B

DA 6.965.46.434====

kmøaMgRbtikmμbBaÄrenARtg; A KW³



column ofweight 2

+==LwVV u

DA kNVA 5.361255.45.04.0

2125.56

=×××+×

= düaRkamm:Um:g;Bt;RtUv)anbgðajenAkñúgrUbTI 16>17.

e. edIm,IBicarNa\T§iBl sideway enAelIeRKag bnÞúkGefrRtUv)andak;enAelIEtBak;kNþalFñwm BC ehIym:Um:g;RtUv)anKNnaenARtg;muxkat;eRKaHfñak;. krNIenHmineRKaHfñak;enAkñúg]Ta- hrN_enHeT.

f. kmøaMgkat;TTWgGtibrmaenAcugTaMgBIrrbs;Fñwm BC ekItmanenAeBlFñwmRtUv)andak;bnÞúkCa mYynwgbnÞúkemKuN uw b:uEnþkmøaMgkat;TTwgGtibrmaekItmanenAeBlEdlFñwmRtUv)andak; bnÞúkCamYynwgEtBak;kNþalbnÞúkGefr nigbnÞúkefreBj³

kNVu 3392

125.56)supportat ( =×

= kNLWVu 72.36

8126.347.1

8)midspanat ( 1 =×××==

g. kmøaMgtamG½kSenAkñúgssrnImYy²KW kNVV DA 5.361== h. ykcMNucm:Um:g;sUnüenAkñúgFñwm BC sßitenAcm¶ay x BI B / enaH

22

2xwxLwM uuB −=

2

5.562

125.566.4342xx

−×= b¤ 0384.15122 =+− xx mx 46.1= BITRm B

3> KNnaFñwm BC a. KNnamuxkat;eRKaHfñak;enAkNþalElVg. mkNM u .4.582= / TTwgRTnugKW mmbw 400=

TTwgsøabKW mmb 2320= nig mmd 43090520 =−= ¬sn μt;eRbIEdkBIrRsTab;¦. RtYtBinitüfaetImuxkat;eFVIkarCaragmuxkat;ctuekaNCamYynwgTTwgRbsiT§PaB

mmb 2320= b¤Gt;? sn μt; mma 25= enaH 2

69.3874

2254304009.0

104.582

)2

(mmadf

MAy

us =

⎟⎠⎞

⎜⎝⎛ −×

⋅=

−=φ

mmmmbf

fAa

c

ys 1202823202885.04009.3874

'85.0<=

×××

==



a snμt;mantémøRbhak;RbEhl a KNna. muxkat;eFVIkarCamuxkat;ragctuekaN dUcenH eRbIEdk 286DB . RtYtBinitü minb ¬edIm,Idak;EdkmYyCYr¦

mmmmb 400408801022811min >=+×+×= dak;EdkBIrCYr/ bgðajenAkñúgrUbTI 16>18.

b. KNnamuxkat;eRKaHfñak;enARtg; B ³ mkNM u .6.434= / mmb 400= nig 60520 −=d mm460= ¬sRmab;EdkmYyRsTab;¦. kRmalxNÐrgkarTaj dUcenHEdkRtUv)andak;enAkñúg

muxkat;EpñkxagelI. MPa

bdMR u

u 135.5460400106.434

2

6

2 =×

⋅==

018.00166.0 max =<= ρρ 24.30544604000166.0 mmAs =××=

eRbI 285DB kñúgmYyCYr. 4> KNnaFñwm BC edaysarkmøaMgkat;TTwg

a. muxkat;eRKaHfñak;enAcm¶ay d BIépÞssrCamYycm¶ayBIG½kSssr mm710460250 =+ dUcenH

298.9kN.71056.5-339d) distanceat ( =×=uV b. ersIusþg;kmøaMgkat;Edlpþl;edayebtug

kNdbfV wcc 7.1211046040028675.0'

63 =⋅××== −φφ

kmøaMgkat;Edlpþl;edayEdkRTnug (web reinforcement) KW kNVVV cus 2.1777.1219.298 =−=−= φφ

kNVs 3.23675.0

2.177==

c. eRCIserIsEdkkg 12DB nig 22 2264

122 mmAv =×=π

dUcenH mmV

dfAs

s

yv 176103.236

4604002263 =

⋅

××== yk mm175

d. KMlatGtibrmaénEdkkg 12DB KW mmds 230

2max == yk mm225

b¤ mmbfA

sw

yv 64640035.0400226

35.0max =××

==



RtYtBinitüsRmab;KMlatGtibrmaén 2d ³ dbfV wcs '

31

≤ b¤

kNVs 5.32410460400328 3 =⋅×≤ −

témø kNVs 5.3243.236 <= . dUcenHeRbI mms 225max = . kN

sdfA

mmsV yvs 8.18410

225460400226)220for (' 3

max =××

=== − kNV s 6.1388.18475.0' =×=φ

cm¶ayBIépÞssreTATItaMgEdl mms 225max = RtUv)aneRbIes μ Inwg m56.1 e. karBRgayEdkkg

EdkkgTImYymanKMlat mms 752/ = 7 EdkkgmanKMlat mmmm 1225175 = 19 EdkkgmanKMlat mmmm 4275225 = ¬srub mm5575 ¦ cm¶ayBIépÞssreTAG½kSrbs;Fñwmes μ Inwg mmmmmm 57502506000 =− . BRgayEdkkg dUcKñasRmab;Bak;kNþalFñwmEdlenAsl; nigdak;EdkkgmYyeTotenAkNþalElVg. cMnYnEdk kgsrubKW 55kg.

5> KNnamuxkat;ssrenAcMNuc B ³ mkNM u .6.434= / kNPu 339= / mmb 400= nig mmh 500=

a. snμt;eRkamGMeBIbnÞúkEdl[eRKagnwgminrgnUv sideway enaH\T§iBlrbs;PaBrlas; (slenderness ration) GacRtUv)anecal nigssrGacRtUv)anKNnaCassrxøIenAeBl

2

112344 M

MKLu −< ¬emIlEpñk 12>5¦

01 =M nig mkNM .6.4342 = yk 8.0=K ¬rUbTI 12>2¦ mLu 24.4

252.05.4 =−= nig mmr 1505003.0 =×= enaH

346.2215.024.48.0 <==

rKLu RbsinebI K RtUv)ansnμt;es μ Inwg 0.1 enaH

343.28 <=r

KLu dUcenH/ karKNnaGgát;CassrxøI.

b. dMeNIrkarKNnaRsedogKñanwg]TahrN_TI 11>16 nig 11>3.



cMNakp©it ( ) mPMe

u

u 282.1339

6.434===

vaCacMNakp©itFM nigvaRtUv)ansn μt;Camuxkat;enAkñúgtMbn; transition region/ 9.0<φ mmd 44060500 =−=

c. edaysar me 282.1= KWFMCag d q¶ayNas;/ kMNt;témøRbhak;RbEhl sA nig sA' EtBI uM nigbnÞab;mkRtYtBinitümuxkat;cugeRkayedaysþaTic Edl)anBnül;enAkñúg]TahrN_

11>3. sRmab; mkNM u .6.434= / mmb 400= / mmh 500= nig mmd 440= / ( ) MPabdMR uu 61.5440400/106.434/ 262 =⋅==

0183.0=ρ nig 28.3220 mmbdAs == ρ eRCIserIs 283DB nig 322DB ¬ 23456mmAs = ¦. eRCIserIs 210743/8.32203/' mmAA ss === nig 223DB ¬ 21140' mmA s = ¦ ¬rUbTI 16>18¦. enAeBlcMNakp©it e mantémøFM/ vaCakarGnuvtþFm μta 3/' ss AA = b¤ 2/sA CMnYs[ ss AA '= .

d. RtYtBinitülT§PaBénmuxkat;cugeRkayedayeRbI 23456mmAs = nig 21140' mmA s = Rsedognwg]TahrN_ 11>3 GaRs½yeTAtamCMhanxageRkam³ i. TCCP scn −+=

aaabfC cc 95204002885.0'85.0 =××== ( ) ( ) kNffAC csss 4288682885.04001140'85.0'' =×−=−=

kNfAT ys 13824004003456 =×== 953532952013824004288689520 −=−+= aaPn (I)

ii. Kitm:Um:g;eFobRtg; sA ³ ( )⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= '

2'1 ddCadCe

P scn

"' dee += Edl "d sßitenAcm¶ay sA eTATIRbCMuTm¶n;énmuxkat;. TIRbCMuTm¶n;ekItman enAcm¶ay mm68.276 BIsréssgát;xageRkAbMput nig mmxdd 32.163" =−=

mme 32.144532.1631282' =+= ( )⎥

⎦

⎤⎢⎣

⎡−+⎟

⎠⎞

⎜⎝⎛ −= 60440428868

24409520

32.14451 aaPn

1127572.28983.3 2 ++−= aa (II)



iii. KNnasmIkar I nig II eKTTYl)an mma 150= nig kNPn 5.474= . epÞógpÞat; ( ) ys fcdcf ≤−= /'600' / mmac 47.17685.0/ == / enaHeyIgTTYl)an

( ) MPaf s 39647.176/6047.176600' =−= EdlmantémøEk,r MPa400 dUc Edl)ansn μt;kñúgkarKNna. eRCIserIsEdkkg 10DB EdlmanKMlat mm400 .

iv. epÞótpÞat; φ ³ mmdt 440= 0045.0003.0

47.17647.176440003.0 =⎟

⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

=c

cdttε

( ) 858.03

250002.065.0 =⎟⎠⎞

⎜⎝⎛−+= tεφ

kNkNPn 3394075.474858.0 >=×=φ muxkat;RKb;RKan;.

6> epÞógpÞat;muxkat;ssrenAkm<s; m25.2 ¬Bak;kNþal¦BI A . mkNM u .3.2172/6.434 == kNPu 25.35025.11339 =+=

eRbIEdk 283DBAs = nig 223' DBA s = . tamviFIedaHRsayRsedogKñakñúgCMhan 5> kNkNPn 25.3508.632 >=φ ¬Edk 32DB Gacpþac;)an EtRtUvBnøÚtRbEvgbgáb;BIeRkam

Bak;kNþalkm<s;ssr¦. 7> KNnasnøak;enARtg;cMNuc A ³ 0=uM / kNH 6.96= / kNPu 5.361=

a. eRCIserIssnøak; Mesnager hinge . edayeRbIsmIkar 16.3 a nig 16.3b/ kNR 3.3051 = nig kNR 1.1122 = ¬eyagtamrUbTI 16>19 CamYynwg o30=θ ¦

211 7.1387

40055.0305300

55.0mm

fRA

ys =

×==

eRCIserIs 253DB ¬ 26.1472 mmAs = ¦ 22

2 5.50940055.0

11210055.0

mmf

RAy

s =×

==

eRCIserIs 222DB ¬ 2760mmAs = ¦. teRmobEdkExVgedaydak; 25DB nigbnÞab;mkdak; 22DB dUcEdlbgðajenAkñúgrUbTI 16>19 ¬b¤eRbI 255DB ¦



b. EdkcMNgTTwgKYrdak;tambeNþaycm¶ay mmDa 2002588 =×== enAkñúgssr nigeCIg

tag. kmøaMgFak;KW

dHaPF u85.0

tan2

+= θ o30=θ / mmd 440= nig mma 200=



kNF o 15644085.02006.9630tan

25.361

=××

+= RkLaépÞmuxkat;EdkcMNg 28.458

40085.0156000 mm=

×=

RbsinebIEdkcMNgbiTCit 10DB ¬eCIgBIr¦ RtUv)anerIs enaHRkLaépÞmuxkat;KW 2157mm . cMnYnEdkcMNgKW 9.2

1578.458= . eRbIEdkcMNg 3kgEdlmanKMlat mm1002/200 =

dUcbgðajenAkñúgrUbTI 16>19. 8> KNnaeCIgtag³ RbsinebIkm<s;eCIgtagRtUv)ansnμt;es μ I 'h enaHkmøaMgEdlmanGMeBIelIeCIgtag

CakmøaMgEkg P nigm:Um:g; '/ hHM = . sMBaFdIRtUv)anKNnaBIsmIkar !#>!$ BIemeronTI 13³ pressure soil allowable≤±+=

IMc

APq

viFIsaRsþKNnaeCIgtagmanlkçN³RsedogKñaeTAnwg]TahrN_TI 13>7.

16>7> esckþIepþImBIkarKNnasßanPaBkMNt; (Introduction to Limit Design)

16>7>1> lkμN³TUeTA (General)



karKNnasßanPaBkMNt;éneRKOgbgÁúMmanbICMhandUcxageRkam³ - karkMNt;bnÞúkKNnaemKuN EdlTTYledayKuNbnÞúkefr nigbnÞúkGefrCamYynwgemKuNbnÞúk.

ACI Code TTYlnUvemKuNdUcEdl[enAkñúgemeronTI3. - viPaKeKOgbgÁúMeRkamGMeBIbnÞúkemKuN (ultimate or factor load) edIm,IkMNt;m:Um:g;emKuN nig

kMmøaMgemKuNenAeBlEdleKOgbgÁúMdYl b¤)ak;. viFIénkarviPaKenHRtUv)aneRbIsRmab;karKNna eRKOgbgÁúMEdk EtsRmab;eRKOgbgÁúMebtugGarem: ACI Code min)anTTYlykviFIenHTaMgGs;eT edaysarkarxVHPaBsVit (ductility) rbs;Ggát;ebtugGarem:. ACI Code GnuBaØatEtEpñkénkar EbgEckeLIgvijnUvm:Um:g;edayEpñk (partial redistribution of moment) enAkñúgrcnasm<½n§eday QrelIPaKryEdl)anmkBIkarBiesaFn_ EdlnwgBnül;kñúgemeronenH.

- KNnaGgát;nImYy²éneRKOgbgÁúMedaysnμt;fava)ak;edaym:Um:g;emKuN nigkmøaMgemKuNEdl)an mkBIkarviPaKeRKOgbgÁúM. viFIenHRtUv)aneRbIR)as;CaTUeTAsRmab;karKNnaebtugGarem: ehIy ACI Code GnuBaØatnUvkareRbIR)as;viFIKNnalT§PaBRTRTg; (strength design method)

dUcEdl)an Bnül;kñúgemeronknøgmk.

16>7> 2> KMniténkarKNnasßanPaBkMNt; (Limit Design Concept) karKNnasßanPaBkMNt;enAknúgebtugGarem:sMedAelIkarEbgEckm:Um:g;eLIgvijEdlekItman enAelIeRKOgbgÁúMTaMgmUl dUcEdlEdkBRgwgenAmuxkat;eRKaHfñak;eFVIkardl; yield strength rbs;va. ersIusþg;cugeRkay (ultimate strength) rbs;eRKOgbgÁúMekIneLIgenAeBlmuxkat;rbs;vaekIneLIg. eTaH bICakaryal (yielding) rbs;EdkeFVI[manPaBdabFM EdlKYrEteCosvageRkambnÞúkeFVIkar (service

load) eRKOgbgÁúMsþaTicminkMNt;mindYlb¤)ak;enAeBlEdlEdkBRgwgénmuxkat;TImYyyal. elIsBIenH ersIusþg;EdlbMrugTuky:ageRcInsßitenAcenøaHkaryaldMbUg nigkar)ak;rbs;eRKOgbgÁúM. kñúgkarKNnaeRKOgbgÁúMEdk BakükarKNna)øasÞic (plastic design) RtUv)aneRbIedIm,Ibgðajkar pøas;bþÚrkñúgkarEbgEckm:Um:g;enAkñúgeRKOgbgÁúMdUcCa steel fiber ¬enARtg;muxkat;eRKaHfñak;¦ rgkugRtaMg rhUtdl;ersIsþg;yal. karekIneLIgnUvkugRtaMgtamkm<s;rbs;muxkat;EdkeRkamkarekIneLIgrbs;bnÞúk RtUv)anbgðajenAkñúgrUbTI 16>20. Portal frame RtUv)anBiesaFn_edIm,IGegátlT§PaBRTRTg;karvil rbs;snøak;)øasÞicrbs;ebtugGarem:. b:uEnþ ACI Code tRmUv[mankarsikSaRsavRCavCaeRcIneTotmun nwgTTYlykkarKNnasßanPaBkMNt;.



16>7> 3> eKalkarN_énsnøak;)aøsÞic (Plastic Hinge Concept) ExSkMeNag φ rbs;Ggát;ekIneLIgCamYynwgm:Um:g;Bt; M . sRmab;FñwmebtugEdlmanbrmaN Edktic düaRkamm:Um:g;-ExSkMeNag nigExSekagbnÞúk-PaBdab RtUv)anbgðajenAkñúgrUbTI 16>21. Fñwm EdlmanbrimaNEdk balanced nigbrimaNEdkeRcInminRtUv)anGnuBaØat[eRbIeday ACI Code eT edaysarva)ak;edaykarpÞúHEbkebtug nigbgðajnUvRbeLaHExSkMeNagtUcenAeBlm:Um:g;emKuN ¬rUbTI 16>22¦.

EpñksMxan;rbs;düaRkamExSrkMeNag-m:Um:g;enAkñúgrUbTI 16>21 KWsßitenAcenøaHcMNuc B nig C Edlm:Um:g; uM rkSatémøefrsRmab;RbeLaHéntémø φ d¾FM. kñúgkarviPaKsßanPaBkMNt; ExSekagExSkM eNag-m:Um:g;GacRtUv)ansnμt;manTRmg; idealized form dUcbgðajenAkñúgrUbTI 16>23 EdlExSkM eNag φ enAcenøaH B nig C RtUv)ansnμt;faefr edIm,IbegáItrUbragsnøak;)aøsÞic. edaysarebtugCa smÖar³RsYy CaTUeTAeK)anKitnUvEdnkMNt;edal[Ggát;)ak;enARtg;ExSkMeNagGtibrmaRtg; C . elak Cranston )anbgðajfaeRKagebtugGarem:EdlKNnaCaTUeTA GacmanlT§PaBTb;nwgkar vil)anFM ehIyExSkMeNagGtibrmaenARtg;cMNuc C nwgminGaceTAdl; Tal;EteRKag)ak;sin. dUcenH enAeBlGgát;RTm:Um:g;es μ Inwgm:Um:g;emKuN uM rbs;va ExSkMeNagbnþekIneLIgcenøaHcMNuc B nig C edayK μankarERbRbYlm:Um:g; edIm,IbegáItsnøak;)aøsÞic. karekIneLIgénExSkMeNagGnuBaØat[EpñkdéT eToténeRKOgbgÁúMsþaTicminkMNt;edIm,ITTYlbnÞúkbEnßm.





16>8> emkanicénkar)ak; (The Collapse Mechanism)

kñúgkarKNnasßanPaBkMNt; Ggát;ebtugGarem:GaceTAdl;ersIusþg;cugeRkay (ultimate

strength) enAeBlvaCitnwgrlM b¤)ak;. Ggát;dYlrlMenAeBlEdlcMnYnsnøak;)aøsÞicRKb;RKan;bMElgva [cUleTACaFñwmemkanicénkar)ak;. cMnYn caM)ac;énsnøak;)aøsÞic n GaRs½yeTAnwgdWeRk redundancy r rbs;eRKOgbgÁúM. TMnak;TMngrvag n nig r edIm,IbegáItFñwmemkanicénkar)ak;KW rn +=1 ]TahrN_ enAkñúgFñwmTRmsamBaØKμanGBaØtielIseT Edl 0=r . dUcenH FñwmkøayeTACaK μansßirPaB ehIy)ak;enAeBlEdlsnøak;)aøsÞicmYyekItmanenARtg;muxkat;énm:Um:g;Gtibrma dUcbgðajenAkñúgrUbTI 16>24 a. karGnuvtþn_eTAelIFñwm nigeRKagk¾RtUv)anbgðajenAkñúgrUbTI 16>24.

16>9> eKalkarN_énkarKNnasßanPaBkMNt; (Principles of Limit Design)

eRkambnÞúkeFVIkar (working load) karEbgEckm:Um:g;enAkñúgeRKagsþaTicminkMNt;KWWWQrelIRTwsþI eGLasÞic ehIyeRKOgbgÁúMTaMgmUlenAEtrkSaenAkñúgEdneGLasÞic. enAkñúgkarKNnasßanPaBkMNt; enA eBlEdlvaeTAdl;emkanicénkarrlM karEbgEckm:Um:g;enAeBl)ak;edaybnÞúkemKuN xusKñaBIkarEbg EckedayQrelIRTwsþIeGLasÞic. karxusKñaenHbgðaj[eXIjnUvkarEbgEckm:Um:g;eLIgvij (moment

redistribution). sRmab;karKNnasßanPaBkMNt;mann½y lkçxNÐ 4 RtUvEteKarBdac;xat

- lkçxNÐemkanicénkar)ak; (Mechanism condition)³ snøak;)aøsÞicRKb;RKan;RtUv)anbegáIteLIg edIm,IbMElgeRKOgbgÁúMTaMgmUl b¤EpñkxøHrbs;eRKOgbgÁúMeTACaGgát;emkanicénkar)ak;.

- lkçxNÐlMnwg (Equilibrium condition)³ karEbgEckm:Um:g;RtUvEtmanlMnwgCamYynwgbnÞúkEdl Gnuvtþ.

- lkçxNÐyal (Yield condition)³ m:Um:g;emKuNminRtUvelIsersIusþg;m:Um:g;enARKb;TItaMgrbs; eRKOgbgÁúM.

- lkçxNÐrgVil (Rotation condition)³ snøak;)aøsÞicRtUvEtmanlT§PaBTb;rgVil (rotation

capacity)RKb;RKan; edIm,IGnuBaØatkarekItmanFñwmemkanicénkar)ak;.



manEtlkçxNÐbIdMbUgeTEdlGnuvtþkñúgkarKNna)aøsÞic edaysarlT§PaBTb;rgVilmanenAkñúg smÖar³sVitdUcCaEdkrYceTAehIy. lkçxNÐTIbYnbegáInEdnkMNt;bEnßmeTAelIkarKNnakMNt;énGgát;eb tugGarem:edayeRbobeFobCamYykarKNna)aøsÞic (plastic design).



16>10> Ednx<s; nigEdnTabénemKuNbnÞúk (Upper and Lower Bounds of Load Factors)

eRKOgbgÁúMEdlCitdYlrlMRtUvEtmancMnYnsnøak;)aøsÞicRKb;RKan;edIm,IbMElgvaeTACaGgát;emkanic énkar)ak;. sRmab;TItaMgNamYyénsnøak;)aøsÞicenAelIeRKOgbgÁúM bnÞúkEdleFVI[rlMGacRtUv)anKNna EdlGacFMCag b¤es μ IbnÞúkBit. edaysarbnÞúkKNnaminGacFMCagbnÞúkEdleFVI[rlMBitsRmab;eRKOg bgÁúM enaHviFIsaRsþKNnabgðajnUvEdnsIueNm:aTic b¤Edkx<s; (upper or kinematic bound) rbs;bnÞúk EdleFVI[rlMBit. dUcenHRKb;Ggát;emkanicénkarrlMEdlGacekItmanRtUv)aneFVIkarGegát uM EdltUc CageK nwgekIteLIgedaybnÞúkBit. elak Horne )anBnül;Ednx<s;edaysnμt;eRKOgbgÁúMCaGgát;emka nicénkar)ak; nigbnÞab;mkKNnakm μnþxageRkA eW EdleFVIedaybnÞúkxageRkA nigkmμnþkñúg iW EdleFVI enAsnøak;)aøsÞic. RbsinebI ie WW = enaHbnÞúkEdlGnuvtþFMCag b¤esμ IbnÞúkEdleFVI[)ak;. RbsinebIdüaRkamm:Um:g;enARtg;cMNucNamYyRtUv)anbegáItedIm,IbRgÁb;lMnwgsþaTiceRkamGMeBIbnÞúkGnuvtþenAeBl)ak; enaHbnÞúkEdlGnuvtþtUcCag b¤esμ IbnÞúkEdleFVI[)ak;Bit. sRmab;düaRkamm:Um:g; epSgeTot eKGacTTYlbnÞúkemKuNepSgeTot. témøEdlFMCagénEdntUc b¤EdnsþaTic (lower or static

bound) RtUv)anTTYlenAeBlm:Um:g;enAmuxkat;CaeRcInsRmab;düaRkamm:Um:g;Edlsn μt;xiteTACitm:Um:g; EdleFVI[rlM. elak Horne )anBnül;EdnTabedaysn μt;karEbgEckm:Um:g;xusKñaedIm,ITTYlnUveRKOg bgÁúMEdlsßitenAkñúgsßanPaBlMnwgCamYybnÞúkxageRkA nigeKarBlkçxNÐyalenAelIeRKOgbgÁúMTaMgmUl. kñúgkrNIenH bnÞúkxageRkAtUcCag b¤esμ IbnÞúkEdleFVI[rlM.

16>11> karviPaKsßanPaBkMNt; (Limit Analysis)

sRmab;karviPaKedaydMeNIrkarKNnasßanPaBkMNt; viFIBIrGacRtUv)aneRbI viFIkmμnþCak;Esþg (virtual work method) nigviFIlMnwg (equilibrium method). sRmab;viFI virtual work km μnþRtUv)an eFVI edaybnÞúkemKuN uP ¬b¤ uw ¦ edIm,IbegáItPaBdab virtual deflection Edl[ Δ RtUv)andak; [esμ IkmμnþEdlRsUbykenAsnøak;)aøsÞic. km μnþxageRkAEdleFVIedaybnÞúkKW ( )∑ Δ= ue wW b¤

( )∑ ΔuP . kmμnþEdlRsUbykedaysnøak;)aøsÞicKWkmμnþ ( )∑== θui MW .

]TahrN_16>3 FñwmEdlbgðajenAkñúgrUbTI 16>25 RTnUvbnÞúkcMcMNucenAkNþalElVg. KNnam:Um:g;EdleFVI[)ak;enA muxkat;eRKaHfñak;.



dMeNaHRsay

1> FñwmCaGgát;sþaTicminkMNt; 1 dWeRk ehIycMnYnsnøak;EdlRtUvkaredIm,IbMElgFñwmeTACaFñwm emkanicénkar)ak;KW 211 =+=n snøak;)aøsÞic enARtg;cMNuc A nig C . snøak;)aøsÞicTI mYyekItmanenARtg;cMNuc A ehIy FñwmeFVIkarCaFñwmTRmsamBaØrhUtdl;vaxiteTArk emkanicénkar)ak;.



2> RbsinebImMurgVil θ ekItmanenAsnøak;)aøsÞicenAcugbgáb; A enaHmMurgVilenARtg;cMNuc θ2=C . PaBdabenARtg;cMNuc C eRkambnÞúkKW ( )θ2/L ¬rUbTI 16>25¦.

∑ ⎟⎠⎞

⎜⎝⎛=Δ==

2 workexternal θLPPW uue

( ) ( )θθθ 2 workinternal 21 uuui MMMW +=== ∑ RbsinebImuxkat;BIrenARtg; A nig C manTMhM nigbrimaNEdkdUcKña enaH

uuu MMM == 21 nig θui MW 3= . eday[ ie WW = uuuu MLPMM 3

22 21 ==+ nig

6LP

M uu =

]TahrN_16>4 KNnam:Um:g;EdleFVI[)ak;enAmuxkat;eRKaHfñak;sRmab;FñwmEdlbgðajenAkñúgrUbTI 16>26 EdlbNþal edaybnÞúkBRgayesμ I uw . dMeNaHRsay

1> cMnYcsnøak;)aøsÞicKW 2 . 2> sRmab;PaBdabenARtg; 0.1=C mMurgVilenARtg;cMNuc A aA /1=θ nig bB /1=θ ehIy

abL

abba

BAc =+

=+= θθθ

3> kmμnþxageRkAKW ∑ =⎟⎠⎞

⎜⎝⎛ ×

=Δ=22

1 LwLwwW uuue

kmμnþxagkñúgKW ∑ +== CuAuui MMMW θθθ 21 ⎟

⎠⎞

⎜⎝⎛ ++=

baM

aM uu

11121

dak;[ eW nig iW ⎟⎠⎞

⎜⎝⎛

−++=

aLM

aM

aM

Lw uuu

u2212 ¬!^>(¦

RbsinebIm:Um:g;TaMgsgçagesμ IKña enaH ( ) ( )⎥⎦

⎤⎢⎣

⎡−−

=⎥⎦

⎤⎢⎣

⎡−

+=aLaaL

LM

aLaLM

w uuu

22122 ¬!^>!0¦





4> edIm,IKNnaTItaMgsnøak;)aøsÞicenARtg; C EdlbegáIttémøGb,brmaénbnÞúkEdleFIV[)ak; uw eFVIedrIevsmIkarTI !^>( eFobnwg a nigdak;[vaesμ IsUnü³

0=a

wuδδ

( )02

22

22

1 =⎟⎟⎠

⎞⎜⎜⎝

⎛

−−+−

aLM

aM

aM uuu

RbsinebI uuu MMM == 21 enaH ( )22

12aLa −

=

b¤ ( ) LLa 586.022 =−= BIsmIkar !^>!0 bnÞúkEdleFVI[)ak;KW ( )2/66.11 LMw uu = nigm:Um:g;EdleFVI[)ak; KW

20858.0 LwM uu = . RbtikmμenAcMNuc A KW Lwu586.0 nig Rbtikm μenARtg;cMNuc B KW Lwu414.0 . enAkñúgviFIlMnwg lMnwgrbs;Fñwm b¤rbs;Ggát;dac;edayELkrbs;FñwmRtUv)ansikSaeRkambnÞúk EdlbgðajenAeBl)ak;. edIm,IbgðajkarviPaKedayviFIenH ]TahrN_BIxagmuxTaMgBIr RtUv)aneFVIeLIgvijenATIenH.

]TahrN_16>5 sRmab;FñwmEdlbgðajenAkñúgrUbTI 16>25 kMNt;m:Um:g;EdleFVI[)ak;edayeRbIviFIlMnwg. dMeNaHRsay snøak;)aøsÞicBIrRtUv)anbegáItenAcMNuc A nigC . edayeyagtamrUbTI 16>25 e kmøaMgRbtikmμenAcMNuc A KW ( ) ( )LMP uu /2/ 1+ nig Rbtikm μenAcMNuc B KW ( ) ( )LMP uu /2/ 1− KitlMnwgénFñwm BC nigKitm:Um:g;eFobcMNuc C /

21

22 uuu ML

LMP

=⎟⎠⎞

⎜⎝⎛⎟⎠⎞

⎜⎝⎛ −

22 21

LPMM uuu =+ EdlRsedogKñanwgsmIkar !^>#. enAeBl uuu MMM == 21 / enaH

23 LPM uu = b¤

2LPM uu =



]TahrN_16>6 KNnam:Um:g;EdleFVI[)ak; (collapse moment) sRmab;FñwmEdlbgðajenAkñúgrUbTI 16>26 edayviFI lMnwg. dMeNaHRsay

1> snøak;)aøsÞicBIrRtUv)anbegáItenARtg;cMNuc A nig C . eyagtamrUbTI 16>26 d / kmøaMgRbtikmμenA Rtg; ( ) ( )LMLwA uu /2/ 1+= nigkmøaMgRbtikmμenARtg;

( ) ( )LMLwB uu /2/ 1−= . bnÞúkenAelI BC KW bwu EdlmanGMeBIenA 2/b BI B Edl aLb −= . edayKitlMnwgénkMNat; BC nigKitm:Um:g; eFobcMNuc C /

( ) 21

22 uuu

u MbbwbL

MLw =−⎟⎠⎞

⎜⎝⎛ −

RbsinebI uuu MMM == 21 enaH ( ) ( )aL

LM

LbMbLbw u

uu −=+=− 2)1(2

( )( )aLa

aLLM

w uu −

−×=

22

EdlRsedogKñanwgsmIkar !^>$ ( )( )aL

aLaLwM u

u −−

×=22

2> TItaMg a GacRtUv)ankMNt;dUcBImun Edl La 586.0= / 20858.0 LwM uu = nig ( )2/66.11 LMw uu = .

16>12> mMurgVilrbs;snøak;)aøsÞic (Rotation of Plastic Hinges)

16>12>1> RbEvgsnøak;)aøsÞic (Plastic Hinge Length) karsnμt;rbs;RTwsþIeBlfamMurgVilminEmneGLasÞic (inelastic rotation) énebtugekItmanenA

cMNucm:Um:g;GtibrmaenAeBlEdlEpñkdéTeTotrbs;Ggát;eFVIkarCalkçN³eGLasÞic. tamBit mMurgVil )aøsÞic (plastic rotation) ekItmanenATaMgsgçagénmuxkat;m:Um:g;GtibrmaelIRbEvgkMNt;mYy. RbEvg enHRtUv)aneK[eQ μaHfa RbEvgsnøak;)aøsÞic pl . RbEvgsnøak;)aøsÞic pl CaGnuKmn_eTAnwgkm<s; RbsiT§PaB d nigcm¶ayBImuxkat;énm:Um:g;x<s;bMputeTAcMNucm:Um:g;sUnü (contra-flexure) .



eyagtamrUbTI 16>27 a RbEvg 2/pl tag[RbEvgsnøak;)aøsÞicenAelIEpñkmçagénG½kS rbs; TRm. uM nig uφ Cam:Um:g;emKuN nigkMeNagemKuNenARtg;muxkat;eRKaHfñak; Edl yM nig yφ Ca m:Um:g; nigkMeNagenARtg;cMNucyaldMbUg (first yield). kMeNag)aøsÞicenARtg;muxkat;eRKaHfñak; pφ esμ I ( )yu φφ − ehIylT§PaBTb;rgVilesμ Inwg ( )pplφ .

RbEvgsnμt;rbs;snøak;)aøsÞicRtUv)ansnμt;famanRbEvgRbEhlkm<s;RbsiT§PaB. Corley )anesñInUvsmIkarxageRkamsRmab;RbEvgsmmUlénsnøak;)aøsÞic ⎟

⎠⎞

⎜⎝⎛+=

dzddl p 2.05.0 ¬!^>!!¦

Edl =z cm¶ayénmuxkat;eRKaHfñak;eTAcMNucm:Um:g;sUnü nig =d km<s;RbsiT§PaBrbs;muxkat;. Mattock )anesñInUvTRmg;d¾smBaØ zdl p 05.05.0 += ¬!^>!@¦



karBiesaFCaeRcInenAelIebtugGarem:Cab;bgðajfa pl GacRtUv)ansn μt;esμ Inwg d06.1 . vak¾)an bgðajEdrfaRbEvgénsnøak;)aøsÞicenAkñúgFñwmebtugGarem:Cab;EdlmanTMBk;enAxagcugekIneLIgCamYynwgnwgkarekIneLIgénbrimaNEdk fibers nigEdkemGaRs½ynwgsmIkarxageRkam³ ( )dl sp ρρ13.006.1 += ¬!^>!#¦ Edl =ρ PaKryEdkemenAkñúgmuxkat; nig =sρ PaKryén fibers EdkedaymaD/

2.10 ≤≤ sρ . ]TahrN_ RbsinebI %1=ρ nig %8.0=sρ enaH dl p 164.1= . 16>12>2> emKuNEbgEckkMeNag (Curvature Distribution Factor )



emKuNsMxan;mYyeTotEdlTak;TgkñúgkarKNnamMurgVil)aøsÞicKWemKuNEbgEckkMeNag β . kM eNagtambeNþaysnøak;)aøsÞicERbRbYly:agFM ehIyenAkñúgkarKNnamMurgVilemKuNenHminRtUv)anKit EdleFVI[karKNnasnøak;)aøsÞicmantémøFM. eyagtamrUbTI 16>27 RkLaépÞqUt ABC tag[mMurgVil minEmneGLasÞicEdlGacekItmanenAsnøak;)aøsÞic b:uEnþRkLaépÞGt;qUt EBF tag[karcUlrYmén lkçN³eGLasÞicrbs;mMurgVilelIRbEvgrbs;Ggát;. RkLaépÞqUt ABC GacRtUv)ansnμt; esμ InwgplKuN rvag β nigRkLaépÞsrub ABCD enAkñúgRbEvgsnøak;)aøsÞic 2/pl EdlenAelIRCugmçag rbs;muxkat; eRKaHfñak;. emKuNEbgEckkMeNag β CapleFobénmMurgVil)aøsÞicBit pcθ elI plφ Edl φ CakMeNag nig pl CaRbEvgénsnøak;)aøsÞic. témø β sßitenAcenøaH 5.0 nig 6.0 . karBiesaF)anbgðajfa β GacRtUv)ansnμt;es μInwg 56.0 . enAeBlEdlEdk fibers EdlmanTMBk;cugRtUv)aneRbIenA kñúgFñwmebtug témø β fycuHGaRs½yeTAnwgsmIkarxageRkam³

sρβ 16.056.0 −= ¬!^>!$¦ Edl sρ CaPaKry fibers Edk/ %2.10 ≤≤ sρ . karfycuHénemKuNEbgEckkMeNagénebtugEdl eRbIEdk fibers min)anbgðajfalT§PaBTb;rgVilfycuHeT. kMeNag)aøsÞicrbs;ebtugEdleRbIEdk fibers EtgEtFMCagkMeNag)aøsÞicrbs;ebtugEdlmineRbIEdk fibers. rUbTI 16>28 bgðajBIkarEbgEckkM eNagtambeNþayRbEvgsnøak;)aøsÞic. RkLaépÞ 1ABC tag[mMurgVil)aøsÞicsRmab;ebtugEdlmin manEdk fibers/ 56.0=β b:uEnþRkLaépÞ 2ABC nig 3ABC tag[mMurgVil)aøsÞicsRmab;ebtugEdl manEdk fibers %8.0 nig %2.1 erogKña. 16>12>3> snÞsSn_énPaBsVit (Ductilty Index ) pleFobénkMeNagemKuNnigkMeNagyaldMbUgRtUv)aneK[eQμaHfasnÞsSn_énPaBsVit/

yu φφμ /= . snÞsSn_énPaBsVitrbs;ebtugGarem:ERbRbYlcenøaH 4 nig 6 . RbsinebIEdk fibers RtUv)aneRbIenAkñúgFñwmebtugGarem: enaHsnÞsSn_énPaBsVitekIneLIgtamsmIkarxageRkam³ ( )μρμ s8.30.1' += ¬!^>!%¦ Edl =μ pleFobkMeNagemKuNelIkMeNagyaldMbUg ='μ snÞsSn_énPaBsViténebtugEdlmanEdk fibers =sρ PaKryénEdk fibers edaymaD/ %2.10 ≤≤ sρ



16>12>4> mMurgVilEdlRtUvkar (Required Rotation) eKRtUvkarmMurgVilénsnøak;)aøsÞicenAeRKOgbgÁúMminkMNt;ebtugGarem:edIm,IGnuBaØat[snøak;)aøsÞic ekItman ehIyeRKOgbgÁúMEdlxiteTArkemkanicénkar)ak;GacRtUv)ankMNt;eday slope deflection BI smIkarxageRkam. sRmab;kMNat; AB cenøaHsnøak;)aøsÞicNIr mMurgVilenARtg; A KW

( ) ( )[ ]FBBFAAc

A MMMMIE

L−+−= 2

6θ ¬!^>!^¦

Edl AM nig =BM m:Um:g;emKuNenARtg;cMNuc A nig B erogKña FAM nig =FBM m:Um:g;bgáb;cugeGLasÞicenARtg;cMNuc A nig B =CE m:UDuleGLasÞicrbs;ebtug cf '4730= =I m:Um:g;niclPaBénmuxkat;eRbH ¬emeronTI 5¦ 16>12>5> lT§PaBTb;mMurgVil (Rotation Capacity Provided) snøak;)aøsÞicrgkarTajKMrUenARtg;muxkat;TRm nigmuxkat;kNþalElVgéneRKagRtUv)anbgðajenA kñúgrUbTI 16>29.lT§PaBTb;mMurgVilGaRs½yCacMbgeTAnwg³

- Ultimate strain capacity rbs;ebtug c'ε EdlGacRtUv)ansnμt;esμ I 003.0 b¤ 0035.0 . - RbEvg pl EdlenAelIRbEvgenHsnøak;)aøsÞiceFVIkardl;yal.

RbEvgenHRtUv)ansnμt;mantémøRbEhlkm<s;RbsiT§PaBénmuxkat;Edlsnøak;)aøsÞicekItman ¬ dl p = ¦

- km<s;rbs;bøúksgát; c enAkñúgebtugenAeBl)ak;enARtg;muxkat;énsnøak;)aøsÞic. mMurgVil θ énsnøak;)aøsÞicRtUv)anKNnatamsmIkarxageRkam³

cI ppεθ = ¬!^>!&¦

Edl pε KWCakMeNInén strain enAkñúgebtugEdlvas;BI initial yielding rbs;EdkenAkñúgmuxkat; ¬rUbTI 16>29 c ¦³

11 0035.0' cccp εεεε −=−= RbsinebI dl p = ehIypleFob dc / es μ Inwg 5.0≤λ /

( )λ

ελ

εθ 11 0035.00035.0 cc

dd −=

−=



BIRtIekaNbERmbRmYlrageFob (strain triangle) rUbTI 16>29/

⎟⎠⎞

⎜⎝⎛−

=⎟⎠⎞

⎜⎝⎛

−=⎟

⎠⎞

⎜⎝⎛

−=

λλ

λλεε

11s

y

s

yyc E

fdd

dEf

cdc

Edl =yf ersIusþg;yalrbs;Edk nig =sE m:UduleGLasÞicrbs;Edk MPa5102 ⋅= . dUcenH

( )λλλε

λθ

−−=−=

10035.00035.0 1

s

ycE

f ¬!^>!*¦

sRmab;Edk MPaf y 280= nigedayeRbItémøGtibrmaén 50.0=λ enaH rad3

5min 102.4)5.01(102

2805.0

0035.0 −⋅=−×⋅

−=θ

sRmab;Edk MPaf y 400= nig 44.0max =λ enaH rad3

5min 1038.4)44.01(102

28044.0

0035.0 −⋅=−×⋅

−=θ



minθ Edl)anKNnaenATIenH)anBIEtmçag ehIymMurgVilGnuBaØatsrubenARtg;snøk;)aøsÞicesμ Inwg min2θ b¤ θ2 . λ BitGacRtUv)anKNnadUcxageRkam

eKman ca 1β= nig 85.01 =β sRmab; MPaf c 28' ≤

( ) bf

fAacc

ys

'85.0 21==

β

5.0'72.0'72.0≤===

c

y

c

ys

ff

bdffA

dc ρ

λ ¬!^>!(¦

Edl bdAs /=ρ . eKnwgTTYl)an maxλ enAeBlEdleRbI maxρ . RbsinebIlT§PaBTb;rgVilminRKb;RKan; eKGacbegáInmuxkat; b¤kat;bnßyPaKryEdkedIm,I TTYl)an c tUc/ λ tUc nig θ FM. RbsinebIeKeRbIEdkkgvNÐ bERmbRmYlrageFobemKuNEdleFVI [EbkebtugnwgekIneLIgx<s;dl; 012.0 . sRmab;snøak;)aøsÞicsgát; ¬dUcenAkñúgssr¦

hl ppεθ = ¬!^>@0¦

Edl =h km<s;srubrbs;muxkat; nig =pl RbEvgEdl yielding ekItman. enAkñúgsnøak;sgát; pl ErbRbYlcenøaH h5.0 nig h . enAeBlebtugrgkugRtaMgemKuNdl; cf ' / 002.0=cε dUcenH 002.0' −= cp εε

0015.0002.00035.0 =−= CamMurgVilGb,brmaenARCugmçag. dUcenH rad

hh 00075.05.00015.0

min =×

=θ CamYynwgEdkkgvNÐ/ θ GacnwgekIneLIgdl;

( ) radh

h 005.05.0002.0012.0max =×−=θ témø 012.0' =cε CatémøEdlFMNas; dUcenHtémøtUcCagenHGacRtUv)aneRbICamYyEdkkgvNÐ.

RbsinebImindUcenHeT eKGaceRbImuxkat;epSgeTot. enAkñúgFñwmCab;ebtugGarem:EdlmanEdk fibers mMurgVil)aøsÞicGacRtUv)anKNnadUcxageRkam³

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−

−=λλ

λβθ1

0035.0

s

yp E

f ¬!^>@!¦

Edl ( )sys f ρρρλ 17.400625.024.23.4 +−+= ¬!^>@@¦ sρβ 16.056.0 −= ¬!^>!$¦



=yf ersIusþg;yalrbs;Edk =sE m:UDúleGLasÞicrbs;Edkem

=ρ PaKryEdkem =sρ PaKryEdk fibers KitmaD

smIkar !^>@! Bgðajy:agc,as;famMurgVil)aøsÞicénebtugGarem:EdleRbIEdk fibers KWGaRs½yeTA nwg PaKryEdkem/ PaKryEdk fibers nigersIusþg;yalrbs;va. karbegáInersIusþg;yalkat;bnßymMu rgVil)aøsÞic. smIkar !^>@! k¾rab;bBa©ÚlnUv\T§iBlénRbEvgsnøak;)aøsÞicenAelImMurgVilEdr.

xageRkamCaTRmg;EdlRtUv)amsRmYledIm,IKNnamMurgVil)aøsÞic³ ⎟⎠⎞

⎜⎝⎛=

λλβθ 003.0

p ¬!^>@#¦

]TahrN_ RbsinebI 0=sρ nig MPaf y 400= enaH λθ /00289.01 =p nigRbsinebI %1=sρ / %5.1=ρ nig MPaf y 400= enaH λθ /01235.02 =p . enHmann½yfa lT§PaBTb;mMurgVilrbs;

FñwmebtugGarem:nwgekIneLIgRbEhlbYndgRbsinebIeKeRbIEdk fibers %1 .

16>13> segçbviFIsaRsþkñúgkarKNnasßanPaBkMNt; (Summary of Limit Design Procedure)

- KNnabnÞúkemKuNedayeRbIemKuNbnÞúkEdl[enAkñúgemeronTI 3³ LDwu 6.12.1 += - kMNt;Ggát;emkanicénkar)ak;/ snøak;)aøsÞic/ nigm:Um:g;emKuN uM - KNnamuxkat;eRKaHfñak;edayeRbIviFIKNnaersIusþg; (strength design method) - kMNt;mMurgVilcaM)ac;énsnøak;)aøsÞic - KNnalT§PaBTb;mMurgVilenARtg;muxkat;énsnøak;)aøsÞic. lT§PaBTb;mMurgVilRtUvEtFMCagmMurgVil

caM)ac;. - RtYtBinitüemKuNRbqaMg yielding rbs;Edk nigsñameRbHFM² ¬EdlCapleFobrvag

load serviceat moment elastic/uMφ - epÞógpÞat;PaBdab nigsñameRbHeRkamGMeBIbnÞúkeFVIkar - RtYtBinitüemIlfaEdkkmøaMgkat;TTwgRKb;RKan;RtUv)andak;enARKb;muxkat;



]TahrN_16>7 FñwmdUcEdlbgðajenAkñúgrUbTI 16>30 RtUv)anbgáb;enAcugTaMgsgçag nigRTbnÞúkBRgayes μ IemKuN

mkN /80 nigbnÞúkcMcMNucemKuN kN5.213 . KNnaFñwmedayeRbIdMeNIrkarKNnasßanPaBkMNt;. eK[ mmb 350= / MPaf c 21' = nig MPaf y 280= . dMeNaHRsay

1> bnÞúkBRgayesμ IemKuN mkNwu /80= . bnÞúkcMcMNucemKuN mkNPu /5.213= . 2> snøak;)aøsÞicekItmanenARtg;cMNuc A / B nig C EdlbNþal[manemkanicénkar)ak;dUc

bgðajenAkñúgrUbTI 16>30. edayeRbIviFIkmμnþCak;Esþg (virtual work method) nigsn μt;PaB dabÉktþaenARtg;cMNuc C enaHkm μnþxageRkAesμ Inwg

mkNWe .5.5097.38015.213 =×+×= km μnþxagkñúgEdlRsUbedaysnøak;)aøsÞicKW

)Cat (2)Bat ()Aat ( θθθ uuui MMMW ++=

7.34

4 uu

MM == θ

eday[ ie WW = enaH mkNM u .3.471= . tamkarviPaKTUeTA[ mkNLP

LwM u

uu .3.471

84.75.213

164.780

816

22=+=+=

3> KNnamuxkat;eRKaHfñak;enARtg;cMNuc A / B nig C sRmab; mkNM u .3.471= . BItaragenA kñúg]bsm<½n§ B nigsRmab; MPaf c 21' = / MPaf y 280= CamYynwgPaKryEdk

013.0=ρ eK)an MPaRu 95.2= ¬ %04.2max =ρ ¦ 2bdRM uu =

mmd 67635095.2103.471 6

=×⋅

= km<s;srubrbs;FñwmKW mmh 73660676 =+= yk mm740

28.3075676350013.0 mmbdAs =××== ρ eRbIEdk 285DB mYyRsTab; ¬ 23079mmAs = ¦/

mmmmb 35034270102289min <=+×+×= mm

bffA

ac

ys 1383502185.0

2803079'85.0

=××

×==



mmac 35.16285.0

== 24.0676

35.162===

dcλ

4> mMurgVilcaM)ac;rbs;snøak;)aøsÞicKW a. ( ) ( )[ ]FBBFAA

cA MMMM

IEL

−+−= 26

θ

MPafE cc 21676214730'4730 === MPaEs 200000= b. kMNt;m:Um:g;cugbgáb;enARtg; A nig B edayeRbIbnÞúkemKuN³ mkNLP

LwMM u

uFBFA .55.562

84.75.213

124.780

812

22=+=+==

m:Um:g;)aøsÞic mkNMM BA .3.471== c. m:Um:g;niclPaBénmuxkat;eRbHGacRtUv)anKNnadUcxageRkam

( )23

3xdnAxbI scr −+=

Edl x Cacm¶ayBIsrésrgkarsgát;eTAG½kSNWt ( )kd . edIm,IkMNt; x ¬emIlemeronTI 6¦/ mmx 4.257= nig 481044.68 mmIcr ⋅=

d. mMurgVilcaM)ac;Gb,brma³ edaycat;Tukm:Um:g;TaMgGs;enARtg; A nig B GviC¢man/ enaH ( ) ( )[ ] 6

8 1055.5623.47155.5623.47121044.68216766

7400⋅+−++−

⋅××=Aθ

rad00227.0=

5> lT§PaBTb;mMurgVilKW³ ( ) ( )24.01200000

28024.0

0035.01

0035.0−

−=−

−=λλ

θs

yA E

f

radrad 00227.00127.0 >= lT§PaBTb;mMurgVilesμ IRbEhl 5.5 dgénmMurgVilcaM)ac; enHbgðajfamuxkat;RKb;RKan;. 6> RtYtBinitüpleFobrvagm:Um:g;emKuNelIm:Um:g;eGLasÞiceRkambnÞúkeFVIkar

mkNLPwLMM BA .6.3518

4.74.13312

4.750812

22=

×+

×=+==

mkNadfAM ysn .471102

13867628030799.02

6 =⋅⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−××=⎥

⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−= φφ

pleFobKW 34.16.351

471= EdltMNag[emKuNsuvtßiPaBRbqaMgnwg yielding rbs;Edk

enARtg;TRm.



7> RtYtBinitüPaBdabGtibrmaEdlbNþalmkBIbnÞúkeFVIkar ¬enAkNþalElVg¦³ ykbnÞúkeFVIkar

BRgayesμ I mkNw /50= nig kNP 4.133= enaH

EIwL

384

4

1 =Δ sRmab;bnÞúkcMcMNucenAkNþalElVg



EI

PL192

3

2 =Δ PaBdabsrubKW mm53.4

1044.68216761927400133400

1044.6821676384740050

8

3

8

4=

⋅××

×+

⋅××

×=Δ

1633

17400

53.4==

ΔL

EdlCapleFobtUcEmnETn 8> brimaNEdkkmøaMgkat;TTwgRKb;RKan;RtUv)andak;edIm,IeCosvagkar)ak;edaykmøaMgkat;TTwg

EdlGacekItman.

16>14> karEbgEckm:Um:g;eLIgvijénm:Um:g;GviC¢manenAkñúgFñwmCab; Moment Distribution of Negative Moments in Continuous Beams

karEbgEckm:Um:g;GviC¢maneLIgvijenAkñúgGgát;rgkarBt;Cab;KWQrelIsac;lUteFobsuT§ (net

tensile strain NTS) tε sRmab;TaMgebtugGarem: nigebtugeRbkugRtaMg. rUbTI 16>31 bgðajlImIt GnuBaØatkñúgkarEbgEckm:Um:g;eLIgvij. vabgðajfaPaKrym:Um:g;GviC¢manekIneLIg b¤fycuHenAelITRm rbs;FñwmCab; 'q EdlKNnaedayRTwsþIeGLasÞicminRtUvFMCag %1000 tε CamYytémøGtibrma %20 . karEbgEckm:Um:g;eLIgvijRtUv)anGnuBaØatEtenAeBlEdl 0075.0≥tε EdlbgðajfavamanPaBsVit RKb;RKan;enARtg;muxkat;Edlm:Um:g;RtUv)ankat;bnßy. enAeBl 0075.0<tε karEbgEckm:Um:g;eLIgvij minRtUv)anGnuBaØateLIy. m:Um:g;GviC¢manEdl)anEktMrYvRtUv)aneRbIsRmab;KNnam:Um:g;viC¢manEdl)an EktRmUv (ACI Code, Section 8.4) . karEbgEckm:Um:g;eLIgvijminRtUv)anGnuvtþcMeBaHGgát;Edl KNnaedayviFIKNnaedaypÞal;sRmab;RbB½n§kRmalxNÐeT ¬eyagtamemeronTI 17¦.

Casegçb PaBryekIneLIg nigPaKryfycuHénm:Um:g;GviC¢manmandUcxageRkam³ - enAeBlEdl 0075.0<tε karEbgEckm:Um:g;eLIgvijminRtUv)anGnuBaØat ¬ 476.0/ >bρρ ¦. - enAeBlEdl 0075.0=tε PaKryénkarEbgEckm:Um:g;eLIgvijKW %5.7 ¬ 476.0/ =bρρ ¦. - enAeBlEdl 020.0>tε PaKryénkarEbgEckm:Um:g;eLIgvijKW %20 ¬ 217.0/ =bρρ ¦. - enAeBlEdl 020.00075.0 << tε PaKryEbgEckm:Um:g;eLIgvijKW

tq ε1000'= ¬!^>@$¦



]TahrN_ RbsinebI 010.0=tε enaHPaKryEbgEckm:Um:g;eLIgvijKW %10 . TMnak;TMngrvag

PaKryEdk ρ enAkñúgmuxkat; nigsac;lUteFobsuT§ tε KWmandUcxageRkam ¬eyagtamEpñk 3>9¦³

003.0003.0

−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

b

s

y

tEf

ρρ

ε ¬#>@$¦

sRmab;Edk MPaf y 400= nig MPaEs 200000= . edaysnμt; 002.0/ =sy Ef enaH

003.0005.0−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛=

b

t

ρρ

ε ¬#>@%¦

sRmab; 0075.0=tε / lImIténPaBsVitKW 75.3002.0/0075.0/ ==yt εε . PaKryEbgEckm:Um:g; eLIgvijERbRbYlGaRs½yeTAnwgkarkMNt;TaMgenH nigsRmab; MPaf y 400= RtUv)an[enAkñúgtaragTI 16>1 nig 16>2.



RKb;PaKryEbgEckm:Um:g;eLIgvijEdlRtUv)aneRbI vacaM)ac;RtUvFanafamuxkat;minrgnUvkarxUc xat b¤mansñameRbHFMedaysarbnÞúkeFVIkar ehIyvaRtUvrkSalT§PaBTb;rgVilenARKb;muxkat;eRKaHfñak;enA kñúgeRKOgbgÁúM. karEbgEckm:Um:g;eLIgvijenAkñúgeRKOgbgÁúMsþaTicminkMNt;eFVI[m:Um:g;GviC¢manenAelITRm nigm:Um:g;viC¢manenAkNþalElVgfycuH. karfycuHenHmin)aneFVI[suvtßiPaBrbs;eRKOgbgÁúMfycuH b¤eFVI [maneRKaHfñak;enaHeT ebIeRbobeFobCamYyeRKOgbgÁúMsþaTickMNt;. CakarBit PaBCab;enAkñúgrcna sm<½n§pþl;nUversIusþg;/ sßirPaB nigesdækic©bEnßmeTotkñúgkarKNna. emKuNEbgEckm:Um:g;eLIgvij q EdlQrelI (ACI Code 318-99) RtUv)anKNnadUcxageRkam

( )⎥⎦

⎤⎢⎣

⎡ −−=

bq

ρρρ '120 ¬!^>@%¦

enAkñúgsmIkarTI !^>@% PaKryEdk ρ b¤ )'( ρρ − enARtg;muxkat;Edlm:Um:g;RtUv)ankMNt; RtwmPaKryGtibrma bρ5.0 . PaKryEdkGb,brmaenAkñúgmuxkat;rgkarBt;RtUv)ankMNt;Rtwm

yyc fff /4.1)4/(' ≥ . edayeRbIkarkMNt;dac;xatTaMgenHPaKryEbgEckm:Um:g;eLIgvijGtibrma nigGb,brmaRtUv)anbgðajenAkñúgtarag 16>3.

taragTI 16>1 karpøas;bþÚrPaKryEbgEckm:Um:g;eLIgvij )'(q MPaf y 400=

tε 0075.0 010.0 0125.0 0150.0 0175.0 020.0 0225.0 bρρ / 476.0 385.0 323.0 278.0 244.0 217.0 196.0

(%)'q 5.7 10 5.12 15 5.17 20 20

taragTI 16>2 karpøas;bþÚrPaKryEbgEckm:Um:g;eLIgvij )'(q sRmab;kar[PaKry bρρ /

bρρ / 48.0 45.0 40.0 35.0 30.0 25.0 20.0 tε 0074.0 0081.0 0095.0 0113.0 0137.0 017.0 022.0 (%)'q 0.0 1.8 5.9 3.11 7.13 0.17 0.20



taragTI 16>3 karEbgEckm:Um:g;eLIgvijGtibrma nigGb,brma q ¬smIkar !^>@%¦ )(' MPaf c )(MPaf y bρ minρ )minρfor %(maxq )5.0%(for min bq ρ

21 400 0215.0 0033.0 9.16 10 28 400 0285.0 0033.0 7.17 10 35 400 0339.0 003.0 9.17 10 ]TahrN_16>8 kMNt;m:Um:g;eGLasÞicGtibrmaenARtg;TRm nigenAkNþalElVgénFñwmCab;EdlmanbYnElVgdUcbgðajenA kñúgrUbTI 16>32 a. Fñwmmanmuxkat;esμI nigRTnUvbnÞúkefrBRgayesμ I mkN /117 nigbnÞúkGefr

kN5.87 . snμt;PaKryEbEckm:Um:g;eLIgvijGtibrma %10 nigBicarNanUvkrNIBIrxageRkam³ - enAeBlEdlbnÞúkGefrRtUv)andak;enAelIElVgqøas;Kña KNnam:Um:g;viC¢manGtibrmaenAkñúgElVg - enAeBlEdlbnÞúkGefrRtUv)andak;enAelIElVgCab;Kña KNnam:Um:g;GviC¢manGtibrmaenAelITRm

dMeNaHRsay 1> Fñwmmanm:Um:g;niclPaB I es μ IKña nigman E dUcKña. dUcenH EI efr. smIkarbIm:Um:g;

sRmab;viPaKFñwmnigsRmab; EI efrKW³ ( )

442

322

311

2211LwLwLMLLMLM CbA −−=+++

edaysarElVgesμ IKña ( )21

2

44 wwLMMM CBA +−=++ ¬!^>@^¦

enAkñúg]TahrN_enH 0== EA MM . krNIénkardak;bnÞúk6EbbepSgKñaRtUv)an BicarNadUcbgðajenAkñúgrUbTI 16>32³ krNITI1> bnÞúkefrRtUv)andak;enAelIFñwm ABCDE TaMgmUl ¬rUbTI 16>32 b¦. krNITI2> bnÞúkGefrRtUv)andak;enAelIElVg AB nig CD sRmab;m:Um:g;GtibrmaenAkñúg

ElVg AB nig CD ¬rUbTI 16>32 c¦. krNITI3> dUckrNITI 2 sRmab;ElVg BC nig DE ¬rUbTI 16>32 d¦. krNITI4> bnÞúkGefrRtUv)andak;enAelIElVg AB / BC nig DE sRmab;m:Um:g;GviC¢manenA

Rtg; B ¬rUbTI 16>32 e¦.



krNITI5> bnÞúkGefrRtUv)andak;enAelIElVg CD nig DE ¬rUbTI 16>32 f¦. krNITI6> bnÞúkGefrRtUv)andak;enAelI BC nig CD

sRmab;m:Um:g;GviC¢manGtibrmaenARtg; C ¬rUbTI 16>32 g¦. 2> krNITI1> GnuvtþsmIkar !^>@^ eTAelIFñwmkMNat; ABC / BCD nig CDE erogKña

mkNMM CB .2106)117117(4

642

−=+−=+ mkNMMM DCB .21064 −=++

mkNMM DC .21064 −=+ KNnasmIkarTaMgeyIgTTYl)an

mkNMM DB .28.451−== nig mkNM C .9.300−= sRmab;karkat;bnßym:Um:g; %10

( ) mkNMM DB .2.40628.4519.0'' −=−×== ( ) mkNM C .81.2709.3009.0' −=−×=

m:Um:g;kNþalElVgEdlRtUvKñanwgm:Um:g;Edl)ankat;bnßyehIyKW ElVg mkNMLwDEAB B

D .4.3232.40621

86117'

21

8

22=−

×=+==

ElVg ( ) mkNCDBC .18881.2702.40621

86117 2

=+−×

== 3> krNITI2> GnuvtþsmIkar !^>@@ eTAelIkMNat;Fñwm ABC / BCD nig CDE erogKña³

mkNMM CB .5.787)5.87(4

642

−=−=+ mkNMMM DCB .5.7874 −=++

mkNMM DC .5.7874 −=+ KNnasmIkarTaMgeyIgTTYl)an

mkNMM DB .75.168−== nig mkNM C .5.112−= m:Um:g;eGLasÞickNþalElVgEdlRtUvKñanwgm:Um:g;xagelIKW Fñwm mkNMLwAB B

L .4.30975.16821

865.87

21

8

22=−

×=+=

mkNBC .6.140)5.11275.168(210 =+−=



mkNLw

CD L .1.253625.1408

65.87)5.11275.168(21

8

22=−

×=+−=

mkNDE .4.8475.168210 =−=

edIm,Ikat;bnßym:Um:g;viC¢mankñúgElVg eKRtUvbegáInm:Um:g;Rtg;TRmeday %10 nigKNnam:Um:g; kñúgElVgEdlRtUvKña. m:Um:g;viC¢manEdlTTYl)anRtUvEtes μ Iy:agtic %90 énm:Um:g;Edl KNnadMbUg.

( ) mkNMM DB .6.18575.1681.1'' −=−== mkNM C .75.123)5.112(1.1' −=−=

m:Um:g;eGLasÞickNþalElVgEdlRtUvKñanwgm:Um:g;xagelIKW Fñwm mkNMLwAB B

L .95.3006.18521

865.87'

21

8

22=−

×=+=

mkNBC .7.154)75.1236.185(210 =+−=

mkNLwCD L .05.2397.1548

65.87)6.18575.123(21

8

22=−

×=+−=

mkNDE .8.926.185210 =−=

4> krNITI3> RsedogKñanwgkrNITI2> ehIym:Um:g;RtUv)anbgðajenAkñúgrUbTI 16>32 d. 5> krNITI4> BicarNaElVg AB / BC nig DE EdlRTbnÞúkGefredIm,IKNnam:Um:g;GviC¢man

GtibrmaenARtg;TM B ³ mkNMM CB .1575)5.87(

264

2−=−=+

mkNMMM DCB .5.7874 −=++ mkNMM DC .5.7874 −=+

KNnasmIkarTaMgeyIgTTYl)an mkNM B .7.379−= / mkNM C .3.56−=

nig mkNM D .8.182−= sRmab;karkat;bnßym:Um:g; %10 Rtg; B

( ) mkNM B .7.3417.3799.0' −=−= m:Um:g;kNþalElVgEdlRtUvKñaKW



Fñwm mkNMLw

AB BL .9.2227.341

21

865.87

21

8

22=−

×=+=

mkNLwBC L .75.1941998

65.87)3.567.341(21

8

22=−

×=+−=

mkNCD .55.119)8.1823.56(210 −=+−=

mkNLwDE L .35.3024.918

65.878.18221

8

22=−

×=−=

6> krNITI5> RsedogKñanwgkrNITI4> elIkElgEtElVgxagcugminRtUv)andak;bnÞúkedIm,I TTYl)anm:Um:g;viC¢manGtibrmarnARtg;TRm B ¬b¤TRm D sRmab;kardak;bnÞúkRsedogKña¦. düaRkamm:Um:g;Bt;RtUv)anbgðajenAkñúgrUbTI 16>32 f.

7> krNITI6> BicarNaElVg BC nig CD EdlRTbnÞúkGefredIm,IKNnam:Um:g;GviC¢man GtibrmaenARtg;TM B ³

mkNMM CB .5.787)5.87(4

642

−=−=+

mkNLw

MMM LDCB .1575

24

2−=−=++

mkNLwMM LDC .5.787

44

2−=−=+

KNnasmIkarTaMgeyIgTTYl)an mkNMM DB .5.112−==

nig mkNM C .5.337−= sRmab;karkat;bnßym:Um:g; %10 Rtg; C

( ) mkNM C .75.3035.3379.0' −=−= ( ) mkNMM DB .25.1015.1129.0'' −=−==

m:Um:g;kNþalElVgEdlRtUvKñaKW Fñwm mkNDEAB .6.502.101

21

−=−==

mkNLwCDBC L .15.1916.2028

65.87)95.3032.101(21

8

22=−

×=+−==

8> m:Um:g;Gtibrma nigGb,brmaeRkaykarEbgEckm:Um:g;eLIgvijRtUv)anbgðajenAkñúgtarag 16>4. Moment envelop RtUv)anbgðajenAkñúgrUbTI 16>32 h.



9> enAkñúg]TahrN_renH muxkat;kNþalElVgRtUv)aneRbIsRmab;PaBgayRsYl. m:Um:g;kNþal ElVgmincaM)ac;Cam:Um:g;viC¢manGtibrmaeT. kñúgkrNIElVgcug AB nig DE m:Um:g;Gtibrma eRkayeBlBIkarEbgEckbnÞúkeLIgvij %10 KWwes μ Inwg 2.12/2LwD nigekItmanenAcm¶ay

L4.0 BI BC nig D . taragTI 16>4 m:Um:g;cugeRkayén]TahrN_TI 16>8 eRkayBIkarEbgEckm:Um:g;eLIgvij

krNI 1 2 3 4 ¬1 + 2¦ 5 ¬1 + 3¦ TItaMg

muxkat; m:Um:;g DL

m:Um:;gGviC¢man Gtibrma LL

m:Um:;gviC¢man Gtibrma LL

m:Um:;gGviC¢man Gtibrma LLDL +

m:Um:;gviC¢man Gtibrma LLDL +

TRm A 0 0 0 0 0 B 2.406− 7.341− 1.28+ *9.747− 1.378− C 9.300− 75.303− - *65.604− 9.300− D 2.406− 7.341− 1.28+ *9.747− 1.378− E 0 0 0 0 0

kNþalElVg

AB 4.323+ 8.92− 95.300+ 6.230+ *35.624+ BC 188+ 7.154− 05.239+ 3.33+ *05.427+ CD 188+ 7.154− 05.239+ 3.33+ *05.427+ DE 4.323+ 8.92− 95.300+ 6.230+ *35.624+

( * ) m:Um:g;KNnaGtibrma nigGb,brmacugeRkay.







]TahrN_16>9 kMNt;karEbgEckm:Um:g;GviC¢maneLIgvijGnuBaØatenAelITRm B / C / D nig E énFñwmCab; ABCDE EdlbgðajenAkñúgrUbTI 1633. FñwmEdlmanmuxkat;ctuekaNEkg mmb 300= / mmh 550= nig

mmd 490= nigvaRtUv)anBRgwgdUcbgðajenAkñúgtarag ¬ MPaf c 28' = nig MPaf y 420= ¦ - edayeRbI]bsm<½n§ B . - edayeRbIkarkMNt; ACI Code.

dMeNaHRsay

1> sRmab; MPaf c 28' = nig MPaf y 420= / 0285.0=bρ . emKuNEbgEckm:Um:g;eLIgvij RtUv)an[dUcxageRkam³

⎥⎦

⎤⎢⎣

⎡ −−=

bq

ρρρ '120 ¬!^>@%¦

2> emKuNEbgEckm:Um:g;eLIgvijrbs; ACI Code CaGnuKmn_énbERmbRmYlrageFobEdksuT§ tε nigERbRbYlcenøaHBI %5.7 nig %20 dUcbgðajenAkñúgrUbTI 16>31

tq ε1000'= ¬!^>@$¦

003.0003.0

−+

=

b

s

y

tEf

ρρ

ε



nig 003.0005.0−=

s

t

ρρ

ε sRmab; MPaf y 420=

taragxageRkambgðajBItémø q nig 'q EdlminRtUvKña.

TRm EdkTaj sA

ρ Edksgát;

sA' 'ρ bρ

ρρ '−

%q tε '%q

B 283DB 0126.0 0 0 44.0 2.11 008.0 8 C 323DB 0164.0 0 0 58.0 4.8 0056.0 0 D 203DB 0064.0 0 0 225.0 5.15 0192.0 2.19 E 254DB 0134.0 203DB 0064.0 246.0 1.15 0173.0 3.17


karKNnakRmalxNÐBIrTis 507 T.Chhay

XVII. karKNnakRmalxNÐBIrTis Design of Two-Way Slabs


kRmalxNÐGacRtUv)anBicarNaCaGgát;eRKOgbgÁúMEdlmankRmas; h tUcCagRbEvg L nigTTwg S . TRmg;d¾samBaØrbs;kRmalxNÐKWkRmalxNÐEdlRtUv)anRTedayTRmQmKña Edlvapþl;nUvPaB dabcMbgkñúgTismYy EdleK[eQ μaHfa kRmalxNÐmYyTis (one-way slab). karKNnakRmalxNÐ mYyTismanniyayenAkñúgemeronTI 9. enAeBlkRmalxNÐRtUv)anRTedayRCugTaMgbYn nigmanpleFobbeNþay L elITTwg S tUc CagBIr ehIykRmalxNÐdabBIrTis elIsBIenHbnÞúkenAelIkRmalxNÐRtUv)anbBa¢ÚneTATRmTaMgbYn RCug. kRmalxNÐEbenHRtUv)aneK[eQ μaHfa kRmalxNÐBIrTis (two-way slab). m:Um:g;Bt; nigPaB dabenAkñúgkRmalxNÐEbbenHtUcCagenAkñúgkRmalxNÐmYyTis kRmalxNÐdUcKñaGacRTbnÞúk)aneRcIn CagenAeBlEdlvamanTRmTaMgbYnRCug. bnÞúkenAkñúgkrNIenHRtUv)anRTBIrTis ehIym:Um:g;Bt;kñúgTis nImYy²tUcCagm:Um:g;Bt;enAkñúgkRmalxNÐRbsinebIbnÞúkrbs;vaRtUv)anRTkñúgTisEtmYy. karteRmob rt-Fñwm-kRmalxNÐ (slab-beam-girder) KMrUénkRmalxNÐmYyTis nigBIrTisRtUv)anbgðajenAkñúgrUbTI 17>1.

17>2> RbePTkRmalxNÐBIrTis (Types of Two-Way Slabs)

kRmalxNÐebtugBIrTisGacRtUv)ancat;cMNat;fñak;dUcxageRkam³ a. kRmalxNÐBIrTisenAelIFñwm (two-way slab on beam)³ krNIenHekItmanenAeBlEdl

kRmalxNÐBIrTisRtUv)anRTedayFñwmenAelIRCugTaMgGs;rbs;va ¬rUbTI17>1¦. bnÞúkBIkRmal xNÐRtUvbBa¢ÚneTATRmFñwmTaMgbYnrbs;va EdlnwgbBa¢ÚnbnÞúkbnþeTAssr.

b. Flat slab³ CakRmalxNÐBIrTisEdlRtUv)anBRgwgBIrTisedayKñanFñwmRT ehIybnÞúkRtUv)an bBa¢ÚnpÞal;eTAssrTRm. ssrcg;TMluHkRmalxNÐ EdlRtUv)ankarBaredaybIviFIxageRkam ¬rUbTI 17>2 nig 17>3¦³ - edayeRbI drop panel CamYynwg column capital.


T.Chhay 508 Design of Two-Way Slab

- edayeRbI drop panel EdlK μan column capital. ebtugEdlB½T§CMuvij column capital KYr EtRkas;RKb;RKan;edIm,ITb;Tl;nwgkugRtaMgTajGgát;RTUgEdlekItBIkmøaMgkat; punching

shear. - edayeRbI column capital edayK μan drop panel EdlCaviFImYyminFm μta.

c. Flat-Plate floor³ CaRbB½n§kRmalxNÐBIrTisEdlmankRmas;kRmalxNÐesμ I nigsßitenABIelI ssredaypÞal;edayK μanFñwm b¤ column capital ¬rUbTI 17>2 a¦. kñúgkrNIenHssrcg;TMluH kRmalxNÐedaykugRtaMgTajGgát;RTUg. dUcenH CaTUeTAeKRtUvkarbegáInkRmas;kRmalxNÐ b¤dak;EdkBiess.

d. Two-way ribbed slabs nig waffle slab system³ kRmalxNÐRbePTenHekItBIkRmalxNÐ EdlmanpleFobbeNþayelITTwgtUcCag 2. CaTUeTA kRmas;rbs;kRmalxNÐsßitenAcenøaH

cm5 eTA cm10 nigRtUv)anRTedayrnUt (rib or joist) TaMgBIrTis. rnUtRtUv)anteRmobkñúgTis nImYy²CamYyKMlatRbEhlBI cmcm 7550 − EdlbegáItragkaer b¤ctuekaNEkg ¬rUbTI 17>2 c¦. rnUtk¾GacRtUv)anteRmobedaymMu o45 b¤ o60 BIG½kSrbs;kRmalxNÐ EdlbegáInesaP½N PaBsßabtükm μ. sRmab; two-way ribbed slabs RbB½n§epSg²GacRtUv)anTTYlyk³ - RbB½n§rnUtBIrTisCamYynwgRbehagcenøaHrnUtEdlTTYledayeRbIBum<Biess EdlCaTUeTA

manragkaer. rnUtRtUv)anRTedayrtTaMgbYnRCugEdlsßitenABIelIssr. kRmalxNÐ RbePTenHRtUv)aneK[eQμaHfa two-way ribbed (joist) slab system .





- RbB½n§rnUtBIrTisCamYyeRKOgbMeBj (filler) enAcenøaHrnUtEdleFVI[Bidanerobes μ I. eRKOg bMeBj (filler) CagRbehag nigeFVIBIebtugTm¶n;Rsal b¤Tm¶n;Fmμta b¤BIsmÖar³Tm¶n;Rsal epSgeTot. rnUtRtUv)anRTedayrtenARCugTaMgbYnEdlRtUv)anRTbnþedayssr. kRmal



xNÐRbePTenHk¾RtUv)aneK[eQμaHfa two-way ribbed slab system b¤ hollow-block

two-way ribbed system . - RbB½n§rnUtBIrTisCamYyRbehagcenøaHrnUt nigKμanrt b¤FñwmRTrnUt. vaQrenAelIssreday

pÞal;CamYynwgbnÞHebtugtan;. kRmalxNÐRbePTenHRtUv)anehAfa waffle slab. 17>3> kareRCIserIsRbB½n§kRmalxNÐebtugEdlmanlkçN³esdækic©

Economical Choice of Concrete Floor Systems

RbB½n§kRmalxNÐCaeRcInRbePTRtUv)aneRbIsRmab;GKarTUeTA dUcCa eKhdæan kariyal½y nigGKar rdæ)alepSg². kareRCIserIsRbB½n§kRmalxNÐEdlmanlkçN³kRmalxNÐ nigRKb;RKan;GaRs½yelI RbePTGKar rUbragsßabtükmμ esaPN½ nigRbEvgElVgEdlenAcenøaHssr. CaTUeTA bnÞúkGefrenAelI GKarERbRbYlcenøaHBI 22 /2.7/8.3 mkNmkN − . karENnaMTUeTAsRmab;kareRbIR)as;RbB½n§kRmal xNÐEdlmanlkçN³esdækic©RtUv)ansegçbdUcxageRkam³

- Flat plate ³ saksmbMputsRmab;ElVgEdlmanRbEvgcenøaHBI mm 5.76 − nigbnÞúkGefrERb RbYlBI 22 /8.4/9.2 mkNmkN − . GtßRbeyaCn_énkarTTYlyk flat plate rYmmankarcM NayelIBum<Gs;éføefak TTYl)anBidanrabes μ I nigkarsagsg;qab;. Flat plate manlT§PaB Tb;kmøaMgkat;TTwgTab nigPaBrwgRkajtUc EdleFIV[manPaBdabFM;. Flat plate RtUv)an eRbIy:agTUlMTUlayenAkñúgGKarCakRmalxNÐBRgwgedayEdk b¤k¾ebtugeRbkugRtaMg.

- Flat slab ³ saksmbMputsRmab;ElVgEdlmanRbEvgBI mm 96 − nigsRmab;bnÞúkGefrERb RbYlBI 22 /2.7/8.3 mkNmkN − . vaRtUvkarBum<eRcInCag flat plate CaBiesssRmab; column capital. kñúgkrNICaeRcIn eKeRbIEt drop panel edayK μan column capital .

- Waffle slab ³ saksmsRmab;ElVgEdlmanRbEvgBI mm 5.149 − nigsRmab;bnÞúkGefrERb RbYlBI 22 /2.7/8.3 mkNmkN − . vaRTbnÞúk)aneRcInCag flat plate nigmanBidanKYr[Tak; TajEtBum<mantémøéfø.

- kRmalxNÐelIFñwm (slab on beam)³ salsmbMputsRmab;ElVgcenøaH mm 96 − nigbnÞúk GefrBI 22 /7.5/9.2 mkNmkN − . FñwmbegáInPaBrwgRkajrbs;kRmalxNÐEdleFVI[man PaBdabtUc. eKRtUvkarBum<bEnßmsRmab;Fñwm.



- kRmalxNÐmYyTisenAelIFñwm (one-way slab on beam)³saksmbMputsRmab;ElVgEdlman RbEvgBI mm 63 − nigbnÞúkGefrcenøaHBI 22 /8.4/9.2 mkNmkN − . vaGacRtUv)aneRbI sRmab;ElVgFMCagenHCamYynwgtémøéføCag elIsBIenHeKnwgTTYl)anPaBdabFM. eKRtUvkarBum< bEnßmsRmab;Fñwm.

- One-way joist floor system³ saksmbMputsRmab;ElVgEdlmanRbEvgBI mm 96 − nigman bnÞúkGefrcenøaH 22 /7.5/8.3 mkNmkN − . edaysarEtrnUteRCA brimaNebtug nigEdkKWtic EtkarcMNayelIBum<Gs;eRcIn. Bidanrbs;kRmalxNÐGacnwgemIleTAKYr[Tak;Taj.

17>4> eKalKMnitkñúgkarKNna (Design Concept)

karviPaKd¾suRkitsRmab;kmøaMg nigbMlas;TIenAkñúgkRmalxNÐBIrTisKWs μúKsμaj edaysarEt PaBminkMNt;x<s;. vaBitCas μ úKsμajebIeTaHbICa\T§iBl creep nig nonlinear behavior rbs;ebtugRtUv )anecalk¾eday. viFI numerical method dUcCa finite element k¾GacRtUv)aneRbI b:uEnþviFId¾samBaØdUc EdlGVI)anbgðajeday ACI Code saksmbMputsRmab;karKNnasRmab;karGnuvtþ. ACI Code,

Chapter 13 snμt;fakRmalxNÐeFVIkarCaFñwmTUlayEtrak;begáItCaeRKagrwg (rigid frame) CamYynwg ssrEdlenABIeRkam nigBIelIva. karsn μt;énkarEckeRKagCaeRKagsmmUlRtUv)anepÞógpÞat;eLIgvij edaykarsikSaRsavRCavCalkçN³viPaK nigBiesaFn_ (analytical and experimental research). va )anbgðajfa lT§PaBRTbnÞúkcugeRkay (ultimate load capacity) énkRmalxNÐBIrTisCamYynwgkar Tb;tamRCug ¬restrained boundary) KWes μ I RbEhlBIrdgénlT§PaBRTbnÞúkcugeRkayEdlKNnaeday karviPaKtamRTwsþI edaysarkarEbgEckm:Um:g;eLIgvijd¾FMEdlekIteLIgenAkñúgkRmalxNÐmunnwg)ak;. enAeBlbnÞúkFMbMlas;TI nigPaBdabFMRtUv)anrMBwgTuk dUcenHeKRtUvkarkRmas;kRmalxNÐGb,brmaedIm,I rkSaPaBdab niglkçxNÐeRbHRKb;RKan; eRkambnÞúkeFVIkar. ACI Code kMNt;viFIsaRsþBIrsRmab;KNnakRmalxNÐBIrTis³

- viFIKNnaedaypÞal; (direct design method DDM, ACI Code, Section 13.6) CaviFIRbhak; RbEhl (approximate procedure) sRmab;karviPaK nigkarKNnakRmalxNÐBIrTis. RtUv )ankMNt;sRmab;RbB½n§kRmalxNÐEdlrgnUvbnÞúkBRgayes μ I nigssrmanKMlates μ IKña b¤esÞIr esμ IKña. viFIenHeRbInUvsMnuMemKuNedIm,IkMNt;m:Um:g;KNnaenARtg;muxkat;eRKaHfñak;.



RbB½n§kRmalxNÐEdlmin RtUvKñanwgkarkMNt;rbs; ACI Code, Section 13.6.1 RtUv)anviPaK edayviFIsaRsþKNnaEdl manlkçN³suRkitCag.

- viFIeRKagsmmUl (equivalent frame method EFM, ACI Code, Section 13.7) CaviFImYy EdlGKarbITMhM (3D) RtUv)anEckecjCaesrIéneRKagsmmUlBIrTMhM (2D) edaykat;GKar tamExSrcenøaHssr. lT§plrbs;eRKagRtUv)anBicarNadac;edayELkBIKñatamTisbeNþay nigTisTTwgrbs;GKar nigRtUv)anKitBImYyCan;eTAmYyCan; dUcEdlbgðajenAkñúgrUbTI 17>4.

viFIsaRsþKNnatam ACI Code BIrKWQrelIelIlT§plénkarviPaKeGLasÞic (elastic analysis) én eRKOgbgÁúMTaMgmUledayeRbIbnÞúkemKuN. viFIEdlEktRmUv (modified approach) viFI direct design

method RtUv)anbgðajenAkñúg commentary én code qñaM 1989 CaviFIPaBrwgRkajEktRmUv (modified

stiffness method MSM). vaQrelIkarbBa©ÚlemKuNEbgEckd¾kMNt;mYyCaGnuKmn_énpleFobPaB rwgRkaj ecα sRmab;KuNnwgm:Um:g;sþaTicsrubenAkñúgElVgxagcug. viFIenHRtUv)anBnül;enAeBleRkay.

bEnßmBIelIviFIrbs; ACI Code eKenAmanviFIepSg²CaeRcIneTotsRmab;KNna nigviPaKkRmal xNÐ. CalT§pl kRmalxNÐnwgmanbrimaNEdkticCag b¤eRcInCag. viFIviPaK (analytical method)

GacRtUvcat;cMNat;fñak;kñúgRkuménTMnak;TMngeKalrvagbnÞúk nigbMlas;TI CaeGLasÞic/ )aøsÞic nig nonlinear .

- enAkñúgkarviPaKeGLasÞic (elastic analysis) kRmalxNÐebtugRtUv)anKitCakRmaleGLa sÞic. karBt;kmøaMgkat;TTwg nigPaBdabRtUv)anKNnaedaysmIkarDIepr:g;EsülTI4 (fourth

differential equation) EdlTak;TgbnÞúkeTAnwgPaBdabsRmab;kRmalesþIgCamYynwgbMlas;TI tUc dUcEdl)anbgðaj eday Timoshenko. dMeNaHRsay finite difference solution k¾dUc CadMeNaHRsay finite element solution RtUv)anesñIeLIgedIm,IviPaKkRmalxNÐ. enAkñúgviFI finite element method kRmalxNÐRtUv)an EbgEckCasMNaj;ragRtIekaN b¤ragkaer (mesh

of triangles or quadrilateral). GnuKmn_bMlas;TIéncMNuc (node) Edlkat;KñaedaycMNuc sMNaj; (intersecting mesh point) RtUv)anbegáIteLIgCaTUeTA ehIym:aRTicénPaBrwgRkaj (stiffness matrices) RtUv)anbegáItsRmab;karviPaKedaykMuBüÚTr½.

- sRmab;karviPaK)aøsÞic eKmanbIviFI. viFI yield line method RtUv)anbegáIteLIgeday Johansen edIm,IkMNt;sßanPaB (limit state) énkRmalxNÐedayBicarNafa yield line EdlekItmanenAkñúgkRmalxNÐCaemkanicénkar)ak; (collapse mechanism). viFIceRmok



(strip method) RtUv)an begáIteday Hillerborg. kRmalxNÐRtUv)anEckecjCaceRmok (strip) ehIybnÞúkenAelIkRmal xNÐRtUv)anEbgEckTisedABIrEkgKña. ceRmokRtUv)anviPaK CaFñwmsamBaØ. viFITIbICaviFI optimal analysis method sRmab;eFVI[brimaNEdlTTYl)anman témøGb,brmaedayQrelIkarviPaK)aøsÞic. dMeNaHRsay optimal solution KWsμ úKsμajkñúg karviPaK nigTTYl)ankarBRgaysrésEdlmYyd¾sμ úKsμaj.

- karviPaK nonlinear analysis KitlkçN³bMlas;TIeRkambnÞúkBiténkRmalxNÐebtugGarem: enAeBlEdlviFI finite element method KitBicarNaEpñk nonlinear énTMnak;TMngkugRtaMg-bERmbRmYlrageFob (stress-strain relationship) énGgát;mYy²dac;edayELkBIKña. kñúgkrNI enH dMeNaHRsaykøayCasμ úKsμaj RbsinebITMnak;TMngEdl)anBIkarBiesaFedayTTYl)ankar sRmYlminRtUv)ansnμt;eTenaH.

viFIEdl)anerobrab;xagelI RtUv)anbgðajedIm,IENnaMGñksikSanUvviFIepSg²énkarviPaKkRmalxNÐ. kargarBiesaFn_elIkRmalxNÐminRtUv)anGPivDÆeTkñúgb:un μanqñaMcugeRkayenH b:uEnþkarsikSaCaeRcInRb-EhlCaRtUvkaredIm,IsRmYldMeNIrkarKNnabc©úb,nñCamYysuvtßiPaB karbMerIkargar niglkçN³esdækic¢.

17>5> ceRmokelIssr nigceRmokkNþal (Column and Middle Strips)

rUbTI 17>5 bgðajkRmalxagkñúgénkRmalxNÐBIrTisEdlRtUv)anRTenAelIssr A / B / C nig D . RbsinebIkRmalRTbnÞúkBRgayes μ I kRmalxNÐnwgdabBIrTis CamYyPaBdabGtibrmaenAtMbn; kNþal O . cMNucx<s;bMputsßitenAelIssr A / B / C nig D dUcenHEpñkénkRmalxNÐEdlenACMuvij ssrnwgmanrage)a:g (convex shape). karpøas;bþÚrrUbragrbs;kRmalxNÐbnþicmþg² ¬BIPaBe)a:genA elIssreTArkPaBptenAkNþalkRmal¦ eFVI[ExSkaMnImYy²kat;Rtg;cMNucrbt;. muxkat;Rtg; O / E / F / G nig H nwgmanm:Um:g;Bt;viC¢man b:uEnþenAmþúMbrievNssrnwgmanm:Um:g;Bt;GviC¢manGtibrma. eday BicarNacMeroktambeNþay AFB ceRmoknwgekagdUcFñwmCab; ¬rUbTI 17>5 b¦ edaymanm:Um:g;GviC¢man enARtg; A nig B nigmanm:Um:g;Bt;viC¢manRtg; F . ceRmokenHlatsn§wgenAcenøaHssrBIr A nig B nigCab;enAelIRCugTaMgsgçagénkRmalEdlbegáIt)anCaceRmokelIssr (column strip).





dUcKñasRmab;ceRmoktambeNþay EOG nwgmanm:Um:g;Bt;GviC¢manenARtg; E nig G ehIy m:Um:g;viC¢manenARtg; O EdlbegáItCaceRmokkNþal. ceRmokTIbItambeNþay DHC nwgeFVIkar RsedogKñanwgceRmok AFB . dUcenH bnÞHkRmalGacnwgRtUv)anEbgEckbIceRmokKW 1enAkNþaltam beNþay EOG Edl eK[eQμaHfaceRmokkNþal nigBIreTotsgçagtambeNþay AFB nig DHC EdleK[eQ μaHfa ceRmokelIssr ¬rUbTI 17>5 a¦. ceRmoknImYy²eFVIkarCaFñwmCab;. tamviFIdUcKña bnÞHkRmalk¾RtUv)anEbgEckCabIcMeroksRmab;TisedAmYyeTotKW ceRmokkNþalmYytambeNþay FOH nigceRmokelIssrBIreTot tambeNþay AED nig BGC erogKña ¬rUbTI 17>5 e¦. tamry³rUbTI 17>5 a eyIgeXIjfaceRmokkNþalRtUv)anRTedayceRmokelIssr EdlbBa¢Ún bnÞúkbnþeTAssr A / B / C nig D enAkñúgbnÞHkRmalenH. dUcenHceRmokssrRTbnÞúkeRcInCag ceRmokkNþal. dUcenH m:Um:g;Bt;viC¢manenAkñúgceRmokelIssrnImYy² ¬enARtg; E / F / G nig H ¦ mantémø FMCagm:Um:g;Bt;viC¢manenARtg; O EdlsßitenAceRmokkNþal. dUcKña m:Um:g;GviC¢manenAelI ssr A / B / C nig D enAkñúgceRmokelIssrmantémøFMCagm:Um:g;GviC¢manenARtg; E / F / G nig H enAkñúgceRmokkNþal. Epñkénm:Um:g;KNnaEdlRtUv)ankMNt;enAmuxkat;eRKaHfñak;nImYy²én ceRmokssr nigceRmokkNþalRtUv)anbgðajenAkñúgEpñkTI 8.

TMhMénceRmokelIssr nigceRmokkNþslnImYy²enAkñúgbnÞHkRmalRtUv)ankMNt;eday ACI

Code, Section 13.2. ceRmokelIssr x EdlRtUv)ankMNt;edayTTwgkRmalxNÐenAelIRCugnImYy² énG½kSssr es μ InwgmYyPaKbYnénTMhMbnÞHkRmal ¬ 1l nig 2l ¦ mYyNaEdltUcCageK rYmbBa©ÚlTaMgFñwm RbsinebIman. =1l RbEvgElVg KitBIG½kSeTAG½kS kñúgTisedAEdlm:Um:g;nwgRtUv)ankMNt; =2l RbEvlElVg KitBIG½kSeTAG½kS kñúgTisedAEkgnwg 1l EpñkénbnÞHkRmalcenøaHceRmokelIssrkMNt;ceRmokkNþal.



17>6> kRmas;kRmalGb,brmaedIm,IkMritPaBdab

(Minimum Slab Thickness to Control Deflection)

ACI Code, Section 9.5.3 kMNt;kRmas;kRmalxNÐsRmab;kRmalxNÐBIrTisedIm,IkMrit PaBdab. TMhMénPaBdabrbs;kRmalxNÐGaRs½ynwgGefrCaeRcInEdlrYmbBa©ÚlTaMgPaBrwgRkaj Tb;karBt; (flexural stiffness) rbs;kRmalxNÐEdlbBa©ÚlCaGnuKmn_énkRmas;kRmalxNÐ h . enAeBlbegáInkRmas; kRmalxNÐ enaHPaBrwgRkajTb;karBt;rbs;kRmalxNÐk¾ekIneLIg ehIyPaB dabrbs;kRmalxNÐnwgRtUvkat;bnßy. edaysarkarKNnaPaBdabsRmab;kRmalxNÐBIrTismanPaB s μúKsμaj nigedIm,IeCosvagPaBdabFM ACI Code kMNt;kRmas;kRmalxNÐTaMgenHedayTTYlykkar



kMNt;Edl)anBIkarBiesaFbI. RbsinebIkarkMNt;rbs;eyIgminsßitenAkñúgEdnkMNt;TaMgbIenHeT eKcaM )ac;RtUvKNnaPaBdab.

a. sRmab; 22.0 ≤≤ fmα /

)2.0(5361400

8.0

−+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=fm

yn

fl

hαβ

¬!&>!¦

b:uEnþminRtUvtUcCag mm125 b. sRmab; 2>fmα

β9361400

8.0

+

⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

yn

fl

h ¬!&>@¦

b:uEnþminRtUvtUcCag mm90 c. sRmab; 2.0<fmα

=h kRmas;kRmalxNÐGb,brmaedayK μanFñwmxagkñúg ¬tarag 17>1¦ ¬!&>#¦ Edl =nl clear span sRmab;TisEvgEdlvas;BIépÞQmKñarbs;ssr =β pleFobén clear span EvgelI clear span xøI =fmα témømFümén fα sRmab;RKb;FñwménRCugTaMgGs;rbs;bnÞHkRmal

=fα CapleFobénPaBrwgRkajTb;karBt;énmuxkat;Fñwm bcb IE lIPaBrwgRkajTb; karBt;énkRmalxNÐ scs IE EdlBT§½CMuvijedayG½kSbnÞHkRmalenABIelIFñwmRCug nImYy².

scs

bcbf IE

IE=α ¬!&>$¦

Edl cbE nig csE Cam:UDuleGLasÞicrbs;ebtugenAkñúgFñwm nigkRmalxNÐ erogKña. =bI m:Um:g;niclPaBTaMgmUlénmuxkat;FñwmeFobG½kSTIRbCMuTm¶n; ¬muxkat;FñwmrYmTaMg

beNþaykRmalxNÐenAelIRCugTaMgsgçagrbs;FñwmEdlesμ Inwgkm<s;FñwmBIelI b¤BI eRkamkRmalxNÐykmYyNaEdlFMCageK b:uEnþminRtUvFMCagbYndgkRmas; kRmalxNÐ¦.

=sI m:Um:g;niclPaBénmuxkat;kRmalxNÐTaMgmUl. b:uEnþ kRmas;kRmalxNÐminKYrtUcCagtémøxageRkam³



- sRmab;kRmalxNÐEdlman 0.2<fmα ³ mm125 - sRmab;kRmalxNÐEdlman 2>fmα ³ mm90 tarag 17>1 kRmas;kRmalxNÐGb,brmaedayK μanFñwmxagkñúg

edayK μan Drop Panel** man Drop Panel*** bnÞHkRmalxageRkA bnÞHkRmalxageRkA Yield

Stress yf * K μanFñwmxag manFñwmxag

bnÞHkRmalxagkñúg K μanFñwmxag manFñwmxag

bnÞHkRmalxagkñúg

280 33nl

36nl

36nl

36nl

40nl

40nl

420 30nl

33nl

33nl

33nl

36nl

36nl

* sRmab;EdkEdlman Yield Stress cenøaH 280 nig 420 kRmas;Gb,brmaTTYl)anBI linear interpolation. ** Drop panel RtUv)ankMNt;enAkñúg ACI Sections 13.3.7.7 nig 13.3.7.2 *** kRmalxNÐEdlmanFñwmcenøaHssrtambeNþayxagkñúg. témøén fα sRmab;FñwmminKYrmantémøtUcCag

8.0 .

RbsinebIFñwmminRtUv)aneRbI dUckñúgkrNI flat plate enaH 0=fα nig 0=fmα . smIkar ACI

Code sRmab;KNnakRmas;kRmalxNÐ h )anKit\T§iBlrbs;RbEvgElVg/ TRmg;bnÞHkRmal/ yield

stress rbs; Edk yf nigPaBrwgRkajTb;karBt;rbs;Fñwm. enAeBlFñwmEdlmanlkçN³rwgxøaMgRtUv)aneRbI smIkar !&>! Gacpþl;nUvkRmas;kRmalxNÐtUc ehIysmIkar !&>@ Gaclub. sRmab; flat plate nig flat slab enAeBl EdlFñwmxagkñúgminRtUv)aneRbI kRmas;kRmalxNÐGb,brmaGacRtUv)ankMNt;eday pÞal;BItarag 9>5 c én ACI Code EdlRtUv)anbgðajenATIenHKWtarag 17>1. karkMNt;rbs; ACI Code epSgeTotRtUv)ansegçbdUcxageRkam³

- sRmab;bnÞHkRmalEdlmanxagminCab;; FñwmxagcugEdlman 8.0=α RtUv)aneRbI ebImindUcenH eT kRmas;kRmalxNÐGb,brmaRtUv)anKNnatamsmIkar !&>! nig !&>@ RtUv)anbegáIn %10 y:ag tic ¬ ACI Code, Section 9.5.3 ¦.

- enAeBl drop panel RtUv)aneRbIedayK μanFñwm kRmas;kRmalxNÐGb,brmaKYrRtUv)anbnßy eday %10 . drop panel KYrRtUv)anlatsn§wgRKb;TisBIG½kSrbs;TRmedaycm¶ayminticCag



RbEvgElVgelI 6 RKb;TiscenøaHG½kSeTAG½kSénTRm nigTMlak;cuHeRkamkRmalxNÐy:agtic 4/h . karbnßyenH)anrYmbBa©ÚleTAkñúgtaragTI 17>1.

- edayminKittémøEdlTTYl)anBIsmIkar !&>! nig !&>@ kRmas;kRmalxNÐBIrTisminRtUvtUcCag krNIdUcteTA³ ¬!¦ mm125 sRmab;kRmalxNÐEdlK μanFñwm b¤ drop panel. ¬@¦ mm100 sRmab;kRmalxNÐK μanFñwmEtman drop panel. ¬#¦ mm90 sRmab; kRmalxNÐmanFñwmenA elIRCugTaMgbYnCamYynwg 2≥fmα nig mm125 sRmab; 2≤fmα ¬ ACI Code, Section

9.5.3¦. CMhanxageRkamsegçbBIkarKNnaTaMgenH³

!> sRmab;kRmalxNÐEdlK μanFwñmxagkñúg ¬ flat plate nig flat slab¦ a. KNnakRmas;kRmalxNÐedaypÞal;BItarag 17>1. b:uEnþsmIkar !&>! nig !&>@ k¾GacRtUv)an

eRbI ehIyCaTUeTAsmIkar !&>! lub. kRmas;kRmalxNÐGb,brmaKYrFMCag b¤esμ Inwg mm125 sRmab;kRmalxNÐEdlKμan drop panel nigFMCagb¤es μ I mm100 sRmab;kRmalxNÐEdlman drop panel.

b. enAxagEdlminCab; FñwmxagEdlman 8.0≥fα KYrRtUv)aneRbI. ebImindUecñaHeT kRmas; kRmalxNÐGb,brmaRtUv)anKNnaedaysmIkar !&>! nig !&>@ KYrRtUv)anbegáIneday %10 . karbegáIn %10 RtUv)anbBa©ÚleTAkñúgCYrQrTI 2 kñúgtaragTI 17>1 rYcehIy.

c. RbsinebI drop panel RtUv)aneRbIenAkñúg flat slab kRmas;kRmalxNÐGb,brmaRtUv)anbnßy eday %10 enAkñúgkrNIEdl drop panel latsn§wgenARKb;TisBIG½kSénTRmCamYycm¶aymin tUcCag 6/1 RbEvgElVg nigTMlak;eRkamkRmalxNÐy:agtic 4/h . karbnßyenH)anbBa¢Úl eTAkñúgemKuNéntarag 17>1.

@> sRmab;kRmalxNÐEdlmanFñwmenARKb;RCug ¬ 0>fmα ¦ a. KNna fmα nigbnÞab;mkKNnakRmas;kRmalxNÐGb,brmaBIsmIkar !&>! nig !&>@. kñúg

krNICaeRcInsmIkar !&>@ lub. b. kRmas;kRmalxNÐKYrFMCag b¤es μ Inwg mm125 sRmab;kRmalxNÐEdlman 0.2<fmα nigKYr

FMCag b¤esμ Inwg mm90 sRmab;kRmalxNÐEdlman 0.2≥fmα .



#> sRmab;RKb;kRmalxNÐ³ kRmas;kRmalxNÐEdltUcCagkRmas;Gb,brmaEdl[enAkñúgCMhan !> nig @> GacRtUv)aneRbI RbsinkarKNnabgðajfaPaBdabminFMCagkarkMNt;rbs; ACI Code,

Table 9.5 b EdlBnül;enAkñúgemeronTI 6.

]TahrN_17>1³ RbB½n§kRmal flat plate EdlmanTMhM m65.7 × RtUv)anRTenAelIssrkaer mm500 . edayeRbIsmIkar ACI Code kMNt;kRmas;kRmalxNÐGb,brmacaM)ac;sRmab;bnÞH

kRmalxagkñúg nigbnÞHkRmalkac;RCug dUcbgðajenAkñúgrUbTI 17>6. FñwmxagminRtUv)aneRbI. eK[ MPaf c 28' = nig MPaf y 420= .

dMeNaHRsay³

1> sRmab;bnÞHkRmalxNÐkac;RCugelx ! kRmas;Gb,brmaKW 30

nl ¬ MPaf y 420= nig K μanFñwmxagRtUv)aneRbI ¬emIltarag 17>1¦.



mmln 700050075001 =−= mmh 233

307000

min == yk mm250 müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbIedIm,IKNnakRmas;Gb,brmaCamYy 0== fmf αα .

2> sRmab;bnÞHkRmalxagkñúgelx #> CamYy MPaf y 420= kRmas;kRmalxNÐGb,brmaKW

mml

h n 21233min == yk mm220

müa:gvijeTot smIkar !&>! nig !&>@ GacRtUv)aneRbI. RbsinebIRKb;bnÞHkRmalxNÐTaMgGs;eRbIkRmas;dUcKña enaHeKGacyk

mmh 250min = .

]TahrN_17>2³ RbB½n§kRmalxNÐdUcbgðajenAkñúgrUbTI 17>7 EdlpSMeLIgedaykRmaltan; nigFñwm enAelITaMgBIrTisEdlRTedayssrkaerEdlmanRCug mm500 . edayeRbIsmIkar ACI Code kMNt; kRmas;kRmalxNÐGb,brmacaM)ac;sRmab;bnÞHkRmalxagkñúg. eK[ MPaf c 21' = nig


1> edIm,IeRbIsmIkar !&>! fmα RtUv)anKNnamun. dUcenH eKcaM)ac;kMNt; bI / sI nig fα sRmab; Fñwm nigkRmalxNÐtamTisEvg nigTisxøI.

2> m:Um:g;niclPaBrbs;FñwmTaMgmUl bI RtUv)anKNnasRmab;muxkat;dUcbgðajenAkñúgrUbTI 17>7 b EdlRtUv)anbegáIteLIgedayFñwm nigEpñksgçagxøHrbs;kRmalxNÐ yx = b:uEnþminRtUvFMCag 4 bYndgkRmas;kRmalxNÐ. sn μt; cmh 18= ehIyvaRtUv)anepÞógpÞat;enAeBleRkay enaH

cmcmyx 72418381856 =×<=−== . dUcenH cmbe 11623840 =×+= nigmuxkat; GkSr T RtUv)anbgðajenAkñúgrUbTI 17>7 c . kMNt;TIRbCMuTm¶n;rbs;muxkat;edayKitm:Um:g;eFobkMBUlrbs;søab³ RkLaépÞsøab 2208811618 cm=×= RkLaépÞRTnug 215203840 cm=×=



RkLaépÞsrub 23608cm y360837152092088 =×+×

cmy 8.20= ( ) ( ) ( ) 42323 6.9289248.219152038

12408.11208818

12116 cmIb =⎥⎦

⎤⎢⎣⎡ −++⎥⎦

⎤⎢⎣⎡ +=

3> m:Um:g;niclPaBénkRmalxNÐtamTisedAEvgKW

12

3bhIl = Edl cmb 600= nig cmh 18= 43 29160018

12600 cmIl ==

flα ¬tamTisedAEvg¦ 19.3291600

6.928924===

s

bEIEI

4> m:Um:g;niclPaBénkRmalxNÐtamTisedAxøIKW



43 3693601812760 cmI s ==

fsα ¬tamTisedAxøI¦ 51.2369360

6.928924===

s

bEIEI

5> fmα CatémømFümén fsα nig flα 85.2

251.219.3

=+

=fmα 6> 29.1

5.065.06.7=

−−

=β 7> kMNt; minh edayeRbIsmIkar !&>@ ¬ mln 1.7= ¦³

( ) mh 148.02.082.229.1536

14004208.01.7

min =−×+

⎟⎠⎞

⎜⎝⎛ +

=

b:uEnþ témøenHminRtUvtUcCag h Edl[edaysmIkar !&>@ ¬ 0.2>fmα ¦ mh 164.0

29.193681.7

=×+

= müa:geTot cmh 90min = . dUcenH cmh 4.16= lub. eKGacTTYlykkRmas;kRmalxNÐEdl)ansnμt; cmh 18= . cMNaMfa enAkñúgkrNIGnuvtþn_CaeRcIn smIkar !&>@ manlkçN³lub.

17>7> ersIusþg;kmøaMgkat;TTwgrbs;kRmalxNÐ (Shear Strength of Slabs)

sRmab;RbB½n§kRmalxNÐBIrTis bnÞHkRmalRtUvEtmankRmas;RKb;RKan;edIm,ITb;nwgm:Um:g;Bt; TaMgBIr nigkmøaMgkat;TTwgenARtg;muxkat;eRKaHfñak;. edIm,IGegátlT§PaBTb;kmøaMgkat;TTwgénkRmal xNÐBIrTis krNIxageRkamRtUv)anBicarNa.

17>7>1> kRmalxNÐBIrTisEdlRTedayFñwm (Two-Way Slabs Supported on Beams) muxkat;eRKaHfñak;rbs;kRmalxNÐBIrTisEdlRTedayFñwmKWsßitenAcm¶ay d BIépÞénFñwmTRm ehIy lT§PaBTb;kmøaMgkat;TTwgénmuxkat;nImYy²KW 6/' bdfV cc φφ = . enAeBlEdlFñwmman lkçN³rwg nigGacbBa¢ÚnbnÞúkkRmaleTAssr vaRtUv)ansnμt;[RTbnÞúkEdleFVIGMeBImkelIépÞkRmal



xNÐEdlB½T§ edaybnÞat; o45 EdlKUsecjBIRCugEkg dUcbgðajenAkñúgrUbTI 17>8. bnÞúkenAelIépÞ ctuekaNBñaynwgRtUv)anRTedayFñwmEvg AB nig CD b:uEnþbnÞúkenAelIépÞRtIekaNnwgRtUv)anRTeday FñwmxøI AC nig BD .

kmøaMgkat;TTwgkñúgmYyÉktþaTTwgrbs;kRmalmantémøx<s;bMputenAcenøaH E nig F tam

TisTaMgBIr ehIy )2/( 2lwV uu = Edl uw CabnÞúkemKuNBRgayesμ IkñúgmYyÉktþaépÞ. RbsinebIEdkTb;kmøaMgkat;TTwgminRtUv)andak; kmøaMgkat;TTwgenAcm¶ay d BIépÞénFñwm udV

RtUvEtes μ Inwg

6' bdf

VV ccud

φφ ≤≤

Edl ⎟⎠⎞

⎜⎝⎛ −= d

lwV uud 2

2

17>7>2> kRmalxNÐBIrTisEdlKμanFñwm (Two-Way Slabs without Beams)

Flat plate nig flat slab K μanFñwmeT dUcenHkRmalxNÐRtUv)anRTedayssredaypÞal;. sRmab; kRmalxNÐEbbenHkugRtaMgkmøaMgkat;TTwgBIrRtUv)aneFVIkarGegát TImYyKWkmøaMgkat;TTwgmYyTis b¤ kmøaMgkat;TTwgFñwm (one-way shear or beam shear). muxkat;eRKaHfñak;RtUv)anykenAcm¶ay d BIépÞ



énssr ehIykRmalxNÐRtUv)anBicarNadUcFñwmEdlmanTTwgFMsßitenAcenøaHTRm dUckñúgkrNIFñwmmYy Tis (one-way beam). lT§PaBTb;kmøaMgkat;TTwgénmuxkat;ebtugKW 6/' bdfV cc φφ = . RbePTTI BIrénkmøaMgkat;TTwgEdlRtUvsikSaKWkmøaMgkat;TTwgBIrTis b¤kmøaMgkat;pug (two-way shear or

punching shear) dUcEdl)anerobrab;enAkñúgkarKNnaeCIgtag. kar)ak;edaykmøaMgkat;ekItmantam beNþaykMNat;ekaN b¤kMNat;BIra:mIt (truncated cone or pyramid) CMuvijssr. muxkat;eRKaHfñak; sßitenAcm¶ay 2/d BIépÞssr/ column capital/ b¤ drop panel ¬rUbTI 17>9 a¦. RbsinebIEdkkmøaMg kat;TTwgminRtUv)andak; ersIusþg;kmøaMgkat;TTwgrbs;ebtugKWtémøEdltUcCageKkñúgcMeNamsmIkar !&>% nig !&>^³

3'

'31

61 dbf

dbfV ococc

φβ

φ ≤⎟⎟⎠

⎞⎜⎜⎝

⎛+= ¬!&>%¦

Edl =ob brimaRténmuxkat;eRKaHfñak; =β pleFobénRCugEvgrbs;ssrelIRCugxøI ¬b¤RkLaépÞbnÞúk¦ dbf

bd

V oco

sc '2

12 ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

αφφ ¬!&>^¦

Edl sα esμ I 40 sRmab;ssrxagkñúg/ es μ I 30sRmab;;ssrxag nigesμ I 20 sRmab;ssrkac;RCug. enAeBlEdlEdkkmøaMgkat;TTwgRtUv)andak; ersIusþg;kmøaMgkat;TTwgminKYrelIs dbfV occ '

2φφ ≤ ¬!&>&¦

17>7>3> EdkkmøaMgkat;TTWgenAkñúgkRmalxNÐBIrTisEdlKμanFñwm

Shear Reinforcement in Two-Way Slabs Without Beams

enAkñúgRbB½n§kRmalxNÐ flat plate nig flat slab kRmas;kRmalxNÐEdl)aneRCIserIsGacnwg minRKb;RKan;edIm,ITb;nwgkugRtaMgkmøaMgkat;TTwgEdlGnuvtþeT. kñúgkrNIenH eKGacbegáInkRmas; kRmalxNÐ b¤dak;EdkTb;kmøaMgkat;TTwg. ACI Code GnuBaØatkareRbIEdkTb;kmøaMgkat;TTwgCa shearhead nig anchored bar b¤ wire.

Shearhead pSMeLIgedayEdkragGkSr I b¤GkSr C EdlpSarExVgCabYn nigRtUv)andak;enAkñúg kRmalxNÐBIelIssr ¬rUbTI 17>9 c, d ¦. karKNna Shearhead minGnuvtþsRmab;ssrxageRkA Edlm:Um:g;Bt; nigm:Um:g;rmYlmantémøFMEdlRtUv)anbMElgcenøaHkRmalxNÐ nigssr. ACI Code,

Section 11.12.4 bgðajfaenARtg;muxkat;eRKaHfñak; ersIusþg;kmøaMgkat; nominal nV minKYrelIs



3/' dbf oc b:uEnþRbsinebIEdk shearhead RtUv)andak; nV minKYrelIs 12/'7 dbf oc . edIm,IkMNt; TMhMrbs; shearhead, ACI Code, Section 11.12.4 pþl;nUvkarkMNt;dUcteTA³





!> pleFob vα rvagPaBrwgRkaj IEs rbs;éd shearhead nigPaBrwgRkajénmuxkat;EdleRbH smasEdlmanTTWg dc +2 minRtUvtUcCag 15.0 .

@> søabrgkarsgát;énEdkragminRtUvmanTItaMgenAmþúM d13.0 énépÞrgkarsgát;rbs;kRmalxNÐ. #> km<s;rbs;EdkragminRtUvFMCag 70 énkRmas;RTnug. $> lT§PaBTb;m:Um:g;)aøsÞic PM énédnImYy²rbs; shearhead RtUv)anKNnaeday

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ ++=

221c

lhn

VM vvv

uP αφ ¬ACI Code, Eq. 11.37 ¦ ¬!&>*¦

Edl 9.0=φ =uV kmøaMgkat;TTwgemKuNCMuvijbrievNénépÞssr n = cMnYnéd =vh km<s;rbs; shearhead =vl RbEvg shearhead Edlvas;BIG½kSssr

%> muxkat;kRmalxNÐeRKaHfñak;sRmab;kmøaMgkat;TTWgRtUvEtkat;éd shearhead enAcm¶ayes μ Inwg )2/)(4/3( 1clv − BIépÞssreTcugénédrbs; shearhead dUcbgðajenAkñúgrUbTI 17>9 c. mux

kat;eRKaHfñak;RtUvEtmanbrimaRtGb,brma ob b:uEnþvaminRtUvenACitCag 2/d BIépÞrbs;ssr. ^> Shearhead RtUv)anBicarNa[cUlrYmkñúgkarEbgEckm:Um:g;eLIgvij vM eTAceRmokkRmalxNÐ

elIssrnImYy²dUcxageRkam³ ⎟

⎠⎞

⎜⎝⎛=

221clV

nM vuvv αφ ¬ACI Code, Eq. 11.38¦ ¬!&>(¦

b:uEnþvaminRtUvtUcCagtémøtUcCageKkñúgcMeNam %30 énm:Um:g;emKuNEdlcaM)ac;enAkñúgceRmok elIssr karpøas;bþÚrm:Um:g;ceRmokelIssrelIRbEvg vl b¤ pM Edl[enAkñúgsmIkar !&>*.

kareRbI anchored bent bar b¤ wire k¾RtUv)anGnuBaØateday ACI Code, Section 11.12.3. Edk Edldak;enAxagEpñkxagelIrbs;ssr niglT§PaBékarteRmobEdkRtUv)anbgðajenAkñúgrUbTI 17>9 e. enAeBlEdl bar b¤ wire RtUv)aneRbICaEdkTb;kmøaMgkat;TTwg enaHersIusþg;kmøaMgkat;TTWg nominal KW³

sdfAdbf

VVV yvocscn +=+=

6' ¬!&>!0¦

Edl vA CaRkLaépÞEdkkgsrub nig ob CaRbEvgénmuxkat;eRKaHfñak;énkmøaMgkat;BIrTisenA cm¶ay 2/d BIépÞssr. ersIusþg;kmøaMgkat; nominal nV minRtUvFMCag 2/' dbf oc .



kareRbIEdkkmøaMgkat;enAkñúg flat plate kat;bnßykRmas;kRmalxNÐ nigenAEtrkSaPaBrabesμ I rbs;BidanedIm,Ikat;bnßyéføBum<. TRmg; stirrup cage sRmab;EdkkmøaMgkat;TTwgRtUv)anbgðajenAkñúg rUbTI 17>9 f . RbePTmü:ageToténEdkkmøaMgkat;pSMeLIgeday studded steel strip ¬rUbTI 17>9 g¦. Steel strip RtUv)andak;CamYy bar chair nigRtUv)anP¢ab;eTAnwgBum< edayCMnYs stirrup gage . ersIusþg; yalrbs;Edk stud RtUv)ankMNt;enAcenøaH MPa280 nig MPa420 edIm,ITTYl)an anchorage eBj eljenAeBlbnÞúkemKuN.

17>8> karviPaKkRmalxNÐBIrTisedayviFIKNnaedaypÞal; Analysis of Two-Way Slabs by the Direct Design Method

Direct design method CaviFIRbhak;RbEhl (approximate method) RtUv)anbegáIteLIgeday ACI Code edIm,IKNnam:Um:g;KNnaenAkñúgkRmalxNÐBIrTisEdlRTbnÞúkBRgayesμ I. edIm,IeRbIviFIenH kar kMNt;xøHRtUv)anelIkeLIgeday ACI Code, Section 13.6.1. 17>8>1> karkMNt; (Limitations)

!> vaRtUvmankRmalxNÐCab;Kñay:agticbIkñúgTismYy² @> kRmalxNÐRtUvEtkaer b¤ctuekaNEkg. pleFobElVgEvgelIElVgxøIrbs;kRmalminRtUvFM

CagBIr #> ElVgEdlenAEk,rkñúgTisnImYy²minRtUvxusKñaedayFMCagmYyPaKbIénElVgEvgCag. $> ssrminRtUvlyecjBIG½kSssrdéTCaeRcIneTotedaytémøGtibrma %10 énRbEvgElVg

enAkñúgTislyecj. %> bnÞúkTaMgGs;RtUvEtBRgayes μ I ehIypleFobénbnÞúkGefrelIbnÞúkefrminRtUvFMCag 2 . ^> RbsinebImanFñwmenARKb;RCug pleFobénPaBrwgRkajEdlTak;TgkñúgTisEkgTaMgBI

212

221 / ll ff αα minRtUvtUcCag 2.0 nigFMCag 0.5 .

17>8>2> m:Um:g;sþaTicemKuNsrub (Total Factored Static Moment)

RbsinFñwmTRmsamBaØRTbnÞúkBRgayesμ I w ¬ mkN / ¦ enaHm:Um:g;Bt;viC¢manGtibrmaekItmanenA



kNþalElVgniges μ Inwg 8/21wlM o = Edl 1l CaRbEvgElVg. RbsinebIRtUv)anbgáb;cugTaMgsgçag b¤Cab;

CamYynwgm:Um:g;GviC¢manesμ IKñaenAcugTaMgsgçag enaHm:Um:g;srub po MM = ¬m:Um:g;viC¢manenAkNþal ElVg¦ nM+ ¬m:Um:g;GviC¢manenAelITRm¦ 8/2

1wl= ¬rUbTI 17>10¦. \LÚvRbsinebIFñwm AB RTbnÞúk W BIkRmalxNÐEdlmanTTwg 2l Ekgnwg 1l enaH 2lwW u=

ehIym:Um:g;srubKW ( ) 8/212 lwlM o = Edl =uw GaMgtg;sIuetbnÞúkKitCa 2/ mkN . kñúgsmIkarenH

m:Um:g;BitR)akdEdlekItmanenAeBl 1l esμ Inwg clear span cenøaHTRm A nig B . RbsinebI clear span RtUv)ankMNt;eday nl enaH

( )8

2

2n

uol

lwM = (ACI Code, Eq. 13.3)

Clear span nl RtUv)anvas;BIépÞeTAépÞTRmkñúgTisedAEdlm:Um:g;RtUv)anBicarNa b:uEnþminRtUvticCag 65.0 dgRbEvgElVgBIG½kSeTAG½kSTRm. épÞénTRmEdlmanm:Um:g;GviC¢manKYrRtUv)anKNna RtUv)an

bgðajenAkñúgrUbTI 17>11. RbEvg 2l RtUv)anvas;kñúgTisedAEkgnwg nl ehIyes μ ITisedAcenøaHG½kSeTA G½kSrbs;TRm ¬TTwgkRmalxNÐ¦. m:Um:g;srub oM EdlKNnakñúgTisedAEvgRtUv)anKitCa olM nigkñúgTisedAxøIRtUv)anKitCa osM .

enAeBlm:Um:gsrub oM RtUv)anKNnakñúgTisedAmYy vaRtUvEbgEckCam:Um:g;viC¢man pM nigm:U m:g;GviC¢man nM GBa¢wgehIyeTIb npo MMM += ¬rUbTI 17>10¦. enaHm:Um:g;nImYy² pM nig

nM RtUv)anEbgEckqøgkat;TTwgkRmalxNÐcenøaHceRmokssr nigceRmokkNþaldUcEdl)anBnül; y:agxøI.



17>8>3> karEbgEckm:Um:g;tambeNþaykñúgkRmalxNÐ (Longitudinal Distribution of Moment in Slabs) enAkñúgkRmalxagkñúg m:Um:g;sþaTicsrub oM RtUv)anEbgEckenAkñúgm:Um:g;BIr m:Um:g;viC¢man pM

enA kNþalElVgesμInwg oM35.0 nigm:Um:g;GviC¢man nM enATRmnImYy²esμ Inwg oM65.0 dUcbgðajenA kñúgrUbTI 17>12. témøm:Um:g;TaMgenHQrelIkarsnμt;fakRmalxagkñúgCab;kñúgTisTaMgBIr ehIyman RbEvgElVg nigbnÞúkRbhak;RbEhlesμ IKña dUcenHtMNxagkñúgK μanmMurgVilFMeT. elIsBIenHeTot m:Um:g;man témøRbEhlnwgm:Um:g;rbs;Fñwmbgáb;cugTaMgBIrEdlrgbnÞúkBRgayes μ I Edlm:Um:g;GviC¢manenAelITRmes μ I BIrdgm:Um:g;GviC¢manenAkNþalElVg. enAkñúgrUbTI 17>12 RbsinebI 21 ll > / enaHkarEbgEckm:Um:g;enA kñúgTisedAEvg nigTisedAxøIKW³

( )

8

21

2n

uoll

lwM = olpl MM 35.0= oln MM 65.01 =

( )8

22

1n

uosl

lwM = osps MM 35.0= osns MM 65.0=



RbsinebITMhMénm:Um:g;GviC¢manenAelITRmxagkñúgmantémøxusKñaedaysarRbEvgElVgminesμ IKña ACI Code kMNt;[eRbIm:Um:g;EdlFMCagsRmab;KNnasrésEdk.

enAkñúgbnÞHkRmalxageRkA bnÞúkkRmalxNÐEdlGnuvtþelIssrxageRkA)anmkEtBIRCugmçag

bNþal[ekItmanm:Um:g;mines μ I (unbalanced moment) nigmMurgVilenAtMNxageRkA. dUcenH m:Um:g; viC¢manenAkNþalElVg nigm:Um:g;GviC¢manenAelITRmxagkñúgTImYynwgekIneLIg.TMhMénmMurgViléntMNxag eRkAkMNt;nUvkarelIneLIgnUvm:Um:g;kNþalElVg nigm:Um:g;enAelITRmxagkñúg. ]TahrN_ RbsinebIRCug xageRkACaTRmsamBaØ dUckñúgkrNIkRmalxNÐenAelICBa¢aMg ¬rUbTI 17>13¦ m:Um:g;kRmalenARtg;épÞ CBa¢aMgesμ I 0 m:Um:g;viC¢manenAkNþalElVgGacykesμ Inwg op MM 63.0= nigm:Um:g;GviC¢manenATRmxag kñúgKW os MM 75.0= . témøTaMgenHbMeBjlkçxNÐsmIkarsþaTic



( )oonpo MMMMM 75.063.0 21

21 +=+=

sRmab;RbB½n§kRmal-ssr (slab-column floor system) tMNxageRkAmankarTb; (restraint) xøH Edlpþl;edayPaBrwgRkaJTb;karBt;énkRmalxNÐ nigedayPaBrwgRkajTb;karBt;énssrxageRkA.

eyagtam ACI Code, Section 13.6.3 m:Um:g;sþaTicsrub oM enAkñúgElVgcugRtUv)anEbgEckeday pleFobepSgKñaedayeyagtamtarag 17>2 nigrUbTI 17>14. emKuNm:Um:g;enAkñúgCYrQrTI 1 sRmab; RCugEdlminmankarTb;KWQrelIkarsnμt;fa pleFobénPaBrwgRkajTb;karBt;rbs;ssrelIPaBrwg RkajTb;karBt;smasrvagkRmalxNÐ nigFñwmenARtg;tMN ecα KWesμ IsUnü. emKuNénCYrQrTI 2 KWQr elIkarsnμt;fapleFob ecα esμ InwgGnnþ. emKuNm:Um:g;enAkñúgCYrQrTI 3/ TI4 nigTI5 RtUv)anbegáIt eLIgedaykarviPaKRbB½n§kRmalCamYynwglkçxNÐragFrNImaRt niglkçxNÐTRmepSgKña.

taragTI 17>2 karEbgEckm:Um:g;enAkñúgbnÞHkRmalxagcug

RCugxageRkA kRmalxNÐEdlK μan FñwmenAcenøaHTRmxag

kñúg minRtUv )anTb;

¬!¦ Tb;eBj

¬@¦

kRmalxNÐ EdlmanFñwm enAcenøaHRKb;

TRm ¬#¦

manFñwm xageRkA

¬$¦

K μanFñwm xageRkA

¬%¦ m:Um:g;emKuNGviC¢manxageRkA 0 65.0 16.0 30.0 26.0

m:Um:g;emKuNviC¢man 63.0 35.0 57.0 50.0 52.0 m:Um:g;emKuNGviC¢manxageRkA 75.0 65.0 70.0 70.0 70.0



17>8>4> karEbgEckm:Um:g;tamTTwgkñúgkRmalxNÐ

(Transverse Distribution of Moment in Slabs) m:Um:g;tambeNþayEdl)anBnül;xagelIKWsRmab;TTwgTaMgmUlrbs;eRKagGKarsmmUl. TTwg

eRKag enHCaplbUkénTTwgceRmokelIssrBIr CamYynwgTTwgceRmokkNþalBIrénbnÞHkRmalBIr Ek,rKña dUcbgðaj enAkñúgrUbTI 17>15. karEbgEcktamTTwgénm:Um:g;tambeNþayeTAceRmok kNþal nigceRmokelIssrKW CaGnuKmn_énpleFob 12 / ll

stiffness slabstiffness beam

==scs

bcbf IE

IEα ¬!&>!@¦



lengthspan beam toequal width of slab a ofrigidity flexuralsection beam edge ofrigidity torsional

2==

scs

cbt IE

CEβ

¬!&>!#¦ Edl ∑ ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−==

363.01constant torsional

3 yxy

xC ¬!&>!$¦

Edl x nig y CaTTwg nigbeNþayrbs;muxkat;ctuekaN. PaKryénm:Um:g;KNnanImYy²Edl nwgRtUvEbgEckeTAceRmokelIssr nigceRmokkNþalsRmab;bnÞHkRmalxagkñúg nigbnÞHkRmal xageRkA RtUv)an[enAkñúgtarag 17>3 dl; 17>6. enAkñúgbnÞHkRmalKMrUxagkñúg EpñkxøHénm:Um:g; KNna EdlminRtUv)andak;eTAkñúgceRmokelIssr ¬tarag 17>3¦ RtUv)anTb;edayceRmokkNþal Bak;kNþalEdlRtUvKña. kareFVI linear interpolation sRmab;témø 12 / ll EdlenAcenøaH 5.0 nig

0.2 nigsRmab;témø 121 / llfα EdlenAcenøaH 0 nig 1 RtUv)anGnuBaØateday ACI Code. BI tarag 17>3 eyIgGacemIleXIjfa enAeBlFñwmminRtUv)aneRbI dUckñúgkrNI flat plate nig flat

slab 01 =fα . PaKrycugeRkayénm:Um:g;enAkñúgceRmokelIssr nigceRmokkNþalCaGnuKmn_én oM RtUv)an[enAkñúgtaragTI 17>4.

sRmab;kRmalxageRkA Epñkénm:Um:g;KNnaEdlminRtUv)andak;enAkñúgceRmokelIssr ¬tarag 17>5¦ RtUv)anTb;edayceRmokkNþalBak;kNþalEdlRtUvKña. mþgeTot kareFVI linear interpola-

tion cenøaHtémøEdlbgðajenAkñúgtarag 17>5 RtUv)anGnuBaØateday ACI Code, Section

13.6.4.2. enAeBlEdl FñwmminRtUv)aneRbIenAkRmalxageRkA dUckrNI flat plate nig flat slab

edayK μanFñwmxag (spandrel beam) 01 =fα / 0=C nig 0=tβ . enHmann½yfacugssr pþl; nUvkarTb;sRmab;cugkRmalxageRkA. témøGnuvtþn_éntarag 17>5 sRmab;krNIBiessenHRtUv)an bgðajenAkñúgtarag 17>6 nigrUbTI 17>15. tarag 17>3 PaKryénm:Um:g;tambeNþayenAkñúgceRmokelIssr sRmab;bnÞHkRmalxagkñúg (ACI Code, Section 13.6.4)

pleFob 12 / ll 121 / llfα 5.0 0.1 0.2

0 75 75 75 m:Um:g;GviC¢manenAelITRmxagkñúg 0.1≥ 90 75 45

0 60 60 60 m:Um:g;viC¢manenAEk,rkNþalElVg 0.1≥ 90 75 45



tarag 17>4 PaKryénm:Um:g;enAkñúgkRmalxNÐxagkñúgBIrTisEdlKμanFñwm ( 01 =α )

m:Um:g;KNnasrub ( ))!(!

!8

21

2 rnrnl

lwM nuo −⎟

⎟⎠

⎞⎜⎜⎝

⎛=

m:Um:g;GviC¢man m:Um:g;viC¢man m:Um:g;tambeNþayenAkñúgkRmalmYy oM65.0− oM35.0±

ceRmokelIssr ( ) oo MM 49.065.075.0 −=− ( ) oo MM 21.035.060.0 =

ceRmokkNþal ( ) oo MM 16.065.025.0 −=− ( ) oo MM 14.035.040.0 =



tarag 17>5> PaKryénm:Um:g;tambeNþayenAkñúgceRmokelIssr sRmab;bnÞHkRmalxageRkA (ACI Code, Section 13.6.4)

pleFob 12 / ll 121 / llfα tβ 5.0 0.1 0.2

0 0 75 75 75 5.2≥ 90 75 45 0.1≥ 0 60 60 60

m:Um:g;GviC¢manenAelITRmxag eRkA

5.2≥ 90 75 45

m:Um:g;viC¢manenAEk,rkNþalElVg 0 60 60 60

0.1≥ 90 75 45

0 75 75 75 m:Um:g;GviC¢manenAelITRmxagkúñg 0.1≥ 90 75 45

tarag 17>6> PaKryénm:Um:g;tambeNþayenAkñúgceRmokelIssr nigceRmokkNþal ¬sRmab;pleFob 12 / ll ¦ eday[ 01 == tf βα

% ceRmokelIssr ceRmokkNþal m:Um:g;cugeRkayCaGnuKmn_én

oM nig ecα ¬ceRmokelIssr¦

m:Um:g;GviC¢manenAelITRmxageRkA 100 oM26.0 0 ( ) oec

M⎥⎦

⎤⎢⎣

⎡+ α11

65.0

m:Um:g;viC¢man¬ oM52.06.0 × ¦ 60 oM312.0 oM208.0 ( ) oec

M⎥⎦

⎤⎢⎣

⎡+

−α11

28.063.0

m:Um:g;GviC¢manenAelIMTRmxagkñúg ¬ oM70.075.0 × ¦ 75 oM52.0 oM175.0 ( ) o

ecM⎥⎦

⎤⎢⎣

⎡+

−α11

10.075.0

BItarag 17>6 eyIgeXIjfaenAeBlEdlFñwmxagminRtUv)aneRbIsRmab;kRmalxageRkA 0=tβ nigm:Um:g;KNna %100 RtUv)anTb;edayceRmokelIssr. ceRmokkNþalnwgminTb;m:Um:g;NamYy eT dUcenHbrimaNEdkGb,brmaRtUv)andak;. ACI Code, Section 13.6.4.3 kMNt;faenAeBlTRm xageRkACassr b¤CBa¢aMgEdlRtUv)anBnøÚtsRmab;cm¶ayes μ InwgbIPaKbYnRbEvgElVgTTwg 2l Edl



eRbIedIm,I kMNt; oM m:Um:g;GviC¢manxageRkAEdlRtUv)anEbgEckes μ Ikat;tam 2l . enAeBlEdlFñwm RtUv)andak;tambeNþayG½kSssr ACI Code, Section 13.6.5 tRmUvfam:Um:g;RtUvEtsmamaRtedIm,I karBarm:Um:g; %85 enAkñúgceRmokelIssr RbsinebI 0.1)/( 121 ≥llfα . sRmab;témø )/( 121 llfα enAcenøaH 0.1 nig 0 m:Um:g;EdlmankñúgFñwmRtUv)ankMNt;edayeRbI linear interpolation . m:Um:g;k¾ RtUvEtsmamaRtedIm,IkarBarm:Um:g;bEnßmEdlekItedaybnÞúkTaMgGs;EdlGnuvtþedaypÞal;eTAelIFñwm edaybBa©Ül TaMgTm¶n;rbs;tYFñwm EdlKitBIeRkamkRmal. Epñkénm:Um:g;Edlmin)andak;eTAkñúgFñwm RtUv)anTb;edaykRmalxNÐenAkñ μ úgceRmokelIssr.

17>8>5> karpþl;rbs; ACI sRmab;\T§iBlrbs;KMrUénkardak;bnÞúk

(ACI Provisions for Effects of Pattern Loading)

enAkñúgrcnasm½<n§Cab; m:Um:g;Bt;Gtibrma nigGb,brmaenARtg;muxkat;eRKaHfñak;RtUv)anTTYl edaykardak;bnÞúkGefrtamKMrUkMNt;mYyedIm,IbegáIttémøx<s;bMput. kardak;bnÞúkGefrenARKb;ElVg TaMgGs; nwgminbegáItm:Um:g;Bt;viC¢man b¤m:Um:g;Bt;viC¢manGtibrmaeT.m:Um:g;Gtibrma nigGb,brma GaRs½yCacMbg nwgkrNIxageRkam³

!> pleFobénbnÞúkGefrelIbnÞúkefr. pleFobx<s;nwgbegáIn\T§iBlrbs;KMrUénkardak;bnÞúk (patter loading).

@> pleFobPaBrwgRkajssrelIFñwm. pleFobtUcnwgbegáIn\T§iBlrbs;KMrUénkardak;bnÞúk. #> KMrUénkardak;bnÞúk. m:Um:g;viC¢manGtibrmaenAkñúgElVgrg\T§iBltictYcBIKMrUénkardak;bnÞúk. edIm,IkMNt;m:Um:g;emKuNKNnaenAkñúgrcnasm<n§½Cab; ACI Code, Section 13.7.6 kMNt;dUc

xageRkam³ !> enAeBlKMrUénkardak;bnÞúkRtUv)ansÁal; eRKagsmmUlKYrRtUv)anviPaKsRmab;bnÞúkenaH. @> enAeBlbnÞúkGefrERbRbYl b:uEnþminFMCagbIPaKbYnénbnÞúkefr DL ww 75.0≤ b¤enAeBl

EdlRKb;kRmalTaMgGs;RtUv)andak;bnÞúkGefrkñúgtMNalKña karviPaKeRKagEdlmandak; bnÞúkGefremKuNeBjeRKagRtUv)anGnuBaØat.

#> sRmab;lkçxNÐénkardak;bnÞúkepSgeTot eKGnuBaØat[sn μt;fa m:Um:g;emKuNviC¢man GtibrmaenAEk,rkNþalElVgekItmanCamYynwg 75.0 énbnÞúkGefremKuNeBjenAelI kRmal nigenAelIkRmalqøas;.



sRmab;m:Um:g;emKuNGviC¢manGtibrmaenAkñúgkRmalxNÐelITRm RtUv)aneKGnuBaØat[ snμt;fa 75.0 énbnÞúkGefremKuNGnuvtþEtenAelIkRmalEk,r.

$> m:Um:g;emKuNminKYryktUcCagm:Um:g;EdlekIteLIgCamYybnÞúkGefremKuNeBjenAelIkRmal EdlCab;TaMgGs;eT.

17>8>6> karlMGitsrésEdk (Reinforcement Details)

eRkayeBlPaKryTaMgGs;énm:Um:g;sþaTicenAkñúgceRmokelIssr nigceRmokkNþalRtUv)an kMNt;brimaNsrésEdkk¾GacRtUv)anKNnasRmab;m:Um:g;viC¢man nigGviC¢manenAkñúgceRmoknImYy² dUcEdl)aneFVIsRmab;FñwmenAkñúgemeronTI4 2

2bdRadfAM uysu =⎟

⎠⎞

⎜⎝⎛ −= φ ¬!&>!%¦

KNna uR nigkMNt;PaKryEdk ρ edayeRbItarag]bsm<½n§ B b¤eRbIsmIkarxageRkam³ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

c

yyu f

ffR

'7.11

ρφρ ¬!&>!^¦

Edl 9.0=φ . RkLaépÞmuxkat;EdkKW bdAs ρ= . enAeBlEdlkRmas;kRmalxNÐRtUvnwgkar kMNt; kRmas;kRmalxNÐEdl)anerobrab;kñúgEpñkTI 4> enaHeK minRtUvkarEdkrgkarsgát;eT. rUbTI 13>3>8 én ACI Code bgðajRbEvgGb,brmaénEdk nigkar lMGitsrésEdksRmab;kRmalEdl K μanFñwm ehIyvak¾RtUvbgðajenATIenHEdr ¬rUbTI 17>16¦. KMlatEdkenAkñúgkRmalxNÐminRtUvFM CaglImItGtibrmarbs; ACI EdlmanKMlat mm450 b¤BIrdgkRmas; kRmalykmYyNaEdltUc CageK. 17>8>7> viFIPaBrwgRkajEdlRtUv)anEktRmUvsRmab;ElVgcug

(Modified Stiffness Method for End Spans)

enAkñúgviFIenH PaBrwgRkajrbs;FñwmxagcugkRmal nigrbs;ssrxageRkARtUv)anCMnYsedayPaB rwgRkajénssrsmmUl ecK . PaBrwgRkajTb;karBt;énssrsmmUl ecK GacRtUv)anKNnaBI smIkarxageRkam³

tcec KKK111

+=∑

b¤ ∑∑

+=

tc

cec KK

KK

/1 ¬!&>!&¦





Edl =ecK PaBrwgRkajTb;nwgkarBt;rbs;ssrsmmUl =cK PaBrwgRkajTb;nwgkarBt;rbs;ssrBitR)akd =tK PaBrwgRkajTb;karrmYlrbs;Fñwmxag plbUkénPaBrwgRkajrbs;ssrxagelI nigxageRkamkRmalxNÐGacRtUv)anykdUcxag

eRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛+=∑

2

2

1

14c

c

c

cc L

ILI

EK ¬!&>!*¦

Edl 1cI nig 1cL Cam:Um:g;niclPaB nigRbEvgrbs;ssrxagelInIv:UkRmalxNÐ nig 2cI nig 2cL Cam:Um:g;niclPaB nigRbEvgrbs;ssrxageRkamnIv:UkRmalxNÐ. PaBrwgRkajTb;nwgkarrmYl

rbs;Fñwmcug tK GacRtUv)ankMNt;dUcxageRkam³ ∑

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= 3

2

22 1

9

lc

l

CEK cs

t ¬!&>!(¦

Edl =2c TMhMrbs;ssrctuekaNEkg b¤ctuekaNEkgsmmUl/ capital column b¤ bracket Edlvas;enAelIElVgTTwgénRCugnImYy²rbs;ssr.

=csE m:UDuleGLasÞicrbs;ebtugkRmal =C efrrmYl (torsion constant) EdlkMNt;BIsmIkarxageRkam³

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=

363.01

3 yxyxC ¬!&>@0¦

Edl x CaTMhMTTwgrbs;ctuekaN nig y CabeNþayrbs;ctuekaN. kñúgkarKNna C vimaRtrbs;muxkat;ctuekaNRtUv)aneRCIserIsy:agNaedIm,IeFVI[)antémø C FMCageK.

smIkarxagedImEdl)anENnaMenATIenH nwgRtUv)anykmkeRbIenAkñúgEpñk 12 “Equivalent

Frame Method” . RbsinebIkRmalmanFñwmRsbKñanwgm:Um:g;EdlRtuvKNna enaHPaBrwgRkajTb;karrmYl tK

Edl[kñúgsmIkar !&>!( RtUv)anCMnYseday taK EdlmantémøFMCag ehIy taK RtUv)anKNna dUcxageRkam³

s

sbtta I

IKK ×=



Edl ==12

32hl

I s m:Um:g;niclPaBrbs;kRmalxNÐEdlmanTTwges μ InwgTTwgeBjcenøaHG½kS kRmal ¬edayminrYmbBa©ÚlEpñkrbs;tYrFñwmEdlbnøayeTAelI b¤eTAeRkamkRmal xNÐ¦.

ssb II = / edaybBa©ÚlTaMgtYrFñwmEdlbnøayeTAelI b¤eTAeRkamkRmalxNÐ. muxkat;énGgát;rgkarrmYlxøHEdlmanP¢ab;mkCamYyRtUv)anbgðajenAkúñgrUbTI 17>17.

enAeBlEdl taK RtUv)anKNna enaHpleFobPaBrwgRkaj ecα RtUv)anTTYldUcxageRkam³

( )∑ +=

bs

ecec KK

Kα ¬!&>@!¦

Edl 1

4l

IEK scs

s = =PaBrwgRkajTb;karBt;rbs;kRmalxNÐ

1

4l

IEK bcb

b = =PaBrwgRkajTb;karBt;rbs;Fñwm

=bI m:Um:g;niclPaBTaMgmUlrbs;muxkat;FñwmbeNþay karEbgEckénm:Um:g;sþaTicsrub oM enAkñúgkRmalxageRkARtUv)an[CaGnuKmn_én ecα

dUcxageRkam³

( ) oec

M⎥⎦

⎤⎢⎣

⎡+

−=α/111.075.0moment factored negativeInterior

( ) oec

M⎥⎦

⎤⎢⎣

⎡+

−=α/11

28.063.0moment factored Positive

( ) oec

M⎥⎦

⎤⎢⎣

⎡+

=α/11

65.0moment factored negativeExterior

témøTaMgenHRtUv)anbgðajenAkñúgkRmalxageRkAKMrUkñúgrUbTI 17>18. emKuNTaMgenHRtUv )anBicarNaBI\T§iBlrbs;PaBrwgRkajrbs;ssrxageRkAk¾dUcCa\T§iBlrbs;PaBrwgRkajrbs;Fñwm cugkRmalEdleFVI[karEbgEckm:Um:g;manlkçN³RKb;RKan;.

17>8>8> segçbviFIKNnaedaypÞal; (Summary of the Direct Design Method (DDM))

krNITI1 kRmalKμanFñwm !> RtYtBinitütRmUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1. RbsinebIvaminRtUvnwg

karkMNt;eT eKminGaceRbIviFI DDM )aneT.





@> kMNt;kRmalxNÐGb,brma minh edIm,IRKb;RKgPaBdabedayeRbItémøenAkñúgtarag

17>1. kRmalxageRkAEdlK μanFñwmxag[ minh x<s;bMput ¬ 30/nl sRmab; MPaf y 420= ¦. vaCa karGnuvtþFm μtaEdleRbIkRmas;kRmalxNÐesμ IKñasRmab;RKb;

kRmalxageRkAnigxagkñúg. #> KNnabnÞúkemKuN LDu WWW 6.12.1 . +=



$> epÞógpÞat;kRmas;kRmalxNÐ h edIm,IkarBarkmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwg BIrTis. RbsinebIkRmas;kRmalxNÐ h minRKb;RKan; eKRtUvbegáInkRmas; h b¤dak;Edk Tb;kmøaMgkat;TTWg.

%> KNnam:Um:g;sþaTicsrub oM sRmab;TisedATaMgBIr ¬smIkar !&>!!¦ ^> kMNt;emKuNEbgEcksRmab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay nig

TisedATTwgsRmab;ceRmokelIssr nigceRmokkNþalnImYy²TaMgenAkñúgkRmalxagkñúg nigkRmalxageRkA dUcxageRkam³ a. sRmab;kRmalxagkñúg eRbIemKuNm:Um:g;Edl[enAkñúgtarag 17>4 b¤rUbTI 17>15 b. sRmab;kRmalxageRkAEdlK μanFñwmxag emKuNm:Um:g;kRmalRtUv)an[enAkñúgtarag

17>2 b¤rUbTI 17>14 ¬krNITI5¦. sRmab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbItarag 17>6 b¤rUbTI 17>15 sRmab;GRtaceRmokelIssr. ceRmokkNþalnwg Tb;Epñkénm:Um:g; EdlminRtUv)andak;eTAkñμúgceRmokssr.

c. sRmab;kRmalxageRkAEdlmanFñwmxag emKuNm:Um:g;kRmalRtUv)an[enAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNITI4¦. sRmab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbItarag 17>5 sRmab;ceRmokelIssr. ceRmokkNþalnwgTb;lMnwgénm:Um:g; kRmal.

&> kMNt;brimaNEdksRmab;RKb;muxkat;eRKaHfñak;;énceRmokelIssr nigceRmokkNþal TaMgGs; nigBnøÚtsrésEdkeBjkRmalxNÐ ¬rUbTI 17>16¦

*> KNna unbalanced moment nigRtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced

moment edaykarBt;RKb;RKan;b¤Gt;. RbsinebIGt;RKb;RKan;eT kMNt;brimaNEdk bEnßmEdlcaM)ac;enAkñúgTTwgeRKaHfñak; ¬eyagtamEpñkTI 10¦.

(> RtYtBinitüemIlfaetIkarbMElgm:Um:g; unbalanced moment edaykmøaMgkat;TTwgRKb; RKan; b¤Gt;. RbsinebIGt;eT begáIn h b¤dak;EdkTb;kmøaMgkat;TTwg. ¬eyagtamEpñkTI 10¦

krNITI2 kRmalEdlmanFñwmxagkñúg nigFñwmxageRkA !> RtYtBinitütRmUvkarénkarkMNt;Edl)anBnül;enAkñúgEpñk 8>1.



@> kMNt;kRmalxNÐGb,brma minh edIm,IRKb;RKgPaBdabedayeRbItémøenAkñúgsmIkar TI !&>! dl; !&>#. kñúgkrNICaeRcIn smIkarTI !&>@ lub. smIkarTI !&>! KYrRtUv)an KNnadMbUgdUcbgðajenAkñúg]TahrN_TI 17>1.

#> KNnabnÞúkemKuN LDu WWW 6.12.1 . += $> epÞógpÞat;kRmas;kRmalxNÐ h tamry³kmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwgBIr

Tis. CaTUeTA kmøaMgkat;TTWgminmanlkçN³eRKaHfñak;sRmab;kRmalxNÐEdlRTeday FñwmeT.

%> KNnam:Um:g;sþaTicsrub oM sRmab;TisedATaMgBIr ¬smIkar !&>!!¦ ^> kMNt;emKuNEbgEcksRmab;m:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgTisedAbeNþay nig

TisedA TTwgsRmab;ceRmokelIssr nigceRmokkNþalnImYy²TaMgenAkñúgkRmalxag kñúg nigkRmalxageRkA dUcxageRkam³ a. sRmab;kRmalxagkñúg eRbIemKuNm:Um:g;kñúgrUbTI 17>14 ¬krNITI 3¦ b¤rUbTI

17>12. sRmab;karEbgEckm:Um:g;kñúgTisedATTwg eRbItaragTI 17>3 sRmab; ceRmokelIssr. cM erokkNþalnwgTb;Epñkénm:Um:g;Edlmin)andak;eTAkñúgceRmok elIssr. KNna 1α BI smIkar !&>!@.

b. sRmab;kRmalxageRkA eRbIemKuNm:Um:g;kRmalenAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNI TI3¦. sRmab;karEbgEckm:Um:g;enAkñúgTisedATTwg eRbItarag 17>5 sRmab;ceRmokelIssr. ceRmokkNþalnwgTb;lMnwgénm:Um:g;kRmal.

c. kñúgkrNITaMgBIr (a) nig (b) FñwmRtUvTb; %85 énm:Um:g;enAkñúgceRmokssr enAeBl Edl 0.1)/( 121 ≥llfα b:uEnþGRtaERbRbYlcenøaH %85 nig %0 enAeBl )/( 121 llfα ERbRbYlcemøaHBI 0.1 nig 0 .

&> kMNt;brimaNEdksRmab;RKb;muxkat;eRKaHfñak;;énceRmokelIssr/ Fñwm nigceRmok kNþalTaMgGs; bnÞab;mkBnøÚtsrésEdkeBjkRmalxNÐ ¬rUbTI 17>16¦

*> KNna unbalanced moment nigbnÞab;mkRtYtBinitüemIlkarbMElgénm:Um:g; edaykar Bt; nigkmøaMgkat;TTwg ¬eyagtamEpñkTI 10¦.



]TahrN_TI17>3³ edayeRbIvIFI direct design method KNnakRmal flat plate xagkñúgKMrUdUc Edl)anbgðajenAkñúgrUb TI 17>6 nig 17>19. RbB½n§kRmalpSMeLIgeday kRmalbYnenARKb;Tis EdlkRmalmYy² manTMhM m65.7 × . kRmalTaMgGs;RtUv)anRTedayssrTMhM cm5050× man RbEvg m6.3 . kRmalxNÐRTbnÞúkGefreFVIkar BRgayesμ I 2/8.4 mkN nigbnÞúkefreFVIkarEdlrYm mankRmalkargarbegðIy (floor finish) 2/5.1 mkN rYmTaMgbnÞúkpÞal;rbs;kRmal. eK[




dMeNaHRsay³ 1> kMNt;kRmas;kRmalxNÐGb,brmaedayeRbItarag 17>1 sRmab; flat plate. BI]TahrN_

TI 17>1 kRmas;kRmalxNÐKW cm25 . 2> KNnabnÞúkemKuN³

2/75.72525.05.1slab ofweight 5.1 mkNwD =×+=+= 2/178.46.175.72.1 mkNwu =×+×=

3> RtYtBinitükmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwgBIrTis³ a. RtYtBinitükmøaMgkat;pugenAcm¶ay 2/d BIépÞssr ¬GMeBIBIrTis¦.

Edaysnμt;kRmas;ebtugkarBarEdk cm2 nigeRbIEdk 16DB . enaH d mFümKW cm4.216.1225 =−− nig ( ) cmbo 6.2854.21504 =+= ¬emIlrUbTI 17>19 c¦

[ ] kNwllV uu 3.7561017)5098600750()4.714.71( 421 =⋅×−×=××−= −

kNdbfV occ 5.80810214.0856.228375.0'

33 =×××==

φφ EdlFMCag uV

b. KNnakmøaMgTTwgFñwmenAcm¶ay d BIépÞssr. d mFümKW cm4.21 . BicarNaceRmok m1 ¬rUbTI 17>19 d¦ CamYyRbEvgceRmokKW³

mx 286.3214.025.075.3 =−−= kNwV uu 862.55286.317)286.31( =×=×=

kNbdfV cc 5.14110214.0128675.0'

63 =×××==

φφ EdlFMCag uV . Kñugkardak;bnÞúkFm μta kmøaMgkat;TTwgmYyTisGt;lub.

4> KNnam:Um:g;sþaTicsrubenAkñúgTisedAEvg nigTisedAxøI kñúgTisedAEvg mkN

llwM nu

ol .75.624768

178

2212 =×==

kñúgTisedAxøI mkNllw

M nuos .11.4825.55.7

817

82

221 =×==

edaysarEt 12 ll < TTwgénBak;kNþalceRmokelIssrenAkñúgTisedAEvgKW mm 5.1625.0 =× ehIyTTwgénceRmokkNþalKW m35.126 =×− . TTwgénBak;kNþal

ceRmokelIssrkñúgTisedAxøI KW m5.1 ehIyTTwgénceRmokkNþalKW m5.45.125.7 =×− . edIm,IKNnakm<s;RbsiT§PaB d kñúgTisedAnImYy² snμt;faEdkenA



kñúgTisedAxøIRtUvBIelIEdk enAkñúgTisedAEvg. dUcenH cmd 2.228.0225)direction long( =−−= nig

)directionshort (d 8.06.1225 −−−= cm6.20= . sRmab;karGnuvtþn_ =)average(d cm5.215.325 =− GacRtUv)aneRbIsRmab;TisedATaMgBIr.

dMeNIrkarKNnaGacRtUv)anerobcMCaTRmg;tarag dUcbgðajenAkñúgtarag 17>7 nig 17>8. karlMGitsRmab;kareRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>20 edayeRbIRbB½n§ EdkRtg;. eKRtUveKarBkardak;RbEvgGb,brmarbs;EdkdUcEdl)anbgðajenAkñúgrUbTI 17>16. Gñksagsg;cUlcitþeRbIEdkRtg; nigEdkEdlmanersIusþg; MPaf y 420= . KMlatGtibrma mm375

83000

bars of no.panel ofwidth

=== taragTI17>7 karKNnabnÞHkRmal flat platexagkñúg ¬kñúgTisEvg¦

mkNM o .75.624= mkNMM on .1.40665.0 −=−= mkNMM op .66.21835.0 =+=

ceRmokelIssr ceRmokkNþal TisEvg

GviC¢man viC¢man GviC¢man viC¢man karEbgEckm:Um:g; % 75 60 25 40

).( mkNM u 6.30475.0 −=nM 2.1316.0 ±=pM 5.10125.0 −=nM 5.876.0 ±=pM TTwgceRmok )(mmb 3000 3000 3000 3000 km<s;RbsiT§PaB )(mmd 222 222 222 222

)(2 MPabdM

R uu = 06.2 89.0 69.0 59.0

PaKryEdk (%)ρ 57.0 24.0 19.0 16.0 )( 2= mmbdAs ρ 2.3796 4.1598 4.1265 6.1065

)(0018.0(min) 2mmbhA ss = 1350 1350 1350 1350 EdkEdleRCIserIs ¬Rtg;¦ 1620DB 168DB 1212DB 1212DB KMlat mmhs 5002 =≤ 150 375 250 250



taragTI17>8 karKNnabnÞHkRmal flat platexagkñúg ¬kñúgTisxøI¦ mkNM o .11.482=

mkNMM on .4.31365.0 −=−= mkNMM op .7.16835.0 =+=

ceRmokelIssr ceRmokkNþal TisEvg

GviC¢man viC¢man GviC¢man viC¢man karEbgEckm:Um:g; % 75 60 25 40

).( mkNM u 05.23575.0 −=nM 2.1016.0 ±=pM 35.7825.0 −=nM 5.676.0 ±=pM TTwgceRmok )(mmb 3000 3000 4500 4500 km<s;RbsiT§PaB )(mmd 206 206 206 206

)(2 MPabdM

R uu = 85.1 79.0 41.0 35.0

PaKryEdk (%)ρ 51.0 21.0 11.0 09.0 )( 2= mmbdAs ρ 8.3151 8.1297 7.1019 3.834

)(0018.0(min) 2mmbhA ss = 1350 1350 2025 2025 EdkEdleRCIserIs ¬Rtg;¦ 1616DB 168DB 1218DB 1218DB KMlat mmhs 5002 =≤ 5.187 375 250 250

KMlatEdkenAkñúgceRmokelIssrkñúgTisxøIKW mm250 . vamanlkçN³RKb;RKan; edaysar vatUcCag mmhs 5002 = nigtUcCag mm450 EdlkMNt;eday ACI Code.

cMNaMfa PaKryEdkTaMgGs;KWticCag 0182.0max =ρ . dUcenH 9.0=φ .

]TahrN_TI17>4³ edayeRbIviFI direct design method KNnakRmal flat plate xageRkAEdlmanTMhM bnÞúk ersIusþg;ebtug nigersIusþg;EdkdUcKñanwgGVIEdl)an[enAkñúg]TahrN_TI 17>3. FñwmminRtUv)aneRbI ¬rUbTI 17>21¦.

dMeNaHRsay³ 1> kMNt;kRmas;kRmalxNÐGb,bramedayeRbItarag 17>1 sRmab; flat plate.

BI]TahrN_TI 17>1 kRmas;kRmalxNÐKW cm25 .



2> KNnabnÞúkemKuN³ 2/17 mkNwu = 3> RtYtBinitükmøaMgkat;TTwgmYyTis nigkmøaMgkat;TTwgBIrTis ¬eyagtam]TahrN_TI 17>3

nigrUbTI 17>9¦.

a. RtYtBinitükmøaMgkat;pugenAssrxagkñúg kNVkNV cu 5.8083.756 =<= φ b. RtYtBinitükmøaMgkat;TTwgmYyTis³ kNVkNV cu 5.141862.55 =<= φ c. RtYtBinitükmøaMgkat;pugenAssrxageRkA³ cmd 4.21=

cmx 7.602

4.2150 =+=



cmy 4.714.2150 =+=



cmyxbo 8.1922 =+= kNVu 6.40017104.717.6025

2750600 4 =×⎥

⎦

⎤⎢⎣

⎡×−⎟

⎠⎞

⎜⎝⎛ += −

kNkNdbfV occ 6.4008.545'3

>==φφ

d. RtYtBinitükmøaMgkat;pugenAssrkac;RCug³ cmd 4.21= cmyx 7.60

24.2150 =+==

cmyxbo 4.121=+= kNVu 7.21417107.607.6025

275025

2600 4 =×⎥

⎦

⎤⎢⎣

⎡×−⎟

⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ += −

kNkNdbfV occ 7.2147.343'3

>==φφ

4> KNnam:Um:g;sþaTicsrub ¬BI]TahrN_TI 17>3¦ mkNM ol .7.624)direction long( = cmd 2.22=

mkNM os .11.482)directionshort ( = cmd 6.20= TTwgrbs;ceRmokelIssrKW cm300 nigTTwgceRmokkNþalKW cm450

5> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ ml 5.71 = ¬eyagtamtarag 17>5 b¤rUb 17>15¦. karEbgEckm:Um:g;srub olM enAkñúgceRmokelIssr nigceRmokkNþalKWRtUv )anKNnadUcxag eRkam³ a. ceRmokelIssr³

m:Um:g;GviC¢manxagkñúg ( ) mkNM o .32875.624525.0525.0 −=−=−= m:Um:g;viC¢manenAkñúgElVg ( ) mkNM o .19575.624312.0312.0 === m:Um:g;GviC¢manxageRkA ( ) mkNM o .4.16275.62426.026.0 =−=−=

b. ceRmokkNþal³ m:Um:g;GviC¢manxagkñúg ( ) mkNM o .3.10975.624175.0175.0 −=−=−= m:Um:g;viC¢manenAkñúgElVg ( ) mkNM o .9.12975.624208.0208.0 === m:Um:g;GviC¢manxageRkA 0=



6> KNnam:Um:g;KNnaenAkñúgTisedAxøI³ mls 6= . vaRtUv)anKitdUckRmalxagkñúgEdr BIeRBaH vaCab;TaMgsgçag. eyagtamtarag 17>4 b¤rUbTI 17>15 karEbgEckm:Um:g;srub osM enAkñúgceRmokelIssr nigceRmokkNþalRtUv)anKNnadUcxageRkam³ a. ceRmokelIssr³

m:Um:g;GviC¢man ( ) mkNM o .2.23611.48249.049.0 −=−=−= m:Um:g;viC¢man ( ) mkNM o .2.10111.48221.021.0 ===

b. ceRmokkNþal³ m:Um:g;GviC¢man ( ) mkNM o .1.7711.48216.016.0 −=−=−= m:Um:g;viC¢man ( ) mkNM o .5.6711.48214.014.0 ===

dMeNIrkarKNnaRtUv)anteRmoby:aggayRsYlenAkñúgtarag 17>9. karlMGitsRmab;kar eRCIserIssrésEdkRtUv)anbgðajenAkñúgrUbTI 17>22 edayeRbIRbB½n§EdkRtg;;enAkñúgTis Evg. karlMGitsrésEdkenAkñúgTisxøImanlkçN³RsedogKñanwgkarBRgaysrésEdkenA kñúgrUbTI 17>20 edayeRbIkareRCIserIssrésEdkenAkñúgtarag 17>9. cMNaMfa RKb;PaKryEdkTaMgGs;tUcCag 0182.0max =ρ . dUcenH 9.0=φ .



tarag 17>9 karKNnakRmal flat platexageRkAsRmab;]TahrN_TI 17>4 ¬ cmd 2.22= ¦ ceRmokelIssr ceRmokkNþal TisEvg xageRkA viC¢man xagkñúg xageRkA viC¢man xagkñúg

).( mkNM u 4.162− 195 328− 0 9.129 3.109− TTwgceRmok )(mmb 3000 3000 3000 3000 3000 3000

)(2 MPabdM

R uu = 10.1 32.1 22.2 0 88.0 74.0

PaKryEdk (%)ρ 30.0 36.0 62.0 0 24.0 20.0 )( 2= mmbdAs ρ 1998 2398 4129 0 1598 1332

)(0018.0(min) 2mmbhA ss = 1350 1350 1350 1350 1350 1350 EdkEdleRCIserIs ¬Rtg;¦ 1610DB 1612DB 1622DB 1212DB 1218DB 1212DB KMlat mmhs 5002 =≤ 300 250 136 250 167 250 TisxøI ceRmokelIssr ceRmokkNþal

).( mkNM u 2.236− 2.101 1.77− 5.67 TTwgceRmok )(mmb 3000 3000 4500 4500 km<s;RbsiT§PaB )(mmd 206 206 206 206

)(2 MPabdM

R uu = 86.1 79.0 40.0 35.0

PaKryEdk (%)ρ 52.0 21.0 11.0 09.0 )( 2= mmbdAs ρ 3214 1298 1020 3.834

)(0018.0(min) 2mmbhA ss = 1350 1350 2025 2025 EdkEdleRCIserIs ¬Rtg;¦ 1616DB 168DB 1218DB 1218DB KMlat mmhs 5002 =≤ 5.187 375 250 250 ]TahrN_TI17>5³ eFVI]TahrN_TI 17>4 eLIgvij edayeRbIviFI modified stiffness method. ¬eKRtUvkarKNnaRsedogKña sRmab;viFI equivalent frame method, EpñkTI 12¦.



dMeNaHRsay³ 1> GnuvtþRsedogKñasRmab;CMhanTI 1 dl; 4 dUckñúg]TahrN_TI 17>4 2> KNnaPaBrwgRkajssrsmmUl/ ecK ³

tcec KKK111

+=∑

eyIgGacsnμt;faEpñkénceRmokkRmalEdlenAcenøaHssrxageRkAeFVIkarCassrTb;nwgkar rmYl. muxkat;rbs;kRmalxNÐ-ssrKW cm50 ¬TTWgrbs;ssr¦ cm25× ¬kRmas;kRmal xNÐ¦ dUcEdlbgðajkñúgrUb. a. kMNt;PaBrwgRkajTb;karrmYl tK BIsmIkar !&>@0³

363.01

3 yxyxC ⎟⎟⎠

⎞⎜⎜⎝

⎛−= mmx 250= mmy 500=

483

1084.173

50025050025063.01 mmC ⋅=

×⎟⎠⎞

⎜⎝⎛ −=

63

8

3

2

22

1047.3

600050016000

1084.179

1

9⋅=

⎟⎠⎞

⎜⎝⎛ −

⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= ccc

t EE

lc

l

CEK

sRmab;kRmalxNÐEk,rKñaBIr ¬enAelIRCugTaMgsgçagrbs;ssr¦ EdleFVIkarCaFñwmTTwg 66 1094.61047.32 ⋅=⋅×= cct EEK

b. KNnaPaBrwgRkajrbs;ssr cK / km<s;ssr mLc 6.3= 6

41079.5

12500

360044

⋅=×== cc

c

ccc E

EL

IEK

sRmab;ssrBIrenABIelI nigBIeRkamkRmalxNÐ 66 1058.111079.52 ⋅=⋅×= ccc EEK

c. KNna ecK ³

66 1094.61

1058.1111

⋅+

⋅=

ccec EEK

61034.4 ⋅= cec EK 3> KNnaPaBrwgRkajrbs;kRmalxNÐ nigemKuN ecα

1

4l

IEK sc

s = mmhs 250= mml 60002 = 12

32 s

shl

I =



63

1017.412

250600075004

⋅=×

×= cc

s EE

K

( )∑ +=

bs

ecec KK

Kα

0=bK ¬edaysarK μanFñwm¦ dUcenH 04.1

1017.41034.4

6

6=

⋅

⋅=

c

cec

EE

α

yk 96.111 =+=ec

Qα

4> KNnam:Um:g;KNnaenAkñúgTisedAEvg³ mll 5.7= . karEbgEckm:Um:g;enAkñúgkRmalmYyRtUv)anbgðajenAkñúgrUbTI 17>18. m:Um:g;GviC¢manxagkñúgKW

mkNMQ

M olni .6.436)7.624(96.110.075.010.075.0 −=⎟

⎠⎞

⎜⎝⎛ −=⎥

⎦

⎤⎢⎣

⎡−=

m:Um:g;viC¢manKW mkNM

QM olp .3.304)7.624(

96.128.063.028.063.0 =⎟

⎠⎞

⎜⎝⎛ −=⎥

⎦

⎤⎢⎣

⎡−=

m:Um:g;GviC¢manKW ( ) mkNM

QM olne .2.2077.624

96.165.0)(65.0

===

5> KNnakarEbgEckm:Um:g;kRmalenAkñúgTisxøIeTAceRmokelIssr nigceRmokkNþal. m:Um:g; niM / pM nig neM RtUv)anEbgEckdUcxageRkam ¬eyagtamtarag 17>6¦³

a. m:Um:g;xagkñúg mkNM nl .6.436−= RtUv)anEbgEck %75 sRmab;ceRmokelIssr nig %25 sRmab;ceRmokkNþal

( ) mkN.5.3276.43675.0stripcolumn −=−= ( ) mkN.1.1096.43625.0strip Middle −=−=

b. m:Um:g;viC¢man mkNM p .3.304= RtUv)anEbgEck %60 sRmab;ceRmokelIssr nig %40 sRmab;ceRmokkNþal

( ) mkN.6.1823.30460.0stripcolumn == ( ) mkN.7.1213.30440.0strip Middle ==

c. m:Um:g;GviC¢manxageRkA mkNM ne .2.207−= RtUv)anEbgEckGaRs½ytamtarag 17>5³



sscs

cbt I

CIECE

22==β ¬ebtugkRmalxNÐ nigebtugssrmanm:UDuleGLasÞicdUcKña¦

483

10125.7812

2506000 mmI s ⋅==

114.010125.782

1084.178

8=

⋅×

⋅=β

01 ==scs

bcbf IE

IEα 0

1

21 =

ll

fα 8.01

2 =ll

BItarag 17>5 nigedayeFVIviFanmUlvacar (interpolation) cenøaH 0=tβ ¬PaKry = %100 ¦ nig 5.2=tβ ¬PaKry %75= ¦ sRmab; 114.0=tβ PaKryKW %9.98 . m:Um:g;GviC¢manxageRkAenAkñúgceRmokelIssrKW ( ) mkN.92.2042.207989.0 −=−× nigenAkñúgceRmokkNþalKW mkN.28.2− . kñúgkrNIenHeKGacKitfaceRmokelIssr RTm:Um:g; neM %100 KWesμ Inwg mkN.2.207−

6> kMNt;srésEdkEdlcaM)ac;enAkñúgTisedAEvgkñúgtaragEdlmanlkçN³RsedogKñanwg]TahrN_TI 17>4. lT§plEdlTTYl)anmanlkçN³ERbRbYlticbMputxusBItarag 17>9.

7> eRbobeFoblT§plrvag]TahrN_TI 17>4 nig 17>5 eyIgeXijfam:Um:g;xageRkAenAkñúg ceRmokelIssr ¬ mkN.2.207− ¦FMCagcMelIyEdlTTYl)ankñúg]TahrN_TI 17>4 ¬ mkN.4.162− ¦ eday %6.27 b:uEnþm:Um:g;viC¢man ¬ mkN.6.182 ¦ RtUv)ankat;bnßyeday

%8.6 ¬eFobnwg mkN .195 ¦ ÉtémødéTeTotesÞIrEtRtUvKña.

]TahrN_TI17>6³ KNnakRmalxagkñúgénRbB½n§kRmalBIrTisEdl)anbgðajenAkñúgrUbTI 17>7. kRmalpSMeLIgeday kRmal EdlmanTMhM m66.7 × cMnYn 6 kñúgTisnImYy². kRmalTaMgGs;RtUv)anRTedayssrEdlman TMhM cm5050× RbEvg m6.3 . kRmalRtUv)anRTedayFñwmtambeNþayG½kSssrEdlmanmuxkat;dUc bgðajkñúgrUb. bnÞúkGefreFVIkarRtUv)anyk 2/8.4 mkN nigbnÞúkefreFVIkarpSMeLIgeday 2/1 mkN sRmab;kargarbegðIybEnßmBIelITm¶n;pÞal;rbs;kRmal. cUreRbI MPaf c 21' = / MPaf y 420= nigviFI direct design method.



dMeNaHRsay³

1> eKRtUveFVItamkarkMNt;rbs; ACI Code. kMNt;kRmas;kRmalxNÐGb,brmaedayeRbIsmIkar 17>1 nig 17>2. kRmas;kRmalxNÐRtUv)anKNnarYcCaeRscenAkñúg]TahrN_TI 17>2 ehIy eyIgTTYlykkRmas; cm18 . CaTUeTA kRmas;kRmalxNÐenAkñúgRbB½n§kRmalRtUv)an RKb;RKgedaykRmalkac;RCugdUcCakarKNna minh kRmalxageRkApþl;nUvkRmas;kRmalFM CagsRmab;kRmalxagkñúg.

2> KNnabnÞúkemKuN 2/5.52518.01 mkNwD =×+=

2/28.148.46.15.52.1 mkNwu =×+×= 3> kugRtaMgkmøaMgenAkñúgkRmalxNÐminmanlkçN³eRKaHfñak;eT. muxkat;eRKaHfñak;mancm¶ay d



BIépÞFñwm. sRmab;TTwg m1 ³ kNdwV uu 84.3715.0

24.0328.14 widthbeam

213 =⎟

⎠⎞

⎜⎝⎛ −−=⎟

⎠⎞

⎜⎝⎛ −−=

kNbdfV cc 9.851015010006

2175.0'6

3 =⋅×== −φφ 4> KNnam:Um:g;sþaTicsrubenAkñúgTisEvg nigTisxøI³

( ) ( ) mkNllw

M nu

ol .9.5391.76828.14

822

12 ===

( ) ( ) mkNllw

M nu

os .4.4105.56.7828.14

822

21 === 5> KNnam:Um:g;KNnaenAkñúgTisEvg³ mll 6.7=

a. karEbgEckm:Um:g;enAkñúgkRmal m:Um:g;GviC¢man mkNMM oln .9.3509.53965.065.0 −=×== m:Um:g;viC¢man mkNMM olp .1899.53935.035.0 =×==

b. karEbgEckm:Um:g;kRmalkñúgTisTTwgeTAFñwm/ ceRmokelIssr nigceRmokkNþal 79.0

6.76

1

2 ==ll 19.31 ===

s

bsf EI

EIαα ¬BI]TahrN_TI 17>2¦

152.279.019.31

21 >=×=

ll

fα

c. karEbgEckm:Um:g;GviC¢man nM . Epñkénm:Um:g;GviC¢manxagkñúgedIm,IkarBaredayceRmok elIssrRtUv)anTTYlBItarag 17>3 edayeFVI interpolation nigesμ Inwg %3.81 ¬sRmab;

79.0/ 12 =ll nig 0.1)/( 121 >llfα ¦. ceRmokelIssr mkNM n .3.2859.350813.0813.0 −=×== ceRmokkNþal mkNM n .6.659.350187.0187.0 −=×==

edaysarEt 1)/( 121 >llfα / ACI Code, Section 13.6.5 bgðajfa %85 énm:Um:g; kñúgceRmokelIssrRtUv)anEck[eTAFñwm nigenAsl; %15 RtUv)anEck[eTAkRmal ceRmokelIssr. Fñwm mkN.5.2423.28585.0 −=×= ceRmokelIssr mkN.8.423.28515.0 −=×= ceRmokkNþal mkN.6.65−=

d. karEbgEckm:Um:g;viC¢man pM . Epñkénm:Um:g;viC¢manxagkñúgEdlRtUv)anTb;edayceRmok



elIssrRtUv)anTTYlBItarag 17>3 edayeFVI interpolation nigesμ Inwg %3.81 ¬sRmab; 79.0/ 12 =ll nig 0.1)/( 121 >llfα ¦.

ceRmokelIssr mkNM n .7.153189813.0813.0 =×== ceRmokkNþal mkNM n .3.35189187.0187.0 =×==

edaysarEt 1)/( 121 >llfα / ACI Code, Section 13.6.5 bgðajfa %85 énm:Um:g; kñúgceRmokelIssrRtUv)anEck[eTAFñwm nigenAsl; %15 RtUv)anEck[eTAkRmal ceRmokelIssr. Fñwm mkN.6.1307.15385.0 =×= ceRmokelIssr mkN .1.237.15315.0 =×= ceRmokkNþal mkN.3.35=

karlMGitm:Um:g;RtUv)anbgðajenAkñúgrUbTI 17>23. 6> KNnam:Um:g;KNnaenAkñúgTisxøI³ ElVg m6= . viFIKNnaRsedogKñanwgCMhanTI5>

m:Um:g;GviC¢man mkNMM osn .8.2664.41065.065.0 −=×== m:Um:g;viC¢man mkNMM osp .6.1434.41035.035.0 =×== EbgEck nM / pM eTAFñwm/ ceRmokelIssr nigceRmokkNþal

27.166.7

1

2 ==ll 51.21 ===

s

bsf EI

EIαα ¬BI]TahrN_TI 17>2¦

119.327.151.21

21 >=×=

ll

fα

PaKryénm:Um:g;GviC¢man nigGviC¢manenAkñúgceRmokelIssrRtUv)anTTYlBItarag 17>3 edaykareFVI interpolation. ¬sRmab; 27.1/ 12 =ll nig ( ) 0.1/ 121 >llfα PaKryEbgKW

%67 ¦. m:Um:g;GviC¢manceRmokelIssr mkNM n .8.1788.26669.067.0 −=×== m:Um:g;GviC¢manceRmokkNþal mkNM n .888.26633.033.0 −=×== eday ( ) 0.1/ 121 >llfα / %85 én mkN.8.178− RtUv)andak;eTAkñúgFñwm. dUcenH m:Um:g;GviC¢manelIFñwm mkN.1528.17885.0 −=×= m:Um:g;GviC¢manceRmokelIssr mkN.8.268.17815.0 −=×= m:Um:g;viC¢manelIFñwm mkN.8.816.14367.085.0 =××=



m:Um:g;viC¢manceRmokelIssr mkN.4.146.14367.015.0 =××= m:Um:g;viC¢manceRmokkNþal mkN.4.476.14333.0 =×=

7> brimaNEdkcaM)ac; nigcMnYnEdkRtUv)anbgðajenAkñúgtarag 17>10. cMNaMfaPaKryEdkTaMgGs;tUcCag 00137.0max =ρ . dUcenH 9.0=φ .

tarag 17>10 karKNnaénkRmalxNÐmanFñwmBIrTisxagkñúg TisEvg

ceRmokelIssr ceRmokkNþal ).( mkNM u 8.42− 1.23 6.65− 3.35

TTwgceRmok )(mmb 3000 3000 3000 3000 km<s;RbsiT§PaB )(mmd 150 150 150 150

)(2 MPabdM

R uu = 0.63 0.34 0.97 0.52

PaKryEdk (%)ρ 0.17 0.09 0.26 0.14

)( 2= mmbdAs ρ 765 405 1170 630

)(0018.0(min) 2mmbhA ss = 972 972 972 972

EdkEdleRCIserIs 9DB12 9DB12 11DB12 9DB12

TisxøI ceRmokelIssr ceRmokkNþal

).( mkNM u 8.26− 4.14 88− 4.47 TTwgceRmok )(mmb 3000 3000 4600 4600 km<s;RbsiT§PaB )(mmd 140 140 140 140

)(2 MPabdM

R uu = 0.46 0.24 0.98 0.53

PaKryEdk (%)ρ 0.12 0.06 0.27 0.14

)( 2= mmbdAs ρ 504 252 1739 902

)(0018.0(min) 2mmbhA ss = 972 972 1490 1490

EdkEdleRCIserIs ¬Rtg;¦ 9DB12 9DB12 16DB12 14DB12



]TahrN_TI17>7³ edayeRbIviFI direct design method kMNt;m:Um:g;viC¢man nigGviC¢mancaM)ac; sRmab; karKNnaénkRmalxageRkA ¬elx @¦ énRbB½n§kRmalBIrTisEdlmanFñwmdUcEdlbgðajenAkñúgrUbTI 17>7. eRbIbnÞúk nig Tinñn½yEdl[enAkñúg]TahrN_TI 17>6. dMeNaHRsay³

1> karkMNt;EdlTamTarbs; ACI Code RtUv)anbMeBjenAkñúg]TahrN_enH. kMNt;kRmas; kRmalGb,brma sh edayeRbIsmIkar !&>! nig !&>@ nigCMhanbnþbnÞab;. snμt; cmhs 18= . muxkat;rbs;Fñwmxagkñúg nigxageRkARtUv)anbgðajenAkñúgrUbTI 17>7. cMNaMfa karbnøykRmalxNÐenARKb;RCugrbs;FñwmKW cmyx 38==

2> a. m:Um:g;niclPaBrbs;Fñwm nigkRmalxagkñúgEdlRtUv)anKNnaenAkñúg]TahrN_TI 17>2 KW TaMgBIrTis 46.928924 cmIb = TisEvg 4291600cmI s = TisxøI 4369360cmI s = b. KNna bI nig sI sRmab;Fñwmxag nigkRmalxNÐxag Fñwmxag ( )( ) ( )( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡×+

×+

⎥⎥⎦

⎤

⎢⎢⎣

⎡×+

×= 2

32

35.143830

1238305.131868

121868

bI

4632987cm= KNna sI sRmab;ceRmokxagcugEdlRsbeTAnwgFñwmxag EdlmanTTwg

2500

27600

+=

mm4050= kRmalxagcug 4

3196830

1218405 cmI s =

×=

3> a. KNna fα ¬ sbf EIEI /=α ¦ TisEvg 19.3

2916006.928924==lα

TisxøI 51.2369360

6.928924==sα

Fñwmxag 22.3196830632987

==α α mFüm 86.2

422.3251.219.3

=+×+

== fmα b. =β pleFob clear span EvgelI clear span xøI



29.15.51.7==

c. KNna sh ³

( ) mmhs 1502.086.229.1536

14004208.07100

min =−×+

⎟⎠⎞

⎜⎝⎛ +

=

b:uEnþtémøenHminRtUvtUcCag

mmhs 16429.1936

14004208.07100

min =×+

⎟⎠⎞

⎜⎝⎛ +

= ¬lub¦ eRbI cmcmhs 918 >= ¬témøGb,brmaEdlkMNt;eday code ¦

4> KNnabnÞúemKuN 2/28.14 mkNwu = ¬BI]TahrN_TI 17>6¦ 5> KNnam:Um:g;sþaTicsrub³ mkNM ol .9.539= mkNM os .4.410= ¬BI]TahrN_mun¦ 6> KNnam:Um:g;KNnaenAkñúgTisxøI ¬ElVg m6= ¦³ edaysarkRmalCab;kñúgTisenH m:Um:g;mantémø

dUcnwgm:Um:g;Edl)anKNnaenAkñúg]TahrN_TI 17>6 ehIyRtUv)anbgðajenAkñúgrUbTI 17>23 sRmab;kRmalxagkñúg.

7> KNnam:Um:g;enAkñúgmYykRmaledayeRbIemKuNEdl[enAkñúgtarag 17>2 b¤rUbTI 17>14 ¬krNITI 3¦³ m:Um:g;GviC¢manxagkñúg mkNMM oni .3789.5397.07.0 −=×== m:Um:g;viC¢mankñúgElVg mkNMM op .7.3079.53957.057.0 =×== m:Um:g;GviC¢manxageRkA mkNMM one .4.869.53916.016.0 −=×== cMNaM³ RbsinebIviFI modified stiffness method RtUv)aneRbI enaH 461027.3857 mmC ⋅= /

61013.39 ⋅= cta Ek / 61079.5 ⋅= cc EK / 61056.1 ⋅= cs EK / 61095.4 ⋅= cb Ek / 61094.8 ⋅= cb Ek nig 37.1=ecα . m:Um:g;GviC¢manxagkñúgkøayCa mkN.7.373− ¬Rbhak;

RbEhlKña¦ m:Um:g;viC¢mankøayCa mkN.75.252 ¬fycuH %18 ¦ nigm:Um:g;GviC¢manxageRkAkøay Ca 86.202 ¬ekIneLIg %235 ¦

8> karEbgEckm:Um:g;kRmaleTAFñwm ceRmokelIssr nigceRmokkNþal³ 79.0

6.76

1

2 ==ll 19.31 == lf αα

0.152.279.019.31

21 >=×=

ll

fα



KNna C ³

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∑

yxyxC

3

363.01

Eckmuxkat;rbs;FñwmxagCactuekaNBIrEdleFVIy:agNaedIm,ITTYl)an C Gtibrma. ykmuxkat;Fñwm mm560300× ¬ mmx 300= / mmy 560= ¦ nigmuxkat;kRmal

mm380180× ¬ mmx 180= / mmy 380= ¦ 46

331027.3857

3380180

38018063.01

3560300

56030063.01 mmC ⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛ ×⎟⎠⎞

⎜⎝⎛ −+⎟

⎟⎠

⎞⎜⎜⎝

⎛ ×⎟⎠⎞

⎜⎝⎛ ×−=

66.0102916002

1038572 4

6=

⋅×

⋅==

scs

cbt IE

CEβ

a. EbgEckm:Um:g;GviC¢manxagkñúg niM ³ eyagtamtarag 17>3 nigedaykareFVI interpolation PaKrym:Um:g;Edldak;enAkñúgceRmokelIssr ¬sRmab; 79.0/ 12 =ll nig 0.1/ 121 >llfα ¦KW %3.81

ceRmokelIssr mkN.3.307378813.0 −=×= ceRmokkNþal mkN.7.70378187.0 −=×= edaysar 0.1/ 121 >llfα / %85 énm:Um:g;enAkñúgceRmokssrKWRtUv)andak;eTAkñúgFñwm dUcenH³ Fñwm mkN.2.2613.30785.0 −=×= ceRmokelIssr mkN.1.463.30715.0 −=×= ceRmokkNþal mkN.7.70−= b. EbgEckm:Um:g;viC¢man pM ³ eyagtamtarag 17>3 nigedayeFVI interpolation PaKry

m:Um:g;EdlRtUvdak;kñúgceRmokelIssrKW %3.81 ¬ %85 éntémøenHRtUv)andak;eTAFñwm¦. dUcenH

Fñwm ( ) mkN.6.2127.307813.085.0 =×= ceRmokelIssr ( ) mkN.5.377.307813.015.0 =×= ceRmokkNþal mkN.5.577.307187.0 =×=



c. EbgEckm:Um:g;GviC¢manxageRkA neM ³ eyagtamtarag 17>5 nigedaykareFVI interpolation PaKrym:Um:g;Edldak;eTAkñúgceRmokelIssr ¬sRmab; 79.0/ 12 =ll nig 0.1/ 121 >llfα ¦KW %5.92 nig %85

Fñwm ( ) mkN.9.674.86925.085.0 −=×= ceRmokelIssr ( ) mkN.124.86925.015.0 −=×=

ceRmokkNþal mkN.48.64.86075.0 =×=

17>9> m:Um:g;KNnaenAkñúgssr (Design Moments in Column)

enAeBlEdlkarviPaKeRKagsmmUl (equivalent frame) RtUv)aneFVIeLIgedayviFI direct

design method m:Um:g;enAkñúgssrEdlbNþalBIbnÞúkminesμ I (unbalanced load) enAelIFñwmEk,rRtUv)an TTYlBIsmIkarxageRkam EdlRtUv)ankMNt;eday ACI Code, Section 13.6.9:

( ) ( )[ ]22

22 '''5.007.0 ndnldu llwllwwM −+= ¬!&>@@ a ¦

RbsinebIviFI modified stiffness method EdleRbI ecK nig ecα enaHm:Um:g; uM RtUv)ankMNt; dUcxageRkam³ ( ) ( )[ ]

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−+=

ec

ndnldu

llwllwwM

α11

'''5.008.0 22

22 ¬!&>@@ b ¦

Edl dw nig =lw bnÞúkefr nigGefremKuNenAelIElVgEdlEvgCag =dw' bnÞúkGefremKuNenAelIElVgEdlxøI nl nig =nl ' RbEvgénElVgEdlEvgCag nigxøICag erogKña ( )∑ +

=bs

ecec KK

Kα ¬!&>@!¦

m:Um:g;enAkúñgsmIkarTI !&>@@ KYrRtUv)anEbgEckrvagssrxagelI nigxageRkamkRmalxNÐRtg; tMNreTAtamsmamaRtPaBrwgRkajrgkarBt;rbs;va ¬rUbTI 17>24¦. sRmab;ElVgEdles μ IKña 22 'll = nig nn ll '= ( )2

25.007.0 nlu llwM = ¬!&>@# a ¦



( )⎟⎟⎠

⎞⎜⎜⎝

⎛+

=

ec

nlu

llwM

α11

5.008.0 22 ¬!&>@@ b ¦

karbegáItsmIkarTaMgenHedayQrenAelIkarsnμt;fabnÞúkGefrBak;kNþaleFVIGMeBIenAelIElVg EvgCag b:uEnþbnÞúkGefreFVIGMeBIenAelIElVgTaMgBIr. smIkar !&>@@ k¾GacRtUv)anGnuvtþsRmab;ssrxag eRkA edaysnμt;faRbEvgElVgEdlxøICagKW 0 ¬rUbTI 17>25¦.



17>10> karbMElgm:Um:g;mines μ IeTAkñúgssr (Transfer of Unbalanced Moments to Columns)

17>10>1> karbMElgm:Um:g; (Transfer of Moment) kñúgkarviPaKeRKagsmmUl (equivalent frame) enAkñúgGKar m:Um:g;ekItmanenARtg;tMNkRmal xNÐ-ssr EdlekItBIkmøaMgxagdUcCa kmøaMgxül; kmøaMgrBa¢ÜydI b¤kmøaMgTMnajmines μI (unbalanced

gravity load) edayeFVI[manm:Um:g;;mines μIenAkñúgkRmalenAelIRCugEdlpÞúynwgssr. mYycMENkén m:Um:g;mines μIRtUv)anbMElgeTAssredaykarBt; ehIycMENkEdleFVI[m:Um:g;manlMnwgRtUv)anbBa¢Ún edaykmøaMgkat;bBaÄrEdlmanGMeBIenAelImuxkat;eRKaHfñak;sRmab;kmøaMgkat;pug. RbEhl %60 énm:U m:g;EdlRtUv)anbMElgeATcugssrTaMgsgçagRtg;tMNRtUv)anbMElgedaykarBt; ehIy %40 EdlenA sl;RtUv)anbMElgedaykmøaMgkat;cakp©it ¬b¤kmøaMgrmYl¦ enARtg;muxkat;EdlmanTItaMg 2/d BIépÞ ssr. ACI Code, Section 13.5.3 bgðajfacMENkén unbalanced moment EdlRtUv)anbMElg edaykarBt; fM enARtg;tMNkRmalxNÐ-ssrEdlRtUv)anKNnadUcxageRkam³ uff MM γ= ¬!&>@$¦

2

1

2

1321

1

321

1

bb

dcdc

f

+

=

⎟⎟⎠

⎞⎜⎜⎝

⎛

++

+

=γ ¬!&>@%¦

ehIym:Um:g;EdlbMElgedaykmøaMgkat;TTwgKW ( ) fuufv MMMM −=−= γ1 ¬!&>@^¦ Edl 1c nig 2c CaRbEvgrbs;RCugBIrénssrctuekaN b¤ssrctuekaNEkgsmmUl/ )( 11 dcb += nig

( )dcb += 22 . enAeBlEdl 21 cc = / uf MM 6.0= ehIy uv MM 4.0= . 17>10>2> karRbmUlpþúMsrésEdkenAelIssr (Concentration of Reinforcement Over the column) sRmab;karbMElgm:Um:g;edaypÞal;eTAssr vaCakarcaM)ac;kñúgkarRbmUlpþúMsrésEdkdak;kñúg ceRmokssrkñúgTTwgkMNt;mYyenAelIssr Epñkénm:Um:g;EdlbMElgedaykarBt; fM RtUv)anBicarNa [ eFVIGMeBItamry³TTwgkRmalxNÐes μ InwgTTwgssr 2c bUknwg sh15.1 enARKb;RCugTaMgGs;rbs;ssr b¤ tamry³TTwgkRmalxNÐes μ Inwg ( )shc 32 + (ACI Code, Section 13.5.3). srésEdkGacRtUv)an RbmUlpþúMenAelIssredayKMlatCit²Kña b¤edayeRbIsrésEdkbEnßm.



17>10>3> kugRtaMgkmøaMgkat;EdlbNþalBI fM (Shear Stress Due to) fM kugRtaMgkmøaMgkat;EdlbegáItedaycMENkén unbalanced moment vM RtUv)anpSMeLIgCa mYynwgkugRtaMgkmøaMgkat;EdlbegáItedaykmøaMgkat; uV Edl)anBIkmøaMgbBaÄr. kugRtaMgkmøaMgkat; TaMgBIrRtUv)ansn μt;[eFVIGMeBIenACMubrievNbøg;EdlmanTItaMgenAcm¶ay 2/d BIépÞssrdUcbgðajenA kñúgrUb 17>26. smIkarsRmab;KNnakugRtaMgkmøaMgkat;KW³

c

v

c

uJ

CMAV

v ±=2,1 ¬!&>@&¦

Edl =cA RkLaépÞmuxkat;eRKaHfñak;enACMuvijssr =cJ m:Um:g;niclPaBb:UElénRkLaépÞEdlRsbeTAnwgm:Um:g;EdlmanGMeBIbEnßmBIelIm:Um:g;nicl

PaBénmuxkat;xagcugEdleFobnwgG½kSTIRbCMuTm¶n;énmuxkat;eRKaHfñak;.



sRmab;ssrxagkñúg ( )yxdAc += 2 ¬!&>@*¦ nig

632

32

3 xdyxxdJc +⎟⎟⎠

⎞⎜⎜⎝

⎛+= ¬!&>@(¦

sRmab;ssrxageRkA ( )yxdAc += 2 ¬!&>#0¦ nig ( )

62

32 3

21

3 xddxyxdxJc ++−= ¬!&>#!¦ Edl 1x / 2x nig y Rtuv)anbgðajenAkñúgrUbTI 17>26. kugRtaMgkmøaMgkat;Gtibrma

cvcu JCMAVv += /1 RtUvEttUcCag 3'cfφ ebImindUecñaHeT EdkTb;kmøaMgkat;RtUv)andak;.

]TahrN_TI17>8³ kMNt;m:Um:g;enAelIssrxagkñúg nigxageRkAkñúgTisedAEvgrbs; flat plate kñúg]Ta-hrN_TI 17>4. dMeNaHRsay³

1> kMNt;m:Um:g;ssrxageRkA. BI]TahrN_TI 17>4 nig 17>5 2/3.975.72.1 mkNwd =×=

2/84.38.46.15.05.0 mkNwl =××= mll 6'22 == mll nn 7' == 96.111 =⎟⎟

⎠

⎞⎜⎜⎝

⎛+

ecα

Unbalanced moment EdlRtUvbMElgeTAssrxageRkAedayeRbIsmIkar !&>@@ b KW ( )[ ] mkNM u .7.15707684.33.9

96.108.0 2 =−×+=

RbsinebIsmIkar !&>@@ a RtUv)aneRbI/ mkNM u .4.270= EdlCatémøEdlsnSMsMéc. 2> enATRmxagkñúg PaBrwgRkajrbs;kRmalenAsgçagssrRtUv)aneRbIedIm,IKNna ecα ³

( )∑ +=

bs

ecec KK

Kα ¬!&>@!¦

BI]TahrN_TI 17>5/ 61034.4 ⋅= cec EK / 61017.4 ⋅= cs EK nig 0=bK dUcenH 52.0

1017.421034.4

6

6=

⋅×

⋅=

c

cec

EE

α

92.211 =⎟⎟⎠

⎞⎜⎜⎝

⎛+

ecα

BIsmIkar 17>22 b m:Um:g; unbalance enAssrxagkμñúgKW³



( )[ ] mkNM u .93.30763.97684.33.992.208.0 22 =××−×+=

RbsinebIsmIkar !&>@@ a RtUv)aneRbI/ mkNM u .79= EdlCatémøEdlsnSMsMéc. ]TahrN_TI17>9³ sRmab; flat plate kñúg]TahrN_TI 17>4 KNnakugRtaMgkmøaMgkat;enAkñúgkRmal xNÐRtg;muxkat;eRKaHfñak;EdlbNþalBI unbalanced moment nigkmøaMgkat;TTWgenAelIssrxagkñúg nig ssrxageRkA. RtYtBinitükarRbmUlpþúMsrésEdk nigkmøaMgrmYlkñúgrbs;ssrxageRkA. eK[

MPaf c 28' = nig MPaf y 420= dMeNaHRsay³

1> m:Um:g;EdleFVI[K μanlMnwg (unbalanced moment) enAssrxagkñúgKW mkNM u .93.30= ¬]TahrN_ TI 17>8¦ Edl 6.0=fγ ¬edaysar cmcc 5021 == ¦. m:Um:g;EdlRtUvbMElgedaykarBt;KW mkNMM uff .56.1893.306.0 =×== γ m:Um:g;EdlbMElgedaykmøaMgkat;KW mkNMMM fuv .37.1256.1893.30 =−=−= müa:gvijeTot m:Um:g;E;dlKNnaBIsmIkar !&>@@ a GacRtUv)aneRbIedIm,IbegáItkugRtaMgkmøaMgkat; FMCag. edayeRbI cmd 2.22= ¬]TahrN_TI 17>4¦

( ) kNVu 1.756722.05.7617 2 =−×= BIrUbTI 17>27

24.64112.222.724 cmAc =××=

632

32

3 xdyxxdJc +⎟⎟⎠

⎞⎜⎜⎝

⎛+=

( ) 46323

107.52.226

2.722.722.7232.72

22.22 cm⋅=+⎟

⎟⎠

⎞⎜⎜⎝

⎛+=

224max /1258

107.52722.037.12

104.64111.756 mkNv =

⋅

×+

⋅=

−−

2min /110034.783.1179 mkNv =−=

22 /1258/1323323.13/2875.03/' mkNmkNMPafv cc >==== φφ



2> sRmab;ssrxageRkA unbalanced moment EdlRtUvbMElgedaykarBt; fM enARtg;tMN kRmalxNÐ-ssrKWesμInwg uf Mγ Edl mkNM u .7.157= . cMNaMfa cmcc 5021 == /

cmd 2.22= enAkñúgTisedAEvg nig 6.0=fα sRmab;ssrkaer. mkNM f .6.947.1576.0 =×=

m:Um:g;EdlRtUvbMElgedaykmøaMgkat;TTwgKW mkNMMM fuv .1.636.947.157 =−=−=

3> sRmab;karbMElgedaykmøaMgkat;enAssrxageRkA muxkat;eRKaHfñak;sßitenAcm¶ay 2/d

BIépÞssr ¬rUbTI 17>28¦. 2/17 mkNwu =

( ) kNVu 390722.0611.09.3617 =×−×= kMNt;TItaMgTIRbCMuTm¶n;rbs;muxkat;eRKaHfñak;edayKitm:Um:g;eFob AB

( ) lx2.721.6122

1.611.612 +×=⎟⎠⎞

⎜⎝⎛ ×

dUcenH cmxl 2.19= . RkLaépÞmuxkat;eRKaHfñak; cA KW ( ) 27.43152.721.6122.22 cm=+× . KNna yxc IIJ += sRmab;RkLaépÞesμ IKñaBIr

1.612.22 × EdlmanRCugRsbeTAnwgTisedAén m:Um:g; CamYynwgRkLaépÞ 2.722.22 × EkgeTAnwgTisedArbs;m:Um:g;. m:Um:g;niclPaBénRkLaépÞTaMgBIrRtUvKiteFobnwgG½kS CD .

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛+=+= 2

3

12AxbhIIJ yxc



2323

2.192.222.722.2212

1.612.192

1.611.612.2212

1.612.222 ××++⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −×+=

461084.1 cm⋅= b¤edayeRbIsmIkar !&>#! sRmab;ssrxageRkA. KNNakugRtaMgkmøaMgkat; nominal Gtibrma nigGb,brmaedayeRbIsmIkar !&>@&³

224max /1.1562

1084.1192.01.63

107.4315390 mkN

JCM

AV

vc

v

c

u =⋅

×+

⋅=+=

−−

2min /3.2454.6587.903 mkN

JCM

AV

vc

v

c

u =−=−= 22 /1.1562/1323323.13/2875.03/' mkNmkNMPafv cc <==== φφ



kugRtaMgkmøaMgkat;TTwgFMCagkugRtaMgkmøaMgkat;GnuBaØat dUcenHeKRtUvbegáInkRmas;kRmalxNÐ b¤eRbIEdkTb;kmøaMgkat;.

4> RtYtBinitükarRbmUlpþúMsrésEdkenAssrxageRkA KWRtYtBinitüPaBRKb;RKan;rbs;lT§PaBTb; karBt;rbs;muxkat;edIm,IbMElgm:Um:g;GviC¢maneTAkñúgssrxageRkA. muxkat;eRKaHfñak;rbs;kM ralxNÐRtUv)anbnøay sh5.1 enAelIRCugnImYy²rbs;ssr Edl[TTwg ( )25350 ×+

cm125= nigkRmas; cm25 . m:Um:g;srubenAkñúgTTwgceRmokelIssr m3 KW mkN.4.162 Edl)anKNnaenAkñúg]TahrN_TI 17>4 ¬CMhan %¦. m:Um:g;enAkñúgTTwg cm125 KWesμ Inwg

3001254.162 mkN.67.67= .

RbsinebIeKeRbIKMlatEdkes μ I²KñaenAkñúgceRmokelIssr enaHeKRtUvkarbrimaNEdkbEnßmenAkñúg TTwg cm125 sRmab;m:Um:g;Edles μ Inwg mkNM f .93.2667.676.9467.67 =−=− . brimaN EdkcaM)ac; 2340mmAs = dUcenH 124DB ¬ 2452mm ¦ GacRtUv)aneRbI. dMeNaHRsayepSgeTotKWedIm,IteRmobEdkenAkñúgceRmokelIssredIm,IbegáInbrimaNEdkenA kñúgTTwkceRmok cm125 . brimaNEdkcaM)ac;enAkñúgTTwgceRmokKYrRKb;RKan;edIm,ITb;nwgm:Um:g;Edles μ Inwg 6.0 dgénm:Um:g; GviC¢manenAkñúgceRmokelIssr b¤ mkN.44.974.1626.0 =× .

⎟⎠⎞

⎜⎝⎛ −

=

2adf

MA

y

us

φ snμt; mma 25=

26

1230

2252224209.0

1044.97 mmAs =⎟⎠⎞

⎜⎝⎛ −×

⋅=

RtYtBinitü³ mmbf

fAa

c

ys 4.1712502885.0

4201230'85.0

=××

×==

eRbI 1211DB enAkñúgTTwg cm125 edayEckes μ IKñasgçagssredayKitBIG½kSssr ¬rUbTI 17>29¦. kardak;EdkbEnßm 124DB Edl)anbgðajxagelICadMeNaHRsaykan;EtRbesI.

5> kmøaMgrmYlenAkñúgkRmalxNÐ³ kmøaMgrmYlBIRCugTaMgsgçagrbs;ssrxageRkAes μ Inwg %40 énm:Um:g;elIceRmokTTwg.

mkNTu .96.644.1624.0 =×= kmøaMgrmYlenAelIRCugmçag³ mkN.48.32

296.64

=



TTwgénmuxkat;kRmalxNÐEdles μ InwgTTwgssrRtUv)ansnμt;[Tb;nwgkugRtaMgrmYl³ ∑= yxvT tuu

3

31

Edl cmx 25= nig cmy 50= . muxkat;eRKaHfñak;KWenAcm¶ay d BIépÞssr ¬rUbTI 17>30¦. edaysnμt;fakmøaMgrmYlERbRbYlmanragCaExSekag)a:ra:bUleTAG½kSkRmalxNÐ enaHkmøaMg rmYlenAcm¶ay d KW³

mkNTu .42.285.3

222.05.348.322=⎟

⎠⎞

⎜⎝⎛ −

=

sRmab;ersIusþg;Tb;karrmYlrbs;ebtug 212505025 cmAcp =×= / ( )50252 +=cpP cm150= tamsmIkar !%>!( ( ) ( )15003/101012502875.0 622 ×⋅⋅= −

cpTφ mkN.78.13= / mkNmkNTa .42.28.445.34/78.13 <== .



eKRtUvkarEdkTb;kmøaMgrmYl. EdkkgbiTCitcaM)ac; nigEdkbeNþaybEnßmRtUv)anKNnadUc Bnül;enAkñúgemronTI 15. muxkat;cugeRkayRtUv)anbgðajenAkñúgrUbTI 17>30. vaCakar RbesIrRbsinebImanFñwmxagenAssrxageRkAedIm,IbegáInPaBrwgRkajTb;karrmYlrbs;kRmal xNÐ.

]TahrN_TI17>10³ kMNt;brimaNEdkTb;kmøaMgkat;TTwgcaM)ac;sRmab;kRmal flat plate xagkñúg edayBicarNadUcteTA³ kmøaMgkat;put kNVu 870= / kRmas;kRmalxNÐ cm23= / cmd 19= /

MPaf c 28' = / ehIyTMhMssrKW cm5050× . dMeNaHRsay³

1> kMNt; 3/' dbfV occ φφ = sRmab;kmøaMgkat;BIrTis ( ) ( ) cmdbo 27619504504 =+=+=

kNVc 7.6933/1019027602875.0 3 =⋅××= −φ edaysar cu VkNV φ>= 870 EdkTb;kmøaMgkat;TTwgRtUvkarcaM)ac;.

2> cVφ GnuBaØatGtibrma EdleRbIEdkkmøaMgkat;TTwges μ Inwg ucoc VkNVdbf >== 6.1040)(5.12/' φφ EdkTb;kmøaMgkat;TTwgGacRtUv)aneRbI.

3> EdkTb;kmøaMgkat;TTWgGacpSMeLIgedayEdksrés Edkrag dUcCaFñwmGkSr I b¤ special

large-head studs welded to a steel strip ¬emIlrUbTI 17>9¦. kñúg]TahrN_enH dMeNaHEdl minéføedayeRbIEdkTb;kmøaMgkat;Fm μtaRtUv)anTTYlykmkeRbI ¬rUbTI 17>9 f ¦. EdkTb;kM laMgkat;TTwgRtUv)andak;enAelIRCugTaMgbYnrbs;ssrxagkñúg ¬b¤bIRCugsRmab;ssrxageRkA¦ sRmab;RbEvg ad + ¬rUbTI 17>31¦. cm¶ay a RtUv)ankMNt;eday[ uc VV =φ enAmux kat; ob EdlbgðajedayExSdac; nigsnμt;fa 6/' dbfV occ φφ = .

( ) ( )aacbo 2500424 +=+= ( ) 8700006/190250042875.0 =+× a

enATIenH cma 87= ehIy ( ) cmda 106=+ dUcenHyk cm110 .



4> KNnaEdkkmøaMgkat;TTwg³

( ) kNVVV cus 3.1767.693870 =−=−= φφ kNVs 235=

sV sRmab;épÞmYyrbs;muxkat;eRKaHfñak; kNVs 75.584=

eRbI 10DB EdkkgGkSr U / 2157mmAv = ¬sRmab;eCIgBIr¦. KMlatKW syv VdfAs /= mm21358750/190420157 =××= . KMlatGtibrmKW mmd 952/1902/ == / yk

mms 90= . 5> karEbgEckEdkkg³ cMnYnEdkkgkñúgmYyRCugrbs;ssrKW 2.129/110 = b¤ 13kg.

cm¶aysrubKW mm11709013 =× ¬rUbTI 17>31¦

]TahrN_TI17>11³ Flat-Slab Floor System edayeRbIviFI direct design method KNnaRbePTkRmalxNÐ flate slab xagkñúgEdlmanEt drop

panel ehIyvamanTMhM m65.7 × ¬rUbTI 17>32¦. RKb;kRmalTaMgGs;RtUv)anRTedayssrTMhM cm5050× RbEvg m6.3 . kRmalxNÐRTnUvbnÞúkBRgayes μ IGefrK μanemKuN 2/8.4 mkN nigbnÞúkefr

K μanemKuN 2/15.1 mkN edayKμanrYmbBa©ÚlTm¶n;pÞal;. eK[ MPaf c 28' = nig MPaf y 420= ¬dMeNaHRsayKWRsedognwg]TahrN_TI 17>3¦.





dMeNaHRsay³ 1> kMNt;kRmas;kRmal nigkRmal; drop panel

a. RbEvg clear span KW m75.05.7 =− . sRmab;kRmalxageRkA témøGb,brmarbs; 33/nlh = cm2.21= b:uEnþkRmalxagkñúg témøGb,brmarbs; cmlh n 4.1936/ == .

eRbIkRmalxNÐEdlmankRmal cm20 kRmas;TMlak;cuHBIeRkamkRmalxNÐKW cmh 54/ = dUcenHkRmas; drop panel KW cm25 .

b. TMhMrbs; drop panel KW mL 25.16/5.76/ == sRmab;TisnImYy²BIG½kSrbs;TRmkñúg TisedAEvg nig m16/6 = enAkñúgTisedAxøI. dUcenHTMhMsrubrbs; drop panel KW

m25.2 × ¬rUbTI 17>32¦. 2> KNnabnÞúkemKuN³

2/15.6252.015.1load slab mkN=×+= 2/06.158.46.115.62.1 mkNWu =×+×=

2/4.72525.015.1load panel drop mkN=×+= 2/56.168.46.14.72.1 mkNWu =×+×=

edaysarEt drop panel manRbEvg 3/L kñúgTisnImYy² témømFüm 2/56.1556.16

3106.15

32 mkNWu =+=

3> RtYtBinitükmøaMgkat;BIrTis ¬enAcm¶ay 2/d BIépÞssr¦³ a. enAkñúg drop panel ³ cmd 2.228.0225 =−−=

( ) cmbo 8.2882.22504 =+= ( )[ ] kNVu 692722.065.756.15 2 =−×= ( ) uocc VkNdbfV >=⋅×== − 1.84810222288828

375.0'

33φφ

b. enAkñúgkRmal³ cmd 2.178.0220 =−−= ehIy ob RtUv)anvas;ecjBI drop panel

enAcm¶ay cm6.82/2.17 = . ( ) ( ) cmbo 8.9682.1720022.172502 =+++=

[ ] kNVu 9.609172.2672.265.756.15 =×−×= ( ) uocc VkNdbfV >=⋅×== − 220410172968828

375.0'

33φφ



tarag 17>11> karKNnaRbB½n§kRmal flat slab xagkñúg

TisEvg mkNM ol .8.571= ceRmokelIssr ceRmokkNþal

emKuNm:Um:g; oM49.0− oM21.0 oM16.0− oM14.0 ).( mkNM u -280.2 120.0 -91.5 80.0

TTwgceRmok )(mmb 3000 3000 3000 3000

km<s;RbsiT§PaB )(mmd 210 160 160 160

)(2 MPabdM

R uu = 2.12 1.56 1.19 1.04

PaKryEdk (%)ρ 0.59 0.43 0.32 0.28

)( 2= mmbdAs ρ 3717 2064 1536 1344

)(0018.0(min) 2mmbhA ss = 1350 1080 1080 1080

EdkEdleRCIserIs ¬Rtg;¦ 19DB16 11DB16 14DB12 12DB

TisxøI mkNM os .3.441= ceRmokelIssr ceRmokkNþal

emKuNm:Um:g; oM49.0− oM21.0 oM16.0− oM14.0 ).( mkNM u -216.2 92.7 -70.6 61.8

TTwgceRmok )(mmb 3000 3000 4500 4500

km<s;RbsiT§PaB )(mmd 210 160 160 160

)(2 MPabdM

R uu = 1.63 1.21 0.61 0.54

PaKryEdk (%)ρ 0.45 0.33 0.16 0.14

)( 2= mmbdAs ρ 2835 1584 1152 1008

)(0018.0(min) 2mmbhA ss = 1350 1080 1620 1620




c. kmøaMgkat;mYyTisminmaneRKaHfñak;. 4> KNnam:Um:g;sþaTicsrubenAkñúgTisEvg nigTisxøI

22

/8.57187656.15 mkNM ol =

×=

22

/3.4418

5.55.756.15 mkNM os =×

= TTwgrbs;ceRmokelIssrkñúgTisnImYy²KW cm300

2600

= b:uEnþTTwgrbs;ceRmokkNþal KW cm300 kñúgTisedAEvg nig cm450 kñúgTisedAxøI.

5> KNnam:Um:g; nigsrésEdkRtUv)anbgðajtarag 17>11. eRbIkm<s;RbsiT§PaBmFüm mmd 21040250 =−= sRmab;ceRmokelIssr nig mmd 16040200 =−= sRmab;

ceRmokkNþal. karBRgaysrésEdklMGitmanlkçN³RsedogKñakñúg]TahrN_ flat plate.



17>11> kRmalxNÐ Waffle (Waffle Slabs)

RbB½n§kRmalxNÐ waffle slab BIrTispSMeLIgedayrnUtebtugEdlFm μtaRbsBVKñaCamMuEkg. kRmalxNÐenHGacsagsg;edayKμanFñwm EdlkñúgkrNIenHk,alssrtan;RtUv)aneFVIenAelIssredIm,I karBarkarpugEdlbNþalBIkmøaMgkat;. FñwmTUlayk¾GacRtUv)aneRbIenAeLIG½kSssrsRmab;km<s;es μI. Bum<canEdkragkaer b¤ fiberglass pan RtUv)aneRbICaTUeTAedIm,IbegáItRTnug. kRmalxNÐesþIgkRmas;

mm75 eTA mm125 RtUv)ancak;CamYyRTnugedIm,IbegáItCa waffle slab. kRmalnImYy²RtUv)anEbgEckCaceRmokelIssr nigceRmokkNþþal. ceRmokelIssrrYm bBa©ÚlRTnugTaMgGs;EdlCab;eTAnwgk,alssrtan; ehIyceRmokkNþalsßitenAcenøaHceRmokelI ssr. EdkRtg; b¤EdkBt;GacRtUv)aneRbICaEdkBRgwgenAkñúg waffle slab. karKNna waffle slab BIrTismanlkçN³ RsedogKñanwgkarKNna flat slabEdr edayKitk,alssrtan;Ca drop panel. edIm,IkarBarkmøaMgTaj FMenAkñúgk,alssr eKRtUveRbITMhMssrFMRKb;RKan; b¤dak; shear cap. kñúgkarKNna waffle slab kRmalxagelI nigrnUtnImYy²begáItCamuxkat;GkSret Edlesμ Ikm<s; kñúg flat plate. dUcenH ElVgEvgEdlRTbnÞúkF¶n;GacRtUv)anKNnaCamYynwgkarsnSMsMécebtug)an eRcIn. kRmal waffle slab k¾)anpþl;nUvBidand¾KYr[Tak;Taj Edl)anBIkarelcecjnUvRTnug b¤eday karlMGePøIg. kRmalsþg;darénBum<canEdlRtUv)aneRbICaTUeTAenAkñúg waffle slab GacsßitenAkñúgCeRmIsBIrxageRkam³

1> Bum<cankaerTMhM cmcm 7575 × CamYynwgkRmas;kRmal mm75 nigTTwgrnUt mm150 manKM lat cm90 KitBIG½kS. sþg;darRbePTenH mankm<s;ERbRbYlBI mm200 eTA

mm500 eday ekIneLIgmþg mm50 . eyagtam]TahrN_TI17>12 nigrUbTI 17>33. 2> Bum<cankaerTMhM cmcm 4848 × CamYynwgkRmas;kRmal mm75 nigTTwgrnUt mm125

manKM lat cm60 KitBIG½kS. sþg;RbePTenH mankm<s;ERbRbYlBI mm150 eTA mm300 edayekIneLIgmþg mm50 . B½t’manepSg²BIkRmalRtUv)anbgðajenAkñúgtarag 17>12.



tarag 17>12 lkçN³muxkat;

sRmab;rnUt ¬Bum<canTMhM cmcm 7575 × ¦ kRmalxag elI ( )mm

km<s;rnUt)(mm

maDxül; ( )panmm /10 36×

RkLaépÞ ( )2410 mm×

cgY

( )mm gI

( )4810 mm× 75 200 107.4 10.09 81.91 5.45

75 250 132.7 11.04 98.58 9.02

75 300 157.4 12.02 116.54 13.85

75 350 181.4 13.05 135.4 20.08

75 400 204.9 14.12 155 27.88

75 500 250 16.39 195.7 48.8

115 200 107.4 13.69 95.12 8.25

115 250 132.7 14.64 109.4 12.89

115 300 157.4 15.62 141.8 19.06

115 350 181.4 16.65 141.8 26.95

115 400 204.9 17.72 159.45 36.72

115 500 250 19.99 196.88 62.59

sRmab;rnUt ¬Bum<canTMhM cmcm 4848 × ¦ 75 150 32 6.56 72.14 2.31

75 250 42.01 7.33 89.11 4.25

75 250 51.57 8.15 107.57 7.03

75 300 60.75 90 127.08 10.78

115 150 32 8.96 87.47 3.84

115 250 42.01 9.73 102.21 6.44

115 250 51.57 10.55 118.53 10.08

115 300 60.75 11.4 136.12 14.91





]TahrN_TI17>12³ Waffle Slab KNnaRbB½n§kRmalxNÐ waffle floor EdlpSMeLIgedaykRmalkaerKμanFñwmedayKitnUvTinñn½yxag Rkam ¬rUbTI 17>33¦³

RbEvgElVgedayKitBIG½kSssreTAG½kSssr= m10 TTwgrnUt = mm150 manKMlat mm900 BIG½kSeTAG½kS km<s;rnUt = mm350 kRmas;kRmalxNÐ = mm75 TMhMssr = mm500500× bnÞúkefr ¬minrYmbBa©ÚlbnÞúkpÞal;¦= 2/4.2 mkN bnÞúkGefr= 2/8.4 mkN MPaf c 35' = MPaf y 420=



dMeNaHRsay³ 1> KNnakRmas;Gb,brmarbs;kRmalxNÐedayeRbItarag 17>1³ 30/min nlh = /

5.010 −=nl m5.9= / mh 317.030/5.9min == sRmab;kRmalxagkñúg ehIy mlh n 288.033/min == sRmab;kRmalxagkñúg. smIkar !&>! nig !&>@ GacRtUv)aneRbI.

edaysnμt;km<s;srub mm425 EdlrYmmankRmalkRmas; mm75 nigrnUtkm<s; mm350 . 2> KNnabnÞúkEdlmanGMeBIenAelI waffle floor ³

a. bnÞúkemKuNénEpñktan;enAelIssr 2/75.1225425.02.1 mkN=××= b. maDxül;rbs;rnUtkm<s; mm350 KW 36104.181 mm⋅ elIRkLaépÞ 2900900 mm× .

Tm¶n;srubrbs;épÞ 2810000mm KW ( ) kN89.410104.1814251081252.1 964 =⋅⋅−×⋅× −

b¤Tm¶n;kñúg 21m KW 2/89.4 mkN c. bnÞúkefrbEnßmemKuNnigbnÞúkGefremKuNKW 2/56.108.46.14.22.1 mkN=×+× .

bnÞúkBRgayesμ IemKuNenAelIépÞtan; 2/5.2331.2375.1256.10 mkNwu ≈=+= bnÞúkBRgayenAemKuNenAelIépÞelIrnUt 2/5.1545.1589.456.10 mkNwu ≈=+=

d. bnÞúkenAelImYykRmal ¬eyagtamrUbTI 17>34¦³ enAelIépÞtan; mkNW /8.1834.65.156.35.23 =×+×=

enAelIépÞelIrnUt mkNW /155105.15 =×= 3> KNnakmøaMgkat; nigm:Um:g;sþaTicsrub³

kNVu 89.7802.315555.18.183)column of faceat ( =×+×= mkNM o .2.1783

22.3155975.355.18.18375.489.780)midspanat (

2=−××−×=

4> RtYtBinitükmøaMgkat;pug ¬eyagtamrUbTI 17>35¦³ a. enAkñúgépÞtan;enAcm¶ay 2/d BIépÞssr mmh 425= / mmd 39530425 =−= /

mmc 500)column( = / ( ) mmbo 35803955004 =+= / kNVu 9.1634895.05.236.38.1834.6155 2 =×−×+×= nig

( ) uocc VkNdbfV >=×== 19523/39535803575.03/'φφ b. enAkñúgépÞelIrnUtenAcm¶ay 2/d BIRCugrbs;épÞtan;. kRmas;kRmalKW mm75 . yk

mmd 60= enaH



( ) mmbo 154406038004 =+=

kNVu 1304860.35.236.38.1834.6155 2 =×−×+×= ( ) uocc VkNdbfV >=×== 13703/60154403575.03/'φφ

5> KNnam:Um:g; nigsrésEdk a. kRmalxageRkA³ mkNM o .2.1783=

m:Um:g;GviC¢manxageRkA mkNM o .6.46326.0 −== m:Um:g;viC¢man mkNM o .3.92752.0 ==



m:Um:g;GviC¢manxagkñúg mkNM o .2.12487.0 −== b. kRmalxagkñúg³ mkNM o .2.1783=

m:Um:g;GviC¢man mkNM o .1.115965.0 −== m:Um:g;viC¢man mkNM o .1.62435.0 == karlMGItBIkarKNnaRtUv)anbgðajenAkñúgtaragTI 17>13 nigrUbTI 17>36. cMNaMfa PaKryEdkTaMgGs;tUc ehIy 9.0=φ

6> KNna unbalanced moment enAkñúgssr nigRtYtBinitükmøaMgkat;sRmab; uV nig vM dUckñúg]TahrN_TI 17>8 nig 17>9.



tarag 17>13> karKNnakRmal waffle slab xagkñúg nigxageRkA ¬rnUt 5enAkñúgceRmokelI ssr nigrnUt 6enAkñúgceRmokkNþal¦

ceRmokelIssr ceRmokkNþal kRmalxageRkA xageRkA

M− M± xagkñúg

M− M− M±

emKuNm:Um:g; 100 60 75 25 40

).( mkNM u 463.6 556.4 936.2 312 370.9

TTwgceRmok )(mmb 3800 5000 3800 900 (6 ribs) 5000

km<s;RbsiT§PaB )(mmd 395 395 395 395 395

)(2 MPabdM

R uu = 0.78 0.71 1.58 2.22 0.48

PaKryEdk (%)ρ 0.21 0.19 0.43 0.61 0.13

)( 2= mmbdAs ρ 3152 3753 6454 2169 2567

)(0018.0(min) 2mmbhA ss = 2907 765/rib 2907 688.5 637.5/rib

EdkEdleRCIserIs ¬Rtg;¦ 11DB20 2DB25/rib 21DB20 7DB20 2DB22/rib

ceRmokelIssr ceRmokkNþal kRmalxagkñúg xageRkA

M− M± xagkñúg M−

M− M± emKuNm:Um:g; - 60 75 25 40

).( mkNM u - 374.5 869.3 289.8 249.6

TTwgceRmok )(mmb - 5000 3800 900 (6 ribs) 5000

km<s;RbsiT§PaB )(mmd - 395 395 395 395

)(2 MPabdM

R uu = - 0.48 1.47 2.06 0.32

PaKryEdk (%)ρ - 0.13 0.40 0.57 0.09

)( 2= mmbdAs ρ - 2567 6004 2026 1777.5

)(0018.0(min) 2mmbhA ss = - 765/rib 2907 688.5 637.5/rib

EdkEdleRCIserIs ¬Rtg;¦ - 2DB25/rib 20DB20 7DB20 2DB22/rib





17>12> viFIeRKagsmmUl (Equivalent Frame Method)

enAeBlEdlRbB½n§kRmalxNÐBIrTismineKarBtamkarkMNt;rbs; direct design method m:Um:g; KNnaRtUv)ankMNt;edayviFI equivalent method. enAkñúgviFIenH GKarRtUv)anEckCaeRKagsmmUltam BIrTis nigbnÞab;mkviPaKeRKagkñúgsßanPaBeGLasÞicsRmab;RKb;lkçxNÐénkardak;bnÞúk. PaBxusKña rvagviFITaMgBIrsßitenAelIviFIénkarKNnam:Um:g;tambeNþayrbs;ElVg. tRmUvkarsRmab;karKNnaRtUv )anBnül;dUcxageRkam³

k> karBiBN’naBIeRKagsmmUl³ eRKagsmmUlCaeRKagGKarkñúgbøg; ¬BIrTMhM¦ EdlTTYl)an edaykarkat;GKarkñúglMhM ¬bITMhM¦tambeNþayExSkNþalElVgcenøaHssr ¬rUbTI 17>4¦. eRKagsmmUlEdlTTYl)anRtUv)anBicarNadac;edayELkenAkñúgTisbeNþay nigTisTTwg rbs;GKar. sRmab;bBaÄr kRmalnImYy²RtUv)anviPaKdac;edayELk edaysn μt;cugsagelI nig cugxageRkamrbs;ssrRtUv)ansnμt;fabgáb;. kRmal-Fñwm (slab-beam) RtUv)ansnμt; fabgáb; enARtg;TRmkRmalBIrEdlQmnwgTRmEdleYigRtUvBicarNa BieRBaHbnÞúkbBaÄrcUlrYm CamYym:Um:g; tictYcenARtg;tMNrenaH. sRmab;bnÞúkedk eRKagsmmUlpSMeLIgedaykRmal TaMgGs;sRmab; km<s;TaMgmUlrbs;GKar edaysarkmøaMgenAkRmalnImYy²CaGnuKmn_én bnÞúkedkenARKb;kRmalBIelInIv:UEdlRtUvBicarNa. karviPaKeRKagk¾GaceFVIeLIgedaykmμviFI kMuBüÚTr½.

x> karsnμt;bnÞúk³ enAeBlpleFob service live load nig service dead load tUcCagb¤es μ Inwg 75.0 KMrUénkardak;bnÞúk pattern loading RtUv)aneRbIedayBicarNanUvlkçxNÐxageRkam³ - manEt %75 énbnÞúkefremKuNTaMgmUlGacRtUv)aneRbIsRmab;karviPaK. - m:Um:g;Bt;GviC¢manGtibrmaenAkñúgkRmalRtg;TRmRtUv)anTTYledaykardak;bnÞúúkEtelI

kRmalxNÐBIrEdlCab;Kña. - m:Um:g;viC¢manGtibrmaenAEk,rkNþalElVgRtUv)anTTYledaykardak;bnÞúkEtenAelIElVg

qøas;. - m:Um:g;KNnaminRtUvtUcCagm:Um:g;KNnaEdlekIteLIgedaykardak;bnÞúkemKuNeBjelIk

Rmal (ACI Code, Sectoion 13.7.6). - m:Um:g;GviC¢maneRKaHfñak;RtUv)anBicarNa[manGMeBIenARtg;épÞssrctuekaN b¤enA

Rtg;ssrkaersmmUlEdlmanRkLaépÞdUcKñasRmab;muxkat;minEmnctuekaNEkg.



K> m:Um:g;niclPaBkRmal-Fñwm³ ACI CodekMNt;fakarERbRbYlm:Um:g;niclPaBtamG½kS beNþay ssr nigFñwmkRmalRtUv)anykmkKitkñúgkarviPaKeRKag. tMbn;eRKaHfñak;sßitenA cenøaHExSG½kSssr nigépÞssr/ bracket b¤ capital. tMbn;enHRtUv)anBicarNaCamuxkat; Rkas;énkRmalxNÐ. edIm,IBicarNakm<s;d¾FMrbs;ssr nigkarkat;bnßyTTwg\T§iBlrbs;va EdlCab;nwg FñwmkRmal ACI Code, Section 13.7.3.3 kMNt;fam:Um:g;niclPaBrbs;Fñwm kRmalrvagG½kSssr nigépÞTRmRtUv)ansn μt;esμ InwgFñwmkRmalenARtg;épÞssredayEcknwg témø ( )2221 lc− Edl 2c CaTTwgssrkñúgTisedATTwg nig 2l CaTTwgrbs;FñwmkRmal. RkLaépÞrbs;muxkat;TaMgmUlGacRtUv)aneRbIedIm,IKNnam:Um:g;niclPaBrbs;FñwmkRmal.

X> m:Um:g;niclPaBrbs;ssr³ ACI Code, Section 13.7.4 bgðajfam:Um:g;niclPaBrbs;ssr RtUv)ansnμt;faesμ IGnnþBIépÞxagelIrbs;kRmaleTA)atrbs; column capital b¤FñwmkRmal ¬rUbTI 17>37¦.

g> PaBrwgRkajrbs;ssr ecK RtUv)ankMNt;eday

tcec KKK111

+=∑

¬!&>!&¦

Edl ∑ cK CaplbUkPaBrwgRkajrbs;ssrxagelI nigssrxageRkamenARtg;cugrbs;va ∑

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= 3

2

22 1

9

lcl

CEK es

t ¬!&>!(¦

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−= ∑

363.01

3 yxyxC ¬!&>@0¦

c> m:Um:g;ssr³ enAkñúgkarviPaKeRKag m:Um:g;EdlkMNt;sRmab;ssrsmmUl enAcugxagelIssr eRkamkRmal nigenA)atssrelIkRmalRtUv)aneRbIkñúgkarKNnassr.

q> m:Um:g;GviC¢manenAelITRm³ ACI Code, Section 13.7.7 bgðajfasRmab;ssrxagkñúgm:Um:g; GviC¢manemKuNRtUv)anykenARtg;épÞssr b¤épÞ capital b:uEnþenAcm¶ayminFMCag 11175.0 l BI G½kSssr. sRmab;ssrxageRkA m:Um:g;GviC¢manemKuNRtUv)anykmkKitenARtg;muxkat; EdlsßitenABak;kNþalcm¶ayrvagépÞssr nigEKmrbs;TRm. ssrmuxkat;mUlRtUv)anKit CassrkaerEdlmanmuxkat;esμ IKña.

C> plbUkm:Um:g;³ RbB½n§kRmalxNÐBIrTisEdleKarBtamkarkMNt;rbs;viFI direct design

method k¾GacRtUv)anviPaKedayviFI equivalent frame method . edIm,IFanafaviFITaMgBIr



pþl;nUvlT§pldUcKña ACI Code, Section 13.7.7 bgðajfam:Um:g;EdlkMNt;edayviFI equivalent frame method GacRtUv)ankat;bnßyedaysmamaRtEdlplbUkénm:Um:g;viC¢man nigm:Um:g;GviC¢manenAkñúgkarKNnaminRtUvFMCagm:Um:g;sþaTicsrub oM .

]TahrN_TI17>13³ edayeRbIviFI equivalent frame method viPaKeRKagKMrUxagkñúgénRbB½n§kRmal flate plate Edl[enA kñúg]TahrN_TI 17>3 EtkñúgTisedAEvg. RbB½n§kRmalpSMeLIgedaykRmalbYnkñúgTisedAnImYy² Edl kRmalnImYy²manTMhM m65.7 × . kRmalnImYy²RtUv)anRTedayssrTMhM cm5050× RbEvg m6.3 . Service live load KW 2/8.3 mkN Service dead load KW 2/6 mkN ¬edayrYmbBa©ÚlTaMgTm¶n;pÞal; rbs;kRmal¦. eK[ MPaf c 21' = / MPaf y 420= . FñwmxagminRtUv)aneRbI. ¬rUbTI 17>38¦ dMeNaHRsay³

1> kRmas;kRmalxNÐ cm25 RtUv)aneRCIserIs dUcEdlBnül;kñúg]TahrN_TI 17>3. 2> bnÞúkemKuNKW 2/28.138.36.162.1 mkNwu =×+×=

pleFob Service dead load elI Service live load KW 75.063.06/8.3 <= . dUcenHeRKag GacRtUvKNnaCamYynwgkarbnÞúkemKuN uw [manGMeBIRKb;kRmalCMnYs[karBRgaybnÞúk tamKMrUénkardak;bnÞúk.

3> kMNt;PaBrwgRkajrbs;kRmal sK ³



s

ss l

EIkK =

Edl k CaemKuNPaBrwgRkaj nig 43

332 1081.7

1225.06

12m

hlI s

s−⋅=

×==

emKuNPaBrwgRkajGacRtUv)ankMNt;edayviFI column analogy method EdlRtUv)anBnül; enAkñúgesovePAviPaKrcnasm<½n§ (structural analysis). edayKitfam:Um:g;niclPaBsRmab;kRmal

sI es μ Inwg 0.1 dUckñúgrUb m:Um:g;niclPaBrvagG½kSssr nigépÞssrKW 19.1

60005001

0.1

1

0.122

2

2

=

⎟⎠⎞

⎜⎝⎛ −

=

⎟⎟⎠

⎞⎜⎜⎝

⎛−

lc

TTwgén analogous column ERbRbYlCamYy I/1 dUcbgðajenAkñúgrUbTI 17>38 b ³ 19.1/1 84.0=

emKuNPaBrwgRkajkRmal ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

aa IMc

Alk 11 ¬!&>#@¦

Edl =aA RkLaépÞénmuxkat; analogous column

=aI m:Um:g;niclPaBrbs; analogous column

=M m:Um:g;EdlekItBIbnÞúkÉktþaenAsrésxageRkAbMputén analogous column

EdlenAG½kSrbs;kRmal.

20.1 1lM ×=

42.742.0784.025.027 =+=××+=aA centerline about the portion) end of()7m ofportion slabfor ( IIIa +=

1.342250.075.342.0

127 23

=⎟⎠⎞

⎜⎝⎛ −+=aI

edayecalm:Um:g;niclPaBénGgát;xøIxagcugeFobnwgTIRbCMuTm¶n;rbs;va. emKuNPaBrwgRkaj 1.409.301.1

1.3475.375.31

42.715.7 =+=⎥⎦

⎤⎢⎣⎡ ××

+=k

emKuN carryover 507.01.4

01.109.3=

−=

dUcenH PaBrwgRkajrbs;kRmalxNÐKW EEKs3

31027.4

5.71081.71.4 −

−⋅=

⋅×=



4> kMNt;PaBrwgRkajrbs;ssr/ cK ³

2' ×⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

cc l

EIkK



sRmab;ssrenABIelI nigBIeRkamkRmal. ='k emKuNPaBrwgRkajrbs;ssr mlc 6.3= 43

4102.5

125.0 mIc

−⋅== emKuNPaBrwgRkaj 'k GacRtUv)ankMNt;dUcxageRkam³

⎟⎟⎠

⎞⎜⎜⎝

⎛+=

aac I

McA

lk 1'

sRmab;ssr 2/clc = nig ( ) 220.1 cc llM == 35.325.06.3 =−=−= sca hlA ( )

133.31235.3

12

33==

−= sc

ahl

I

8.4133.3

8.18.135.316.3' =⎟

⎠⎞

⎜⎝⎛ ×

+=k

EEKc 0139.026.3

102.58.43

=⋅

=−

enAkñúg flat-plate floor system PaBrwgRkajrbs;ssr cK GacRtUv)anKNnaedaypÞal; dUcxageRkam ( ) ( )3

23

cc

cc

sc

c

c

c

hllI

hlI

EK

−+

−= ¬!&>##¦

5> KNnaPaBrwgRkajTb;karrmYl tK rbs;kRmalenARtg;épÞrbs;ssr

32

2 1

9

⎟⎟⎠

⎞⎜⎜⎝

⎛−

= ∑

c

cst

lc

l

CRK ehIy ∑ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

363.01

3 yxyxC

enAkñúg]TahrN_enH mmx 250= ¬kRmas;kRmalxNÐ¦ nig mmy 500= ¬TTWgssr¦ emIlrUbTI 17>17.

433

1042.33

5.025.05.025.063.01 mC −⋅=⎟

⎟⎠

⎞⎜⎜⎝

⎛ ×⎟⎠⎞

⎜⎝⎛ +=

EE

K cst

33

31066.6

65.016

1042.39 −−

⋅=

⎟⎠⎞

⎜⎝⎛ −

⋅=

sRmab;kRmalxNÐBIrCab;Kña EEKt33 1032.131066.62 −− ⋅=⋅×=

6> KNnaPaBrwgRkajssrsmmUl/ ecK ³



EEKKK tcec31032.13

10139.0

1111−⋅

+=+=∑

EKec3108.6 −⋅=

7> emKuNEbgEckm:Um:g; (D.F) ³ - sRmab;tMNxageRkA

386.0108.61027.4

1027.4)slab(. 33

3=

⋅+⋅

⋅=

+=

−−

−

ecs

sKK

KFD

( ) 614.0columns. ==∑KK

FD ec

ssrxagelI nigssrxageRkamkRmalxNÐmanPaBrwgRkajdUcKña dUcenHemKuNEbgEck 614.0 RtUv)anEckes μ IKñarvagssrTaMgBIr EdlmYy²TTYl)an D.F= 307.02/614.0 = .

- sRmab;tMNxagkñúg 278.0

108.61027.421027.4)slab(. 33

3=

⋅+⋅×

⋅=

+=

−−

−

ecs

sKK

KFD

( ) 444.0108.61027.42

108.6columns. 33

3=

⋅+⋅×

⋅==

−−

−

∑KK

FD ec

ssrmYy²man D.F= 222.02/444.0 = .

8> m:Um:g;cugbgáb;³ edaysar LDLL ./. tUcCag 0.75 m:Um:g;emKuNTaMgmUlRtUv)ansnμt;faman GMeBIelIElVgTaMgGs;.

212 )moment endFixed (Llk"wu=−

emKuN "k GacRtUv)ankMNt;eday column analogy method ³ sRmab;bnÞúkÉktþa mkNw /1= enAelIbeNþayElVg m5.7 düaRkamm:Um:g;Bt;samBaØRtUv)anbgðajenAkñúgrUbTI

17>38 b . RkLaépÞénm:Um:g;Bt; edayBicarNabERmbRmYlm:Um:g;niclPaBtambeNþayElVgKW RkLaépÞsrub ( ) 321 2AAAAm ++=

( ) 98.3484.091.025.021291.0791.077

32

=⎟⎠⎞

⎜⎝⎛ ××+×+−×=

emKuNm:Um:g;bgáb;cug 21lA

A

a

m=

Edl aA sRmab;kRmalxNÐKW 42.7 dUcEdl)anKNnaenAkñúgCMhanTI 3. 0838.0

5.742.798.34" 2 =×

=k



eyIgeXIjfaemKuNm:Um:g;bgáb;cug 0838.0"=k mantémøEk,rnwgemKuN 833.012/1 = Edl eRbICaTUeTAedIm,IKNnam:Um:g;bgáb;rbs;Fñwm. eK)anrMBwgTuknUvlT§plenH edaysarEpñkénElVg manm:Um:g;niclPaBERbRbYltUcenAkúñg flat plate EdlK μan column capital b¤ drop panel. enAkñúg flat plate EdlmanpleFobElVgelITTwgssrFMCag 20 enaHeKGacykemKuNm:Um:g; bgáb;cug 0833.0 mkeRbIedIm,IKNnam:Um:g;cugRbhak;RbEhl. m:Um:g;bgáb;cug ¬EdlbNþalBI

2/28.13 mkNwu = ¦ mkN.6.3755.7628.130838.0 2 =×××= 9> karEbgEckm:Um:g;GaceFVIeTA)ansRmab;Bak;kNþaleRKag edaysarvamanlkçN³sIuemRTI. enA

eBlEdlm:Um:g;cugGviC¢manRtUv)ankMNt; m:Um:g;viC¢manenAkNþalElVgGacTTYl)anedaydk témømFüménm:Um:g;cugGviC¢manBIm:Um:g;viC¢manFñwmTRmsamBaØ. karEbgEckm:Um:g;RtUv)anbgðaj enAkñúgrUbTI 17>39. m:Um:g;Bt; nigkmøaMg kat;TTwgcugeRkayRtUv)anbgðajenAkñúgrUbTI 17>40.

10> kRmalxNÐCagRtUv)anKNnasRmab;m:Um:g;GviC¢manenARtg;épÞssrdUcbgðajenAkñúgrUbTI 17>40.



]TahrN_TI17>14³ edayeRbIviFI direct design method edIm,IKNnakRmal flate slab xagkñúgEdlman drop panel edIm,I RTbnÞúkefr 2/6.8 mkN nigbnÞúkGefr 2/11 mkN . RbB½n§kRmalpSMeLIgedaykRmalcMnYn ^ kñúgTis nImYy² EdlkRmalmYy²manTMhM m4.56× . RKb;kRmalTaMgGs;RtUv)anRTeday ssrEdlmanGgát; p©it m4.0 ehIy column capital manGgát;p©it m0.1 . km<s;Can;KW m0.3 . eK[ MPaf c 28' = nig

MPaf y 400=



dMeNaHRsay³

1> RKb;karkMNt;rbs; ACI edIm,IeRbI direct design method RtUv)anbMeBj. kMNt;kRmas; kRmalGb,brma sh edayeRbIsmIkar !&>! nig !&>@. Ggát;p©itrbs; column capital es μ Inwg

m0.1 . muxkat;ssrkaersmmUlEdlmanRkLaépÞesμ IKñamanRCuges μ Inwg ( )22 500ππ =r



mm885= b¤ mm900 . m1.59.00.6direction) (longspan clear =−= m5.49.04.5direction)(short span clear =−=

edaysarFñwmminRtUv)aneRbI 0=fmα / 0.1=sβ nig 11.14.5/6 ==β BItarag !&>!/ kRmas;Gb,brma mmlh ns 15533/1.533/ === b:uEnþedaysarman drop panel sh GacRtUv )ankat;bnßy %10 RbsinebI drop panel latsn§wgcm¶ayy:agtic 6/l kñúgTisnImYy²BIG½kS rbs;TRm nigTMlak;cuHBIeRkamkRmaly:agtic 4/sh . dUcenH eRbIkRmas;kRmal

1559.0 ×=sh mm140= ehIyRbEvgbeNþay nigTTwgrbs; drop panel KW m

l2

30.6

3direction Long 1 ===

ml

8.134.5

3directionShort 2 ===

kRmas;rbs; drop panel KW mmhs 17514025.125.1 =×= . begáInkRmas;rbs; drop panel

dl; mm220 edIm,Ipþl;nUvkRmas;RKb;RKan;sRmab;kmøaMgkat;pug nigedIm,IecosvagnUvkareRbInUv PaKryEdkFM. TMhMTaMgGs;RtUv)anbgðajenAkñúgrUbTI 17>41.

2> KNnabnÞúkemKuN 2/28116.16.82.1 mkNwu =×+×=

3> RtYtBinitükmøaMgkat;BIrTis. dMbUgenAkñúg drop panel ³ muxkat;eRKaHfñak;enAcm¶ay 2/d CMuvij column capital. yk mmd 19030220 =−= . Ggát;p©itrbs;muxkat;rgkmøaMgkat;KW

m19.119.01 =+ kNVu 87619.1

44.5628 2 =⎥⎦

⎤⎢⎣⎡ −×=

π

mbo 74.3219.12 =⎟

⎠⎞

⎜⎝⎛= π

uocc VkNdbfV >=×××

=×= 9301903740281000

33.075.0'33.0φφ bnÞab;mkeTotepÞógpÞat;kmøaMgkat;BIrTisenAkñúgkRmalxNÐ. muxkat;eRKaHfñak;KWsßitenAcm¶ay

2/d BIeRkA drop panel

( ) mmd 11030140slab =−=

RkLaépÞeRKaHfñak; ( )( ) 203.411.08.111.02 m=++=



( ) mbo 04.891.111.22 =+= ( ) kNVu 79403.44.5628 =−×=

uc VkNV >=×××

= 11581108040281000

33.075.0φ

kmøaMgkat;mYyTismineRKaHfñak;eT. 4> KNnam:Um:g;sþaTicsrubenAkñúgTisEvg nigTisxøI³

mkNllw

M nu

ol .6.4911.54.5828

822

12 =×==

mkNllw

M nu

os .2.4255.46828

822

21 =×== edaysar 12 ll < TTwgrbs;ceRmokelIssrkñúgTisedAEvgKW ( ) m7.24.525.02 =× . TTwgcM erokelIssrkñúgTisedAxøIKW m7.2 . edaysnμt;Ggát;p©itEdk mm12 ehIyEdkkñúgTisedAxøI sßitenABIelIEdkkñúgTisedAEvg enaHkm<s;RbsiT§PaBkñúgTisedAxøIKWtUcCagkm<s;RbsiT§PaBkñúg TisedAEvgRbEhl mm10 . témørbs; d nigdMeNIrkarKNnaRtUv)anbgðajenAkñúgtarag 17>14. RbEvgGb,brmarbs;EdkEdl)aneRCIserIsRtUveKarBtamRbEvgtRmUvkarrbs; ACI

Code Edl)anbgðajenAkñúgrUbTI 17>16. cMNaMfaPaKryEdkTaMgGs;tUcCag maxρ . dUcenH 9.0=φ .

5> PaBrwgRkajrbs;ssrKW 782.0

116.8

L.LD.Lratio == ehIy 11.1

2

1 =ll

kMNt; 15.111.1782.0

1min =

×=α

viFIRbhak;RbEhlRtUv)aneRbIenATIenHedIm,IkMNt;PaBrwg Rkajrbs;ssrCamYynwg capital

rbs;va.

sI ¬m:Um:g;niclPaBrbs;kRmalkñúgTisxøI¦ 463

10137212

1406000 mm×==

ccsc

s EE

lIE

K 36

2101016

540010137244

⋅=⋅×

==

cI ¬sRmab;ssrmUlEdlmanGgát;p©it mm400 ¦ ( ) 464

4101257400

6464mm

D⋅===

ππ

cc

c

ccc E

El

IEK 3

6101676

300010125744

⋅=⋅×

==



tarag 17>14 karKNnaénkRmal flat plate xagkñúgEdlman drop panel TisEvg mkNoM .6.491=

mkNoMnM .5.31965.0 −=−=

mkNoMpM .1.17235.0 +=+= ceRmokelIssr ceRmokkNþal

emKuNm:Um:g; nM75.0− pM60.0 nM25.0− pM40.0 ).( mkNM u -239.6 103.3 -79.9 68.8

TTwgceRmok )(mmb 190 110 110 110

km<s;RbsiT§PaB )(mmd 2.7 2.7 2.7 2.7

)(2

MPabd

MR u

u = 2.46 3.16 2.44 2.10

PaKryEdk (%)ρ 0.71 0.93 0.7 0.6

)( 2= mmbdAs ρ 3642 2762 2079 1782

)(0018.0(min) 2mmbhA ss = 1070 680 680 680


KMlat )(mm 150 193 135 170

TisxøI mkNM o .2.425= mkNMM on .4.27665.0 −=−=

mkNMM op .8.14835.0 +== ceRmokelIssr ceRmokkNþal

emKuNm:Um:g; nM75.0− pM60.0 nM25.0− pM40.0 ).( mkNM u -207.3 89.3 -69.1 59.5

TTwgceRmok )(mmb 180 100 100 100

km<s;RbsiT§PaB )(mmd 2.7 2.7 3.3 3.3

)(2

MPabd

MR u

u = 2.37 3.30 2.10 1.80

PaKryEdk (%)ρ 0.69 1.00 0.60 0.50

)( 2= mmbdAs ρ 3353 2700 1980 1650

)(0018.0(min) 2mmbhA ss = 1070 680 680 680


KMlat )(mm 150 195 185 205



pleFobrvagPaBrwgRkajrbs;ssrnigPaBrwgRkajrbs;kRmal 65.1

101016101676

3

3=

⋅

⋅==

s

cKK

EdlFMCag 15.1min =α . RbsinebI sI kñúgTisEvgRtUv)aneRbI pleFobénPaBrwgRkajssr elIPaBrwgRkajkRmalEdl)anKNnanwgFMCag 65.1 . dUcenHssrKWRKb;RKan;.

6> kMNt; balanced moment enAkñúgssr nigRtYtBinitükugRtaMgkmøaMgkat;enAkñúgkRmal dUc Edl)anBnül;enAkñúg]TahrN_TI 17>8 nig 17>9.


T.Chhay 606 Stairs

XVIII. CeNþIr Stairs


RKb;GKarTaMgGs; TaMgTab nigx<s;EtgEtmanCeNþIr eTaHbICamanCeNþIreyagRKb;RKan;k¾eday. CeNþIrpSMeLIgeday km<s;kaM (rise), CMhankaM (run or tread) nigfasCeNþIr (landing)¬rUbTI 18>1¦.


CeNþIr 607 T.Chhay

TMhMFm μtarbs;km<s;kaM nigCMhankaMenAkñúgGKarEdlTak;Tgnwg empirical rule xøH. mm430run Rise =+

mm356run 2Rise =+ 205.0run Rise m=× km<s;kaMGaRs½ynwgRbePTGKar. ]TahrN_ sRmab;GKarsaFarN³ km<s;kaMKWRbEhl cm15

b:uEnþsRmab;GKarsñak;enAvaERbRbYlcenøaH cm15 eTA cm19 . CMhankaMKWRbEhl cm25 enAkñúgGKar saFarN³ nigERbRbYlcenøaH cm23 eTA cm32 sRmab;GKarsñak;enA. CaTUeTA km<s;kaMminRtUvFMCag

cm20 nigminRtUvtUcCag cm10 ehIycMnYnkm<s;kaM)anBIkarEckTMhMCan;eTACan;rbs;GKarnwgkm<s;kaM snμt;. kargarbegðIyrbs;kaMCeNþIrman f μdus (troweling Alundum grit) kar:U asphalt kar:U terrazzo

kar:U marble b¤RBM. bEnßmBIelIbnÞúkefr CeNþIrRtUv)anKNnasRmab;bnÞúkGefrGb,brma 2/8.4 mkN .

18>2> RbePTCeNþIr (Types of Stairs)

eKmanCeNþIrCaeRcInRbePTEdlGaRs½yCacMbgeTAnwgRbePT nigtYnaTIrbs;GKar nigGaRs½y eTAelItRmUvkarsßabtükm μ. RbePTCeNþIrFm μtabMputmandUcxageRkam³

!> Single-flight stair³ kareFVIkarrbs;rcnasm<½n§éntYCeNþIrRsedogeTAnwgkRmalxNÐmYyTisEdl RtUv)anRTenAcugsgçag. kRmalrbs;kRmalRtUv)aneKehAfa waist ¬rUbTI 181¦. enAeBltY CeNþIrmanfas eKRtUvdak;FñwmenARtg; B nigC edIm,IlkçN³esdækic© ¬rUbTI 18>2¦. RbsinebI FñwmTaMgBIrenHminRtUv)andak; enaHRbEvgElVgCeNþIrnwgekIneLIgedaysarTTwgrbs;fasBIrEdl latsn§wgcenøaH A nig D . enAkñúgGKarsñak;enATTwgfasKWsßitenAcenøaH m2.1 eTA m8.1 ehIy cm¶aysrubcenøaH A nig D KWRbEhl m6 .

viFIepSgeTotkñúgkarRT Single-flight stair KWRtUveRbI stringer b¤Fñwmxag (edge beam) enARCugBIrtambeNþayCeNþIr. kaMRtUv)anRTedayFñwm ¬rUbTI 18>3¦.

@> Double-flight stair³ GñkeRbInwgmanlkçN³gayRsYlkñúgkareRbIR)as;GKarEdlman double-

flight stair. RbePTEdlRtUv)aneRbIR)as;CaTUeTAKWRbePT quarter-turn ¬rUbTI 18>4¦nig closed-well stair b¤ open-well stair dUcbgðajenAkñúgrUbTI 18>5. sRmab;karviPaKeRKOgbgÁúM CeNþIr tYmYy²RtUv)anKitdUc single-flight ehIyRtUv)anBicarNaedayRTenAelIFñwmBIr b¤eRcIn


T.Chhay 608 Stairs

dUcbgðajenAkñúgrUbTI 18>2. fasCeNþIrlatsn§wgkñugTisedATTwgcenøaHTRmBIr ehIyRtUv)an KNnadUc one-way slab. kñúgkrNI open-well stair EpñkkNþalrbs;fasCeNþIrRTbnÞúkeBj cMENkÉsgçagBIrRTbnÞúkEtBak;kNþal dUcbgðajenAkñúgrUbTI 18>5 d. bnÞúkBak;kNþaleTot RtUv)anRTenAkñúgTisbeNþayedaytYCeNþIr ¬muxkat; A-A nig B-B¦.


CeNþIr 609 T.Chhay

#> Three or more flight of stair³ kñúgkrNIxøH EdlTMhMTaMgmUlrbs;CeNþIrRtUv)ankMNt; three or

more flight of stair GacRtUv)anTTYlyk ¬rUbTI 18>6¦. tYCeNþIrmYy²RtUv)anKitdac;eday ELkBIKñadUckñúgkrNI double-flight staircase.

$> Cantilever stair³ RtUv)aneRbICaTUeTAsRmab;CeNþIr fire-escape stair ehIyvaRtUv)anRTeday

CBa¢aMg b¤Fñwmebtug. CeNþIrRbePTenHGac full-flight EdltYCeNþIrQrelIEtCBa¢aMgmçag nigGac half-flight EdltYCeNþIrQrelICBa¢aMgsgçag b¤RbePT semispiral dUcbgðajenAkñúgrUbTI 18>7. enAkñúgCeNþIrRbePTenH kaMnImYy²eFVIkarCaFñwm cantilever ehIyEdkemRtUv)andak;enAkñúgtMbn; rgkarTajénCMhankaM nigEdkRtUv)anf<k;eTAkñúgCBa¢aMgebtug. EdkTb;sItuNðPaB nigkarrYmmaD RtUv)andak;kñúgTisedATTwg.


T.Chhay 610 Stairs

TRmg;epSgeTotrbs;CeNþIr cantilever stair KWeRbI open-riser step EdlRTedayFñwm kNþaldUcbgðajenAkñúgrUbTI 18>8. FñwmmanCRmaldUctYCeNþIr ehIyEpñkxagelIrbs;Fñwm GnuBaØat[kaMCeNþIrKgelI. kñúgkrNICaeRbIkaMebtugGarem:cak;eRscGacRtUv)aneRbICamYynwg karpþl;BiesssRmab;rwtb‘ULúgedIm,IP¢ab;kaMeTAnwgFñwm.


CeNþIr 611 T.Chhay

%> Precast flights of stair³ el,Ónkñúgkarsagsg;enAkñúgKMeragxøHtRmUv[eRbI precast flights of

stair ¬rUbTI 18>8¦. tYCeNþIrGacRtUv)ancak;edayELk ehIybnÞab;mkRtUv)anP¢ab;eTAnwgfas CeNþIrEdlcak;enAnwgkEnøg. kñúgkrNIepSgeTot tYCeNþIrrYmTaMgfasCeNþIr RtUv)ancak;nig bnÞab;mkdak;enAelICBa¢aMg b¤FñwmTMr. vaRtUv)anKNnaCakRmalxNÐmYyTisEdlmanTRm samBaØCamYynwgEdkemenA)at waist rbs;CeNþIr. brimaNEdkRKb;RKan;RtUv)andak;enAelI tMN dUcbgðajenAkñúgrUbTI 18>9.

TMBk;RtUv)aneKeFVIedIm,IkargarelIkdak; nigdMeLIg. EdkBiessRtUvdak;enARtg;mux kat;eRKaHfñak; edIm,ITb;nwgkugRtaMgTajEdlekItmanenAkñúgCeNþIrkñúgdMNak;karelIkdak;.


T.Chhay 612 Stairs

^> Free standing stair³ sRmab;CeNþIrRbePTenH fasCeNþIrsßitenAkñúgxül;edayKμanTRmenA xagcug ¬rUbTI 18>10¦. CeNþIreFVIkarkñúglkçN³Cakþaelat (springboard) EdlbegáItCa kugRtaMgrmYlenAkñúgkRmalxNÐ.

RbB½n§énkardak;bnÞúkbIRbePT RtUv)anykmkBicarNakñúgkarKNnaCeNþIrRbePTenH

edayKitBicarNafam:Um:g;rmYlnwgekItmanenAkñúgkRmalRKb;lkçxNÐ³ - enAeBlbnÞúkGefreFVIGMeBIEtenAelItYCeNþIrxagelI nigBak;kNþalfas ¬rUbTI 18>12¦

tYCeNþIrxagelInwgrgnUvkmøaMgTajbEnßmBIelIm:Um:g;Bt; EttYCeNþIrxageRkamnwgrgnUv kmøaMgsgát; EdlGacbegáItCakmøaMgPøat; (buckling) enAkñúgkRmal .


CeNþIr 613 T.Chhay

- enAeBlbnÞúkGefreFVIGMeBIEtenAelItYCeNþIrxageRkam nigBak;kNþalfas tYCeNþIrxag elInwgrgkmøaMgTaj EttYCeNþIrxageRkamnwgrgm:Um:g;Bt; nigkmøaMgsgát;.

- enAeBlbnÞúkGefreFVIGMeBIenATaMgelItYCeNþIrxagelI nigxageRkam kardak;bnÞúkenAelI tYCeNþIrmYynwgbNþal[tYrCeNþIrmYyeTotrmYl. kugRtaMgrmYlekItenAkñúgCeNþIr TamTarsrésEdkRKb;RKan;enAkñúgépÞTaMgsgçagrbs;CeNþIr nigfas. srésEdkTTwg enAkñúgkRmal nigfasRtUv)andak;enAkñúgépÞTaMgsgçagrbs;ebtugkñúgTRmg;CaEdlGkSr U biTCit enABak;kNþalTTwgrbs;CeNþIr. srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>13.

sßabtükrcUlcitþCeNþIrRbePTenH ehIyCeNþIrRbePTenHeBlxøHRtUv)aneKehAfa pliers-

shaped staircase b¤ jackknife staircase. &> Run-riser stair³ CaRbePTCeNþIrEdlpSMeLIgedaycMnYn km<s;kaM nigCMhankaMCaeRcInEdl

P¢ab;KñaedaypÞal;y:agrwgedayK μankRmal waist ¬rUbTI 18>14 a¦. CeNþIrRbePTenHTTYl karcab;GarmμN_edaysßabtükredaysarrUbragxageRkArbs;va. karviPaKeRKOgbgÁúMrbs; run-riser stair GacRtUv)ansRmYledaysnμt;fa\T§iBlrbs;kmøaMgtamG½kSRtUv)anecal nig snμt;fabnÞúkenAelICMhankaMnImYy²RtUv)anRbmUldak;enAxagcugrbs;CMhankaM ¬rUbTI 18> 14 b¦. sRmab;karviPaKéntYCeNþIrEdlRTedayTMrsamBaØ edayBicarNatYCeNþIrsamBaØén CMhankaMBIr ABC EdlrgnUvbnÞúkcMcMNuc P enARtg;cMNuc B’ ¬rUbTI 18>14 b¦. edaysar tMN B nig B’ CatMNrwg m:Um:g;enARtg;tMN B es μ Im:Um:g;enARtg;tMN B’ b¤ 'BB MM =

2/PS= Edl S CaTTwgrbs;CMhankaM. m:Um:g;enAkñúgkm<s;kaM 'BB mantémøefr ehIyesμ I nwg 2/PS .

enAeBlEdlKμankm<s;kaM CeNþIr ABC eFVIkarCaFñwmTMrsamBaØ ehIym:Um:g;Bt;Gtibrma EdlekItmanenAkNþalElVgCamYytémø 2/4/ PSPLM B == . sRmab;tYCeNþIrEdlpSM eLIgedaykm<s;kaM nigCMhankaMeRcIn viFIdUcKñaRtUv)aneRbIdüaRkamm:Um:g;Bt;RtUv)anbgðaj enAkñúgrUbTI 18> 15 a. m:Um:g;enAkñúg 'BB mantémøefrs μ Inwgm:Um:g;enARtg;tMN B b¤ PS2 . dUcKña PSMM CC 3' == / PSMM DD 3' == nig PSMM EE 2' == .


T.Chhay 614 Stairs


CeNþIr 615 T.Chhay

RbsinebImanvtþmanfasCeNþIrenAcugmçag b¤cugsgçag bnÞúkenAelIfask¾RtUv)anRbmUl CabnÞúkcMcMNucdUckrNICMhankaMEdr. karviPaKrcnasm<½n§k¾GaceFVIedayBicarNabnÞúkBRgay es μ IenAelItYCeNþIr. m:Um:g;enAkñúgkm<s;kaMTaMgGs;mantémøefr nigTTYl)anBIrdüaRkamm:Um:g; Bt;énFñwmTMrsamBaØEdlrgbnÞúkesμ I ¬rUbTI 18>15 b¦. ]TahrN_TI 18>3 bgðajBIkar KNnaCeNþIredayeRbIkarsnμt;BIr KWbnÞúkcMcMNuc nigbnÞúkBRgayesμI.

RbsinebItYCeNþIrRtUv)anbgáb; b¤Cab;enAcugmçag b¤cugTaMgBIr m:Um:g;GacRtUv)anTTYl edayeRbIviFIviPaKeRKOgbgÁúMNamYyk¾)an. edIm,IBnül;krNIenH cat;TuktYCeNþIrEdlpSMeLIg edayCMhankaMBIr nigRtUvbgáb;enAcugTaMgBIr ¬rUbTI 18>16 a¦. m:Um:g;enAcugbgáb; A nig B EdlbNþalBIbnÞúkenARtg; B esμ Inwg 4/8/ PSPL = . lT§plenHRtUv)anTTYledaysnμt; faCeNþIrminmankm<s;kaM ABC eFVIkarCaFñwmbgáb;cugEdlrgnUvbnÞúkcMcMNucenAkNþalElVg ¬rUbTI 18>16 b¦. m:Um:g;enAkNþalElVg muxkat; B es μ Inwg

4424

PSPSPSMPLA =−=−

m:Um:g;Bt;éntYCeNþIrEdlmankm<s;kaMmYyRtUv)anbgðajenAkñúgrUbTI 18>16 a. cMNaMfam:Um:g; enAkñúgkm<s;kaM 'BB mantémøefr ehIy 4/' PSMM BB == .

sRmab;tYCeNþIrEdlmanlkçN³sIuemRTI cugbgáb;TaMgsgçag ehIyrgnUvbnÞúkcMcMNucenA Rtg;cMNucCMhankaM m:Um:g;enAcugbgáb;GacRtUvKNnadUcxageRkam³

( ) )1(12

end fixed 2 −= nPSM Edl =P bnÞúkcMcMNucenARtg;cMNucCMhankaM =S TTwgCMhankaM =n cMnYnCMhankaM enAeBl 2=n enaH ( ) ( )

414

12end fixed PSPSM =−=

EdllT§pldUcnwglT§plTTYl)anBIxagedIm. RbsinebImanfasCeNþIrenAcugmçag b¤cugsgçag bnÞúkenAelIfasCeNþIrGacRtUv)an

dak;CabnÞúkcMcMNucenAKMlat S .


T.Chhay 616 Stairs

*> Helical stair (open-spiral stair)³ CaRbePTeRKOgbgÁúMbITMhM EdlCaTUeTAmanragCargVg;enA kñúgbøg; ¬rUbTI 18>17¦. vaCaRbePTCeNþIrEdleKeRbIenAkñúg entrance hall, theater foyer

nigGKarkariyal½yEdlmankm<s;Tab. témørbs;vaéføCagCeNþIrRbePTFm μta. CeNþIrGacRtUv)anRTenARCugxøHEdlCab;nwgCBa¢aMg b¤GacKNnaCa free-standing

helical staircase EdlTTYlkareBjniymCaeK. eRkamGMeBIrbs;bnÞúk tYCeNþIrGacrgnUvkug RtaMgrmYl. tYCeNþIrxagelInwgrgnUvkugRtaMgTaj ÉcMENkÉkugRtaMgsgÁt;ekItmanenAEpñk xageRkamrbs;CeNþIr. kmøaMgEdleFVIGMeBIenARtg;muxkat;NamYyGacpSMeLIgedaym:Um:g; bBaÄr m:Um:g;edk m:Um:g;rmYl kmøaMgtamG½kS kmøaMgkat;TTwgEdlkat; waist rbs;CeNþIr nigkM laMg radial horizontal shearing force. EdkbeNþayempSMeLIgedayEdk helical bar Edldak;enAkñúg waist rbs;CeNþIr nigCMhankaMBIfasxagelIeTATMrxageRkam. EdkTTwgRtUv EtmanTMrgCaEdkkgbiTCitedIm,ITb;kugRtaMgrmYl b¤CaTRmg;EdkGkSr U pÁÜbKñadak;enA kNþalTTwgrbs;CeNþIr.

viFIepSgeTotsRmab;pþl;[ helical stair KWeRbIFñwm helical girder enAkNþalTTwg rbs;CeNþIr. kaMnImYy²RtUv)anKitCaFñwm cantilever ehIyEdkRtUv)andak;enAEpñkxagelI rbs;kaM.


CeNþIr 617 T.Chhay


T.Chhay 618 Stairs


CeNþIr 619 T.Chhay


T.Chhay 620 Stairs


CeNþIr 621 T.Chhay


T.Chhay 622 Stairs

]TahrN_TI 18>1³ KNnaCeNþIrdUcbgðajenAkñúgrUbTI 18>18 edIm,IRTbnÞúkGefrBRgayes μI

2/8.4 mkN . snμt;km<s;kaMes μInwg cm15 ehIyCMhankaMes μ Inwg cm30 . eK[ MPaf c 21' = nig MPaf y 400= .

dMeNaHRsay³ 1> bnÞúk³ snμt;kRmas;kRmal ¬waist¦ esμ Inwg cm10 .

Tm¶n;rbs;kaMmYy 25area ltrapezoida ×= mkN /4.1253.0

22618.01118.0

=××⎟⎠⎞

⎜⎝⎛ +

=

eyagtamrUbTI 18>18 b snμt;Tm¶n;kargarbegðIyEdlRKbBIelIkaMCeNþIrKW mkN /3.0 . dUcenHbnÞúkefrsrub mkNLD /7.1.. =

mkNLDWu /35.43.08.46.17.12.16.12.1 =××+×=+=


CeNþIr 623 T.Chhay


T.Chhay 624 Stairs

2> m:Um:g;Bt;GtibrmaenAkñúgmYykaMKW 2/2lWu mkNM u .05.78.1

235.4 2 ==

kRmas;mFümrbs;kaMCeNþIrKW cm68.182

18.2618.11=⎟

⎠⎞

⎜⎝⎛ + .

yk cmd 1.166.0268.18 =−−= ⎟⎠⎞

⎜⎝⎛ −=

2adfAM ysu φ snμt; mma 5.12=

26

127

25.121614009.0

1005.7 mmAs =⎟⎠⎞

⎜⎝⎛ −×

⋅=

RtYtBinitü mmbf

fAa

c

ys 5.93002185.0

400127'85.0

=××

×== ¬mantémøRbEhlkarsn μt;¦

brimaNEdkGb,brma ( )( ) 216116130000333.0 mmAs == eRbI 122DB sRmab;mYykaM. kRmas;kRmalGacyktUcCagkarsnμt;enH b:uEnþedIm,IeCosvag PaBdabFM nigPaBrMj½rrbs;CeNþIr eKRtUveRCIserIskRmas;kRmalsmrmü.

3> KNnakmøaMgkat;enAcm¶ay d BIépÞTRm ( ) kNVu 13.7161.08.135.4 =−=

( ) kNbdfV cc 7.271016130021675.0'

675.0 3 =⋅×== −φ

edaysarEt 2/cu VV φ< dUcenHeKminRtUvkarEdkkgeT. b:uEnþeKRtUvdak;Edkkg 100@10DB edIm,IcgCamYyEdkembeNþay.

4> CeNþIrRtUvrkSalMnwgedayTm¶n;rbs;CBa¢aMg b¤edayFñwmebtugGarem:enAkñúgCBa¢aMg. kñúgkrNIenH FñwmrgnUvm:Um:g;rmYl mmkN /.05.7 .

5> srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>18.

]TahrN_TI 18>2³ KNnaCeNþIrdUcbgðajenAkñúgrUbTI 18>19 EdlRTbnÞúkGefrBRgayes μ I 2/7.5 mkN . snμt;km<s;kaMes μInwg cm18 ehIyCMhankaMes μ Inwg cm5.27 . eK[ MPaf c 21' = nig MPaf y 400= .


CeNþIr 625 T.Chhay

dMeNaHRsay³ 1> RbB½n§eRKOgbgÁúM³ RbsinebIeKmineRbIFñwm stringer enaH eKGacTTYlykdMeNaHRsaymYykñúgcM

eNam dMeNaHRsaybYnEdl)anbgðajenAkñúgrUbTI 18>2. enAeBlTRmkNþalminRtUv)aneRbI tYCeNþIrRtuv)anRTenAxagcugénfasCeNþIrxagelI nigxageRkam. RbB½n§rcnasm<½n§enHRtUv)an ykmkeRbIkñúg]TahrN_enH.

2> bnÞúk³ snμt;kRmas;kRmal (waist) KW cm20 Tm¶n;rbs;kaMmYy 25area ltrapezoida ×= mkN /26.225275.0

218.02239.0

=×⎟⎠⎞

⎜⎝⎛ +×

=

Tm¶n;rbs;tYCeNþIr 2/2.8275.026.2 mkN==

Tm¶n;fasCeNþIr 2/5252.0 mkN=×= edaysnμt;kargarbegðIyRKbelICeNþIrKW 2/1 mkN .

( ) 2/16.207.56.112.82.1)stairon ( mkNWu =×++= ( ) ( ) 2/32.167.56.1152.1landingon mkNWu =×++=

edayKNnaCeNþIrkñúg m1 TTwgrbs;CeNþIrdUcenH mkNWu /16.20)stairon ( =

( ) mkNWu /32.16landingon = edaysarbnÞúkenAelIfasCeNþIrRtUv)anRTBIrTis dUcenHbnÞúkBak;kNþalRtUv)anKitenAkñúgTis mYy².

3> KNnam:Um:g;Bt;Gtibrma nigEdkBRgwg ¬rUbTI 18>19 d¦³ a. m:Um:g;enAkNþalElVgKW

mkNM u .65.5421.116.2085.15.116.86.242.34

2=×−××−×=

yk mmd 174620200 =−−=


T.Chhay 626 Stairs


CeNþIr 627 T.Chhay


T.Chhay 628 Stairs

b. ( );2/adfAM ysu −=φ edaysnμt; mma 20=

( )2

6926

101744009.01065.54 mmAs =

−××⋅

=

RtYtBinitü mmbf

fAa

c

ys 75.2010002185.0

400926'85.0

=××

×== mmc 4.24=

brimaNEdkGb,brma 22 92657417410000033.0 mmmmAs <=××= eRbIEdk 120@12DB ¬ 2942mmAs = ¦. sRmab;CeNþIrTTwg m5.1 eRbI 1213DB .

mmdt 174= mmc 4.24= bERmbRmYlrageFobTajsuT§ (net tensile strain)

005.00184.0003.0 >=⎟⎠⎞

⎜⎝⎛ −

=c

cdttε dUcenH 9.0=φ

c. EdkTTwgRtUv)andak;edIm,ITb;karrYmmaD 236020010000018.0 mmAs =××=

eRbIEdk 12DB EdlmanKMlat mm300 ¬ 2377mmAs = ¦ d. RbsinebICeNþIr nigFñwmEdlRTvaRtUv)ancak;CamYyKña EdkbEnßmRtUv)andak;enAEpñkxagelI

nigEpñkxageRkamrbs;fasCeNþIr. srésEdklMGitRtUv)anbgðajenAkñúgrUbTI 18>19. 4> kRmas;kRmalxNÐGb,brmasRmab;karBarPaBdabKW

mL 208.025

2.525

== ¬sRmab;kRmalxNÐTRmsamBaØ¦ kñúgkrNIEdlbgðajenATIenH edaysarcugkRmaltYCeNþIrRtUv)ancak;CamYynwgFñwmEdlRTva ehIymandak;EdkbEnßmsRmab;m:Um:g;GviC¢man enaHkRmas;kRmalGb,brmaGacRtUv)ansnμt; esμ Inwg

mmL 2.0186.028

<= Edl)aneRbI 5> KNnafasCeNþIr³ edayBicarNafasCeNþIrkñúgRbEvgTTwg m1 bnÞúkenAelIfasCeNþIRtUv)an

bgðajenAkñúgrUbTI 18>20. EpñkkNþal m6.0 RTbnÞúkeBj EtEpñksgçag m5.1 RTbnÞúkEtBak; kNþal. m:Um:g;Bt; mkN.08.15

26.032.1605.15.116.88.115.17

2=×−××−×=

edaysarEdkenAkñúgfasCeNþIrRtUv)andak;enABIelIEdkCeNþIrem enaH mmd 4.1676.01220200 =−−−=


CeNþIr 629 T.Chhay

edaysnμt; mma 10=

( )2

6258

54.1674009.01008.15 mmAs =

−××⋅

= 2574(min) mmAs =<

eRbIEdk 12DB KMlat mm180 ¬ 2628mmAs = ¦ 6> FñwmTTwgenAcugfasCeNþIrRtUv)anKNnaeday[RTbnÞúkBICeNþIr mkN /42.34 bEnßmBIelI

bnÞúkpÞal;rbs;va nigbnÞúkrbs;CBa¢aMgEdlenABIelIva. 7> RtYtBinitükmøaMgkat;dUcFmμta.

]TahrN_TI 18>3³ KNnaCeNþIr run-riser stair EdlRTedayTRmsamBaØdUcbgðajenAkñúgrUbTI 18>21 sRmab;RTbnÞúkGefrBRgayesμ I 2/7.5 mkN . eK[ MPaf c 21' = nig MPaf y 400= . dMeNaHRsay³

1> bnÞúk³ sn μt;kRmas;rbs;CMhankaM nigkm<s;kaMes μInwg cm15 . bnÞúkcMcMNucenAelICMhankaMnImYy²RtUv)anKNnadUcxageRkam ¬eyagtamrUbTI 18>21 a ¦. edayKitkñúg m1 TTwgrbs;CeNþIr

( ) kNPD 6.12515.0025.04.015.0 =××+×= cMNaMfa bnÞúkefrcMcMNucenAelIfasCeNþIrmantémøtUcCag kN6.1 buEnþvaGacRtUv)ansnμt;esμ I nwg DP edaykarKNnay:agsRmYl. KitbnÞúkGefrenAelITTwgCeNþIr m1 ehIyRbmUlvaCa bnÞúkcMcMNuc enaHeK)an

kNPL 425.125.07.5 =×= bnÞúkemKuN kNPPP LDu 2.4425.16.16.12.16.12.1 =×+×=+=


T.Chhay 630 Stairs


CeNþIr 631 T.Chhay

2> KNnam:Um:g;Bt;enAkNþalElVg³ bnÞúkenAkñúg]TahrN_enHmanlkçN³sIuemRTIeFobnwgkNþal ElVgRtg;muxkat; B . RbtikmμenARtg;cMNuc A

kNRA 5.312.42

15==

m:Um:g;enARtg;cMNuc B ( ) ( )SPSR uA 478 −= ( ) ( ) mkN.6.3325.042.4725.085.31 =××−×=

3> KNnasrésEdkcaM)ac;enARtg;muxkat;kNþalElVg³ sRmab; cmh 15= / 12525150 =−=d MPa

bdMR u

u 15.21251000106.33

2

6

2 =×

×==

sRmab; MPaf c 21' = / MPaf y 400= nig 15.2=uR enaHPaKryEdkKW 0135.00064.0 max =<= ρρ / ¬ 9.0=φ ¦

280012510000064.0 mmAs =××= eRbIEdk 12DB nigmanKMlat cm14 ¬ 2807mmAs = ¦ tamTisedk nigTisQrkñúgTRmg;Edk kgbiTCit. sRmab;Edkrg eRbIPaKryEdkGb,brmasRmab;Tb;nwgsItuNðPaB nigkarrYmmaD 0018.0=ρ

21081504000018.0 mmAs =××= eRbIEdk 10DB manKMlat cm15 ¬ 23.209 mmAs = ¦. dak;Edk 10DB enARCugmYy²rbs; kaM ¬ 25.235 mmAs = ¦ dUcbgðajenAkñúgrUbTI 18>21 c.

4> m:Um:g; nigsrésEdkEdlcaM)ac;sRmab;muxkat;muxkat;epSgeTotRtUv)aneFVICataragdUcxag eRkam³

TItaMg A 1 2 3 4 5 6 7 8

)..(. mkNMB 0 7.88 14.7 20.48 25.2 28.88 31.5 33.08 33.6

)(MPaRu 0 0.5 0.94 1.31 1.61 1.85 2.02 2.12 2.15

( )%ρ 0 0.14 0.27 0.38 0.47 0.55 0.60 0.63 0.64

( )2mmAs 0 175 338 475 588 688 750 788 800


T.Chhay 632 Stairs

eRbIEdk 200@12DB sRmab;fas nig 150@12DB sRmab;kaMCeNþIr. sRmab; 2588mmAs = eRbIEdk 200@12DB enAkñúgfasCeNþIr. karlMGitsrésEdkRtUv)anbgðaj

enAkñúgrUbTI 18>21 c. 5> RtYtBinitübrimaNEdkcaM)ac;enAkñúgTisTTwgrbs;fas³ bnÞúkenAelIfaskñúgmYyÉktþaRbEvgKW mkN /8.16

25.02.4= dUcenH

mkNM u .2.276.38

8.16 2 =×=

MPaRu 74.11251000102.27

2

6=

×

⋅=

0051.0=ρ 2638mmAs = eRbIEdk 175@12DB 2646mmAs = 6> RbsinebIbnÞúkBRgayesμ IRtUv)ansn μt;famanGMeBIelItYCeNþIr eKnwgTTYl)anlT§plRsedog

Kña. ]TahrN_ bnÞúkemKuNcMcMNucEdl)anKNnaKW kN2.4 manGMeBIelITTwgCMhankaM m25.0 . dUc enHbnÞúkkñúgmYyÉktþaRbEvgKW mkN /8.1625.0/2.4 = . m:Um:g;GtibrmaenAkNþalElVgRtg; muxkat; B ³ mkNM u .6.334

88.16 2 =×=

m:Um:g;enAmuxkat;déTeTotGacRtUv)anKNnay:agRsYl ehIykarKNnaGacRtUv)anerobcMCa taragdUcBnül;kñúgCMhan 4.


CeNþIr 633 T.Chhay


T.Chhay 634 Introduction to Prestressed Concrete

XIX. esckþIENnaMBIebtugkugRtaMg Introduction to Prestressed Concrete

19>1> ebtugeRbkugRtaMg (Prestressed Concrete)

19>1>1> eKalkarN_énkareFVIeRbkugRtaMg (Principles of Prestressing) karGnuvtþeRbkugRtaMgeTAelIGgát;eRKOgbgáúMKWCakarbegáItkugRtaMgGciéRnþy_xagkñúgEdlmanGMeBI RbqaMgnwgkugRtaMgTajenAkñúgebtugEdl)anbnÞúkxageRkA. karGnuvtþeRbkugRtaMgenHbegáItCaEdnkug RtaMgEdlGgát;GacTb;Tl;)any:agmansuvtßiPaB. eKGacGnuvtþkmøaMgeRbkugRtaMgmun b¤kñúgeBldMNal KñaénkarGnuvtþbnÞúkxageRkA. kugRtaMgenAkñúgGgát;eRKOgbgÁúMRtUvEtenAsl; ¬RKb;TIkEnøg nigsRmab; RKb;sßanPaBénkardak;bnÞúk¦ enAkñúgEdnkMNt;rbs;kugRtaMgEdlsmÖar³GacRTRTg;)anK μanTIkMNt;. Ca TUeTA karGnuvtþkugRtaMg ¬PaKeRcInCakugRtaMgsgát;¦ RtUv)anbegáIteLIgeday high-strength steel

tendon EdlrgkarTaj nig anchor eTAnwgGgát;ebtug. kugRtaMgRtUv)anepÞreTAebtugeday bond tamépÞrbs; tendon b¤eday anchorage enAxagcugrbs; tendon. edIm,IgayRsYlkñúgkarBnül; cUrBicarNaFñwmmYyEdleFVIBIebtugsuT§ ehIyFñwmenaHRtUvRTnUv bnÞúkTMnajxageRkA (external gravity load) dUcbgðajkñúgrUbTI 19>1 a. muxkat;FñwmRtUv)aneRCIs erIsCamYynwg tensile flexural stress EdlCalkçxNÐeRKaHfñak;sRmab;karKNna dUcenHeKTTYl)an muxkat;EdlminmanlkçN³esdækic©. mUlehtuKWedaysarebtugxøaMgkñúgkarsgát;CagkarTaj. flexural

tensile strength b¤m:UDuldac; (module of rupture) rbs;ebtug rf es μ Inwg cf '62.0 ¬rUbTI 19>1a¦. kñúgkarKNnaebtugGarem:Fm μta eKminKit tensile strength rbs;ebtugeT ehIyEdksrés RtUv)andak;enAkñúgtMbn;Tajrbs;ebtugedIm,ITb;Tl;nwgkugRtaMgTaj b:uEnþebtugTb;Tl;nwgkugRtaMgsgát; ¬rUbTI 19>1 b¦. kñúgkarKNnaebtugeRbkugRtaMg kugRtaMgsgát;dMbUgRtUv)anGnuvtþeTAkñúgFñwmedIm,I[manGMeBITb; nwgkugRtaMgTajEdlekIteLIgedaysarbnÞúkxageRkA ¬rUbTI 19>1 c¦. RbsinebIkugRtaMgEdldak; dMbUgenHes μ InwgkugRtaMgTajenAsréseRkambMput enaHkugRtaMgTaMgBIrRtUv)anlubecal b:uEnþkugRtaMg sgát;enAsrésEpñkxagelIbMputnwgmantémøDub. kñúgkrNIenH muxkat;Ggát;TaMgmUlrgkarsgát;. Rb sinebIkugRtaMgsgát;EdlGnuvtþdMbUgtUcCagkugRtaMgTajenAsrésEpñkxageRkambMput enaHsrésenA EpñkxageRkamenHrgkarTaj ÉsrésEpñkxagelIbMputrgkarsgát;.


esckþIENnaMBIebtugeRbkugRtaMg 635 T.Chhay

kñúgkarGnuvtþ Ggát;ebtugGacrgeRbkugRtaMgtamviFImYykñúgcMeNamviFIxageRkam³



!> karTajeRkay (Posttensioning): kñúgkareFVI posttensioning, eKTaj steel tendon eRkayeBlebtugRtUv)ancak; nigkkrwg. kareFVI posttensioning RtUv)aneFVIeLIgtamviFI saRsþdUcteTA³ dMbUgeKeRbI hydraulic jack Taj steel wire b¤ strand [lUt bnÞab;mk CMnYs jack eday anchorage EdlGacrkSa[ steel strand enAEtrgkarTaj. CaTUeTA tendon RtUv)aneFVIeLIgBI wire, strand b¤ bar. eKGacTaj wire nig strand CaRkum)an Et eKTaj bar mþg)anEtmYy. kñúgdMeNIrkareFVI posttensioning, eKdak; steel tendon eTAkñúg Bum<muneBlcak;ebtug ehIy tendon RtUv)ankarBarkars¥itCab;eTAnwgebtugeday water-

proof paper wrapping b¤ metal duct (sheath). tendon Edls¥itCab;eTAnwgebtugRtUv)an eKehAfa boded tendon. Unbonded tendon/ RtUv)andak;edayKμan grout b¤RtUv)anlab eRbg.

@> karTajmun (pretensioning): kñúgkareFVI prettensioning eKTaj steel tendon muneBlcak; ebtug. eKTb; tendon CabeNþaHGasnñeday abutment ehIyeKkat;va bnÞab;ebtugRtUv)an cak; nigkkrwg. kmøaMg prestessing RtUv)anepÞreTAebtugeday PaBs¥itenAtamRbEvgrbs; tendon. CaTUeTA eKeRcIneFVI prettensioning enAkñúgkardæan b¤eragcRkpliteRKOgbgÁúMebtug eRbkugRtaMgcak;eRsc EdlmankRmalrwgmaMCaGciéRnþy_.

#> kareFVIeRbkugRtaMgxageRkA (external prestressing): kñúgkareFVI external pretessing, eK GnuvtþkmøaMgeRbkugRtaMgeday flat jack EdlRtUv)andak;enAcenøaHcugGgát;ebtug nig permanent rigid abutments. Ggát;minman prestressing tendon dUcviFITaMgBIrxagelI EdleKGacehAfakareFVIeRbkugRtaMgxagkñúgeT. External prestressing mingayRsYlkñúg karGnuvtþeT edaysar shrinkage nig creep enAkñúgebtugEdlnaM[mankarkat;bnßykug RtaMgsgát;EdlGnuvtþdMbUg.

Profile rbs; tenden GacRtg; ekag b¤ragrgVg;GaRs½yeTAelIkarKNnaGgát;eRKOgbgÁúM. CaTU eTAeKeRbI straight tendon enAkñúg solid slab nig hollow-cored slab b:uEnþeKeRbI bent tendon enA kñúgFñwm nigGgát;eRKOgbgÁúMPaKeRcIn. eKeRbI circular tendon enAkñúgeRKOgbgÁúMEdlmanTRmg;mUldUcCa tank, silo nig pipe. eKGacGnuvtþkmøaMgeRbkugRtaMgEtkñúgmYydMNakkal b¤eRcIndMNakkaledIm,Ikar BarebtugkMu[rgkugRtaMgelIs.



eK)anbegáItnUvRbB½n§eRbkugRtaMgCaeRcIn EdlkñúgcMeNamenaHman Freyssinet, Magnel Blaton,

B.B.R.V., Dywidag, CCL, Morandi, VSL, Western Concrete, Prescon, nig INRYCO. eBlxøH eKCYbnUvbBaðakñúgkareRCIserIsRbB½n§eRbkugRtaMgsRmab;kargarBiess.

visVkrKYrBicarNanUvktþacMbgbIEdlnaMdl;kareRCIserIsRbB½n§enH³ !> GaMgtg;sIueténkmøaMgeRbkugRtaMgEdlRtUvkar @> ragFrNImaRtrbs;muxkat; nigKMlatEdlGacmansRmab; tendon

#> témøénRbB½n§eRbkugRtaMg ¬smÖar³ nigkmøaMgBlkmμ¦ ]TahrN_xageRkambgðajBIlkçN³Biessrbs;ebtugeRbkugRtaMg.

]TahrN_ 19>1³ sRmab;FñwmTMrsamBaØEdlbgðajenAkñúgrUbTI 19>2 cUrkMNt;kugRtaMgRtg;muxkat; kNþalElVgEdlbNþalmkBITm¶n;pÞal;xøÜnva nigkrNIénkardak;bnÞúk nigeRbkugRtaMg³ !> bnÞúkGefrBRgayesμ I mkN /15.13 @> bnÞúkGefrBRgayesμ I mkN /15.13 nigkmøaMgsgát;tambeNþaycMp©it kNP 1132=

#> bnÞúkGefrBRgayesμ I mkN /61.30 nigkmøaMgsgát;tambeNþaycakp©it kNP 1132= Edl manGMeBIRtg;cMNakp©it cme 10=

$> bnÞúkGefrBRgayesμ I mkN /28.39 nigkmøaMgsgát;tambeNþaycakp©it kNP 1132= Edl manGMeBIRtg;cMNakp©itGtibrmasRmab;muxkat; cme 15=

%> bnÞúkGefrGtibrmaenAeBl kNP 1132= EdlmanGMeBIRtg; cme 15= eRbI cmb 30= / cmh 60= / MPaf c 31' = nigkugRtaMgGnuBaØat MPaf c 14.14' =

dMeNaHRsay³ !> kugRtaMgEdlbNþalmkEtBIbnÞúkefr nigbnÞúkGefr

bnÞúkpÞal;rbs;Fñwm ( ) mkN /32.4246.03.0 =×= m:Um:g;bnÞúkefr ( ) mkNwLM LD .28

82.732.4

8

22

.. === kugRtaMgenARtg;srésEpñkxageRkAbMputEdlbNþalBIbnÞúkefrKW ( )

236

12/2/

bhM

bhhM

IMc

===σ



MPaD 56.1106.03.0

286 32 ±=

×

×= −σ

m:Um:g;EdlbNþþalBIbnÞúkGefr mkNL /15.131 = KW mkNM LL .2.85

82.715.13 2

.. =×

= kugRtaMgEdlbNþalBIbnÞúkGefrKW MPa

bhM

L 73.4106.03.02.8566 3

221 ±=×

×== −σ

edayeFVIkarbUkbBa©ÚkkugRtaMgEdl)anBIbnÞúkefr nigbnÞúkGefr ¬rUbTI 19>2 a¦ eyIg)an kugRtaMgxagelI MPa29.673.456.1 −=−−= ¬rgkarsgát;¦ kugRtaMgxageRkam MPa29.673.456.1 =++= ¬rgkarTaj¦ edaysarkugRtaMgTajFMCagm:UDuldac;rbs;ebtug MPafr 45.33162.0 == dUcenHFñwmnwg)ak;.

@> kñúgkrNIEdlkugRtaMgbNþalBIeRbkugRtaMgesμ I RbsinebIeKGnuvtþkmøaMgsgát; KNP 1132= Rtg;TIRbCMuTm¶n;rbs;muxkat; enaHmuxkat;tambeNþyFñwmnwgrgkugRtaMgesμ I MPa

areaP

p 29.6106.03.0

1132 3 ±=×

== −σ kugRtaMgcugeRkayEdlbNþalBIbnÞúkGefr nigbnÞúkefrbUknwgbnÞúkeRbkugRtaMgenARtg;srés

xagelI nigxageRkambMputKW MPa58.12 nig 0 erogKña ¬rUbTI 19>2 b¦. kñúgkrNIenH kmøaMg eRbkugRtaMg)anebgáInkugRtaMgsgát;enARtg;srésEpñkxagelIbMput[mantémøBIrdg nig)ankat; bnßykugRtaMgTajenARtg;srésEpñkxageRkam[esμ Inwg 0 . kugRtaMgsgát;Gtibrma MPa58.12 mantémøtUcCagkugRtaMgGnuBaØat MPaf c 14.14' = .

#> sRmab;kugRtaMgEdlbNþalBIeRbkugRtaMgcMNakp©it ¬ mme 100= ¦ RbsinebIeKGnuvtþkmøaMgeRbkugRtaMg KNP 1132= enARtg;cMNakp©it mme 100= BI eRkamTI RbCMuTm¶n;rbs;muxkat; kugRtaMgenARtg;srésEpñkxagelI nigEpñkxageRkambMputRtUv)ankMNt; dUcxageRkam. m:Um:g;EdlbNþalBIeRbkugRtaMgcMNakp©itKW Pe ( ) ( )

26bh

PeAP

IcPe

AP

p ±−=±−=σ ( ) 3

23 10

6.03.01.01132610

6.03.01132 −−

×

×±

×−=

29.629.6 ±−= enAsrésEpñkxageRkam MPap 58.12−=σ nig 0=pσ enAsrésEpñkxageRkambMput.



BicarNaGMBIkardak;bnÞúkGefr mkNL /61.302 = mkNM LL .36.198

82.761.30 2

.. =×

= ( ) MPaL 02.1110

6.03.036.1986 3

22 ±=×

= −σ kugRtaMgcugeRkayEdlbNþalBIbnÞúkefr/ bnÞúkGefr nigkmøaMgeRbkugRtaMgenAsrésEpñkxagelI nigEpñkxageRkambMputKW MPa58.12 nig 0 erogKña ¬rUbTI 19>2 c¦. cMNaMfa kugRtaMgcug eRkaydUcKñanwgkrNIelIkmunenAeBlEdlbnÞúkGefresμ Inwg mkN /15.13 . edayGnuvtþkmøaMg eRbkugRtaMgenARtg;cMNalp©it cm10 FñwmenHGacRTbnÞúkGefrEfmeTot ¬ mkN /46.17 ¦.



$> sRmab;kugRtaMgEdlbNþalBIeRbkugRtaMgcakp©itRtg;cMNakp©itGtibrma snμt;facMNakp©itGtibrmasRmab;muxkat;enHKW cme 15= .

m:Um:g;Bt;EdlekItedaysarkmøaMgeRbkugRtaMgcakp©itKW mkNPe .8.16915.01132 =×=



kugRtaMgEdlbNþalBIkmøaMgeRbkugRtaMgKW ( ) 3

23 10

6.03.08.169610

6.03.01132 −−

×±

×−=pσ

41.929.6 ±−= MPa7.15−= nig 12.3+

begáInbnÞúkGefrdl; mkNL /28.393 = . m:Um:g;Edl)anBIbnÞúkenHKW mkNM LL .5.254

82.728.39 2

.. =×

= kugRtaMgEdlbNþalmkBIbnÞúkGefrKW ( ) MPaL 14.1410

6.03.05.2546 3

23 ±=×

= −σ kugRtaMgcugeRkayenAsrésEpñkxagelI nigEpñkxageRkambMputEdlbNþalBIbnÞúkefr nigbnÞúk GefrKW MPa58.12 nig 0 erogKña ¬rUbTI 19>2 d¦. cMNaMfa kugRtaMgcugeRkaydUcKñanwgkrNI mun²Edr b:uEnþbnÞúkGefr)anekIneLIgdl; mkN /28.39 . kugRtaMgTaj MPa56.1 RtUv)an begáIteLIgenAsrésEpñkxagelIbMput enAeBlEdleKGnuvtþkmøaMgeRbkugRtaMg. kugRtaMgenH mantémøtUcCagm:UDuldac;rbs;ebtug MPafr 45.3= dUcenHvaminekItmansñameRbHenAelIFñwm eT.

%> eKkMNt;bnÞúkGefrGtibrmaenAeBlkmøaMgeRbkugRtaMgcakp©iteFVIGMeBIenARtg; cme 15= dUct eTA. kñúgkrNImun² kugRtaMgsgát;cugeRkayesμ Inwg MPa58.12 EdltUcCagkugRtaMgGnuBaØat

MPaf c 14.14' = . dUcenH bnÞúkGefrGacekIneLIgdl; mkNL /6.434 = . mkNM LL .5.282

82.76.43 2

.. =×

= MPaL 7.1510

6.03.05.2826 324 =

×

×= −σ

kugRtaMgcugeRkayEdlbNþalBIbnÞúkefr nigbnÞúkGefr 4L ehIynigkmøaMgeRbkugRtaMg KW MPa14.14− nig MPa56.1+ ¬rUbTI 19>2 e¦. kugRtaMgsgát;KWes μ InwgkugRtaMgGnuBaØat

MPa14.14 ehIykugRtaMgTajKWtUcCag modulus of rupture rbs;ebtug MPa45.3 . kñúg krNIenH eKGacKNnabnÞúkGefrBRgayEdlesμ μ Inwg mkN /6.43 dUcteTA³ bUkkugRtaMgsgát; GnuBaØatGtibrma MPa14.14 CamYynwgkugRtaMgTajdMbUgenARtg;srésEpñkxagelIbMput

MPa56.1 edIm,ITTYl)an MPa7.15 . m:Um:g;EdlnwgbegáItkugRtaMgenAsrésEpñkxagelIbMput



MPa7.15 es μ Inwg ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

6

2bhM σ

( )( ) mkN.6.282106.03.06

7.15 32 =⋅=

8

2LWM L= eyIgTTYl)an mkNWL /6.43

2.76.2828

2 =×

= cMNaMfa³ !> muxkat;ebtugTaMgmUlKWskm μkñúgkarTb;Tl;CamYykmøaMgxageRkA @> kugRtaMgTajcugRkayenAkñúgmuxkat;tUcCag modulus of rupture rbs;ebtug Edlbgðaj

famuxkat;ebtugminmansñameRbHeRkamGMeBIrbs;bnÞúkGtibrma #> bnÞúkGnuBaØatenAelIFñwmekIneLIgeRcInKYrsmedaysarkarGnuvtþrbs;kmøaMgeRbkugRtaMg $> karekIneLIgnUvcMNakp©itrbs;kmøaMgeRbkugRtaMgk¾begáInkmøaMgGnuvtþn_GnuBaØat EdleFVI[kugRtaMg

enAelImuxkat;minFMCagkugRtaMgGnuBaØat.

19>1>2> karGnuvtþeRbkugRtaMgedayEpñk (Partial Prestressing) eKkMNt;Ggát;ebtugeRbkugRtaMgedayEpñk (partially prestressed concrete member) CaGgát; Edl³

- kugRtaMgxagkñúgEdlmanGMeBITb;EpñkénkugRtaMgEdlekItBIbnÞúkxageRkA - kugRtaMgTajekItmanenAkñúgebtugeRkamGMeBIbnÞúkeFVIkar (service load) - EdkBRgwgminEmnCaEdkeRbkugRtaMgRtUv)andak;bEnßmedIm,IbegáInlT§PaBrbs;Ggát; edIm,ITb;

nwgm:Um:g; eKGacBicarNa partially prestressed concrete tamBIrkrNI³ !> eKeRbIEdkeRbkugRtaMg nigEdkminEmneRbkugRtaMgenAkñúgmuxkat;EtmYy. ExSkabeRbkugRtaMg

begáItkugRtaMgxagkñúgRtUv)anKNnaedIm,ITTYl)an ultimate capacity rbs;muxkat;ebtugEt mYyEpñkb:ueNÑaH. cMENkÉ capacity EdlenAsl;RtUv)anTTYlBIEdkminEmneRbkugRtaMg Edldak;tamTisdUcKñanwgkabeRbkugRtaMg. EdkEdleRbICaEdkminEmneRbkugRtaMgGacCaRb



ePTEdkFm μta dUcCaEdk carbon steel b¤CaEdk high-tensile-strength. kabeRbkugRtaMgk¾ CaRbePTEdkFmμtadUcEdkminEmneRbkugRtaMgEdr Etvaman ultimate strength esμ Inwg

MPa1725 ¬ ksi250 ¦. kareRCIserIsGaRs½ynwgktþacMbgBIrKW³ PaBdabGnuBaØat nigTMhM sñameRbHGnuBaØat. dUcKña ACI Code kMNt;nUvpleFobGtibrmaénRbEvgElVgelIkkm<s;én Ggát;ebtugGarem: sRmab;PaBdab. eKminGnuBaØat[manPaBdabFMelIslubCamYynwgkm<s; rbs;muxkat;ebtugeRbkugRtaMgtUc nigedaysarkareRbIPaKryEdktic. sñameRbHekItmanenA tMbn;rgkarTajrbs;muxkat;ebtug b¤enARtg;nIv:UEdkedaysareKGnuBaØat[kugRtaMgTajekIt maneRkamGMeBI working load. eKGnuBaØatsñameRbHGtibrmaRtwm .016.0 in )41.0( mm sRmab;Ggát;xagkñúg nig .013.0 in )33.0( mm sRmab;Ggát;xagkñúg.

@> kugRtaMgxagkñúgEdleFVIGMeBIelIGgát;)anEtBI prestrssed steel b:ueNÑaH b:uEnþvaRtUv)anTajCa mYynwgEdnkMNt;TabCag. kñúgkrNIenHsñameRbHekItmanelOnCagGgát;rgeRbkugRtaMgeBj eljeRkambnÞúkdUcCaKña.

eKGacBicarNa partially prestresssed concrete kñúgTRmg;kNþalrvagebtugGarem: nigebtug eRbkugRtaMgeBj (fully prestressed concrete). enAkñúgGgát;ebtugGarem: sñameRbHekItmaneRkamGMeBI bnÞúkeFVIkar dUcenHeKdak;EdkBRgwgenAkñúgtMbn;Taj. CaTUeTAenAkñúgGgát;ebtugeRbkugRtaMg sñameRbH minekItmaneRkamGMeBIbnÞúkeFVIkareT. kugRtaMgsgát;EdlbNþalBIkmøaMgeRbkugRtaMgGaces μ I b¤elIsBI kugRtaMgTajEdlbNþalBIbnÞúkxageRkA. dUcenHeKGacBicarNaGgát; partially prestressed concrete CaGgát;ebtugGarem:EdlkugRtaMgxagkñúgrbs;vamanGMeBITb;nwgEpñkxøH rbs;kugRtaMgEdl)anBIbnÞúkxag eRkA dUcenHkugRtaMgTajenAkñúgebtugminRtUvFMCagtémøkMNt;eRkambnÞúkeFVIkareT. eKKitvaCaebtug Garem:enAeBlNaEdlminmankugRtaMgxagkñúgeFVIGMeBIelIGgát;. ebtugeRbkugRtaMgeBjCakRmitx<s;bMput rbs;ebtugeRbkugRtaMgedayEpñk EdlenAkñúgenaHEdkminEmneRbkugRtaMgRtUv)ankat;bnßydl;sUnü.

enAcenøaHGgát;ebtugGarem:EdlmaneRbH nigGgát;ebtugeRbkugRtaMgeBjEdlminmaneRbH eK manEdnd¾FMsRmab;KNnaebtugeRbkugRtaMgedayEpñk ¬rUbTI 19>3¦. kareRCIserIskRmiténkareFVIeRb kugRtaMgd¾l¥ nwgbegáItnUveRKOgbgÁúMEdlmansuvtßiPaB nigmanlkçN³esdækic©.

rUbTI 19>3 bgðajBIExSekagPaBdab-bnÞúkrbs;FñwmebtugGarem:EdlmanbrimaNEdk nigRbePT EdkxusKña. ExSekag a bgðajBIFñwmebtugGarem: EdlmansñameRbHFmμtaeRkambnÞúktUc crW . eKGackM Nt;m:Um:g;EdleFVI[eRbH (cracking moment) dUcxageRkam³



c

IfM rcr =

Edl =rf m:UDuldac;rbs;ebtug cf '62.0= =I m:Um:g;niclPaBén gross concrete section =c cm¶ayBIG½kSNWteTAsrésrgkarTajxageRkAbMput eKGackMNt;ebtugEdleFVI[eRbH (cracking load) BI cracking moment enAeBlRbEvg ElVg nigRbePTénkardak;bnÞúkRtUv)ankMNt;. sRmab;FñwmTRmsamBaØEdlrgbnÞúkcMcMnugenAkNþalElVg

( ) LMW crcr /4= . ExSekag e nig f bgðajBIFñwmebtugeRbkugRtaMgeBjEdlmanEdktic nigEdkeRcIn erogKña. Fñwm ebtugGarem:EdlmanbrimaNEdkeRcIn)ak;edaysarkarEbkebtugmunnwgEdkeTAdl; yield strength b¤



proof stress rbs;va. FñwmmanPaBdabtUc nwgrgkar)ak;edayPaBRsYy (brittle failure). FñwmEdlman brimaNEdktic)ak;edaysarEdkeFVIkardl; yield nig ultimate strength rbs;va. vabgðajnUv)abdab nigsñameRbHEdlbNþalBIkarlUtsac;rbs;EdkmuneBlebtugEbkCabnþbnÞab; ehIyFñwm)ak;rlM. enAcenøaHExSekag a nig e CaEdnd¾FMrbs;FñwmebtugCamYynwgbrimaNERbRbYlrbs;Edk nigrg nUvbrimaNERbRbYlrbs;kmøaMgeRbkugRtaMg. FñwmEdlrgkmøaMgeRbkugRtaMgtUcenAEk,rExSekag a ehIy FñwmEdlmaneRbkugRtaMgFMenAEk,rExSekag e . eKeRCIserIsbnSMEdkeRbkugRtaMg nigEdkminEmneRbkug RtaMgsRmab;karKNnaKWGaRs½yelIkugRtaMgebtugGnuBaØat PaBdab nigTMhMsñameRbHGtibrma. ExSekag b tMNag[FñwmEdlnwgeRbHeRkamGMeBIénbnÞúkeFVIkareBjelj. RbsinebIEtEpñkxøH rbs;bnÞúkGefrekItmanenAelIeRKOgbgÁúMCaerOy² enaH 1W tMNag[bnÞúkefrsrub nigEpñkxøHrbs;bnÞúk Gefr 1L . ExSekag c tMNag[Fñwmcab;epþImeRbHeRkamGMeBI working load. kugRtaMgTajGtibrmaenA kñúgebtug cr ff '62.0== . ExSekag d tMNag[FñwmEdlmankmøaMgeRbkugRtaMgkMNt;. muxkat;eRKaHfñak;rbs;Fñwmnwgmin eRbHeRkambnÞúkeFVIkareBjeljeT b:uEnþvanwgmankugRtaMgTajGtibrma cr ff '62.00 << . ACI

Code GnuBaØatkugRtaMgTajGtibrmaenAkúñgebtugRtwm cf '5.0 . ExSekag e nig 'e tMNag[FwñmebtugeRbkugRtaMgeBjeljEdlminmankugRtaMgTajeRkam bnÞúkeFVIkar ¬emIlrUbTI 19>4¦. sar³RbeyaCn_d¾sMxan;bMputrbs;kmøaMgeRbkugRtaMgedayEpñkKWlT§PaBkúñgkarRKb;RKgkMeNag (camber). edaykat;bnßykmøaMgeRbkugRtaMg camber nwgRtUv)ankat;bnßy ehIysnSMnUvbrimaNEdk eRbkugRtaMg brimaNkargarkúñgkarTaj nigcMnYn end anchorage. GaRs½ynwgGaMgtg;sIueténkmøaMgeRbkugRtaMg sñameRbHenAkñúg partially prestressed member

ekIteLIgelOnCagenAkñúg fully prestressed concrete member eRkamGMeBIrbs; service load. enA eBlEdlsñameRbHekItman m:Um:g;niclPaBRbsiT§PaBrbs;muxkat;eRKaHfñak;RtUv)ankat;bnßy ehIyeK nwgTTYl)anPaBdabFMCagmun. b:uEnþ kareRbIkmøaMgeRbkugRtaMgedayEpñkKWeKTTYl)anlT§plKYrCaTI eBjcitþ ehIyvaTTYl)ankareBjniym.



19>1>3> karcat;cMNat;fñak;Ggát;rgkarBt;ebtugeRbkugRtaMg (Classification of Prestressed Concrete Flexural Members)

ACI Code, Section 18.3 )anEckGgát;ebtugeRbkugRtaMgCabIfñak;edayQrelIkugRtaMgTaj enAelIsrésxageRkAbMput tf enAkñúgtMbn;TajeRkamGMeBIbnÞúkeFVIkardUcxageRkam³

!> fñak; U (uncracked section) Edlman ct ff '62.0≤ . enAkñúgmuxkat;ebtugEdlK μansñam

eRbHenH eKeRbIlkçN³én gross section edIm,IRtYtBinitüPaBdabeRkamGMeBIbnÞúkeFVIkar. Kμan sñameRbHekItmanenAkñúgmuxkat; nigeKminRtUvkar skin reinforcement eT.

@> fñak; T (muxkat;enAkñúg transition zone) Edlman ctc fff ''62.0 ≤< . muxkat; RbePTenHmankugRtaMgTajenAkñúgebtugFMCagm:UDuldac; (modulus of rupture) rbs;ebtug

cr ff '62.0= EdlbegáItnUvkrNIcenøaHmuxkat;eRbH nigmuxkat;Gt;eRbH. enAkñúgkrNIenH eKeRbIlkçN³én gross section edIm,IRtYtBinitükugRtaMg ehIyeKeRbI bilinear section rbs; muxkat;eRbHedIm,IKNnaPaBdab. eKmincaM)ac;eRbI skin reinforcement enAkñúgtMbn;TajeT.

#> fñak; C (cracked section) Edlman ct ff '> . kugRtaMgTajenAkúñgmuxkat;FMCag modulus of rupture rbs;ebtug 6.1 dg. dUcenH sñameRbHnwgekItmandUckñúgkrNIGgát;eb tugeRbkugRtaMgedayEpñk. enAkñúgkrNIenH eKeRbIlkçN³énmuxkat;eRbHedIm,IRtYtBinitükug



RtaMg sñameRbH nigPaBdab. eKKYreRbIkarpþl;[edIm,IRKb;RKgsñameRbH nigeRbI skin

reinforcement dUckarBnül;enAkñúgEpñk 6>7 sRmab;Ggát;ebtugGarem:Edlmankm<s; RbsiT§PaB mmd 915> .

19>2> smÖar³ nigtRmUvkarsRmab;beRmIbRmas; (Material and Serviceability Requirement)

19>2>1> ebtug (Concrete) lkçN³rbs;ebtugRtUv)anbgðajenAkñúgCMBUk 2. eTaHbICaerOy² Ggát;ebtugGarem:RtUv)anplit

BIebtugEdlmanersIusþg;sgát; MPa21 eTA MPa35 k¾eday k¾Ggát;ebtugeRbkugRtaMgRtUv)anplitBI smÖar³EdlmanersIusþg;x<s;Cag CaTUeTAsßitenAcenøaH MPa28 eTA MPa56 . eKeRbIebtugersIusþg;x<s; sRmab;Ggát;ebtugcak;eRsc nigGgát;ebtugeRbHkugRtaMg Edlkarlay karcak; karbgðab; nigkarEfTaM ebtugsßiteRkamkarRtYtBinitüy:agm:t;ct;.

kugRtaMgGnuBaØatenAkñúgebtugEdleyagtam ACI Code, Section 18.4 mandUcxageRkam³ !> kugRtaMgeRkayeBlepÞreRbkugRtaMg (prestress transfer) nigmuneBl)at;bg;eRbkugRtaMg

(prestress losses): a. kugRtaMgsgát;Gtibrmaesμ Inwg cif6.0 b. kugRtaMgTajGtibrma ¬elIkElgGVIEdl)anGnuBaØatdUcxageRkam¦ esμ Inwg cif25.0 c. kugRtaMgTajGtibrmaenARtg;cugénGgát;TRmsamBaØesμ Inwg cif5.0 Edl cif CaersIusþg;rbs;ebtugenAeBlepÞr RbsinebIkugRtaMgTajmantémøFMCagenH eKRtUvdak;EdkenAtMbn;sgát;edIm,ITb;Tl;kmøaMgTaj srubenAkñúgebtug ¬edayQrelI uncracked gross section¦.

@> kugRtaMgeRkamGMeBIbnÞúkeFVIkareRkayeBlkMhatbg; (loss) TaMgGs; ¬sRmab;fñak; U nigfñak; T ¦ mandUcteTA³ kugRtaMgsgát;Gtibrma cf '45.0 EdlbNþalBIkmøaMgeRbkugRtaMgbUknwgbnÞúk efr nigkugRtaMg cf '05.0 EdlbNþalBIkmøaMgeRbkugRtaMgbUknwgbnÞúksrub.

#> kugRtaMgTaMgenHGacmantémøFMCagenH RbsinebIkarBiesaF nigkarviPaKbgðajfakaRbRBwtþeTA rbs;vaRKb;RKan;.



19>2>2> EdkeRbkugRtaMg (Prestressing Steel) Edk tendon EdleKniymeRbICageKenAkñúgebtugeRbkugRtaMgCa strands ¬b¤kab¦ Edlplit

eLIgCamYynwglYssrésr (wire) CaeRcIn CaTUeTAmancMnYn 7 b¤19 . Wire nig bar k¾RtUv)aneKeRbI R)as;pgEdr. Stand nig wire RtUv)anpliteLIgedayeKarBtam ASTM Standard 421A sRmab; uncoated stress-relieved wire nig 416A sRmab; uncoated seven-wire stress-relieved strand. lkçN³rbs;EdkeRbkugRtaMgRtUv)an[enAkñúgtarag 19>1.

EdkeRbkugRtaMgEdleRbIenAkñúgebtugeRbkugRtaMgRtUvEtmanersIusþg;x<s; CaTUeTAman

ultimate strength puf enAcenøaH MPa1730 eTA MPa1860 . eKcaM)ac;GnuBaØat[EdkersIusþg;x<s; mansac;lUtFM nigrkSakugRtaMgenAkñúgebtug[RKb;RKan; nigGciéRnþy_bnÞab;BI inelastic shortening rbs;

tarag 19>1 Type Diameter

(mm) Area

(mm2) Mass

(kg/m) Seven-wire strand (grade 250) 6.350 23.2 0.179 7.950 37.4 0.298 9.525 51.6 0.402 11.125 69.7 0.551 12.700 92.9 0.729 15.240 139.4 1.101 Seven-wire strand (grade 270) 9.525 54.8 0.432 11.125 74.2 0.595 12.700 98.7 0.789 15.250 138.7 1.101 Prestressing wire grades (250) 4.877 18.7 0.146

(250) 4.978 19.4 0.149 (240) 6.350 31.6 0.253 (235) 7.010 38.7 0.298

Prestressing bars (smooth) 19.050 283.9 2.232 (grade 145 or 160) 22.225 387.1 3.036 25.400 503.2 3.973 28.575 638.7 5.030 31.750 793.5 6.206 34.925 954.8 7.515 Prestressing bars (deformed) 15.875 180.6 1.458 (grade 150-160) 19.050 271.0 2.218 25.400 548.4 4.480 31.750 806.5 6.535 34.925 1006 8.274



ebtug. kugRtaMgGnuBaØatenAkñúgEdkeRbkugRtaMgeyagtam ACI Code, Section 18.5 mandUcxageRkam³ !> kugRtaMgGtibrmaEdlbNþalBI tendon jacking force minRtUvFMCagtémøEdltUcCageKkñú

gcMeNam puf8.0 nig pyf94.0 . témøEdltUcCagminRtUvFMCagkugRtaMgEdlENnaMedayGñk plit tendon b¤ anchorage eT.

@> kugRtaMgGtibrmaenAkñúg pretensioned tendon Pøam²eRkayeBlepÞrminRtUvFMCagtémøtUc CageKkñúgcMeNam puf74.0 nig pyf82.0 .

#> kugRtaMgGtibrmaenAkñúg postensioned tendon eRkayeBl tendon RtUv)an anchor KW puf70.0 .

19>2>3> EdkBRgwg (Reinforcing Steel) CaTUeTA eKeRbIEdkBRgwgminEmneRbkugRtaMgenAkúñgGgát;eRKOgbgÁúMebtugeRbkugRtaMg Ca BiessenAkñúgsMNg;ebtugeRbkugRtaMgcak;eRsc. eKeRbIEdkBRgwgCaEdkkmøaMgkat;TTwg Ca EdkbEnßmsRmab;kardwkCBa¢Ún nigkarelIkdak;Ggát;cak;eRsc ehIynigeRbIenAkñúgGgát;ebtugeRb kugRtaMgedayEpñkEdlcUlrYmCamYynwgEdkeRbkugRtaMg. RbePT nigkugRtaMgGnuBaØatrbs;Edk RtUvENnaMenAkñúgCMBUk 2 nigCMBUk 5 rYcehIy.

19>3> kMhatbg;eRbkugRtaMg (Loss of Prestress)

19>3>1> Lump-sum losses kMhatbg;énkmøaMgeRbkugRtaMgCabnþbnÞab;ekItmaneRkayeBlkmøaMgeRbkugRtaMgRtUv)an epÞrBI jack eTaGgát;ebtug. kMhatbg;eRbkugRtaMgCakarkat;bnßykmøaMgeRbkugRtaMgkñúgmYy CIviténeRKOgbgÁúM. brimaNkMhatbg;enAkñμ úg tendon ERbRbYlcenøaHBI %15 eTA %30 énkugRtaMg edIm edayGaRs½ynwgktþaCaeRcIn. sRmab;eRKOgbgÁúMebtugGarem:Tm¶n;FmμtaPaKeRcInEdlsagsg; eday standard method, tendon stress loss bNþalmkBI elastic shortening, shrinkage, creep nig relaxation rbs;EdkKWmantémøRbEhlnwg ( )MPaksi 24135 sRmab; pretensioned member



nigsRmab; posttensioned member KWRbEhlbwg ( )MPaksi 17225 . kmøaMgkkit nig anchorage slip minRtUv)an rab;bBa©ÚleT. karENnaMBIrsRmab;kar)a:n;s μankMhatbg;srubenAkñúgGgát;ebtugeRbkugRtaMgRtUv)anbgðajeday AASTHO nig Posttensioning Institute (PTI). AASTHO ENnaM[ykkMhatbg;srub (edayminKitkmøaMgkkit) ( )MPaksi 31045 sRmab; pretensioned strand nig ( )MPaksi 22833 sRmab; postentioned strand nig wire enAeBlEdleKeRbIersIusþg;sgát;ebtug MPaf c 35' = . PTI ENnaM lump-sum prestress loss sRmab; posttensioned member ( )MPaksi 24135 sRmab;Fñwm nig

( )MPaksi 20730 sRmab;kRmalxNÐ ¬edayminKitkmøaMgkkit¦. eKGaceRbItémøTaMgGs;enH)anluH Rta EteK)aneFVIkar)a:n;RbmaNkMhatbg;eRbkugRtaMgedayRbPBénkMhatbg;nImYy²dac;edayELkBI Kña)anl¥ dUcEdl)anENnaMy:agsegçb. CaTUeTA RbPBénkMhatbg;eRbkugRtaMgKW

- Elastic shortening rbs;ebtug - Shrinkage rbs;ebtug - Creep rbs;ebtug - Relaxation rbs;Edk tendon - kmøaMgkkit - Anchorage set

19>3>2> kMhatbg;edaysar (Elastic Shortening of Concrete)

kar)a:n;RbmaNkMhatbg; elastic shortening rbs;ebtugenAkñúg pretensioned member RtUv)aneFVIeLIgdUcteTA. BicarNa pretensioned concrete member énmuxkat;efr nigkugRtaMgBRgay es μ ItambeNþayG½kSTIRbCMuTm¶n;rbs;vaedaysarkmøaMg oF . eRkayBIkarepÞrkmøaMgeRbkugRtaMgFñwmebtug nig prestressing tendon rYjxøIedaybrimaNes μIKña edaysarPaBs¥itrvagsmÖar³TaMgBIr. dUcenH kmøaMg eRbkugRtaMgEdlcab;epþIm oF Føak;mkRtwm iF ehIykMhatbg;kmøaMgeRbkugRtaMgKW io FF − . dUcKña strain enAkñúgebtug cε RtUvEtesμ InwgbERmbRmYlrageFob (strain) rbs; tendon sεΔ . dUcenH

sc εε Δ= b¤ ( ) ( )sscc EfEf // Δ= ehIykMhatbg;kugRtaMgEdlbNþalBI elastic shortening KW



c

o

c

icc

c

ss A

nFAnFnff

EEf ≈==×=Δ (19.1)

Edl =cA RkLaépÞrbs;muxkat;ebtug == cs EEn / pleFobm:UDul (modular ratio) =cf kugRtaMgrbs;ebtugenARtg;TIRbCMuTm¶n;rbs;EdkeRbkugRtaMg KuNkugRtaMgnwgRkLaépÞrbs;EdkeRbkugRtaMg spA edIm,ITTYl)ankmøaMgsrub . Elastic loss KW ( ) sp

c

ospcspsio A

AnFAnfAfFFES ⎟⎟

⎠

⎞⎜⎜⎝

⎛≈=Δ=−= (19.2)

( ) spcoi AnfFF −= (19.3) sRmab;karKNnaGnuvtþn_ kMhatbg;kugRtaMgénkmøaMgeRbkugRtaMg ¬ sfΔ kñúgmYyktþaépÞ spA ¦ mantémø Rbhak;RbEhlnwg co AnF / . RbsinebI kmøaMg oF manGMeBIRtg;cMNakp©it e enaH elastic loss Edl bNþalBIvtþmanén oF nigbnÞúkefrGnuvtþn_enAeBlepÞrKW ( ) spc AnfES −= ¬EdlbNþalBIeRbkugRtaMg¦ ( ) spc Anf+ ¬bnÞúkefr¦

spD

spii

io nAI

eMnAIeF

AFFFES ⎟

⎠⎞

⎜⎝⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛+−=−=

2 (19.4)

eKGaceRbItémøRbhak;RbEhlén ( ) sppui AfF 63.0= enAkñúgsmIkarxagelI.

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++=+

Ie

AnAFnAfF spispco

211D.L. (19.5) ( ) ( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++

+=

Ie

AnA

fnAFF

sp

cspoi 211

D.L.

sRmab; posttensioned member Edl tendon nig individual strand minrgkugRtaMgdMNalKña enaHeK GackMhatbg;eRbkugRtaMges μ InwgBak;kNþaléntémø ES sRmab; prestensioned member. dUcKña eKGacyk elastic shortening loss enAkñúgkRmalxNÐesμ InwgmYyPaKbYnéntémø ES sRmab; prestensioned member edaysarkarlUtrbs; tendon mYyman\T§iBltictYceTAelIkugRtaMgén tendon d¾éTeTot.

19>3>3> kMhatbg;edaysarkarrYmmaD (Loss Due to Shrinkage)

kMhatbg;eRbkugRtaMgEdlbNþalBIkarrYmmaDKWGaRs½ynwgeBl. eKGac)a:n;RbmaNvadUcxag eRkam³



sfSH Δ= (shrinkage) sshEε= (19.6) Edl MPaEs

5102 ⋅= nig =shε shrinkage strain enAkñúgebtug eKGacsnμt; Strain mFümEdlbNþalBIkarrYmmaDmantémødUcxageRkam³

- 0003.01 =shε sRmab; pretensioned member - 0002.02 =shε sRmab; posttentioned member RbsinebIeKGnuvtþ posttensioning kñúgcenøaH 5 eTA 7 éf¶eRkayBIcak;ebtug/ eKGacyk shrin-

kage strain es μ Inwg 18.0 shε . RbsinebIeKGnuvtþ posttensioning kñúgcenøaH 1 s)aþh_eTA 2 s)aþh_ eK GaceRbI 17.0 shsh εε = nigRbsinebIeKGnuvtþ posttensioning eRkayeBlcak;ebtugeRcInCag 2 s)aþh_ enaHeKGacyk 2shsh εε = . eKk¾Gac)a:n;RbmaNkMhatbg;edaykarrYmmaD SH dUcxageRkam³

( )RHS

VEKSH ssh −⎟⎠⎞

⎜⎝⎛ −×= − 10006.01102.8 6

Edl =SV / pleFobmaDelIépÞ nig =RH average relative humidity. 0.1=shK sRmab; pretensioned member nigesμ Inwg 8.0 / 73.0 / 64.0 nig 58.0 sRmab; posttensioned member RbsinebIeKGnuvtþ posttensioning eRkayeBlcak;ebtug 5 / 10 / 20 nig 30 éf¶ erogKña.

19>3>4> kMhatbg;edaysar creep rbs;ebtug

Creep CakMhUcRTg;RTayGaRs½ynwgeBlEdlekIteLIgenAkñúgebtugeRkamGMeBIbnÞúkefr. kMhUc RTg;RTayEdlekIteLIgedaysar creep eFVI[)at;bg;kmøaMgeRbkugRtaMgBI %5 eTA %7 . Creep strain ERbRbYlCamYynwgGaMgtg;sIueténkugRtaMgedImenAkñúgebtug relative humidity nigeBl. eKGackMNt;kMhatbg;kugRtaMgEdlbNþalBI creep dUcxageRkam³ sfCR Δ= (creep) ( ) ( )scrccc ECnfC ε== (19>7) Edl =cC emKuN creep

i

cp

εε

strain, elastic initial n,creepstrai

=

eKGacyktémø cC dUcxageRkam³

ersIusþg;ebtug MPaf c 28' ≤ MPaf c 28' > Relative humidity %100 %50 %100 %50

cC 21− 42 − 5.17.0 − 35.1 −



eKGaceFVI interpolation sRmab;témøEdlenAcenøaHtémøEdlenAkñúgtaragxagenH. edayKitfa creep EtBak;kNþalekIteLIgkñúgGMLúg 134 ExdMbUgén 6 ExdMbUgbnÞab;BIkarepÞreRbkugRtaMgeTAebtug nigeRkamlkçxNÐsMeNImFmμta enaHeKGacsn μt; creep strain sRmab;karKNnaGnuvtþn_dUcxageRkam³ !> sRmab; pretensioned members, ×⋅= −5107crε kugRtaMgenAkñúgebtug

@> sRmab; postensioned members, ×⋅= −5102.5crε kugRtaMgenAkñúgebtug. eKeRbItémøenH enAeBlEdleKGnuvtþ posttensionning kñúgGMLúg 2 eTA3s)aþh_. sRmab;karGnuvtþ postensioning elOnCagenH eKGaceRbItémøkNþal.

eKeRbItémøTaMgenH enAeBlEdlersIusþg;rbs;ebtugenAeBlepÞrKW MPaf c 28' ≥ . enAeBlEdl MPaf c 28' < creep strain KYrekIneLIgkñúgGRta /4 ersIusþg;Cak;Esþg.

kMhatbg;eRbkugRtaMgsrubEdlbNþalBI creep scr Eε= (19.8)

19>3>5> kMhatbg;edaysar Relaxation rbs;Edk

Relaxation rbs;EdkbNþal[mankMhatbg;enAkñúgEdkeRbkugRtaMgGaRs½ynwgeBl Edl RsedogKñanwg creep enAkñúgebtugEdr. kMhatbg;edaysar relaxation ERbRbYleTAtamRbePTEdk. CaTUeTA témørbs;vaRtUv)anpþl;[edayGñkplitEdk. CaFm μta eKsn μt;kMbaatbg;enHes μ Inwg %3 én kugRtaMgedImrbs;EdksRmab; posttensioned member nig %2 eTA %3 sRmab; pretensioned

members. RbsinebIeKminmanB½t’manBIkarBiesaFeT eKGacPaKrykMhatbg;sRmab; relaxation enA h1000 dUcxageRkam³

!> enAkñúg low-relaxation strands, enAeBlEdleRbkugRtaMgedImes μ Inwg puf7.0 nig puf8.0 / relaxation (RE) KW %5.2 nig %5.3 erogKña.

@> enAkñúg stress-relieved strand b¤ wire, enAeBlEdleRbkugRtaMgedImesμ Inwg puf7.0 nig puf8.0 / relaxation (RE) KW %8 nig %12 erogKña.

19>3>6> kMhatbg;edaysarkmøaMgkkit (Loss Due to Friction)

CamYynwgEdkrg pretensioning kMhatbg;edaysarkmøaMgkkitekItmanenAeBlEdl wires b¤ strand dabtam diaphragm. CaFmμtakMhatbg;enHmantémøtUc ehIyeKGacecalva)an.



enAeBlEdl strand dabtam concordant profile enaHkMhatbg;edaysarkmøaMgkkitGacmantémøFM. enAkrNIEbbenH CaFm μtaeKeRbI]brkrN_Edlvas;bnÞúkCak;EsþgedIm,IkMNt;kmøaMgenAkñúg tendon. CamYynwgEdkrg posttensioning, \T§iBlénkmøaMgkkitmantémøFMedaysarktþacMbgBIrKW kMeNagrbs; tendon nigkar)at;bg;PaBRtg;rbs;bMBg; (wobble). RbsinebIeKTb;cugbgáb;mçagrbs; tendon edaykmøaMg 2P nigeKTajcugTMenrmçageTotrbs; tendon edaykmøaMg 1P edIm,I[ tendon enaHrGiltamTisrbs;kmøaMg 1P )anluHRtaEt pxePP μα

21 = (19.9) Edl =μ emKuNmMukkitsþaTic nig =pxα mMurvag 1P nig 2P . CaTUeTAeKKit wobble effect tamviFI RsedogKña ( )xKl

sx ePP +−= μα ( )pxppxKl

pxpj ePP αμ++=

( )pxppxKlpjpx ePP αμ+−

= (19.10) Edl =pjP kmøaMgeRbkugRtaMgenARtg;cMNuc x =pxP kmøaMgeRbkugRtaMgenARtg; jacking end =pμ emKuNkmøaMgkkitedaysarkMeNag

=pxα bMErbMrYlmMusrubénragtambeNþayrbs;EdkeRbkugRtaMgBI jacking end eTAdl;cMNuc x KitCara:düg;

kaMkMeNaggRbEvgkMeNa

= =K emKuNkmøaMgkkit wobble kñúgmYyÉktþaRbEvgrbs; tendon CakarsRmYl ACI Code

[nUvsmIkarxageRkamsRmab;krNI ( ) 30.0≤+ xpxp Klαμ . lT§plEdlTTYl)anBI smIkarCatémøRbEhl

( ) 11 −++= pxppxpjpx KlPP αμ (AIC Code, eq. 18.2) (19.11) emKuNkmøaMgkkit μ nig K GaRs½ynwgRbePTén strand b¤ wire, RbePTbMBg; niglkçxNÐépÞ b:H. ACI Commentaru, Sectin 18.6 nigenAkñúgtarag 19.2 [nUvtémøRbhak;RbEhlrbs; μ nig K . kMhatbg;edaysarkmøaMgkkitenAkñúg jack ERbRbYl nigGaRs½ynwgktþaCaeRcIn edayrab;bBa©Úl TaMgRbEvgrbs; tendon. eKENnaM[eRbI accurate load ceel edIm,Ivas;kmøaMgedaypÞal;. kareRbI pressure gauge pþl;nUvlT§plminsuRkit luHRtaEteKeFVIkarEktRmUveTAtamkmøaMgEdleKsÁal; enAkúñúg



tendon. kMhatbg;edaysarkmøaMgkkitenAkñúg cnchorage KWGaRs½ynwgRbePT anchorage nigbrimaN én deviation rbs; tendon Edlqøgkat; anchorage. CaFmμtakMhatbg;enHmantémøtUcEdlGac ecal)an. karENnaMkñúgkrNIBiessKYrTTYl)anBIplitkr. tarag 19>2 emKuNkmøaMgkkitsRmab; post-tensioned tendon

RbePT tendon emKuNkmøaMgkkit wobble K kñúgmYyÉktþaRbEvg ( )310−

emKuNkmøaMgkmøaMgkkit edaysarkMeNag μ

Tendon in flexible metal sheathing (grouted)

Wire tendon 0.533.3 − 25.015.0 −

Seven-wire strand 67.667.1 − 25.015.0 −

High-strength bars 233.0 − 30.008.0 −

Pregreased unbonded tendon Wire tendon and seven-wire strand

67.61− 15.005.0 − Mastic-coated unbonded tendon

Wire tendon and seven-wire strand67.033.0 − 15.005.0 −

19>3>7> kMhatbg;edaysar Anchor set

enAeBlkmøaMgenAkñúg tendon RtUv)anepÞrBI jack eTA anchorage unit, clnart;cUlkñúgbnþic rbs; tendon ekIteLIgedaysarkardak; gripping device b¤ wedge. karrGilenHbNþal[man tendon rYjxøI EdleFVI[)at;bg;kmøaMgeRbkugRtaMg. RbEvgrGilERbRbYlBI mm5.2 eTA mm6 ehIy CaTUeTARtUv)ankMNt;edayplitkr. eKGacKNnakMhtabg; anchor set edayrUbmnþxageRkam³ sss E

LLEf ×

Δ=Δ=Δ ε (19.12)

Edl =Δε GaMgtg;sIueténkarrGil anchor

MPaEs5102 ⋅=

=L RbEvgrbs; tendon



edaysarkMhatbg;eRbkugRtaMgCacMras;smamaRteTAnwgRbEvgrbs; tendon ¬b¤RbEhlCaBak;kNþal énRbEvgrbs; tendon RbsinebIvargkugRtaMgBIcugsgxagkñúgeBlEtmYy¦PaKrykMhatbg;enAkñúgkug RtaMgEdknwgRtUv)ankat;bnßyenAeBlEdlRbEvgrbs; tendon ekIneLIg. RbsinebI tendon lUteday εΔ enAeBlepÞr enaHeKecalkMhatbg;eRbkugRtaMgedaysarkarrGil.

]TahrN_ 19>2³ FñwmTRmsamBaØrg pretensionning RbEvg m11 manmuxkat;ctuekaNEkgCamYynwg

cmb 45= nig cmh 80= . KNnakMhatbg;eGLasÞic nigkMhatbg;EdlGaRs½ynwgeBlTaMgGs;. eK [³ kmøaMgeRbkugRtaMgenAeBlepÞrKW kNFi 1935= / RkLaépÞrbs;EdkeRbkugRtaMgKW =psA

21935mm / MPaf c 35' = / MPaEc 34500= / MPaEs5102 ⋅= / profile rbs; tendon manrag

Ca)a:ra:bUl/ cMNakp©itenAkNþalElVg cm15= nigcMNakp©itenAcug 0= . dMeNaHRsay³ !> kMhatbg;edaysar elastic shortening: kugRtaMgEdl)anBIkmøaMgeRbkugRtaMgenAeBlepÞrKW MPa

AF

ps

i 10001019351935 3 ==

strain rbs;EdkeRbkugRtaMg 35 105

1021000 −⋅=⋅

==s

sEf

edayeRbIsmIkar 19>1 8.5

34500102 5

=⋅

==c

sEEn yk 6

MPaAnFf

c

is 25.3210

80045019356 3 =×

×==Δ

edayKitbERmbRmYlcMNakp©ittambeNþayFñwm strain enAmuxkat;xagcug 43 1056.110

345008004501935 −⋅=

××==

cc

iEA

F

strain enAkNþalElVg c

i

cc

iIE

eFEA

F 2+=

( ) 41033

1092.112800450

12mmbhI ⋅===

strain 4310

24 1022.210

345001092.115019351056.1 −− ⋅=×⋅

×+⋅=

strain mFüm ( ) 44 1089.11022.256.121 −− ⋅=+=



kMhatbg;eRbkugRtaMg = strain MPaEs 8.371021089.1 54 =⋅×⋅=× − PaKrykMhatbg; %78.3

10008.37==

@> kMhatbg;edaysar shrinkage: shrinkage strain 0003.0=

MPaEf sshs 602000000003.0 =×==Δ ε PaKrykMhatbg; %6

100060

== #> kMhatbg;edaysar creep rbs;ebtug³ edaysnμt; 0.2=cC enaH ( )scrcs ECf ε=Δ Elastic strain 41056.1 −⋅==

cc

iEA

F

( ) MPafs 4.622000001056.12 4 =×⋅=Δ − PaKrykMhatbg; %24.6

10004.62==

b¤edaytémøRbhak;RbEhl eyIgyk ×⋅= −5107crε kugRtaMgenAkñúgebtug 435 1076.310

8004501935107 −− ⋅=⎟

⎠⎞

⎜⎝⎛

×⋅=crε

MPaEf scrs 2.752000001076.3 4 =×⋅==Δ −ε PaKrykMhatbg; %52.7

10002.75==

vaCatémøEdlmansuvtßiPaB ehIyeKnwgTTYl)anGRtadUcKñasRmab;karKNnaxagelIRbsinebIeKyk 41.2=cC .

$> kMhatbg;edaysar relaxation rbs;Edk³ sRmab; low-relaxation strand eKsnμt;ykkMhatbg; es μ Inwg %5.2

MPafs 25%5.21000 =×=Δ %> sn μt;kMhatbg;edaysarkarBt; kmøaMgkkitrbs; cable spacer nigbøúkxagcugrbs;RbB½n§

pretensioning KW %2 . MPafs 20100002.0 =×=Δ ^> kMhatbg;edaysarkmøaMgkkitenAkñúg tendon KWsUnü. &> kMhatbg;srubmandUcxageRkam



Elastic Shortening 37.8MPa 3.78% Shrinkage loss 60.0MPa 6.00% Creep of concrete loss 62.4MPa 6.24% Relaxation of steel loss 25.0MPa 2.50% Other loss 20.0MPa 2.00% Total loss 205.2MPa 20.52%

eRbkugRtaMgRbsiT§PaB MPa6.8324.1671000 =−= kmøaMgeRbkugRtaMgRbsiT§PaB kNF 16111019356.832 3 =⋅×= −

( ) ii FFF 833.0167.01 =−= sRmab; iFF η=

dUcenH 833.0=η ]TahrN_ 19>3³ KNnakMhatbg;TaMgGs;én post-tensioned beam EdlmanRbEvg m36 . RkLaépÞ rbs;muxkat;ebtug ( ) 241049 mmAc ⋅= / m:Um:g;niclPaB ( ) 4101083.6 mmI g ⋅= / kmøaMgeRbkugRtaMg enAeBlepÞr ( ) kNFi 4950= / RkLaépÞEdkeRbkugRtaMg ( ) 24840mmAps = / MPaf c 35' = /

MPaEc 34500= / nig MPaEs5102 ⋅= . Profile rbs; tendon manragCa)a:ra:bUl/ cMNakp©itenA

kNþalElVg cm50= nigcMNakp©itenAxagcug 0= . dMeNaHRsay³ !> kMhatbg;eday elastic shortening:

kugRtaMgEdkenAeBlepÞr MPaAF

ps

i 7.10221048404950 3 ===

kugRtaMgenAkúñgebtugRtg;muxkat;xagcug MPa1.10101049

4950 34 =

⋅=

kugRtaMgenAkúñgebtugRtg;muxkat;kNþalElVg I

eMIeF

AF Di

c

i −+=2

Tm¶n;rbs;Fñwm mkN /25.12251049 2 =×⋅= − mkNM D .5.1984

83625.12

2==

kugRtaMgenAkNþalElVg 610

310

23

4 101083.6

5005.1982101083.6500495010

10494950

⋅

×−

⋅

×+

⋅=

MPa72.135.1412.181.10 =−+= kugRtaMgmFüm MPa9.11

272.131.10

=+

=



strain mFüm 41045.334500

9.119.11 −⋅===cE

kMhatbg;eGLasÞicKW MPaEf scs 691021045.3 54 =⋅×⋅==Δ −ε edaysn μt;faeKTaj tendon mþgBIrkñúgeBlEtmYy. KUTImYynwgmankMhatbg;FMCageK b:uEnþKUcugeRkaynwgmankMhatbg;es μ IsUnü. dUcenH kMhatbg;eGLasÞicmFüm MPafs 5.342/69 ==Δ . PaKrykMhatbg; %37.3

7.10225.34

== @> kMhatbg;edaysarkarrYmmaDrbs;ebtug sfΔ (shrinkage) MPaEs 402000000002.00002.0 =×==

PaKrykMhatbg; %91.37.1022

40==

#> kMhatbg;;edaysar creep rbs;ebtug³ sn μt; 5.1=cC elastic strain 43

4 1093.210345001049

4950 −⋅=×⋅

==cc

iEA

F

sfΔ (creep) ( ) ( ) MPaEC scrc 9.872000001093.25.1 4 =×⋅== −ε PaKrykMhatbg; %59.8

7.10229.87

== $> kMhatbg;edaysar relaxation rbs;Edk³ sRmab; low-relaxation strand, kMhatbg;KW %5.2

MPafs 6.257.1022025.0 =×=Δ %> karrGilrbs; anchorage: sRmab;karTajEtBIcugmçag snμt;RbEvgrGil mm8.3

MPaELLf ss 1.21200000

360008.3

==Δ

=Δ edIm,IGnuBaØat[mankarrGilrbs; anchorage eKRtUvkMNt;kugRtaMgkñúgkarTaj 1.217.1022 +

MPa8.1043= enAelI pressure gauge edIm,ITTYl net stress MPa7.1022 enAkñúg tendon. ^> kMhatbg;EdlbNþalBIkmøaMgkit³ smIkar parabolic profile KW ( )2

24 xLxL

eex −= Edl =xe cMNakp©itenARtg;cm¶ay x Edlvas;BITRm nig =e cMNakp©itenAkNþalElVg ( ) ( )xL

Le

dxed x 24

2 −= CaCRmal (slope) rbs; tendon enARKb;cMNucTaMgGs;. enARtg;TRm 0=e eyIgTTYl)an slop ( )

056.036000

50044=

×==

Le

dxed x



slope enAkNþalElVgesμ IsUnü. dUcenH 056.0=pxα . edayeRbI flexible metallic sheath, 5.0=pμ nig 00333.0=K . enAkNþalElVg mx 18= . RtYtBinitüfaetI ( ) 30.0≤+ xpxp Klαμ

3.0088.01800333.0056.05.0 <=×+×=+ xpxp Klαμ ( )pxppxpjpx KlPP αμ++= 1 ( ) xx PP 088.1088.01 =+=

MPa7.11127.1022088.1 =×= ¬kmøaMgenAcug jacking¦ MPafs 907.10227.1112 =−=Δ

PaKrykMhatbg; %8.87.1022

90==

&> kMhatbg;srub Elastic Shortening 34.5MPa 3.37% Shrinkage loss 40.0MPa 3.91% Creep of concrete loss 87.9MPa 8.59% Relaxation of steel loss 25.6MPa 2.50% Friction loss 90.0MPa 8.80% Total loss 278.0MPa 27.17%

eRbkugRtaMgRbsiT§PaB MPa2.7795.2439.1022 =−= kmøaMgeRbkugRtaMgRbsiT§PaB ( ) ( ) ii FFF 762.0238.01 =−=

kNF 37724950762.0 =×= sRmab; iFF η= dUcenH 762.0=η

19>4> viPaKGgát;rgkarBt;begáag (Analysis of Flexural Members)

19>4>1> kugRtaMgEdlbNþalBIlkçxNÐmanbnÞúk niglkçxNÐKμanbnÞúk Stresses Due to Loaded and Unloaded condition

enAkñúgkarviPaKFñwmebtugeRbkugRtaMg CaTUeTAkardak;bnÞúkBIrmaneRKaHfñak;CageK. TImYyKWekIt manenAeBlepÞr KWenAeBlFñwmrgkmøaMgeRbkugRtaMg iF ehIyTm¶n;rbs;Fñwm b¤bnÞúkefrGnuvtþn_enAxN³én karepÞrkmøaMgkugRtaMg. eKminKitlkçxNÐbnÞúkefrbEnßm b¤bnÞúkGefreT. kñúglkçxNÐKμanbnÞúkenH kug RtaMgenAsrésEpñkxagelIbMput nigEpñkxageRkambMputénmuxkat;eRKaHfñak;minRtUvFMCagkugRtaMgenA eBlepÞr cif nig tif sRmab;kugRtaMgrgkarsgát; nigkugRtaMgrgkarTajrbs;ebtugerogKña.



krNITIBIrénkardak;bnÞúkekIteLIgenAeBlEdlFñwmrgkmøaMgeRbkugRtaMgeRkayBIekItmankMhat bg;TaMgGs; nigrgnUvbnÞúkefr nigGefr. enAkñúglkçxNÐmanbnÞúkenH kugRtaMgenAsrésEpñkxagelIbM put nigEpñkxageRkambMputénmuxkat;eRKaHfñak;dac;xatminRtUvFMCagkugRtaMgGnuBaØat cf nig tf sRmab;kugRtaMgrgkarsgát; nigkugRtaMgrgkarTajrbs;ebtugerogKña. lkçxNÐTaMgenHGacsresrCaTRmg;KNitviTüadUcxageRkam³ !> sRmab;lkçxNÐK μanbnÞúk ¬enAeBlepÞr¦

- enAsrésEpñkxagelIbMput ( )

titDtii

ti fI

yMI

yeFAF

≤−+−=α (19.14) - enAsrésEpñkxageRkambMput

( )ci

bDbiibi f

IyM

IyeF

AF

−≥−−−=α (19.15)

@> sRmab;lkçxNÐmanbnÞúk ¬bnÞúkTaMgGs;RtUv)andak;eRkayBIkMhatbg;eRbkugRtaMg¦ - enAsrésEpñkxagelIbMput - ( )

ctLtDt

t fI

yMI

yMI

yFeAF

−≥−−+−=σ (19.16) - enasrésEpñkxageRkambMput - ( )

tbLbDb

b fI

yMI

yMI

yFeAF

≤−−−−=σ (19.17) Edl iF nig =F kmøaMgeRbkugRtaMgenAeBlepÞr nigeRkayBIkMhatbg; tif nig =tf kugRtaMgrgkarTajenAkñúgebtugenAeBlepÞr nigeRkayBIkMhatbg; cif nig =cf kugRtaMgrgkarsgát;enAkúñgebtugenAeBlepÞr nigeRkayBIkMhatbg; DM nig =LM m:Um:g;EdlbNþalBIbnÞúkefr nigbnÞúkGefr

ty nig =by cm¶ayBIG½kSNWteTAsrésEpñkxagelIbMput nigEpñkxageRkambMput enAkúñgkarviPaK eKsnμt;fasmÖar³manlkçN³eGLasÞicenAkúñgEdneFVIkarénkugRtaMgEdlGnuvtþ. 19>4>2> EdnkMNt;sñÚl (Kern Limits) RbsinebIeKGnuvtþkmøaMgeRbkugRtaMgenARtg;TIRbCMuTm¶n;rbs;muxkat; vanwgekItmankugRtaMg BRgayes μ I. RbsinebIGnuvtþkmøaMgeRbkugRtaMgenARtg;cMNakp©it e BIeRkamTIRbCMuTm¶n; EdleFVIy:agNa [kugRtaMgenAsrésEpñkxagelIbMputesμ IsUnü enaHeKcat;TukkmøaMgeRbkugRtaMgenHmanGMeBIRtg;cMNuc



lower kern ¬rUbTI 19>5¦. enAkñúgkrNIenH e RtUv)ansMKal;eday bK ehIIykarBRgaykugRtaMgman ragRtIekaN EdlmankugRtaMgsgát;GtibrmaenAsréseRkameKbMput. kugRtaMgenAsrésxagelIbMputKW ( )

0=+−=I

yeFAF tii

tσ == bKe lower kern

tAyI

= (19.17)

dUcKña RbsinebIeKGnuvtþkmøaMgeRbkugRtaMgenARtg;cMNap©it 'e BIelITIRbCMum¶n; EdleFVIy:agNa[kug RtaMgenAsrésEpñkxageRkambMputesμ IsUnü enaHkmøaMgeRbkugRtaMgRtUv)aneKcat;TukfamanGMeBIRtg;cMNuc upper lower ¬rUbTI 19>5¦. enAkñúgkrNIenHcMNap©it 'e RtUv)ansMKal;eday tK ehIykarBRgaykug RtaMgmanragRtIekaN EdlmankugRtaMgsgát;GtibrimaenAsrésEpñkxagelIbMput. kugRtaMgenAsrés EpñkxageRkambMputKW ( )

0=+−=I

yeFAF bii

bσ == tKe' upper kern

bAyI

= (19.18)

Kern limits énmuxkat;RtIekaNRtUv)anbgðajenArUbTI 19>5.

19>4>3> karkMNt;témøéncMNakp©it (Limiting Values of Eccentricity) eKGacsresrsmIkarkugRtaMgTaMgbYn ¬BIsmIkar 19.13 dl; 19.16¦CaGnuKmn_éncMNakp©it e sRmab;lkçxNÐénkardak;bnÞúkepSg². Ca]TahrN_ eKGacsresrsmIkar 19.13 dUcxageRkam



( )ti

tDtiiti f

IyM

IyeF

AF

≤−+−=σ

( )I

yMAF

fI

yeF tDiti

ti ++≤

⎟⎠⎞

⎜⎝⎛ ++≤ ti

tDi

tif

IyM

AF

yFIe (19.19)

RbsinebIeKeRbI lower kern limit tb AyIK /= / enaH

i

bti

i

Db F

AKfF

MKe ++≤ (19.20)

témø e CacMNakp©itGtibrmaEdlQrelIsrésEpñkxagelIbMputsRmab;lkçxNÐKμanbnÞúk. dUcKña BIsmIkar 19.14

⎟⎠⎞

⎜⎝⎛ ++−≤ ci

bDi

bif

IyM

AF

yFIe (19.21)

i

tci

i

Dt F

AKfF

MKe ++−≤ (19.22)

témø e CacMNakp©itGtibrmaEdlQrelIsrésEpñkxageRkambMputsRmab;lkçxNÐK μanbnÞúk. eKKNna témøGtibrma e BIsmIkarelITaMgBIredayyktémøEdltUcCagmkeRbI. BIsmIkar 19.15 ⎟

⎠⎞

⎜⎝⎛ −+≥ c

tT

tf

IyM

AF

FyIe (19.23)

FAKf

FMKe bcT

b −+≥ (19.24) Edl =TM m:Um:g;EdlbNþalBIbnÞúkefr nigbnÞúkGefr ( )LD MM += . témøenHCacMNakp©itGb,-brma EdlQrelIsrésEpñkxagelIbMputsRmab;lkçxNÐRTbnÞúk. BIsmIkar 19.16 ⎟

⎠⎞

⎜⎝⎛ −+−≥ t

bT

bf

IyM

AF

FyIe (19.25)

FAKf

FMKe ttT

t −+≥ (19.26) témøenHCacMNakp©itGb,brmaEdlQrelIsrésEpñkxageRkambMput sRmab;lkçxNÐmanbnÞúk. eKKYr KNnatémøGb,brma e TaMgBIrenHBIsmIkarTaMgBIrxagelI ehIyeKykcMNakp©itGb,brmaNaEdl mantémøFMCageKmkeRbI.



19>4>4> témøkMNt;émkmøaMgeRbkugRtaMgenAeBlepÞr (Limiting Values of the Prestessing Force at Transfer)

edayKitfa iFF η= Edl η CapleFobén net prestressing force eRkayBIkMhatbg; nig sRmab;krNIepSg²énkardak;bnÞúk eKGacsresrsmIkar 19.20, 19.22, 19.24 nig 19.26 eLIgvijdUc xageRkam³ ( ) btiDib AKfMFKe +≤− (19.27) ( ) tciDit AKfMFKe +≤+ (19.28)

( ) ( )bcLD

ib AKfMMFKeηηη1

−+≥− (19.29)

( ) ( )ttLD

it AKfMMFKeηηη1

−+≥+ (19.30)

CMnYsmIkar 19.27 eTAkñúgsmIkar 19.30 eKTTYl)an ( ) tti

ttLDtbi AKfAKfMMKKF −−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−≥+

ηηη11

b¤ ( ) ( )⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+≥ bti

ttLD

tbi AKfAKfMM

KKF

ηηη111 (19.31)

témø iF CatémøGb,brmaénkmøaMgeRbkugRtaMgenAeBlepÞredaymin[FMCagkugRtaMgGnuBaØateRkam lkçxNÐmanbnÞúk nigKμanbnÞúk. CMnYssmIkar 19.29 eTAkñúgsmIkar 19.28 edIm,ITTYl)an ( ) ( )⎥

⎦

⎤⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+≤ tci

bcLD

tbi AKfAKfMM

KKF

ηηη111 (19.32)

témø iF CatémøGtibrmaénkmøaMgeRbkugRtaMgenAeBlepÞredaymin[elIskugRtaMgGnuBaØateRkam lkçxNÐmanbnÞúk nigKμanbnÞúk. edayCMnYssmIkar 19.31 eTAkñúgsmIkar 19.32 02211 ≥⎟⎟

⎠

⎞⎜⎜⎝

⎛++⎟⎟

⎠

⎞⎜⎜⎝

⎛++−⎟⎟

⎠

⎞⎜⎜⎝

⎛− t

tcib

cti

LD AKffAKffMM

ηηηη (19.33)

smIkarenHbgðajfa 0minmax ≥− ii FF . eKeRbIsmIkarenHsRmab;bgðajfamuxkat;NamYymanlkçN³ RKb;RKan;. ]TahrN_ 19>4³ FñwmTRmsamBaØEdlrgeRbkugRtaMgmunEdlmanRbEvg m4.14 manmuxkat;dUcbgðaj enAkñúgrUbTI 19>6 a. FñwmenHRTnUvbnÞúkefr mkN /15.13 ¬edayminrYmbBa©ÚlTm¶n;pÞal;¦ nigrgnUvbnÞúk Gefr mkN /16 . edaysnμt;faEdkeRbkugRtaMgpSMeLIgeday tendon 20 Edl tendon mYymanGgát;



p©it mm125.11 CamYynwg MPaEs5102 ⋅= / MPaFo 1200= nig ultimate strength

MPaf pu 1725= .

!> kMNt;TItaMgEdnkMNt;xagelI nigEdnkMNt;xageRkamrbs; tendon profile ¬TIRbCMuTm¶n;rbs;

EdkeRbkugRtaMg¦ sRmab;muxkat;enAkNþalElVg nigsRmab;muxkat;bIepSgeTotenAcenøaH muxkat;kNþalElVg nigcugFñwm.

@> dak; tendon cMTItaMgedIm,IbMeBjEdnkMNt;TaMgenH eday[ tendon xøHegIbeLIgcab;BIcMNuc mYyPaKbIénRbEvgElVg. RtYtBinitütémøkMNt;énkmøaMgeRbkugRtaMgenAeBlepÞr.

#> RtYtBinitüeLIgvijnUvkMhatbg; edayKit tendon profile Edl)aneRCIserIs nigbERmbRmYl cMNakp©it e .



eRbI cif ¬enAeBlepÞr¦ MPa28= / MPaf c 35' = / MPaEc 27600= nig MPaEci 24800= .

dMeNaHRsay³ !> kMNt;lkçN³rbs;muxkat; RkLaépÞ 241025.23250300150450150600 mm⋅=×+×+×=

kMNt;TIRbCMuTm¶n;rbs;muxkat;edayKitm:Um:g;eFob)atrbs;muxkat; ( ) mmyb 522925105.6755010901251075

1025.231 333

4 =×⋅+×⋅+×⋅⋅

=

mmyt 4785221000 =−= KNna gross moment of inertia gI



( ) ( )( )( ) ( ) ( )( )( )⎥⎥⎦

⎤

⎢⎢⎣

⎡++

⎥⎥⎦

⎤

⎢⎢⎣

⎡+= 2

32

328600150

12600150403150450

12150450

gI

( ) ( )( )( )⎥⎥⎦

⎤

⎢⎢⎣

⎡++ 2

3397250300

12250300

41010607.2 mm⋅=

mmAyIK

tb 6.235

4781025.2310607.24

10=

×⋅⋅

==

mmAy

IKb

t 8.2145221025.23

10607.24

10=

×⋅⋅

==

@> )a:n;RbmaNkMhatbg;eRbkugRtaMg eday MPaFo 1200= a. snμt; elastic loss esμ I %4 b¤ MPa48120004.0 =× b. kMhatbg;edaysarkarrYmmaDKW MPaEs 601020003.00003.0 5 =⋅×= c. kMhat;bg;edaysar creep rbs;ebtug ³ kar)a:n;RbmaNdMbUgd¾l¥bMputénkMhatbg;eday

sar creep KW 67.1 dgén elastic loss MPa804867.1 ≈×

d. kMhatbg;edaysar relaxation énEdkKW %4 ³ MPa48120004.0 =× kMhatbg;GaRs½ynwgeBlKW MPa188488060 =++ PaKrykMhatbg; %7.15

1200188

== e. kMhatbg;srubKW MPa23648188 =+

PaKryénkMhatbg;srubKW %7.19

1200236

= f. kugRtaMgkmøaMgeRbkugRtaMg

MPaFi 1152481200 =−= ¬enAeBlepÞr¦ MPaF 9642361200 =−=

iFF η= −=1η pleFobkMhatbg;GaRs½ynwgeBl

837.01152964

==



#> EdnkMNt;éncMNakp©it e Rtg;kNþalElVg³ kMNt;kugRtaMgGnuBaØat nigm:Um:g;. enAeBlepÞr MPaf ci 28' = / MPafci 8.16286.0 =×= nig MPaff citi 32.1'25.0 == . enAeBlrgbnÞúk

eFVIkar MPaf c 35' = / MPaff cc 75.15'45.0 == nig MPaff ct 96.2'5.0 == . bnÞúkpÞal;rbs;Fñwm mkN /81.5251025.23 2 =×⋅= −

DM ¬bnÞúkpÞal;¦ ( ) mkN.6.1508

4.1481.5 2==

aM ¬bnÞúkbEnßm nigbnÞúkGefr¦ 8

2Lwa= ( ) mkN.6.755

84.141615.13 2

=+

= m:Um:g;srub ( ) mkNMMM LDT .2.906=+=

=iF kugRtaMgenAeBlepÞr× RkLaépÞEdkeRbkugRtaMg RkLaépÞrbs; tendon 20 Edl tendon nImYy²manGgát;p©it mm125.11 KW

213947.6920 mm=× kNFi 16061011521394 3 =⋅×= −

kNF 1344109641394 3 =⋅×= − a. BicarNamuxkat;enAkNþalElVg

srésxagelIbMput kñúglkçxNÐminrgbnÞúk

i

bti

i

Db F

AKfF

MKe ++≤ ( )( ) mm4.37410

16066.2351025.2332.110

16066.1506.235 3

43 ≤

⋅++≤ −

srésxageRkambMput kñúglkçxNÐK μanbnÞúk

i

tci

i

Dt F

AKfF

MKe ++−≤ ( ) mm4.40110

16068.2141025.238.1610

16066.1508.214 3

43 ≤

⋅++−≤ −

yktémø e EdltUcCageKkñúgcMeNamlT§plTaMgBIrxagelICatémøGtibrma. dUcenH témøGtibrmarbs; mme 374=

srésxagelIbMput kñúglkçxNÐrgbnÞúk

FAKf

FMKe bcT

b −+≥



( ) mm268101344

6.2351025.2375.15101344

2.9066.235 34

3 ≥⋅

−+≥ − srésxageRkambMput kñúglkçxNÐmanbnÞúk

FAKf

FMKe ttT

t −+−≥ ( ) mm5.34910

13448.2141025.2396.210

13442.9068.214 3

43 ≥

⋅−+−≥ −

témøGb,brmarbs; e CatémøtUcCageKkñúgcMeNamlT§plTaMgBIrxagelI. dUcenH témøGb,brmarbs; mme 350=

b. BicarNamuxkat;EdlenAcm¶ay m4.2 BIkNþalElVg ¬muxkat;elx @ kñúgrUbTI 19>6 a¦³ DM ¬bnÞúkpÞal;¦ ( ) ( )28.4

28.4 D

AwR −=

( )( )( ) ( ) mkN.9.1338.4281.58.42.781.5 2 =−=

( )( )( ) ( ) mkNM a .6.6718.4215.298.42.715.29 2 =−=

mkNMT .5.8056.6719.133 =+= srésxagelIbMput sRmab;lkçxNÐminrgbnÞúk³ ( )( ) mme 36410

16066.2351025.2332.110

16069.1336.235 3

43 ≤

⋅++≤ −

srésxageRkambMput sRmab;lkçxNÐminrgbnÞúk ( ) mme 39110

16068.2141025.238.1610

16069.1338.214 3

43 ≤

⋅++−≤ −

témøGtibrmarbs; mme 364= srésxagelIbMput sRmab;lkçxNÐRTbnÞúk ( ) mme 19310

13446.2351025.2375.1510

13445.8056.235 3

43 ≥

⋅−+≥ −

sésrxageRkambMput sRmab;lkçxNÐRTbnÞúk ( ) mme 5.27410

13448.2141025.2396.210

13445.8058.214 3

43 ≥

⋅−+−≥ −

témøGb,brmarbs; mme 5.274= c. BicarNamuxkat;Rtg;cm¶ay m8.4 BIkNþalElVg ¬muxkat;elx # kñúgrUbTI 19>6 a¦³

DM ¬bnÞúkpÞal;¦ mkN.7.83=



mkNM a .8.419= mkNMT .5.503=

- srésxagelIbMput sRmab;lkçxNÐK μanbnÞúk mme 333≤ ¬Gtibrma¦ - srésxageRkambMput sRmab;lkçxNÐKμanbnÞúk mme 360≤ - srésxagelIbMput sRmab;lkçxNÐrgbnÞúk mme 32−≥ - srésxageRkambMput sRmab;lkçxNÐrgbnÞúk mme 50≥ ¬Gb,brma¦

d. BicarNamuxkat;Rtg;cm¶ay m9.0 BIcugFñwm ¬RbEvg anchorage¦³ DM ¬bnÞúkpÞal;¦ mkN.3.35= / mkNM a .1.177= nig mkNMT .4.212=

- srésxagelIbMput sRmab;lkçxNÐK μanbnÞúk mme 303≤ ¬Gtibrma¦ - srésxageRkambMput sRmab;lkçxNÐKμanbnÞúk mme 330≤ - srésxagelIbMput sRmab;lkçxNÐrgbnÞúk mme 248−≥ - srésxageRkambMput sRmab;lkçxNÐrgbnÞúk mme 167−≥ ¬Gb,brma¦

$> Tendon profile RtUv)anbgðajenAkñúgrUbTI 19>6 b. cMNakp©itEdl)aneRCIserIsenAkNþalElVgKW mme 364= EdlvaRKb;RKan;sRmab;muxkat; B enAcm¶ay m4.2 BIkNþalElVg. TIRbCMuTm¶n;énEdk

eRbkugRtaMgmanlkçN³edkcenøaH A nig B nigbnÞab;mkeTreLIgEdlmanlkçN³CabnÞat;cenøaHBI B eTA E . cMNakp©itenARtg;muxkat; C nig D RtUv)anKNnaedayeRbIbnÞat;eRTt BE Edlman CRmal mmm /83.758.4/364 = . cMNakp©itRtg; C KW mm182 nigRtg; D KW mm68 . Tendon

profile Edl)aneRCIserIsbMeBjlkçxNÐEdnkMNt;xagelI nigEdnkMNt;xageRkamrbs;cMNakp©it enARKb;muxkat;TaMgGs;.

karelIk tendon eLIgRtUv)aneFVIdUcxageRkam³ a. dak; tendon TaMg 20 ¬Ggát;p©it mm125.11 ¦

enAmYyPaKbIénkNþalElVgrbs;FñwmedaymanKMlat mm50 BIKñadUcbgðajenAkñúgrUbTI 19>6 a. edIm,IKNnacMNakp©itCak;EsþgenARtg;muxkat;kNþalElVg Kitm:Um:g;sRmab; tendon eFob nwg)at rbs;muxkat;³

cm¶ayBI)at ( ) mm155275412516201

=×+×= e ¬kNþalElVg¦ mmyb 367155522155 =−=−=



EdlvaEk,rnwg mm364 Edl)ansn μt;. RbsinebIebIeKdak; tendon BIrenAcm¶ay mm75 BI tendon EdlenAxageRkam enaHcm¶ayBI)atkøayeTACa

( ) mm1583252250212516201

=×+×+× enaHcMNakp©itnwgkøayeTACa mm364158522 =− Edles μ IweTAnwgcMNakp©itEdl)ansnμt;. Ca karGnuvtþ eKdak; tendon TaMgGs;edaymanKMlatBIKña mm50 .

b. elIkEt tendon EdlenAkNþalcMnYn 12 [egIbeLIg. karBRgay tendon enAmuxkat;xagcug RtUv)anbgðajenAkñúgrUbTI 19>6 a. RtYtBinitücMNakp©itrbs; tendon edayKitm:Um:g;eFobTI RbCMuTm¶n;rbs;muxkat;ebtugsRmab; tendon 12 enAxagelI nig tendon 8 eTotEdlRtUv)andak; enAxageRkam³

( ) mme 10226123648201

=×−×= témø e enHtUc nigRKb;RKan;. cMNakp©itCak;EsþgenAcm¶ay m9.0 BImuxkat;xagcug ( ) mme 761010364

8.49.0

=+−= cMNakp©itCak;EsþgenAcm¶ay m4.2 BImuxkat;xagcugKW ( ) mme 1871010364

21

=+−= %> témøkMNt;rbs; iF ³ témørbs; iF EdleRbIsRmab;karKNnaBIxagelIKW kNFi 1606= .

RtYtBinitü iF Gb,brmaedayeRbIsmIkar 19.31: ( )

( ) ( )⎥⎦

⎤⎢⎣

⎡−−+⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+= bti

ttLD

tbi AKfAKfMM

KKF

ηηη111

min

( )

( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

×⋅×−

⋅×−

⋅+⋅⎟

⎠⎞

⎜⎝⎛ −

+=

−

6.2351025.2332.1

837.08.2141025.2396.2

837.0106.755106.1501

837.01

8.2146.23510

4

4663

kN8.1516=

vamantémøtUcCag iF EdleRbI. RtYtBinitü iF GtibrmaedayeRbIsmIkar 19.32: ( ) ⎥

⎦

⎤⎢⎣

⎡++−⎟⎟

⎠

⎞⎜⎜⎝

⎛−

+= tci

bcLD

tbi AKfAKfMM

KKF

ηηη111

max



( )

( )

( ) ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅+

⋅+

⋅−⋅⎟

⎠⎞

⎜⎝⎛ −

+=

−

8.2141025.238.16

837.06.2351025.2375.15

837.0106.755106.150

837.011

8.2146.23510

4

4663

kN9.2081= vamantémøFMCag iF EdleRbI. dUcenHmuxkat;eRKaHfñak;enAkNþalElVgKWRKb;RKan;. ^> RtYtBinitükMhatbg;eRbkugRtaMg edayeyIgman MPaFo 1200= nig 21394mmAps =

kmøaMg oF srub kN8.16721013941200 3 =××= − MPaEc 27600=

25.727600200000

===c

sEEn yk 7=n

DM enAkNþalElVg mkN.6.150= ( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++

×+=

Ie

AnA

LDfnAFF

ps

cpsoi 211

32..

témørbs; cf Edl)anBIkarBRgaybnÞúkefrRtUvKuNnwg 3/2 edIm,IbgðajBIbERmbRmYlrag)a:ra: bUl rbs;kugRtaMgbnÞúkefrtambeNþayFñwm Edlpþl;[nUvtémøRbhak;RbEhlrbs; iF )an RbesIrCag.

a. kMNt;témømFümrbs; 2e EdlTTYlenAkñúgFñwm. ExSekagtMNag[ 2e RtUv)anbgðajenAkñúgrUb TI 19>6 c³

2e ¬mFüm¦ ( ) ( ) ( )

( ) ⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

×+

×+×+×=

1324964.2

9.3126720319.357769.05776

31

2.71

27.70414 mm= mme 265=

RkLaépÞrbs;)a:ra:bUlesμ InwgRkLaépÞrbs;ctuekaNEkg. b. kugRtaMgEdlbNþalBIbnÞúkefrenARtg;nIv:Urbs; tendon KW

( ) MPaLDfc 53.11010607.22656.150.. 6

10 =⋅×

=



dUcenH ( )

( )kNFi 1.157510

10607.27.70414

1025.231139471

3253.113947108.1672

3

104

3

=⎟⎠⎞

⎜⎝⎛

⋅+

⋅+

××+⋅= −

elastic loss KW %8.57.971.15758.1672 ==− kN . témøenHKWFMCag elastic loss Edl)an snμt; %4 .

elastic loss kñúgmYyÉktþaRkLaépÞEdk MPa70101394

7.97 3 ==

iF kñúgmYyÉktþaRkLaépÞ MPa1130101394

1.1575 3 == c. kMhatbg;GaRs½ynwgeBl

kMhat;bg;edaysarkarrYmmaDebtug MPa60= ¬dUcelIkmun¦ kMhatbg;edaysar creep elastic strain ( )

434 1045.210

276001025.231.1575 −⋅=

⋅==

cc

iEA

F

( )scrcs ECf ε=Δ yk 5.1=cC enaH ( ) MPafs 5.732000001045.25.1 4 =⋅=Δ −

PaKrykMhatbg; %5.61130

5.73==

kMhatbg;edaysar relaxation rbs;EdkKW MPa48 ¬dUcelIkmun¦. kMhatbg;GaRs½ynwgeBl esμ Inwg MPa5.181485.7360 =++ ehIyPaKrykMhatbg;KW

%161130/5.181 = Edlman témøEk,rnwgtémøEdl)ansn μt; %7.15 . ( ) iii FFFF 84.016.01 =−==η 84.0=η

19>5> KNnaGgát;rgkarBt;begáag (Design of Flexural Members)

19>5>1> sBaØaNTUeTA (General) EpñkBIedIm)anbBa¢ak;fakugRtaMgenAsrésxagelIbMput nigsrésxageRkambMputénmuxkat;eRKaH

fñak;rbs;Ggát;ebtugeRbkugRtaMgminRtUvFMCagkugRtaMgGnuBaØatsRmab;RKb;krNITaMgGs; b¤dMNak;kalén kardak;bnÞúk. bEnßmBIelIlkçxNÐTaMgenH eKRtUvKNnaGgát;ebtugeRbkugRtaMgCamYynwgemKuNsuvtßi-



PaBRKb;RKan;edIm,IRbqaMgnwgkar)ak;. ACI Code tRmUv[m:Um:g;Edl)anBIbnÞúkemKuN uM minRtUvFM CagersIusþg;rgkarBt; nMφ énmuxkat;Edl)anKNna.

sRmab;krNI tension-controlled section, FñwmebtugeRbkugRtaMgcab;epþIm)ak;enAeBlEdlkug RtaMgEdkFMCag yield strength rbs;EdkEdleRbIenAkñúgmuxkat;ebtug. EdkeRbkugRtaMgersIusþg;nwgmin bgðajcMNuc yield c,as;las;dUcEdkFm μtaEdleRbIenAkñúgebtugGarem:eT. b:uEnþeRkamkarbEnßmbnÞúk strain enAkñúgEdkekIneLIgedayGRtay:agelOn ehIykar)ak;ekIteLIgenAeBl compressice strain Gtibrmarbs;ebtugmantémøes μ Inwg 003.0 ¬rUbTI 19>7¦.

EdnkMNt;sRmab;EdkBRgwgrbs;Ggát;rgkarBt;ebtugeRbkugRtaMgEdlGaRs½yeTAtam ACI

Code, Section 18.8 KWQrelI net tensile strain sRmab; tension-controlled, transition b¤ compression-controlled section edayeKarBtam ACI Code, Section 10.3



dUcEdl)anBnül;enAkñúgCMBUk 3. em KuNkat;bnßyersIusþg; φ RtUv)an[enAkñúgCMBUkTI 3 edayQrelI ACI Code, Section 9.3.

19>5>2> muxkat;ctuekaN (Rectangular Sections) eKGackMNt; Nominal moment capacity rbs;muxkat;ctuekaNdUcxageRkam ¬eyagtamrUb TI 19>7¦³ ⎟

⎠⎞

⎜⎝⎛ −=⎟

⎠⎞

⎜⎝⎛ −=

22adTadCM n (19.34)

Edl sps fAT = nig abfC c'85.0= . sRmab; TC = d

ff

bffA

ac

psp

c

psps

'85.0'85.0ρ

== (19.35|

EdlpleFobEdkeRbkugRtaMgKW bdApsp /=ρ ehIy psA nig psf CaRkLaépÞ nigkugRtaMgTajrbs; EdkeRbkugRtaMg. yk 132.0

'βρω ≤⎟⎟

⎠

⎞⎜⎜⎝

⎛=

c

pspp f

f

bnÞab;mk da p

85.0ω

= (19.36)

témø pω CakmøaMgenAkñúg tendon EdlRtUv)anvas;edaypÞal;. edIm,IFananUv tesion-controlled

behavior, ACI Code, Section 18.8.1 kMNt;fa pω minRtUvFMCag 132.0 β EdkRtUvKñanwg net tensile

strain 005.0=tε . cMNaMfa 85.01 =β sRmab; MPaf c 28' ≤ nwgkat;bnßyeday 05.0 sRmab;ral; MPa7 sRmab; MPafMPa c 56'28 << ehIyes μ Inwg 65.0 sRmab; MPaf c 56' > .

eKk¾Gacsresr ⎟⎠⎞

⎜⎝⎛ −=

2adfAM pspsn

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

c

psppspsn f

fdfAM

'7.11

ρ (19.37)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

7.11 p

pspsn dfAMω (19.38)

nig nu MM φ=



enAkúñgsmIkarBImun psf CakugRtaMgenAkñúgEdkeRbkugRtaMgenAeBl)ak;. eKminGackMNt;témø Cak;Esþgrbs; psf edaygayRsYleT. dUcenH ACI Code, Section 18.7.2 GnuBaØat[)a:n;RbmaN témø psf dUcxageRkam. sRmab; bonded tendons

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛×−=

c

pup

ppups f

fff

'1

1ρ

βγ (19.39)

sRmab; unbonded tendon enAkñúgGgát;EdlmanpleFobElVgelIkm<s;tUcCag b¤es μI 35

pyp

cseps ffff ≤⎟

⎟⎠

⎞⎜⎜⎝

⎛++=

ρ100'69 (19.40)

RbsinebI puse ff 5.0≥ nigRbsinebI psf sRmab; unbonded tendon minFMCag pyf b¤ MPafse 415+ . sRmab; unbonded tendon enAkñúgGgát;EdlmanpleFobElVgelIkm<s;FMCag 35

⎟⎟⎠

⎞⎜⎜⎝

⎛++=

p

cseps

fffρ300'69 (19.41)

b:uEnþminRtUvFMCag pyf b¤ MPafse 207+ Edl =pγ emKuNsRmab;RbePTrbs; tendon eRbkugRtaMg

55.0= sRmab; pupy ff / EdlmintUcCag 8.0 4.0= sRmab; pupy ff / EdlmintUcCag 85.0 28.0= sRmab; pupy ff / EdlmintUcCag 9.0

=puf ersIusþg;TajEdlkMNt;rbs;EdkeRbkugRtaMg =sef kugRtaMgRbsiT§PaBenAkñúgEdkeRbkugRtaMgeRkayeBlkMhatbg;TaMgGs; =pyf specified yield strength rbs;EdkeRbkugRtaMg enAkñúgkrNIEdl 132.0 βω >p FñwmebtugeRbkugRtaMgCa compression-controlled section. edIm,IFananUv ductile failure eKkMNt; pω RtwmtémøGtibrma 132.0 β . sRmab; 132.0 βω = nig

da 1377.0 β= eyIgTTYl)an ⎟

⎠⎞

⎜⎝⎛ −=

7.132.01 1βdfAM pspsn

( ) ( )1188.01 βρ −= dfbd psp ( ) 2

1188.01' bdf cp βω −= ( ) 22

11 '06.032.0 bdf cββ −= (19.42)



sRmab; MPaf c 35' = / 8.01 =β . enaH 22 09.1'22.0 bdbdfM cn == dUcKña/ sRmab; MPaf c 28' = / 2915.0 bdM n = nigsRmab; MPaf c 42' = / 2238.1 bdM n = 19>5>3> muxkat;Edlmansøab (Flanged Sections) sRmab;muxkat;mansøab (T- or I-section) RbsinebIkm<s;bøúk a sßitenAkñúgsøab eKnwgKitvaCa muxkat;ctuekaNEkg. RbsinebI a sßitenAkñúgRTnug enaHeKKitRTnugCamuxkat;ctuekaNEkgedayeRbI TTwgRTnug nigTTwgsøabEdlelIs ( )wbb − RtUv)anKitdUcKñanwgebtugGarem: T-section Edl)anBnül; enAkñúgCMBUk 3 nig4. eKGacKNna design moment strength rbs; flanged section dUcxageRkam ¬emIlrUbTI 19>7¦. 1nn MM = ¬ersIusþg;m:Um:g;rbs;RTnug¦ 2nM+ ¬ersIusþg;m:Um:g;rbs;søabEdlelIs¦ ⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ −=

22f

ppspfppspwnh

dfAadfAM (19.43)

nu MM φ= nig wc

pspw

bffA

a'85.0

=

Edl pfpspw AAA −= ( )[ ] psfwcpf fhbbfA /'85.0 −= =fh kRmas;rbs;søab cMNaMfaRkLaépÞEdkeRbkugRtaMgsrub psA EckecjCaBIrEpñk pwA nig pfA EdlbegáIt web

moment capacity nig flange moment capacity. sRmab;muxkat;Edlmansøab snÞsSn_EdkBRgwg (reinforcement index) pwω minRtUvFMCag 132.0 β sRmab; tension-controlled section Edl =⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

ps

w

pwpw f

fdb

A'

ω GRtaEdkRTnugeRbkugRtaMg ⎟⎟⎠

⎞⎜⎜⎝

⎛×

c

ps

ff

'

19>5>4> EdkBRgwgrgeRbkugRtaMg (Nonprestressed Reinforcement) kñúgkrNIxøH eKdak;EdkminrgeRbkugRtaMg sA enAkñúgtMbn;Tajrbs;Ggát;rgkarBt;ebtugeRbkug RtaMgCamYynwgEdkeRbkugRtaMg psA edIm,IbegáInersIusþg;m:Um:g; (moment strength) rbs;Fñwm. enAkñúg krNIenH Edksrub ¬ psA nig sA ¦ RtUv)anBicarNaenAkñúgkarviPaKm:Um:g;.



sRmab;muxkat;ctuekaNEdl manEdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMg eKKNna design

moment strength nMφ dUcxag eRkam³ ⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −=

22adfAadfAM ysppspsn (19.44)

Edl bf

fAfAa

c

yspsps

'85.0+

= / ehIy pd nig d Cacm¶ayBIsrésrgkarsgát;xageRkAbMputeTATIRbCMuTm¶n;

rbs;EdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMg erogKña. sRmab;muxkat;Edlmansøab ⎟⎟

⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −=

222f

ppspfssppspwnh

dfAadfAadfAM (19.45)

Edl pfpspw AAA −=

wc

yspsps

bffAfA

a'85.0+

=

sRmab;muxkat;ctuekaNEkgEdlmanEdkrgkarsgát; ehIym:Um:g;RtUv)anKiteFobnwgkmøaMg C ⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −+⎟

⎠⎞

⎜⎝⎛ −= '

2'

22dafAadfAadfAM ysysppspsn (19.46)

Edl bf

fAfAfAa

c

ysyspsps

'85.0'−+

=

smIkarenHmann½yEtenAeBlEdlEdkrgkarsgát; yield. lkçxNÐsRmab;Edkrgkarsgát; yield KW

⎟⎟⎠

⎞⎜⎜⎝

⎛

−≥⎟⎟

⎠

⎞⎜⎜⎝

⎛ −+

y

cysyspsps

fddf

bdfAfAfA

600600''85.0

'1β

RbsinebIeKminCYblkçxNÐenHeT enaHEdkrgkarsgát;min yield eT. enAkñúgkrNIenH eKGacecal sA' ¬yk 0' =sA ¦ b¤mü:ageTot eKGackMNt;kugRtaMgenAkñúg sA' edaykarviPaKTUeTA dUcEdlBnül;enAkñúg CMBUk 3. enAeBleKeRbIEdkrgeRbkugRtaMg nigEdkminrgeRbkugRtaMgenAkñúgmuxkat;dUcKña eKKYrGansmIkar 19.39 dUcxageRkam³

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+−= '

'1

1ωωρ

βγ

pc

pup

ppups d

dff

ff (ACI Code, Eq. 18.3) (19.47)

RbsinebIeKKitEdkrgkarsgát;TaMgGs; enAeBlKNna psf enaHtY ( ) 17.0'

'≥−+ ωωρ

pc

pup d

dff

nig pdd 15.0'≤



Edl d / 'd nig pd Cacm¶ayBIsrésrgkarsgát;xageRkAbMputeTATIRbCMuTm¶n;rbs;EdkTajEdlminrg eRbkugRtaMg Edkrgkarsgát; nigEdkrgeRbkugRtaMg erogKña. =pγ emKuNsRmab;RbePTrbs; tendon eRbkugRtaMg

55.0= sRmab; pupy ff / EdlmintUcCag 80.0 4.0= sRmab; pupy ff / EdlmintUcCag 85.0 28.0= sRmab; pupy ff / EdlmintUcCag 9.0

85.01 =β sRmab; MPaf c 28' ≤ nwgkat;bnßyeday 05.0 sRmab;ekIneLIg MPa7 rbs; cf ' Et 65.01 ≥β .

!> sRmab;muxkat;ctuekaNEkg ACI Cose,Section 18.8 kMNt;pleFobEdkdUcxageRkam ¬ 005.0≥tε sRmab; tension –controlled section¦³

132.0 βω ≤+p

p ddw

Edl ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

pspp f

f'

ρω nig bdAps

p =ρ ¬EdkrgeRbkugRtaMg¦

⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

ff'

ρω nig bdAs=ρ ¬EdkminrgeRbkugRtaMg¦

@> RbsinebIeKeRbIEdkFm μta sA' enAkñúgtMbn;sgát; enaHlkçxNÐkøayeTACa ( ) 132.0' βωωω ≤−+

pp d

d

Edl ( )cy ff '/'' ρω = nig bdA s /''=ρ . EdnkMNt;Edk (reinforcement limitation) mansar³sMxan;edIm,I Fana plastic failure rbs;FñwmebtugGarem:EdkmanEdktic.

#> sRmab;muxkat;mansøab RkLaépÞEdlcaM)ac;edIm,IbegáItersIusþg;rbs;RTnug pwA RtUv)aneRbI edIm,IRtYtBinitü reinforcement index.

pwω ¬RTnug¦ 132.0'

βρ ≤⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

pspw f

f

Edl dw

pwpw db

A=ρ

RbsinebIeKeRbIEdkminrgeRbkugRtaMg enaH reinforcement limitation KW ( ) 132.0' βωωω ≤−+ ww

pwpw d

d



Edl ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

w

sw f

fdb

A'

ω nig ⎟⎟⎠

⎞⎜⎜⎝

⎛=

c

y

w

sw f

fdb

A'

''ω

enAeBleKmineRbIEdkrgkarsgát; sA' enaH 0' =wω . kñúgkarKNna nigkarviPaKGgát; ebtugeRbkugRtaMgedayEpñk (partially prestressed concrete member) eKRtUvEtCYb lkçxNÐEdkxagelI.

sRmab;fñak; C énGgát;ebtugeRbkugRtaMgrgkarBt; Edl ct ff '> ¬muxkat;Edl eRbH¦ eKKYreRbI crack control provision EdlBnül;enAkñúgEpñk 6>7 . enAeBleRbIsmIkar 6.18 sRmab;KMlatGtibrma s / ACI Code, Section 18.4 kMNt;dUcxageRkam³ a. sRmab; tendon eRbIKMlat mms 17= . b. sRmab;bnSMénEdkminrgeRbkugRtaMg nig tonden eRbIKMlat mms 20= . c. sRmab; tendon eRbI psfΔ CMnYs[ sf Edl psfΔ CaPaBxusKñarvagkugRtaMgEdl

KNnaenAkñúg tendon eRbkugRtaMgeRkambnÞúkeFVIkaredayQrelImuxkat;eRbH nig decompression stress dcf enAkñúg tendon eRbkugRtaMg EdlRtUv)anKit[es μ InwgeRb kugRtaMgRbsiT§PaB (effective prestress) sef . cMNaMfa psfΔ minKYrelIsBI MPa250 . RbsinebIvaticCag b¤esμ Inwg MPa140 eKminGacGnuvtþKMlatEdlTamTareT.

eKGacsresrsmIkar 8.18 dUcxageRkam³

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟

⎟⎠

⎞⎜⎜⎝

⎛

Δ⎟⎠⎞

⎜⎝⎛= c

psC

fs 5.23700

32

19>6> m:Um:g;eRbH (Cracking Moment)

sñameRbHekItmanenAkñúgFñwmebtugeRbkugRtaMgenAeBlEdlkugRtaMgTajenAsrésEpñkxageRkAbMputrbs;muxkat;eRKaHfñak;esμ I b¤elIs modulus of rupture rbs;ebtug rf . eKGacsnμt;témørbs;

rf sRmab;ebtugTm¶n;Fm μta[es μ Inwg cf '62.0 . kugRtaMgenAsrésxageRkambMputrbs;FñwmTRm samBaØEdlbegáItedaykmøaMgeRbkugRtaMg nig cracking moment KW ( )

IyM

IyFe

AF bcrb

b +−−=σ enAeBlEdl crb ff '62.0==σ enaH cracking moment KW



( )⎟⎠⎞

⎜⎝⎛ ++=

IyFe

AFf

yIM b

cb

cr '62.0 (19.48)

kugRtaMgTajGtibrmaeRkayBIkMhatbg;KW cf '62.0 EdltMNag[ rf . enAkñúgkrNIenH Fñwmebtug eRbkugRtaMgenArkSamuxkat;minmansñameRbHeRkamGMeBIbnÞúkefr. edIm,IFanaPaBRKb;RKan;ersIusþg;Rb qaMgnwgsñameRbH ACI Code, Section 18.8.3 TamTarfa ultimate moment strength rbs;Ggát; nMφ y:agticRtUves μ Inwg moment cracking 1.2 dg. ]TahrN_ 19>5³ sRmab;Fñwmén]TahrN_ 19>4 cUrRtYtBinitü design strength nigtRmUvkarrbs; ACI

Code EdlRbqaMgnwg cracking moment. dMeNaHRsay³ !> RtYtBinitüemIlfakm<s;bøúkkugRtaMg a sßitenAkñúgsøabb¤Gt;.

bffA

ac

psps

'85.0= (19.35)

psA ¬én 20 tendon Edl tendon mYy²manGgát;p©it mm125.11 ¦= 21394mm yk 85.0/ =upy ff / 4.0=pρ nig 5.08.0/4.0/ 1 ==βγ p . sRmab; bonded tension ⎟⎟

⎠

⎞⎜⎜⎝

⎛×−=

c

pdp

ppups f

fff

'1

1ρ

βγ (19.39)

mmd 8421581000 =−= 31068.3

8424501394 −⋅=×

==bdAps

pρ edayeK[ MPaf pu 1725= ( ) MPaf ps 6.1568

3517251068.35.011725 3 =⎥⎦

⎤⎢⎣⎡ ⋅−= −

( )( ) mma 3.163

4503585.06.15681394

==

edayvamantémøFMCakRmas;søab mm150 . dUcenH muxkat;enHeFVIkarCamuxkat;mansøab. @> sRmab;muxkat;mansøab

⎟⎟⎠

⎞⎜⎜⎝

⎛−+⎟

⎠⎞

⎜⎝⎛ −=

22f

pspfpspwnh

dfAadfAM

Edl pfpspw AAA −= ( )[ ]fwc

pspf hbbf

fA −= '85.01



( )( )[ ] 25.8531501504503585.06.1568

1 mm=−= 25.5405.8531394 mmApw =−= ( )

( ) mmbf

fAa

wc

pspw 1901503585.0

6.15685.540'85.0

===

( ) ( ) mkNM n .2.1660102

1508426.15685.85310

2190

8426.15685.540 66 =⎟⎠

⎞⎜⎝

⎛−+⎟

⎠

⎞⎜⎝

⎛−= −−

( ) mkNM n .2.14942.16609.0 ==φ RtYtBinitü reinforcement index sRmab;muxkat;mansøab 31028.4

8421505.540 −⋅=

×==

dbA

w

pwpwρ

256.08.032.032.0' 1 =×=≤= βρωc

pspwpw f

f ¬ 9.0=φ ¦

#> KNnam:Um:g;emKuNxageRkAEdl)anBIbnÞúkefr nigGefr bnÞúkefr = Tm¶n;pÞal; + bnÞúkefrbEnßm

mkN.96.1815.1381.5 =+= bnÞúkGefr mkN /16= LDU 6.12.1 +=

[ ] mkNMu .3.1253166.196.182.184.14 2

=×+×= m:Um:g;emKuNxageRkAenHmantémøtUcCag ultimate moment capacity rbs;muxkat; mkN.2.1494 dUcenHmuxkat;enHRKb;RKan;.

$> cracking moment ¬smIkar !(>$*¦ KW ( ) ⎟

⎠⎞

⎜⎝⎛ ++=

IyFe

AFf

yIM b

cb

cr '62.0

BI]TahrN_ 19>4 kNF 1344= / 241025.23 mmA ⋅= / mme 364= / mmyb 522= / 41010607.2 mmI ⋅= / MPaf c 35' = nig MPaf c 67.3'62.0 =

( ) 610

34

31010

10607.2522364101344

1025.2310134467.3

52210607.2 −

⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅×⋅+

⋅⋅

+⋅

=crM

mkN.2.961= RtYtBinitüemIlfa ncr MM φ≤2.1 ( ) mkNM cr .4.11532.9612.12.1 ==



témøenHKWtUcCag mkNM n .2.1494=φ . dUcenH FñwmenHRKb;RKan;kñúgkarTb;nwgkareRbH.

19>7> PaBdab (Deflection)

PaBdabrbs;cMNucmYyenAelIFñwmCabMlas;TIsrubrbs;cMNucenaH eTaHCaeLIgelI b¤cuHeRkam EdlbNþalBIkarGnuvtþrbs;bnÞúkenAelIFñwmenaH. enAkñúgFñwmebtugeRbkugRtaMgEdlRTedayTRmsamBaØ CaTU eTAkmøaMgeRbkugRtaMgRtUv)aneKGnuvtþenABIeRkamTIRbCMuTm¶n;rbs;muxkat; EdlbegáItCaPaBdabeLIg elI EdleK[eQ μaHfa camber. Tm¶n;pÞal;rbs;Fñwm nigbnÞúkTMnajxageRkAEdlmanGMeBIenAelIFñwmnwg eFVI[manPaBdabcuHeRkam. Net deflection CaplbUkBiCKNiténPaBdabTaMgBIr. enAkñúgkarKNnaPaBdab eKcaM)ac;RtUvBicarNaTaMgPaBdabry³eBlxøI(short-term deflection) b¤PaBdabPøam² (immediate deflection) nigPaBdabry³eBlyUr (long-term deflection). edIm,IFa na[eRKOgbgÁúMGaceFVIkareTA)an PaBdabry³eBlxøIGtibrma nigPaBdabry³eBlEvgGtibrmaenARKb; dMNak;kalénkardak;bnÞúkEdlmanlkçN³eRKaHfñak;TaMgGs;minRtUvFMCagtMénkMNt;Edl)ankMNt; eday ACI Code ¬emIlEpñk 6>3¦. eKGacKNnaPaBdabrbs;Ggát;ebtugeRbkugRtaMgedaysmIkarPaBdabsþg;dar b¤eday con-

ventional method EdlmanenAkñúgesovePAviPaKeRKOgbgÁúM. ]TahrN_ PaBdabenAkNþalElVgrbs; FñwmTRmsamBaØEdlrgbnÞúkTMnajBRgayesμ I w esμ Inwg EIwL 384/5 4 . m:UDuleGLasÞicrbs;ebtugKW

ccc ffwE '4780'043.0 5.1 == sRmab;ebtugTm¶n;Fm μta. eKKNnam:Um:g;niclPaBrbs;muxkat;ebtug I edayQrelIlkçN³rbs; gross section sRmab; FñwmEdlKμansñameRbH. eKGaceRbIkrNIenH)anenAeBlEdlkugRtaMgTajGtibrmaenAelIsrésxageRkA bMputrbs;ebtugminelIs modulus of rupture rbs;ebtug cr ff '62.0= ¬Fñwmfñak; U ¦. enAeBl EdlkugRtaMgTajGtibrmaenAelIsrésxagelIrbs; gross section FMCag cf '62.0 eKRtUveRbIm:Um:g; niclPaBRbsiT§PaB (effective moment of inertia) eI EdlQrelImuxkat;EdlmansñameRbH b¤Gt; mansñameRbH dUcEdl)anBnül;enAkñúgCMBUk 6 ¬Fñwmfñak; T nig C ¦. PaBdabkNþalE;lVgsRmab; FñwmTRmsamBaØEdlbNþalBIbnÞúkTMnaj nigkmøaMgeRbkugRtaMgRtUv)anbgðajenAkñúgtarag 19>3.



]TahrN_ 19>6³ sRmab;FñwmenAkñúg]TahrN_ 19>4 cUrKNna camber enAeBlepÞr nigbnÞab;mk KNnaPaBdabPøam²EdlrMBwgTukcugeRkayEdlrgbnÞúkeFVIkar. dMeNaHRsay³ !> PaBdabenAeBlepÞr

a. KNnaPaBdabcuHeRkamEdlbNþalBIbnÞúkefrenAeBlepÞr ¬kñúgkrNIenHbnÞúkefrCabnÞúkpÞal;¦ sRmab;FñwmTRmsamBaØEdlrgbnÞúkBRgayesμ I DΔ ¬bnÞúkefr¦

EIwL

3845 4

= BI]TahrN_ 19>4/ mkNwD /81.5= / mL 4.14= / MPaEci 24800= nig

41010607.2 mmI ⋅= ( )

( )mmD 5

10607.2248003841440081.55

10

4=

⋅=Δ ¬cuHeRkam¦

b. KNna camber EdlbNþalBIkmøaMgeRbkugRtaMg sRmab;FñwmTRmsamBaØEdleKelIk tendon xøHenAcMNucmYyPaKbI CamYynwgcMNakp©itenAcMENkmYyPaKbIkNþalFñwm mme 3641 = nigenAcugFñwm 02 =e . ( )

IELeF

ci

ip 216

23 21=Δ

( )( )

mm2010607.224800216

144003641016062310

23−=

⋅×⋅

= ¬eLIgelI¦

Camber cugeRkayenAeBlepÞrKW mm15520 −=+− ¬eLIgelI¦ c. PaBdabeRkambnÞúkeFVIkar

bnÞúkeFVIkarBRgayesμ IsrubKW mkNWT /351615.1381.5 =++= nig MPaEc 27600= . PaBdabcuHeRkamEdlbNþalBI TW KW ( )

( )mm

IELW

c

Tw 27

10607.22760038414400355

3845

10

44=

⋅==Δ ¬cuHeRkam¦

Camber EdlekItBIkmøaMgeRbkugRtaMg kNF 1344= nig MPaEc 27600= KW ( )

( )mmp 15

10607.2276002161440036410134423

10

23−=

⋅×⋅

=Δ ¬eLIgelI¦

PaBdabPøam²cugeRkayeRkambnÞúkeFVIkarKW mmpw 121527 =−=Δ−Δ=Δ ¬cuHeRkam¦



19>8> KNnasRmab;kmøaMgkat;TTwg (Design for Shear)

viFIKNnaedIm,IkMNt;EdkkmøaMgTTwg (shear reinforcement) enAkñúgFñwmebtugeRbkugRtaMgesÞIr EtdUcKñanwgviFIKNnasRmab;FñwmebtugGarem:. eKsnμt;sñameRbHedaysarkmøaMgkat;TTwg (shear

crack) ekIteLIgtammMu o45 edayvas;BIG½kSrbs;Fñwm. CaTUeTA TRmg;énsñameRbHEdlTak;TgnwgkmøaMg kat;TTwgcMnYnBIrRbePT. mYyRbePTKWbNþalBI\T§iBlEdlrYmpSMénkarBt; nigkmøaMgkat;TTwg³



sñameRbHcab; epþImeLIgedaysñameRbHedaykarBt; ehIybnÞab;mksñameRbHenHcab;epþImgak ehIy raltamTiseRTt EdlbNþalBI\T§iBlénkmøaMgTajGgát;RTUg. RbePTTIBIrCa web-shear cracking ekItmanenAkñúgFñwm EdlkugRtaMgTajem b¤kugRtaMgTajGgát;RTUg (principal tensile stress) enAkñúg RTnugd¾tUcrbs;vamantémøFMebIeRbobeFobnwgkugRtaMgBt;. eKRtUveRbIEdkkgedIm,IFana principal

tensile stress enAkñúgkrNI TaMgBIr. eyIgnwgeRbIlkçNvinicä½ykñúgkarKNnarbs; ACI sRmab;kmøaMg kat;TTwg. 19>8>1> viFIcMbg (Basic Approach) ACI design approach QrelItRmUvkarersIusþg;cugeRkay (ultimate strength requirement) edayeRbIemKuNbnÞúkEdl)anbgðajenAkñúgCMBUk 3. enAeBlEdlkmøaMgkat;TTwgemKuN uV FMCagBak; kNþalén nominal shear strength ( 2/cVφ ) eKmindak;EdkkgeT. . kmøaMgkat;TTwgKNnaEdlRtUv kar uV enARtg;muxkat;nImYy²minRtUvFMCag nominal design strength nVφ rbs;muxkat;EdlQrelI nominal shear capacity Edl)anBIkarbUkpSMénebtug nigEdkRTnug. ( )scnu VVVV +≤≤ φφ (19.49) Edl =cV nominal shear strength rbs;ebtug =sV nominal shear capacity rbs;Edk =φ emKuNkat;bnßyersIusþg; 75.0= enAeBlEdlkmøaMgkat;emKuN uV tUcCag 2/uVφ eKRtUvkardak;EdkkmøaMgkat;Gb,brma. 19>8>2> ersIusþg;kmøaMgkat;Edlpþl;edayebtug

Shear Strength Provided by Concrete ACI Code, Section 11.4 bgðajsmIkary:agsamBaØEdl)anBIkarBiesaFedIm,I)a:n;RbmaN nominal shear capacity rbs;Ggát;ebtugeRbkugRtaMg EdlenAkñúgGgát;enaH tendon mankmøaMgeRb kugRtaMg sef y:agtic %40 ersIusþg;Taj puf ³ db

MdVfV wu

ucc ⎟⎟

⎠

⎞⎜⎜⎝

⎛+= 8.4'05.0 (ACI Code, Eq. 11.9) (19.50)

Edl uV nig =uM kmøaMgkat;emKuN nigm:Um:g;emKuNenARtg;muxkat;EdlBicarNa =wb TTwgrbs;RTnug



d ¬kñúgtY u

uM

dV ¦=cm¶ayBIsrésrgkarsgát;eTATIRbCMuTm¶n;rbs;EdkeRbkugRtaMg

d ¬enAkñúgsmIkar ciV b¤ cwV ¦ =témøEdlFMCageKkñúgcMeNam d xagelI nig h8.0 (ACI Code, Section 11.4.2)

kareRbIsmIkar 19.50 RtUv)ankMNt;tamlkçxNÐxageRkam³ !> 0.1/ ≤uu MdV ¬edIm,IKittémøtUcén uV nig uM ¦ @> ( ) dbfV wcc '17.0≥ ¬ cV Gb,brma¦ #> ( ) dbfV wcc '42.0≤ ¬ cV Gtibrma¦

karERbRbYlén shear capacity rbs;ebtugsRmab;FñwmebtugeRbkugRtaMgEdlRTedayTRmsamBaØrgnUv bnÞúk BRgayesμ IRtUv)anbgðajenAkúñgrUbTI 19>8. cMNaMfa eKcaM)ac;dak;EdkkmøaMgkat;GtibrmaEk,rTRm nig Ek,rcMNucmYyPaKbYnénElVgEdl sVφ manxiteTArktémøGtibrma. pÞúymkvij FñwmebtugGarem: RtUvkar EdkkmøaMgkat;TTwg ¬b¤KMlatGb,brma¦ EtEk,rTRmEdl sVφ mantémøGtibrma.



eBlxøH témø cV EdlKNnaedaysmIkar 19.50 GacmantémøtUc dUcenH ACI Code, Section

11.4.2 [nUvviFImü:ageTotsRmab;KNna cV EdlKitBicarNaersIusþg;bEnßmrbs;ebtugenAkñúgmuxkat;. enAkñúgviFIenH cV CatémøEdltUcCageKkñúgcMeNamersIusþg;kmøaMgkat;rbs;ebtug ciV nig cwV ¬rUbTI 19>8¦. ersIusþg;kmøaMgkat; ciV RtUv)anQrelIkarsnμt;fa flexural-shear cracking ekIteLIgEk,rEpñk q¶aybMputrbs; flexural cracking EdlenAcm¶ayRbEhl 2/d BIcMNucrgbnÞúkénkarfycuHm:Um:g;. ACI Code kMNt;fa ciV RtUv)anKNnadUcxageRkam³ ( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛++=

max'05.0

MMVVdbfV cri

dwcci (19.51)

b:uEnþvaminRtUvtUcCag ( ) dbf wc'14.0 Edl =dV kmøaMgkat;TTwgEdlbNþalBIbnÞúkefrKμanemKuN

=iV kmøaMgkat;TTwgemKuNEdlbNþalBIbnÞúkEdlGnuvtþBIxageRkA EdlekItmandMNalKña CamYynwg maxM =maxM m:Um:g;emKuNGtibrmabNþalBIbnÞúkEdlGnuvtþxageRkA

=crM m:Um:g;eRbH (cracking moment) eKGackMNt; cracking moment BIsmIkarxageRkam³ ( )dpec

tcr fff

yIM −+= '5.0 (ACI Code, Eq. 11.11) (19.52)

Edl =I m:Um:g;niclPaBEdlTb;Tl;nwgbnÞúkemKuNxageRkA =ty cm¶ayBIG½kSTIRbCMuTm¶n;én gross section EdlminKitsrésEdkeTAsrésrgkarTajeRkA

bMput =pef ersIusþg;rgkarsgát;enAsrésxageRkAbMputrbs;muxkat;ebtugedaysarkmøaMgeRbkug RtaMgeRkaykMhatbg;

=df kugRtaMgEdlbNþalBIbnÞúkefrKμanemKuNenAsrésxageRkAbMput EdlkugRtaMgTaj bNþalBIbnÞúkxageRkA

Web-shear strength cwV KWQrelIsñameRbHedaykmøaMgkat;TTwgenAkñúgFñwmEdlminEmneRbH edaysarkarBt;eT. sñameRbHEbbenHekItmanenAEk,rTRmEdlmanRTnugtUc. ACI Code, Section

11.4.2 bBa¢ak;fa cwV RtUv)anKNnatamsmIkarxageRkam³



( ) pwpcccw VdbffV ++= 3.0'29.0 (19.53) Edl =pV bgÁMúkM;laMgeRbkugRtaMgbBaÄrenARtg;muxkat;EdlBicarNa

=pcf kugRtaMgsgát;enAkñúgebtug ¬eRkaykarGnuBaØatsRmab;kMhatbg;eRbkugRtaMg¦ enARtg;TI RbCMuTm¶n;rbs;muxkat;EdlTb;Tl;nwgbnÞúkEdlGnuvtþ b¤enARtg;TIRbsBVrvagRTnug nig søabenAeBlEdlTIRbCMuTm¶n;sßitenAkñúgsøab

müa:gvijeTot eKGackMNt; cwV CakmøaMgkat;EdlbegáItkugRtaMgTajem (principle tensile

stress) cf '33.0 enARtg;G½kSTIRbCMuTm¶n;rbs;Ggát; b¤Rtg;RbsBVénsøab nigRTnugenAeBlEdlTIRbCMu TMgn;sßitenAkñúgsøab. eKGacsresrsmIkarG½kSdUcxageRkam³

22

'33.02

2 pcpccwct

ffvff −⎟⎟

⎠

⎞⎜⎜⎝

⎛+==

b¤ dbf

ffV w

t

pctcw ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛+= 1 (19.54)

Edl ct ff '33.0= . enAeBlGnuvtþsmIkar 19.51 nig 19.53 b¤ 19.54 témørbs; d RtUv)anKitCa cm¶aycenøaHsrésrgkarsgát; nigTIRbCMuTm¶n;rbs; tendon eRbkugRtaMg b:uEnþvaminRtUvtUcCag h8.0 . muxkat;eRKaHfñak;sRmab;kmøaMgkat;GtibrmaRtUv)anykRtg; 2/h BIépÞrbs;TRm. eKRtUveRbI EdkkmøaMgkat;dUcKñaRtg;muxkat;cenøaHTRm nigmuxkat;Rtg; 2/h .

19>8>3> EdkkmøaMgkat; (Shear Reinforcement) eKRtUvKNnatémø sV edIm,IkMNt;RkLaépÞcaM)ac;rbs;EdkkmøaMgkat; ( )scu VVV += φ (19.49) ( )cus VVV φ

φ−=

1 (19.55)

sRmab;EdkkgbBaÄr

sdfA

V yvs = (19.56)

nig dfsVA

y

sv = b¤

s

yv

VdfA

s = (19.57)

Edl =vA RkLaépÞrbs;EdkkgbBaÄr nig =s KMlatrbs;Edkkg. smIkarsRmab;Edkkg eRTt dUcKñanwgsmIkarEdl)anbgðajenAkñúgCMBUk 8.



19>8>4> EdnkMNt; (Limitation)

!> KMlatGtibrma maxs rbs;EdkkgminRtUvFMCag 4/3h b¤ cm60 . RbsinebI sV FMCag ( ) dbf wc'4 enaHKMlatGtibrmaxagelIRtUv)ankat;bnßymkRtwmBak;kNþal (ACI Code, Section 11.5.4).

@> kmøaMgkat;Gtibrma sV minRtUvFMCag ( ) dbf wc'8 . RbsinebImindUcenaHeT eKRtUvbegáInTMhM rbs;muxkat; (ACI Code, Section 11.5.6).

#> EdkkmøaMgkat;Gb,brma vA EdlTamTareday ACI Code KW

⎟⎟⎠

⎞⎜⎜⎝

⎛≤=

y

wc

y

wv f

sbff

sbA '062.035.0min (19.58)

enAeBlEdlkmøaMgeRbkugRtaMgRbsiT§PaB pupe ff 4.0≥ EdkkmøaMgkat;Gb,brma vA Kw

wy

pupsv b

ddf

sfAA

80= (19.59)

eKmincaM)ac;ykkm<s;RbsiT§PaB hd 8.0< eT. CaTUeTA smIkar 19.59 pþl;[nUvEdkkmøaMg kat;Gb,brmaFMCagkarpþl;[edaysmIkar 19.58.

]TahrN_ 19>7³ sRmab;FñwmenAkñúg]TahrN_ 19>4 cUrkMNt; nominal shear strength nigEdkkmøaMg kat;caM)ac;. RtYtBinitümuxkat;Rtg; 2/h nig m3 BIcugrbs;Fñwm. eRbI MPaf y 400= sRmab;Edk kmøaMgkat; nigbnÞúkGefr mkN /4.19= . dMeNaHRsay³ !> sRmab;muxkat;enARtg; 2/h mmh 500

21000

2== BIxagcug

@> bnÞúkBRgayesμ IemKuNenAelIFñwm ( ) mkNWu /8.534.196.115.1381.52.1 =×++= uV enAcm¶ay ( ) kNh 5.3605.02.78.53

2=−=

kMNt; uM enARtg;muxkat; 2/h ( ) mkNMu .187

25.08.535.02.78.53

2=−=

témørbs; d Rtg;muxkat; 2/h BIxagcug ¬rUbTI 19>6 b¦ KW



( ) ( ) mmd 5163648.4

5.08.41581000 =−

−−= 0.1995.0

187516.05.360

≤=×

=u

uM

dV

dUckarTamTarrbs; ACI Code db

MdVfV wu

ucc ⎟⎟

⎠

⎞⎜⎜⎝

⎛+= 8.4'05.0

( ) kN6.39210516150995.08.43505.0 3 =×××+= − témøGb,brmarbs; ( ) kNdbfV wcc 8.77105161503517.0'17.0 3 =⋅== − témøGtibrmarbs; ( ) kNdbfV wcc 3.192105161503542.0'42.0 3 =⋅== − témøGtibrmarbs; kNVc 3.192= manlkçN³lub.

#> viFIepSgeTotEdlbgðajeday ACI Code KWfaeKGacyktémø cV CatémøtUcCageKkñúgcMeNam ciV nig cwV a. edayQrelI flexural-shear cracking strength

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++=

max'05.0

MMVVdbfV cri

dwcci

KNnatYnImYy²dac;edayELkBIKña ( ) ( ) kNdbf wc 9.22105161503505.0'05.0 3 =⋅= − =dV kmøaMgkat;efrK μanemKuN ( )( ) kN4.1295.02.715.1381.5 =−+= =maxM m:Um:g;emKuNGtibrma ¬elIkElgTm¶n;rbs;Fñwm¦ bnÞúkemKuN mkN /8.464.196.115.132.1 =×+×= mkNM .6.162

25.05.02.78.46

2

max =⎥⎥⎦

⎤

⎢⎢⎣

⎡−×=

( ) kNVi 6.3135.02.78.46 =−= ( )dpec

tcr fff

yIM ++= '5.0

41010607.2 mmI ⋅= / mmyb 522= =pef kugRtaMgrgkarsgát;EdlbNþalBIkmøaMgeRbkugRtaMg

IFey

AF b+=

MPa8.610607.2

522381013441025.23101344

10

3

4

3=

⋅××⋅

+⋅⋅

=



=df kugRtaMgbnÞúkefrI

yM bD=

mkNM D .9.6525.05.02.796.18

2=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−×=

( ) MPafd 32.110607.2

105229.6510

6=

⋅⋅

=

( ) mkNM cr .4.4121032.18.6355.0522

10607.2 610

=⋅−+⋅

= − dUcenH kNVci 7.947

6.1624.4126.3134.1299.22 =++=

ciV minRtUvtUcCag ( ) ( ) kNdbf wc 1.64105161503514.0'14.0 3 =⋅= − b. ersIusþg;kmøaMgkat;EdlQrelI web-shear cracking KW

( ) pwpcccw VdbffV ++= 3.0'29.0 MPaf pc 78.5

1025.23101344

4

3=

⋅⋅

= mmd 516= b¤ mmh 8008.0 =

yk mmd 800= kNVp 8.101

2.1311344 =×=

Edl =2.13/1 slop rbs; tendon profile 4800/364= MPa72.13529.0 = dUcenH ( ) kNVcw 3.5168.1011080015078.53.072.1 3 =+⋅×××+= −

c. edaysar cicw VV < dUcenH kNVcw 3.516= Ca nominal shear strength enARtg;muxkat; 2/h BIcugrbs;Fñwm. kñúgkrNICaeRcIn cwV lubRtg; 2/h BITRm.

$> EdkRTnug (web reinforcement) kNVu 5.360= kNVcw 2.3873.51675.0 =×=φ edaysar cwu VV φ< / 0=sV dUcenHeRbIEdkkgGb,brma. eRbIEdkkg 10DB . 22 1574/102 mmAv =×= π KMlatGtibrmaCatémøEdltUcCageKkñúgcMeNam mmhs 750

43

1 == mms 6002 = KNna 3s BIsmIkarEdkRTnugGb,brma



wy

pupsv b

dds

ffA

A ×××=80min

150516

5164001725

801394157 3s

××= mms 5813 = yk mms 5003 =

müa:gvijeTot ⎟⎟⎠

⎞⎜⎜⎝

⎛≤=

y

wc

y

wv f

sbff

sbA '062.035.0min 367.0'062.0 =cf

mmb

fAs

w

yv 1140150367.0

400157367.04 =

××

==

dUcenHeyIgeRbI 500@10DB . %> sRmab;muxkat;enAcm¶ay m3 BIxagcug viFIsaRsþkñúgkarKNnaKWRsedogKñasRmab;muxkat;enARtg;

2/h . edayeRbIviFIEdlsRmYlrbs; ACI ( ) kNVu 22632.78.53 =−= mkNMu .920

2332.78.53

2=

⎥⎥⎦

⎤

⎢⎢⎣

⎡−×=

( ) ( ) mmd 7053648.4

38.41581000 =−

−−= 0.1173.0

920705.0226

<=×

=u

uM

dV

( ) kNdbM

dVfV wu

ucc 1.11910705150173.08.43505.08.4'05.0 3 =×××+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+= −

kNVc 8.77min = nig kNVc 3.192max = dUcenH kNVc 1.119= ¬lub¦ ^> eRbIsmIkar ACI Code edIm,IKNna ciV nig cwV . dMbUgKNna ciV ¬EdllubsRmab;muxkat;enH¦ ( ) ( ) kNdbf wc 3.31107051503505.0'05.0 3 =⋅= − =dV ( )( ) kN6.7932.715.1381.5 =−+ mkNM .3.800

2332.78.46

2

max =⎥⎥⎦

⎤

⎢⎢⎣

⎡−×=

( ) kNVi 6.19632.78.46 =−= MPaf pe 9.11

10607.25225.227101344

1025.23101344

10

3

4

3=

⋅××⋅

+⋅⋅

=



mkNM D .2.3242

332.796.182

=⎥⎥⎦

⎤

⎢⎢⎣

⎡−×=

( ) MPafd 5.610607.2

105222.32410

6=

⋅⋅

=

( ) mkNM cr .4.417105.69.11355.0522

10607.2 610

=⋅−+⋅

= − dUcenH kNVci 4.213

3.8004.4176.1966.793.31 =++=

=minciV ( ) ( ) kNdbf wc 6.87107051503514.0'14.0 3 =⋅= − dUcnH kNVci 4.213=

bnÞab;mkKNna cwV MPaf pc 78.5= kNVp 8.101= ¬dUcelIkmun¦

mmd 705= b¤ mmh 8008.0 = yk mmd 800=

dUcenH ( ) kNVcw 3.5168.1011080015078.53.072.1 3 =+⋅×××+= − témørbs; cwV minmaneRKaHfñak;eT. enARtg;mYyPaKbYnénRbEvgElVg témøkmøaMgkat;eRKaHfñak;KW

ciV ¬rUbTI 19>8¦. &> KNnaEdkRTnug

kNVu 226= kNVci 1604.21375.0 =×=φ ( )scu VVV += φ ( ) kNVs 88160226

75.01

=−= Edkkg 10DB / 2157mmAv = . RtYtBinitüKMlatGtibrma mms 500max = ¬dUcelIkmun¦ muxkat;EdlEdlRtUvkar 156

7054005001088 3

=××⋅

==dfsVA

y

sv

vA EdleRbIKW 22 156157 mmmm > . dUcenH yk 400@10DB .



19>9> KNnaCMhandMbUgénGgát;ebtugeRbmugRtaMgrgkarBt; Preliminary Design of Prestressed Concrete Flexural Members

19>9>1> rUbrag nigTMhM (Shapes and Dimensions)

kar)a:n;sμanTMhMrbs;muxkat;d¾RtwmRtUveFVI[karKNnacMNayeBltic nigmins μ úKsμaj. dUc enH karKNnaCMhandMbUgmansar³sMxan;Nas; edIm,IFanafaTMhMmuxkat;manlkçN³smrmümunnwgcab;epþIm KNnalMGit.

enAkñúgdMNak;kalKNnaCMhandMbUg CaFmμtaeKmanTinñn½yxøHEdlGacCYykñúgkareRCIserIsTMhM d¾smRsb. ]TahrN_ m:Um:g;Bt;Edl)anBIbnÞúkGnuvtþn_xageRkA kugRtaMgGnuBaØat nigTinñn½ysRmab; kMNt;kMhatbg;RtUv)andwg b¤RtUv)ankMNt;.

rUbragrbs;muxkat;Ggát;ebtugeRbkugRtaMgGacCactuekaNEkg GkSr T GkSr I b¤RbGb;. km<s; srubrbs;muxkat; h RtUv)ankMNt;edaykarBicarNakm<s;rbs;lMh b¤k¾minRtUv)ankMNt;. kareRCIs erIsTMhMrbs;muxkat;sRmab;karKNnaCMhandMbUgmandUcxageRkam ¬rUbTI 19>9¦³

!> km<s;srubénmuxkat;KW 20/1=h eTA 30/1 énRbEvgElVg. sRmab;karrgbnÞúkF¶n; 20/Lh =

nigsRmab;karrgbnÞúkRsal 30/Lh = b¤ LD MMh += 6.43 Edl h KitCa mm nig M KitCa mkN. .

@> kRmas;rbs;søabxagelIKW 8/hh f = eTA 6/h . #> TTwgrbs;søabxagelIKW 5/2hb ≥ . $> kRmas;rbs;RTnugKW mmbw 100≥ . CaTUeTA eKyk 10030/ += hbw .



%> kareRCIserIs wb nig t KWERbRbYleTAtamkarBRgay tendon eRbkugRtaMg edayeFVIy:agNa rkSakRmas;ebtugkarBarEdk.

^> RkLaépÞEdlsmrmürbs;muxkat;ebtugEdlRtUvkarKW

hMMmA LD

c 1450)( 2 += ¬Edl LD MM + KitCa mkN. nig h KitCa m ¦

sRmab;karKNnakñúgkarGnuvtþ nigkarKNnaEdlmanlkçN³esdækic© ]sSahkmμpliteRKOg sMNg;BIebtug)anbegáItnUvrUbrag nigTMhMbTdæanCaeRcIn EdlGñkKNnaGaceRCIserIsnUvGgát;NaEdl RtUvkar. taragénmuxkat;sþg;darmanenAkñúg PCI Design Handbook. AASTHO k¾)anENnaMnUv girder sþg;daredIm,IeRbIR)as;enAkñúgsMNg;s<an ¬tarag 19>4¦.

tarag 19>4 AASTHO Girders, ebtugTm¶n;Fm μta

RbePT A ( )2.in

I ( )4.in

by ( ).in

bZ ( )3.in

tZ ( )3.in

Tm¶n; ( )ftlb /

Type II 369 50979 15.83 3220 2527 384

Type III 560 125390 20.27 6186 5070 593

Type IV 789 260741 24.73 10544 8908 822

19>9>2> kmøaMgeRbkugRtaMg nigRkLaépÞEdk (Shapes and Dimensions)

enAeBlEdleKeRCIserIsrUbrag km<s; nigTMhMepSgeTotrbs;muxkat;rYcehIy eKGac)a:n;sμantM-élRbhak;RbEhlrbs;kmøaMgeRbkugRtaMg nigRkLaépÞrbs;EdkeRbkugRtaMg psA . BIm:Um:g; couple



xagkñúg m:Um:g;srub TM EdlekItBIbnÞúkefr nigbnÞúkGefreFVIkares μ InwgkmøaMgTaj T KuNnwgédXñas; jd .

( ) ( )jdCjdTMT == ( )jdfAM sepsT = ( )jdf

MAse

Tps =

Edl psA CaRkLaépÞEdkeRbkugRtaMg nig sef CakugRtaMgeRbkugRtaMgRbsiT§PaBeRkaykMhatbg;. témørbs;édXñas; jd ERbRbYlBI h4.0 eTA h8.0 EdlkñúgkarGnuvtþeKykvaenAkñúgcenøaH h6.0 eTA

h7.0 . eKGaceRbItémømFüm 65.0 )an. dUcenH ( ) se

Tps fh

MA65.0

= (19.60)

ehIykmøaMgeRbkugRtaMgKW

hMfATF T

seps 65.0=== (19.61)

kmøaMgeRbkugRtaMgenAeBlepÞrKW η/FFi = Edl η CaemKuNénkMhatbg;GaRs½ynwgeBl. kmøaMgsgát; C enAelImuxkat;esμ InwgkmøaMgTaj T ³ seps fATC == KitCakugRtaMg 1c

c

seps

cf

AfA

AC

==

Edl 1cf CakugRtaMgBRgayes μ IEdlsnμt;enAelImuxkat; sRmab;karKNnaCMhandMbUg eKsnμt;srésxageRkArbs;karEbgEckkugRtaMgragRtIekaNes μ Inwg kugRtaMgsgát;GnuBaØatGtibrma caf . dUcenHkugRtaMgmFümKW 15.0 cca ff = . kugRtaMgsgát;GnuBaØat enAkñúgebtugKW cca ff '45.0= . dUcenH eKGacsnμt;RkLaépÞebtugEdlRtUvkar cA BIkmøaMgTaj T dUc xageRkam³

c

seps

ca

seps

c

seps

cc f

fAffA

ffA

fTA

'225.05.011==== (19.62)

( )( ) c

T

ca

T

ca

T

cac f

Mf

Mfh

Mf

TA'15.033.05.065.05.0

==== (19.63)

karviPaKenHKWQrelIkarKNnasRmab;bnÞúkeFVIkar minEmnsRmab;bnÞúkemKuNeT. cMNakp©it e RtUv)an vas;BITIRbCMuTm¶n;rbs;muxkat;eTATIRbCMuTm¶n;rbs;EdkeRbkugRtaMg ehIyeKGacKNnaCatémøRbhak; RbEhl dUcxageRkam³



i

Db F

MKe += (19.64)

Edl bK Ca lower kern limit ehIy DM Cam:Um:g;Edl)anBIbnÞúkefrK μanemKuN.

19>10> kugRtaMgbøúkxagcug (End-Block Stresses)

19>10>1> Ggát;rgkugRtaMgTajmun (Pretensioned Members)

dUcKñanwgEdkenAkñúgGgát;ebtugGarem:EdlRtUvkarRbEvgbgáb;Cak;lak; enaHkmøaMgeRbkugRtaMg enAkñúgGgát;ebtugrgkugRtaMgmunRtUv)anepÞreTAebtugedaykarbgáb; b¤edaykarf<k;cug b¤edaybnSMTaMgBIr. enAkñúgGgát;rgkugRtaMgmun eKehARbEvgrbs;EdkeRbkugRtaMgEdlkmøaMgeRbkugRtaMgRtUv)anepÞreTAeb-tugfa RbEvgepÞr (transfer length) tl . eRkayeBlepÞr kugRtaMgenAkñúg tendon Rtg;cugbMputrbs;Ggát; es μ InwgsUnü b:uEnþkugRtaMgenARtg;cm¶ay tl BIcugGgát;es μ InwgkmøaMgeRbkugRtaMgRbsiT§PaB pef . transfer

length tl GaRs½ynwgTMhM nigRbePTrbs; tendon, lkçxNÐépÞb:H ersIusþg;ebtug cf ' kugRtaMg nigviFIén karepÞrkmøaMg. kar)a:n;RbmaN tl EdlGacTTYlyk)anKWes μ Inwg 50dgénGgát;p©itrbs; tendon b:uEnþ sRmab; single wires eKyk tl esμ Inwg 100dgénGgát;p©itrbs; wire. edIm,I[kmøaMgTajenAkñúgEdkeRbkugRtaMgbegáIt ultimate flexural strength eBjelj vaRtUv karnUvRbEvgcMNg (bond length). eKalbMNgKWedIm,IkarBarkarrGilTUeTAmunnwgkar)ak;rbs;Fñwm eRkam design strength eBjelj. RbEvgbgáb; dl (development length) es μ InwgplbUkrvag bond

length nig transfer length. edayEp¥kelIkarBiesaF ACI Code, Section 12.9.1 [nUvsmIkarxag eRkamsRmab;KNnaRbEvgbgáb;én three- or seven-wire pretensioning strand: esepsd dffl ⎟

⎠⎞

⎜⎝⎛ −=

32 (19.65)

Edl =psf kugRtaMgenAkñúgEdkeRbkugRtaMgeRkam nominal strength =sef kugRtaMgRbsiT§PaBenAkñúgEdkeRbkugRtaMgeRkaykMhatbg; =bd nominal diameter rbs; wire b¤ strand enAkñúg pretensioned member kugRtaMgTajx<s;manenAtMbn;xagcug EdleKRtUvkardak;EdkBiess. EdkenHmanTRmg;CaEdkkgbBaÄrehIyRtUv)anBRgayesμ IkñúgKMlat 5/h Edlvas;BIxagcugrbs;Fñwm. CaTUeTA eKdak;EdkkgTImYyenAcm¶ay mm25 eTA mm75 BIxagcugFñwm. vaCaKarGnuvtþFm μtakñúgkar



bEnßm nominal reinforcement sRmab;cm¶ay d Edlvas;BIcugrbs;Fñwm. RkLaépÞrbs;EdkbBaÄr vA EdlRtUv)aneRbIenAtMbn;xagcugGacRtUv)anKNnaedaytémøRbhak;RbEhlBIsmIkarxageRkam³

tsa

iv lf

hFA 021.0= (19.66)

Edl =saf kugRtaMgGnuBaØatenAkñúgEdkkg ¬CaTUeTA MPa140 ¦ nig 50=dl dgénGgát; tendon

]TahrN_ 19>8³ kMNt;EdkkgcaM)ac;EdlRtUvkarenAtMbn;xagcugrbs;FñwmEdl[enAkñúg]TahrN_ 19>4. dMeNaHRsay³ kNFi 1606= / mmh 1000= / MPafsa 140= / mmlt 556125.1150 =×= dUcenH 2

3433

5561401000101606021.0 mmAv =

××⋅

= mmh 200

51000

5==

eRbIEdkkgbiTCit 10DB cMnYnbYnkg EdlEdkkgTImYysßitenAcm¶ay mm200 BITRm vA ¬Edldak;¦ 26284157 mm=×=

19>10>2> Ggát;rgkugRtaMgTajeRkay (Post-tensioned Members)

enAkñúg post-tensioned concrete member kmøaMgeRbkugRtaMgRtUv)anepÞrBI tendon ¬sRmab; bonded nig unbonded tendon¦ eTAebtugRtg;cugrbs;Ggát;eday special anchorage device. enA kñúg anchorage zone Rtg;cugrbs;Ggát; kugRtaMgsgát;mantémøx<s;Nas; ehIy transverse tensile stress ekItmandUcbgðajenAkñúgrUbTI 19>10. enAkñúgkarGnuvtþ eKeXIjfaRbEvgén anchorage zone minFMCagkm<s;rbs;cugGgát;eT RbsinebImindUcenaHeT sßanPaBénkugRtaMgenAkñúgtMbn;enaHnwgman lkçN³sμ úKs μaj.

karBRgaykugRtaMgEdl)anBI tendon mYyenAkñúg anchorage zone RtUv)anbgðajenAkñúgrUbTI 19>11. enARtg;cm¶ay h BImuxkat;xagcug eKsnμt;kugRtaMgBRgayesμ IelImuxkat;TaMgmUl. edayKit ExSkmøaMg (trajectories) CaFatumYy²EdlmanGMeBICa curved strut enaHExSkmøaMgmanGMeBItamTisedk eTArkExSG½kSrbs;FñwmenAkñúgtMbn; A edaybegáItCakugRtaMgsgát;. enAkñúgtMbn; B ExSkmøaMg)anbEgVr



Tis ehIy strut manGMeBIecjeRkAEdlbegáItCakugRtaMgTaj. enAkñúgtMbn; C strut esÞIrEtRtg;eday begáItkarBRgaykugRtaMgesμ I.



EdkBRgwgEdlRtUvkarsRmab; anchorage zone xagcugrbs; posttentioned member CaTU eTApSM eLIgedayRkLaénEdkbBaÄr nigEdkedkEdlmanKMlatCit²KñaeBjRbEvgénbøúkxagcugedIm,I Tb;Tl;nwgkugRtaMgpÞúH (bursting stress) nigkugRtaMgTaj. CakarGnuvtþTUeTAeKmin[KMlatEdkFMCag

mm75 enAkñúgTisnImYy²eT ehIyminRtUvdak;EdkenAcm¶ayFMCag mm50 BIépÞxagkñúgrbs; bearing

plate eT.


T.Chhay 702 Appendix

]bsm<½n§


]bsm<½n§ 703 T.Chhay













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Reinforced concrete (khmer).pdf

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