Beam Design

Beam Datawidth 230 mmdepth 300 mm d' 29 mm .= cc+ sdia + mdia/2

15 mm eff depth 271 mm .= d - d'

Material GradesConcrete 20 MPa

Steel 415 MPa

Moment 153 KN-m 9.06xumax 130 .= (700/(1100 * (0.87 * fy)) * dMulim 47 .= 0.36*fck*b*xumax*(d-(0.42*xumax))

2.76

Area of Steel Tension (Ast) Compr (Asc)Percentage Area of Steel

Tension Reinforcement Type Bar dia Nos Area of Steel

Layer 1 16 mm 5Layer 2 - 0Layer 3 - 0

Total Steel Provided

Compression ReinforcementType Bar dia Nos Area of Steel

Layer 1 16 mm 2Layer 2 - 0Layer 3

Total Steel Provided

Shear Force (Vu) 300 KNζv .=Vu / (b * d)ζc Refer Table 61 SP 16 pg 179ζcmax Refer Table J SP 16 pg 175

Type Bar Dia Nos Area of SteelLayer 1 25 mm 0Layer 2 25 mm 0Layer 3 20 mm 0

Total Steel Provided

Type of stirrup 2 leggedStirrup diameter 6 mmSpacing

clear cover to main reinf.

Mu/bd2

Mulim/bd2

or =(0.85*√(0.8*fck)*√(1+5β)-1)) / (6β)

Steel Calculation

Grade Check7.1

SRB DRBa 0.75 a 0.75b -3.611 b -3.611c 9.058 c 2.762-p Err:502 -p 0.955

Ast Err:502 .=(p*b*d)/100 Astlim 595 .=(p*b*d)/100

Mu2 106 .=Mu - MulimAst2 1217 .=Mu2/((0.87*fy)*(d-d'))Ast 1813 .=Astlim+Ast2

0.1070 d'/d 0.150.15 fsc 342 Refer Table F SP 16 pg 13

fcc 8.92 .=0.466*fckAsc 1319 .=Mu2/((fsc-fcc)*(d-d'))

Min steel % 0.205 .=0.85% / fyAst 1813Asc 1319

Min Steel 128 .=(0.85*b*d) / fyMax Steel 2493.2 .=0.04*b*d)

Ast 1813Asc 1319

Shear Calculations

Pt provided #VALUE! .=(Ast*100)/(b*d)Pc provided .=(Asc*100)/(b*d)

β #VALUE! .=(0.8*fck)/(6.89*Pt)

Shear Capacity of Concrete (Vs) #VALUE! .=ζc*b*dShear Stg to be caried by Stirrup (Vus) #VALUE! .=Vu-Vs

Spacingactual req 255 .=(Asv*0.87fy*d)/Vus

min 222 .=(Asv*0.87fy)/(b*0.4)max 203 .=0.75dmax 300 .=300mm

.=(0.87435/100) * (fy/fck)2 .=(0.87435/100) * (fy/fck)2

.=(0.87/100) * (fy) .=(0.87/100) * (fy)

.=Mu/bd2 .=Mulim/bd2

.=-(b±√(b2-4ac))/2a .=-(b±√(b2-4ac))/2a

prov

ide

the

leas

t of t

he 4

Slab Design

Slab thickness t 125 mm Sunken Depth 325 mmfck 20 MPafy 415 MPa

LoadingSlab Load Sunken Slab LoadDead Load DL 3.125 KN/m Dead Load DL 3.125 KN/mLive Load LL 3.000 KN/m Filler Load FL 5 KN/mFinishes Load WL 1.000 KN/m Live Load LL 3.0 KN/mTotal Load Ws 7.125 KN/m Finishes Load WL 1.0 KN/mFactored Load Wsu 11 KN/m Total Load Wsk 11.74 KN/m

Factored Load Wsku 18 KN/m

Slab DataSlab Type Regular

Load 11 KN/mLonger Span (ly) 8.20 m ly/lx ratio 2.05Shorter Span (lx) 4.00 m Slab type -

Loading on edges one way two way

21 KN/m .=w*lx/2

.=w*lx/3

Moments one way two wayMx 21 KN-m

Thickness Check OK .=Mulim > Mux or Muy

Deflection 10 mm

Area of SteelAstx Refer Chart 4 SP 16 pg 21 or

647 sqmm Refer Table 5-44 SP 16 pg 51-80

Spacing required in mm

x y x y x y x x78 c/c 121 c/c 175 c/c 311 c/c

.=ast of bar*1000/ast req

x y

Concrete Steel

Wlonger .=(w*lx/2) + (1-(1/3)*(lx/ly)2)

Wshorter

.=w*lx2/ 8 .=αx * w*lx2

.=αy * w*lx2

.= 5*W*l4/(384EI)

8# 10# 12# 16#

Final Ast provided

Design Calculations

ONE WAY TWO WAYa 0.75 a 0.75b -3.611 b -3.611

cx 1.939 cy #VALUE!-px 0.616 -py #VALUE!Ast 647 .=(p*b*d)/100 Ast #VALUE! .=(p*b*d)/100

Min Ast %0.12 150

Interpolation

Tabl

e 26

IS 4

56 p

g 91

1 0.056ly/lx 1.1 0.064

1.2 0.0720.00 0.00 2.05 #N/A #N/A #N/A 0.056 1.3 0.079

1.4 0.0851.5 0.089

2 0.107

xumax 50 .= (700/(1100 * (0.87 * fy)) * d

Mulim 30 KN-m .= 0.36*fck*b*xumax*(d-(0.42*xumax))

2.761.94

#VALUE!

E 2.24E+07

I 1.63E-04Defln 9.79

.=(0.87435/100) * (fy/fck)2 .=(0.87435/100) * (fy/fck)2

.=(0.87/100) * (fy) .=(0.87/100) * (fy)

.=Mu/bd2 .=Mu/bd2

.=-(b±√(b2-4ac))/2a .=-(b±√(b2-4ac))/2a

mm2

αx αylower value

upper value

exact value

lower value

upper value

interptn. value

Mulim/bd2

Mux/bd2

Muy/bd2

.= bd3/12

.= 5*W*l4/(384EI)

Column Design

Design LoadsLoad Pu 2000 KN

Moment Mu 20 KN-m

Column Datawidth b 200 mmdepth d 200 mmlength l 3.00 meters

GradeConcrete fck 20 MPa

Steel fy 415 MPa

Pu/(fckbd) 2.50 Minimum eccentricity0.01 ex 1.27 mm OK

d'/d 0.05 ey 1.27 mm OK

Refer Chart 31 of SP 16, Page no: 116

pt/fck 0.18

pt 3.60%Ast 1440 sqmm

Number of bars dia nos ast

25 mm 4 1963 sqmm ● ● ● ● ● ● 4- ###

20 mm 4 1257 sqmm 4- ###

20 mm 4 1257 sqmm ● ● ● ● ● ● 4- ###

Total 12 4477 sqmm

Steel provided OK

Mu/(fckbd2)

ACE GROUP ARCHITECTS (P) Ltd.Architects & Consulting Engineers

GAT M27.2m lvlFahim H. Bepari7-Apr-2023

Slab thickness t 150 mmfck 20 MPafy 415 MPa

LoadingSlab LoadDead Load DL 3.75 KN/mLive Load LL 2.00 KN/mGarden Load GL 7.20 KN/mWater Proofing Load WL 1.00 KN/mTotal Load Ws 13.95 KN/mFactored Load Wsu 21 KN/m

Design & Reinforcement Details of Slabs

Slab Data

ly/lx

Sla

b ty

pe Loading on edges Moments Area of SteelSpacing required in mm

Sla

b ty

pe

Sla

b N

ame

Sl.No Sl. Id ThicknessLoad

Wsu / Wsku ly lx Mx My Astx Asty x y x y x y x y

1 Sunk 150 mm 21 KN 5.20 m 5.00 m 1.04 + 36 KN/m 35 KN/m 31 KN-m 29 KN-m OK 753 sqmm 706 sqmm 67 c/c 71 c/c 104 c/c 111 c/c 150 c/c 160 c/c +2 Regular 150 mm 21 KN 5.20 m 2.50 m 2.08 - 26 KN/m 16 KN-m OK 372 sqmm 135 c/c 211 c/c 304 c/c -3 Regular 150 mm 21 KN 6.50 m 5.80 m 1.12 + 45 KN/m 41 KN/m 46 KN-m 40 KN-m OK 1231 sqmm 1005 sqmm 41 c/c 50 c/c 64 c/c 78 c/c 92 c/c 113 c/c +

3A Regular 150 mm 21 KN 2.00 m 1.10 m 1.82 + 10 KN/m 8 KN/m 3 KN-m 1 KN-m OK 180 sqmm 180 sqmm 279 c/c 279 c/c 436 c/c 436 c/c 628 c/c 628 c/c +3B Regular 150 mm 21 KN 5.30 m 4.30 m 1.23 + 35 KN/m 30 KN/m 29 KN-m 22 KN-m OK 691 sqmm 504 sqmm 73 c/c 100 c/c 114 c/c 156 c/c 164 c/c 224 c/c +4 Regular 150 mm 21 KN 35.00 m 2.60 m 13.46 - 27 KN/m 18 KN-m OK 404 sqmm 124 c/c 194 c/c 280 c/c -5 Regular 150 mm 21 KN 9.20 m 4.10 m 2.24 - 43 KN/m 44 KN-m OK 1154 sqmm 44 c/c 68 c/c 98 c/c -6 Regular 150 mm 21 KN 9.20 m 4.00 m 2.30 - 42 KN/m 42 KN-m OK 1083 sqmm 46 c/c 73 c/c 104 c/c -7 Regular 150 mm 21 KN 8.00 m 3.20 m 2.50 - 34 KN/m 27 KN-m OK 638 sqmm 79 c/c 123 c/c 177 c/c -

Project :Title :Designer :Date :

Concrete Steel

Thickness Check

Spacing provided in mm c/cLonger

SpanShorter Span 8# 10# 12#

Wlonger Wshorter

Project NCCDate 07-Apr-23

Grid Floor Analysis & Design

Data x direction y directionLength of beams 14.00 meters 14.00 metersNumber of beams 6 nos 6 nosSpacing of ribs 2.00 meters 2.00 metersDepth of beam 900 mmWidth of beam 200 mmWidth of flange 2000 mmThickness of flange 150 mmGrade of Concrete 20 MPaGrade of Steel 415 MPa

Modulas of Elasticity E = 2.2E+07 KN/sqm

LoadsLive Load 3.00 KNFloor Finish 1.00 KNOther 0.00 KN

Loading CalculationTotal weight of slab 735.00 KNTotal weight of beams in x direction 378.00 KNTotal weight of beams in y direction 345.60 KNTotal weight of Live load 588.00 KNTotal weight of Floor Finish 196.00 KNOther loadTotal Load 2242.60 KNTotal Load/sqm q = 11.44 KN/sqmTotal Factored Load/sqm Q = 17.16 KN/sqm

Design ParametersRatios

0.16710.000

Moment of Inertia

2.3 refer Chart 88 of SP 16 pg 215I = 2.79E-02

Flexural Rigidity of ribs

Dx = 3.12E+05 Dy = 3.12E+05

Modulus of Shear

G = 9.72E+6 KN/sqm

Torsional Constants (Polar Sectional Modulus)

C1 = 2.06E-3 cum C2 = 4.18E-2 cum

Torsional Rigidity

Cx = 1.00E+4 Cy = 2.03E+5

2H = 2.13E+5

8.138.135.55

Deflection CheckCentral Deflection

13.09 mm

Long Term Deflection

39.28 mm

span/deflection (Clause 23.2 IS 456)

s/d = 56.00 mm

Maximum deflection including long term effects is within permissible limits i.e. Ltdefl < s/d ratio

Maximum Moment & Shear Values

Max Bending Moments

Mx = 206 KN-m My = 206 KN-m

Max Torsional Moments

Mxy = 7 KN-m

Shear Force

Qx = 48 KN Qy = 48 KN

Lx = Ly =Nx = Ny =a1 = b1 =D =bw =bf =Df =fck =fy =

ws =wbx =wby =wll =wff =wol =

ws+wbx+wby+wll+wff+wol =

Df/D =bf/bw =

I = (kx*bw*D3)/12kx =

Dx=EI/a1 Dy=EI/b1

G=E / (2(1+μ)

C1=(1-(0.63*(bw/D))*(bw3*D/3) C2=(1-(0.63*(bw/D))*(D3*bw/3)

Cx=GC1/b1 Cy=GC2/a1

2H=Cx+Cy

Dx / Lx4 =

Dy / Ly4 =

2H / (Lx2*Ly

2) =

ω=(16*Q/π)/((Dx/Lx4)+(2H/(Lx

2*Ly2))+(Dy/Ly4))

ω =

Ltdefl. = 3*ωLtdefl. =

Mx=Dx*(π/Lx)2*ω My=Dy*(π/Ly)2*ω

Mxy=(Cx*π2*ω1)/(Lx*Ly)

Qx=[(Dx*(π/Lx)3)+(Cy*(π3/(a*b2)))]*ω Qy=[(Dy*(π/Ly)3)+(Cx*(π3/(b*a2)))]*ω

bw

Df

D

bf

a1

b1

Ly

Lx

Staircase Design

DataEffective Span (l) 5.00 mmRiser (R) 150 mmThread (T) 300 mmWaist Slab thickness (t) 150 mmClear Cover 15 mmEffective Depth of Waist Slab (d) 135 mm

Grade of Concrete (fck) 20 MPaGrade of Steel (fy) 415 MPa

LoadingLoads on going Loads on waist slabSelf weight of waist slab 4.19 KN/m Self weight of landing slab 3.75 KN/mSelf weight of steps 1.88 KN/m Live Load 2.00 KN/mLive Load 3.00 KN/m Floor Finish Load 1.00 KN/mFloor Finish Load 1.00 KN/m Total Load 6.75 KN/m

Total Load 10.07 KN/m Factored Load 10.13 KN/mFactored Load 15.10 KN/m

Bending Moment

###Bending Moment = 47 KN-m

Reactionto be used as UDL = 38 KN ###

60 KN-m

Area of Main SteelAst 1184 sqmm

SpacingDiameter of bar

Spacing across x 96 c/c 170 c/c

Provded Main Steel:

Area of Distribution SteelAst 180 sqmm

SpacingDiameter of bar

Spacing across y 279 c/c 436 c/c

Provided Distridution Steel:

12ø 16ø

8ø 10ø

Calculate Bending Moment using the equation (W*L*L )/8

Seismic Zone II Table 2 IS 1893 2002 pg 16Seismic Intensity z 0.1

Importance factor I 1.5 Table 6 IS 1893 2002 pg 18

Response Reduction Factor R 3 Table 7 IS 1893 2002 pg 23

Lateral Dimension of Building d 65.6 metersHeight of the of Building h 50.4 meters

with brick infillFundamental Natural Period 0.560

Type of Soil Medium Soil

Spectral Acceleration Coefficient 0.000

Design Horizontal Seismic Coefficient 0

Seismic Weight of Building W 680034 KN

Design Seismic Base Shear 0 KN

Ta

Sa/g

Ah

VB

Date 07-Apr-23Footing No. F2

1 Footing Size Design

Load 1 Pu1 2000 KNLoad 2 Pu2 1850 KNCombine load Pcu 3850 KNDesign Load Pc 2823 KN

Moment in x dir Mux 40 KN-mMoment in y dir Muy 40 KN-m

c/c dist b/w col in x dir 2.725 metersc/c dist b/w col in y dir 0.000 meters

Col Dim x dir 0.20 metersy dir 0.20 meters

SBC q 150 KNm2

Footing Size required A req 18.82 sqmm

Footing Size Provided L 6.00 metersB 3.20 meters

Area Provided A prvd 19.20 meters

x bar 1.309y bar 0.000

Zx 10.24Zx 19.20

Nup 151 KNm2

Increase the Footing Size

2 Beam Design

Total Load W 151 KNm2Factored Load Wu 725 KNm2

1.691 meters 2.725 meters 1.584 meters

3.20 meters

6.00 meters

725 KNm2

1.69 meters 2.73 meters 1.58 meters

Beam Size width 600 mmdepth 900 mm

Moment Mb 898 KN-m

Design the beam from the BEAM DESIGN SHEET

Bottom ReinforcementType Bar dia Nos Area of Steel

Layer 1 25 mm 6 2945 sqmmLayer 2 25 mm 6 2945 sqmmLayer 3 -

Total Steel Provided 5890 sqmmPercentage of Steel 1.148 %

Top ReinforcementType Bar dia Nos Area of Steel

Layer 1 25 mm 6 2945 sqmmLayer 2 20 mm 6 1885 sqmmLayer 3 -

Total Steel Provided 4830 sqmm

3 Slab Design

Net upward pressure Nup 151 KNm2l 1.30 meters /=width of footing from col face

Bending Moment Ms 128 KN-mFactored Moment Mus 191 KN-m 1.5*Ms

Concrete fck 20 MPafy 415 MPa

Minimum Depth Required dmin 264 d=sqrt(Ms/Rumax*1000*b)

Depth Provided D 600 mmClear Cover c 50 mmEffective Cover d' 56 mmEffective Depth d' 544 mm

Area of Steel across x dir Spacing c/c in mm 20#

1014 sqmm 112 c/c 198 c/c 310 c/c

Ast across x direction 12 mm dia @ 100 mm c/c 1131 sqmmDist Ast across y direction 8 mm dia @ 175 mm c/c 287 sqmm

4 Shear Check for Slab

Vu1 171 KNζv 0.315 MPa

ζc 0.316 MPa

Shear Check OK

M=Nup*l2/2

Steel

12# 16#

56.00 meters

3.20 meters 600 mm

1.7 meters 2.73 meters 1.6 meters

600 mm

6 - 25 mm dia6 - 20 mm dia

900

mm

6 - 25 mm dia6 - 25 mm dia

600

mm

250 mm

8 mm dia @ 175 mm c/c 12 mm dia @ 100 mm c/c

6 - 25 mm dia6 - 20 mm dia

6 - 25 mm dia6 - 25 mm dia

Design Of Isolated Footing 15 of 40

1 Footing Size Design

Load Pu 2500 KNDesign Load P 1833 KN

Moment in x dir Mux 30 KN-mMoment in y dir Muy 30 KN-m

Column size cx 450 mmcy 450 mm

SBC q 150 KN/sqm

Footing Size required A req 12.22 sqmm

Footing Size ProvidedL 3.30 metersB 2.40 meters

Area Provided A prvd 7.92 meters

Zx 3.17Zx 4.36

Net upward pressure Nup 242 KNm2

Change Footing Dimensions

2 Slab Designlx 1.425ly 0.975

Bending Moment in x dir Mx 369 KN-mBending Moment in y dir My 173 KN-m

Concrete fck 20 MPafy 415 MPa

Minimum Depth Required dmin 366

Depth Provided D 650 mmClear Cover c 50 mmEffective Cover d' 58 mmEffective Depth d' 592 mm

Area of SteelSpacing c/c in mm

20#1847 sqmm 61 c/c 109 c/c 170 c/c833 sqmm 136 c/c 241 c/c 377 c/c

Ast across x direction 16 mm dia @ 125 mm c/c 1608 sqmm XAst across y direction 16 mm dia @ 125 mm c/c 1608 sqmm

Steel

12# 16#

Design Of Isolated Footing 16 of 40

3 One Way Shear along x direction

Vu1 727 KNζv 0.512 MPa

ζc 0.395 MPa

Vc1 561 KN

Increase Depth

4 One Way Shear along y direction

Vu1 460 KNζv 0.235 MPa

ζc 0.279 MPaVc1 546 KN

One Way Shear Check OK

5 Two Way ShearVu2 2485 KNζv 1.007 MPa

ks*ζc 1.118 MPaVc1 2759 KN

Two Way Shear Check OK

Design Of Isolated Footing 17 of 40

L= 3.30 meters

450

B= 2.40 meters 450

650

mm

250 mm

16 mm dia @ 125 mm c/c 16 mm dia @ 125 mm c/c

Dimensions of DomeDiameter d = 15600 mmHeight h = 3000 mmThickness t = 150 mm

Radius of Sphere r = 11640 mm

h =

3.00

m

Φ = 42.08Ѳ = 0 to 42.08

Loading d = 15.60 mDead Load DL = 3.75 KN/mLive Load LL = 0.10 KN/m 42.08 r = 11.64 mWind Load WL = 0.10 KN/mTotal Load W = 3.95 KN/mFactored Load Wu = 5.93 KN/m

Meridional Stress Hoop StressѲ Mt Ѳ Mt

42.08 0.264 MPa 42.08 0.049 MPa45.00 0.269 MPa 45.00 0.035 MPa40.00 0.260 MPa 40.00 0.058 MPa35.00 0.253 MPa 35.00 0.078 MPa30.00 0.246 MPa 30.00 0.096 MPa25.00 0.241 MPa 25.00 0.111 MPa20.00 0.237 MPa 20.00 0.123 MPa15.00 0.234 MPa 15.00 0.133 MPa5.00 0.230 MPa 5.00 0.144 MPa0.00 0.230 MPa 0.00 0.146 MPa

Maximum Meridional Stress 0.269 MPa Maximum Hoop Stress 0.146 MPa

fck 20 MPaFy 415 MPa

230.00

Area of steel 176 sqmm Area of steel 95 sqmm

Bar Dia 10 mm Bar Dia 10 mmSpacing 447 c/c Spacing 828 c/c

Meridional Thrust @ Base 40 KN/mHorizontal Component on Ring Beam 29 KN/mHoop Tension on Ring Beam 229 KN

Area of steel 996 sqmm

Bar Dia 16 mmNo of Bars 5 nos

бst

r = 11640.00 m

04/07/2023 Page 20 of 40

ACE GROUP ARCHITECTS (P) Ltd.Architects & Consulting Engineers

MVJL-Block7-Apr-2023Fahim H. Bepari

Design & Reinforcement Details of Columns

Load Moment Column Data GradeDesign Constants

Ast Req RemarkArea of Steel

Check Figd'/d Type 1 Type 2 Total Reinf Provided

1 - - C1 R 1500 KN 30 KN-m 30 KN-m 200 mm 750 mm 750 mm 50 mm 3.60 m 20 MPa 415 MPa 0.50 0.01 0.1 0.02 0.40% 600 sqmm 1200 sqmm 4 12 mm 452 sqmm 2 12 mm 226 sqmm 6 679 sqmm

Project :Block :Date :Designer :

Sl No.

Grid No Col Nos. Col

typeCol Shape

Design

Paramenters

Final Ast

RequiredPu/(fckbdl) Mu/(fckbdl2)

Ast less than

min Ast req.

Steel provided NOT OK

19.7 KNm2

Dimensions of DomeDiameter d = 12600 mmHeight h = 5000 mm

Radius of Sphere r = 6469 mmΦ = 76.87Ѳ = 0 to 76.87

LoadingDead Load DL = 3.00 KN/mLive Load LL = 0.10 KN/mOther Load OL = 10.00 KN/mTotal Load W = 13 KN/mFactored Load Wu = 20 KN/m

Vertical Reaction VA = VB = 123.8 KNHorizontal Reaction HA = HB = 234.0 KN

Ѳ x y Moment76.87 0.00 0.00 075.00 0.05 0.21 -4260.00 0.70 1.77 -33150.00 1.34 2.69 -48140.00 2.14 3.49 -59630.00 3.07 4.13 -68020.00 4.09 4.61 -73710.00 5.18 4.90 -7695.00 5.74 4.98 -7770.00 6.30 5.00 -780

Max Values 780 KN-m

h =

5.00

m

d = 12.60 m

76.87 r = 6.47 m

Radial Shear Normal Thrust 0 67 17467 174 42 59 18059 180 331 10 224-10 224 481 56 245-56 245 596 100 259

-100 259 680 141 265-141 265 737 178 262-178 262 769 209 252-209 252 777 222 244-222 244 780 234 234-234 234

234 KN 265 KN

r = 6469.00 m

INNOVATIVE ENGINEERS PHAGWARAArchitects & Consulting Engineers

Jnana VikasTerrace FloorFahim H. Bepari7-Apr-2023

CB11

Dimensions of Ring BeamRadius r = 6.30 mtsNo of supports n = 8 nos

Constants Ѳ = 23 deg 0.3927 radians9 1/2 0.1658 radians

C1 = 0.066C2 = 0.03C3 = 0.005

LoadingWu = 10 KN/m

Shear Force

deg KN KN-m KN-m0 24.74 -20.62 0.009 1/2 14.29 -0.05 1.57

22 1/2 0.00 10.39 0.00

Beam Datawidth 300 mmdepth 600 mm

Equivalent ShearVe = V+1.6(T/b) = 33 KN

Equivalent MomentMt = T((1+D/b)/1.7) = 1 KN-m Mt = BM due to torsion

22 KN-m20 KN-m

Project :Title :Designer :Date :

Beam :

Φm =

ΦFΦ MΦ Mm

t

Bending Moment

Torsional Moment

T=MΦ

Me1 = M+Mt = Me1 = Equivalent BM on tension sideMe2 = M-Mt = Me2 = Equivalent BM on compression side

A Load 2700Moment x-dir y-dirBottom 0 29Top 6 137

Col Type Rectangular Column (reinf. on 2 sides)

x-dir y-dirUnsupported Length 8250 8250Col Size 200 900

d'/D 0.05 0.20d' 40

Concrete 20Steel 415

D

Effective Length Ratio0.80 from IS Code0.90 manual Calculation

Effective Length to be considered from Manual CalculationEffective Length (le) lex Ley

7425 7425E Slenderness Ratio

le/D 8 Short Columnle/b 37 Slender ColumnMoment due to Slen Muax 0

Muay 372

Min Ecc ex 46.5ey 23.2

Moment due to ecc Mux 125.55Muy 62.55

G Reduction of MomentsPercentage assumed 2.18

Asc 3924

Puz 2841

k1 K2 Pbx-x 0.219 0.096 367y-y 0.184 -0.022 291

Kx 0.06Ky 0.06

Additional Moments due to ecc Max 0May 21

Modified Initial Moments Mux 3.6Muy 70.6

Summary of MomentsA Moment due to eccentricity + Modified additional moments

Mux 126Muy 83

B Modified initial moments + Modified additional momentsMux 4Muy 91

C 0.4Muz + Modified additional momentsMux 0Muy 32

Final Design LoadsPu 2700Mux 126Muy 91

Delhi Public SchoolIndoor Sports Block7-Apr-2023Fahim H. BepariC6a

Design LoadsPu = 2400 KN

Mux = 192 KN-mMuy = 517 KN-m

Col Datab = 600 mmD = 750 mmd' = 40.0 mm

d'/D = 0.10d'/b = 0.10

Material Gradesfck = 20 MPafy = 415 MPa

Design ConstantsSteel % pt = 1.2 Ast = 5400 sqmm

pt/fck = 0.06 Min Ast = 3600 sqmmPu/fck*b*D = 0.27

0.110.11

Puz = 5682743594

Pu/Puz = 0.420.260.87

1.37

0.98

Steel Percentage OK

Steel Detailsnos dia ast

Type 1 4 20 mm 1257 sqmmType 2 8 16 mm 1608 sqmm

Total Steel 12 - 2865 sqmmPercentage 0.64%

Project :Block :Date :Designer :Column :

Mux/fck*b*D2 = Muy/fck*b*D2 =

Mux1 = Muy1 =

Mux/Mux1 =Muy/Muy1 =

αn =

(Mux/Mux1)αn + (Muy/Muy1)αn

Load W 30 KN/m 10 KN/mLength l 5.60 m 5.00 m

Ec 22000000 MPa 22000000 MPa

Width b 0.20 m 0.20 mDepth d 0.45 m 0.60 mMoment M 126.42 m 40.63 mReaction R 90.30 m 32.50 m

Ixx 0.0015 mm4 0.0036 mm4

Deflectiondy

11.5 mm 0.3 mmFormula

Simply supported beam with UDL

Simply supported beam with Point Load

Elasticity of Concrete = 5000(√fck)

Moment of Inertia = bd3/12

5Wl4/384EI Wl3/48EI

1400 KN/m 10 KN/m3.80 m 5.00 m

22000000 MPa 22000000 MPa

1.50 m 0.20 m1.10 m 0.60 m2601.46 m 40.63 m2738.38 m 32.50 m

0.1664 mm4 0.0036 mm4

10.0 mm 5.3 mm

Cantilever beam with UDL

Cantilever beam with Point Load

Wl4/8EI Wl3/3EI

Span

125 mm 150 mm 175 mm 200 mm

Spacing Spacing Spacing Spacing

3 16 1.45 46512# @ 243 c/c

17 1.01 38612# @ 293 c/c

18 0.75 33712# @ 336 c/c

19 0.59 36912# @ 306 c/c

16# @ 432 c/c 16# @ 521 c/c 16# @ 597 c/c 16# @ 546 c/c

3.5 22 2 66912# @ 169 c/c

23 1.36 53612# @ 211 c/c

25 1.04 44712# @ 253 c/c

26 0.8 42112# @ 269 c/c

16# @ 301 c/c 16# @ 375 c/c 16# @ 450 c/c 16# @ 479 c/c

4 28 2.54 89912# @ 126 c/c

30 1.78 72312# @ 156 c/c

32 1.33 62412# @ 181 c/c

34 1.05 55912# @ 202 c/c

16# @ 224 c/c 16# @ 278 c/c 16# @ 322 c/c 16# @ 360 c/c

4.5 38 2.25 95612# @ 118 c/c

41 1.71 82412# @ 137 c/c

44 1.36 74112# @ 153 c/c

16# @ 210 c/c 16# @ 244 c/c 16# @ 271 c/c

5 50 2.08 103912# @ 109 c/c

54 1.67 93112# @ 121 c/c

16# @ 194 c/c 16# @ 216 c/c

5.5 61 2.54 132712# @ 85 c/c

65 2.01 115512# @ 98 c/c

16# @ 152 c/c 16# @ 174 c/c

6 77 2.38 141812# @ 80 c/c

16# @ 142 c/c

Moment (KNm) Mu/bd2 Ast

(mm2)Moment (KNm) Mu/bd2 Ast

(mm2)Moment (KNm) Mu/bd2 Ast

(mm2)Moment (KNm) Mu/bd2 Ast

(mm2)

Span 150 mm 175 mm 200 mm

312# @ 293 c/c 12# @ 336 c/c 12# @ 306 c/c

16# @ 521 c/c 16# @ 597 c/c 16# @ 546 c/c

3.512# @ 211 c/c 12# @ 253 c/c 12# @ 269 c/c

16# @ 375 c/c 16# @ 450 c/c 16# @ 479 c/c

412# @ 156 c/c 12# @ 181 c/c 12# @ 202 c/c

16# @ 278 c/c 16# @ 322 c/c 16# @ 360 c/c

4.512# @ 118 c/c 12# @ 137 c/c 12# @ 153 c/c

16# @ 210 c/c 16# @ 244 c/c 16# @ 271 c/c

512# @ 109 c/c 12# @ 121 c/c

16# @ 194 c/c 16# @ 216 c/c

5.512# @ 85 c/c 12# @ 98 c/c

16# @ 152 c/c 16# @ 174 c/c

612# @ 80 c/c

16# @ 142 c/c

DESIGN OF RETAINING WALL

1 Preliminary Datai) Height of RW h 3.00 metersii) Soil Density 18 KN/cumiii) SBC 250 KN/sqm

iv) Angle of repose Ø 30 degrees0.524 radians

v) Surcharge Angle Ө 0 degrees0.000 radians

vi) Coefficient of friction µ 0.5vii) Surcharge Load 4 KN/sqm

2 Pressure Coefficients

i)Active Pressure Coefficients

Ca 0.333

ii) Passive Pressure Coefficients Cp 3.00 = (1+SinØ) / (1+SinØ)

3 Preliminary DimensionsProposed Adopted

i) Thickness of Stem - 0.20 metersii) Thickness of footing base slab 0.24 meters 0.30 meters

iii)Length of base slab L = 1.5 * √(Ca/3) * (h + hs) 1.61 meters

2.00 metersor L = 0.6h to 0.65h 2.09 meters

iv) Extra Height of Retaining Wall due to Surcharge 0.22 metersv) Total Height of Retaining Wall due to Surcharge 3.22 meters

vi) Extra Height of RW due to inclined back fill 0.00 metersvii) Total Height of RW due to inclined back fill 3.00 meters

viii) 3.22 meters

4 Stability against Overturningi) Active pressure due Surcharge Load 4 KNii) Active pressure due Backfill Load 27 KNiii) Total Load on stem 31 KN

iv) Overturning Moment 33 KNm

v) Load Lever arm from end of stem Moment

Backfill Load = (L-ts)*(h-tb)*γs 87 KN 0.90 meters 79 KNmSurcharge Load = Ca*Ws*h 4 KN 0.90 meters 4 KNmInclined Backfill Load = ((L-ts)*hi)/2*γs 0 KN 0.60 meters 0 KNm

= ts*(h-tb)*γconc 14 KN 0.95 meters 13 KNmBase self weight = L*tb*γconc 15 KN 1.00 meters 15 KNmDownward component = Pa*sinӨ 0 KN 0 KNmOther Load 0 KNm

∑W 120 KN 110 KNm

vi) Distance of Resultant Vertical Force from end of heel 0.92 meters

vii) Stabilizing Moment 130 KNm

viii) Factor of Safety against OVERTURNING3.54 > 1.4 Safe against Overturning

5 Stability against Slidingi) Sliding Force Pa*CosӨ 31 KNii) Resisting Force 60 KN

iii) Factor of Safety against SLIDING1.74 > 1.4 Safe against Sliding

Shear Key not required

iv) Shear key Design

a) Shear Key Sizex 0.00 metersy 0.00 meters

b) Distance from stem z 0.00 metersc) Heigth of exacavation 0.00 metersd) Heigth of exacavation 0.00 meterse) Passive Pressure 0 KN

v) Revised Factor of Safety against SLIDING1.74 > 1.4

Safe against Sliding

6 Soil Pressures at footing basei) Resultant Vertical Reaction ∑W = R 120 KNii) Distance of R from heel Lr = (Mw+Mo)/R 1.19 metersiii) Eccentricity e = Lr- L/2 0.19 meters

Eccentricity lies within middle third of the base hence OK

iv) Pressure Distridution on soil 95 KN/sqm25 KN/sqm

Max Pressure qmax<SBC hence pressure on base is OK

v) 88 KN/sqm

γs

qo

Ws

=(cosӨ-√(cos2Ө-cos2Ø)*cosӨ) / (cosӨ+√(cos2Ө-cos2Ø))

ts tb = 0.08 * (h + hs)

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi

Design Height of RW considered H = Max of H1 & H2

Pa1 = Ca*Ws*hPa2 = Ca*γs*h2 / 2Pa = Pa1 + Pa2

Mo= (Pa1 * h/2) +(( Pa2*CosӨ)* h/3)

W1 (L-ts) / 2W2 (L-ts) / 2W3 (L-ts) / 3W4 Stem self weight (L- (ts/2))/2W5 L / 2W6

W6

∑Mw

xw=∑Mw/∑W

Mr =∑W * (L - xw)

(FS)OT = 0.9 * (Mr/Mo)

F = µ*∑W

(FS)SL=0.9*(F/(Pa*CosӨ))

h1

h2 = h1 + y + (z * tanØ)

Pp = Cp*γs*(h12-h2

2) / 2

(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))

qmax = R/L * (1+(6*e/L))qmin = R/L * (1-(6*e/L))

Pressure at junction of stem and heel qsh=qmax-((qmax-qmin)/L)*ts)

DESIGN OF L Shaped Cantilever RETAINING WALL

1 Preliminary Datai) Height of Retaining Wall h 3.00 metersii) Soil Density 18 KN/cumiii) SBC 250 KN/sqmiv) Angle of repose Ø 30 degrees

0.524 radiansv) Surcharge Angle Ө 0 degrees

0.000 radiansvi) Coefficient of friction µ 0.5vii) Surcharge Load 4 KN/sqm

2 Pressure Coefficientsi) Active Pressure Coefficients Ca 0.333

ii) Passive Pressure Coefficients Cp 3.00 = (1+SinØ) / (1+SinØ)

3 Preliminary DimensionsProposed Adopted

i) Thickness of Stem min 200mm 0.20 metersii) Thickness of footing base slab 0.24 meters 0.30 metersiii) Length of base slab L = 1.5 * √(Ca/3) * (h + hs) 1.61 meters 2.20 meters

L = 0.6h to 0.65h 2.09 meters

iv) Extra Height of Retaining Wall due to Surcharge 0.22 metersv) Total Height of Retaining Wall due to Surcharge 3.22 meters

vi) Extra Height of RW due to inclined back fill 0.00 metersvii) Total Height of RW due to inclined back fill 3.00 meters

viii) 3.22 meters

4 Stability against Overturningi) Active pressure due Surcharge Load 4 KNii) Active pressure due Backfill Load 31 KNiii) Total Load on stem (Force) 35 KNiv) Overturning Moment due to Imposed load 7 KNv) Overturning Moment due to Backfill load 33 KNvi) Overturning Moment 50 KN

v) Load Lever arm at end of stem MomentBackfill Load = (L-ts)*(h-tb)*γs 105 KN 1.20 meters 126 KNmInclined Backfill Load = ((L-ts)*hi)/2*γs 0 KN 0.87 meters 0 KNm

= ts*(h-tb)*γconc 15 KN 0.10 meters 1 KNmBase self weight = L*tb*γconc 17 KN 1.10 meters 18 KNm

∑W 136 KN 146 KNm

viii) Safe against Overturning -clause 20.1 page 33 of IS 456 2000

5 Stability against Slidingi) Sliding Force 35 KNii) Resisting Force 68 KN

iii) 1.73 > 1.4 Safe against Sliding -clause 20.2 page 33 of IS 456 2000

6 Soil Pressures at footing basei) Net Moment at toe Mn = Mw - Mo 105 KNii) Point of application of Resultant R x = Mn/W 0.77 metersiii) Eccentricity e = (L/2) - x 0.33 meters L/6= 0.37

e<L6 Eccentricity lies within middle third of the base hence OK

iv) Pressure Distridution on soil 117 KN/sqm7 KN/sqm

Max Pressure qmax<SBC hence pressure on base is OK

v) 107 KN/sqm

γs

qo

Ws

=(cosӨ-√(cos2Ө-cos2Ø)*cosӨ) / (cosӨ+√(cos2Ө-cos2Ø))

ts tb = 0.08 * (h + hs)

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi

Design Height of RW considered H = Max of H1 & H2

PHS = Ca*Ws*hPH = Ca*γs*h2 / 2Pa = PHS + PH

MOIL = PHS*h/2MODL = PH*h/3Mo = (1.2*MDIL) + (1.4*MOIL)

W1 ((L-ts) / 2) + tsW2 ((L-ts) / 3) + tsW3 Stem self weight ts / 2W4 L / 2

∑Mw

Mw not less than (1.2*MODL) +(1.4*MOIL)

Pa = PHS + PH

F = µ*∑W

(FS)SL= (0.9*F)/(Pa)

qmax = W/L * (1+(6*e/L))qmin = W/L * (1-(6*e/L))

Pressure at junction of stem and heel qsh=qmax-((qmax-qmin)/L)*ts)

7 Constants for Working Stress Method

Design Constantsi) Grade of concrete 20 MPaii) Grade of steel 415 MPa

iii) Compr stress in concrete c 7.0 table 21 page 81 IS 456iv) Tensile stress in steel t 230v) Modular ratio m = 280/3c 13.33vi) Neutral axis depth factor k=mc/(mc+t) 0.289vii) Lever arm j = 1 - k/3 0.904viii) Factor R= cjk / 2 0.913

8 Design

A) Stemi) Beanding Moment at base of stem 40 KN/m

ii) Thickness required 0.01 metersiii) Thickness provided ts 0.20 meters

Thickness of Stem is OK

iv) Ast required 1387 sqmmv) Ast provided 16 mm dia @ 125 mm c/c 1608 sqmmvi) Percentage of Steel 0.99 %

Steel OK

B) Base SlabForce Lever arm from end of stem Moment

i) Force due to backfill+surcharge 105 1.00 meters 105 KNmii) Force due to inclined backfill 0 0.67 meters 0 KNmiii) Self Weight of base slab 17 1.10 meters 18 KNm

∑Ws 122 Md 123 KNmvi) Upward soil pressure 114 1.59 meters 181 KNm

Downward Pressure is greater Mu 181 KNm

v) Bending Moment Msh = Mu-Md 58

vi) Thickness required 0.25 meters Thickness of Stem is OKvii) Thickness provided ts 0.30 meters

viii) Ast required 1157 sqmmix) Ast provided 16 mm dia @ 150 mm c/c 1340 sqmmx) Percentage of Steel 0.48 %

Steel OK

C) Reinforcement Details

M = MODL + MOIL

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

= (H2-tb)*(L-ts)*γs (L-ts) / 2

= hi/2*(L-ts)*γs (L-ts) / 3 =L *tb*γconc L / 2

Nup = ((qsh+qmin)/2)*(L-ts) ((qsh+(2*qmin))/(qsh+qmin)) / ((L-ts)/3)

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

FILL

DESIGN OF Reverse L Shaped Cantilever RETAINING WALL

1 Preliminary Datai) Height of Retaining Wall h 3.00 metersii) Height of Plinth Fill hp 0.50 metersiii) Soil Density 18 KN/cumiv) SBC 250 KN/sqm

v)Angle of repose Ø 30 degrees

0.524 radians

vi)Surcharge Angle Ө 0 degrees

0.000 radiansvii) Coefficient of friction µ 0.5vii) Surcharge Load 4 KN/sqm

2 Pressure Coefficientsi) Active Pressure Coefficients Ca 0.333

ii) Passive Pressure Coefficients Cp 3.000 = (1+SinØ) / (1+SinØ)

3 Preliminary DimensionsProposed Adopted

i) Thickness of Stem min 200mm 0.20 metersii) Thickness of footing base slab 0.24 meters 0.45 metersiii) Length of base slab if sloped backfill -0.60 meters

2.45 meters0.00 meters

if horizontal backfill -0.96 meters0.00 meters

L = 0.6h to 0.65h 2.09 meters

iv) Extra Height of Retaining Wall due to Surcharge 0.22 metersv) Total Height of Retaining Wall due to Surcharge 3.22 meters

vi) Extra Height of RW due to inclined back fill 0.00 metersvii) Total Height of RW due to inclined back fill 3.00 meters

viii) 3.22 meters

4 Stability against Overturningi) Active pressure due Surcharge Load 4 KNii) Active pressure due Backfill Load 31 KNiii) Total Load on stem (Force) 35 KNiv) Overturning Moment due to Imposed load 7 KNv) Overturning Moment due to Backfill load 33 KNvi) Overturning Moment 50 KN

v) Load Lever arm at start of heel MomentFront fill Load = (L-ts)*(hp-tb)*γs 2 KN 1.13 meters 2 KNm

= ts*(h-tb)*γconc 14 KN 2.35 meters 33 KNmBase self weight = L*tb*γconc 28 KN 1.23 meters 34 KNmOther Load PT Beam Load 0 KN

∑W 43 KN 69 KNm

viii) Safe against Overturning -clause 20.1 page 33 of IS 456 2000

5 Stability against Slidingi) Sliding Force 35 KNii) Resisting Force 22 KN

iii) 0.55 < 1.4 Unsafe against Sliding -clause 20.2 page 33 of IS 456 2000

5a Shear key Design

a) Shear Key Sizex 0.30 metersy 0.30 meters

b) Distance from stem z 0.30 metersc) Heigth of exacavation 0.60 metersd) Heigth of earth mobilization 1.07 meterse) Passive Pressure 21 KN

v) Revised Factor of Safety against SLIDING

γs

qo

Ws

=(cosӨ-√(cos2Ө-cos2Ø)*cosӨ) / (cosӨ+√(cos2Ө-cos2Ø))

ts tb = 0.08 * (h + hs)α = 1 - (q0/2.7*γs*H)L = H*sqrt((Ca*cosβ)/((1-α)*(1+3α))α = 1 - (q0/2.2*γs*H)L = 0.95*H*sqrt((Ca)/((1-α)*(1+3α))

hs = Ws/γs

Hs = h+hs

hi = (L-ts)* tanӨ

Hi = h+hi

Design Height of RW considered H = Max of H1 & H2

PHS = Ca*Ws*hPH = Ca*γs*h2 / 2Pa = PHS + PH

MOIL = PHS*h/2MODL = PH*h/3Mo = (1.2*MDIL) + (1.4*MOIL)

W1 ((L-ts) / 2)W3 Stem self weight (ts/2) + (L-ts)W4 L / 2W5

∑Mw

Mw not less than (1.2*MODL) +(1.4*MOIL)

Pa = PHS + PH

F = µ*∑W

(FS)SL= (0.9*F)/(Pa)

h1

h2 = h1 + y + (z * tanØ)

Pp = Cp*γs*(h12-h2

2) / 2

v)1.09 > 1.4

Unsafe against Sliding. Shear Key Required

6 Soil Pressures at footing basei) Net Moment at toe 28 KNii) Point of application of Resultant R x = Mn/W 0.65 metersiii) Eccentricity e = (L/2) - x 0.58 meters L/6= 0.41

e>L6 Eccentricity lies outside the middle third of the base. Revise the base dimensions

iv) Pressure Distridution on soil 43 KN/sqm-7 KN/sqm

Max Pressure qmax<SBC hence pressure on base is OK

v) 39 KN/sqm

(FS)sliding = 0.9 * ((F+Pp)/(Pa*CosӨ))

Mn = Mw - (MOIL+MODL)

qmax = W/L * (1+(6*e/L))qmin = W/L * (1-(6*e/L))

Pressure at junction of stem and heel qsh=qmax-((qmax-qmin)/L)*ts)

7 Constants for Working Stress Method

Design Constantsi) Grade of concrete 20 MPaii) Grade of steel 415 MPa

iii) Compr stress in concrete c 7.0 table 21 page 81 IS 456iv) Tensile stress in steel t 230v) Modular ratio m = 280/3c 13.33vi) Neutral axis depth factor k=mc/(mc+t) 0.289vii) Lever arm j = 1 - k/3 0.904viii) Factor R= cjk / 2 0.913

8 Design

A) Stemi) Beanding Moment at base of stem 40 KN/m

ii) Thickness required 0.01 metersiii) Thickness provided ts 0.20 meters

Thickness of Stem is OK

iv) Ast required 1387 sqmmv) Ast provided 16 mm dia @ 120 mm c/c 1676 sqmmvi) Percentage of Steel 0.99 %

Steel OK

B) Base SlabForce Lever arm from end of stem Moment

i) Force due to Frontfill 2 1.13 meters 2 KNmiii) Self Weight of base slab 28 1.23 meters 34 KNm

∑Ws 30 Md 36 KNmvi) Upward soil pressure 35 1.03 meters 36 KNm

Upward Pressure is greater Mu 36 KNm

v) Bending Moment Msh = Mu-Md 0

vi) Thickness required 0.01 meters Thickness of Stem is OKvii) Thickness provided ts 0.45 meters

viii) Ast required 2 sqmmix) Ast provided 12 mm dia @ 150 mm c/c 754 sqmmx) Percentage of Steel 0.00 %

Steel OK

C) Reinforcement Details

M = MODL + MOIL

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

= (L-ts)*(hp-tb)*γs (L-ts) / 2 = L* tb * γconc L / 2

Nup = ((qsh+qmin)/2)*(L-ts) ((qsh+(2*qmin))/(qsh+qmin)) / ((L-ts)/3)

dreq=√(Ms/(R*b)

Ast = M/(t*j*tse)

pt = Ast/(b*d)

FILL