Calculation of L20-H0.75m_new

7/31/2019 Calculation of L20-H0.75m_new

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6. Summary of Loading Effects

LOAD CASES DENOTATIONS

No. LOAD CASE CLARIFICATION

1 G_DC Girder Self-weight

2 S_DC Self-weight of Deck Slab+Diaphragms

3 DW Self-weight of Surface + Railings

4 SH_D Shrinkage Differential5 CR_D Creep Differential

6 TG Temperature differential 50C

7 CR Secondary force due to Creep

8 LL_MAX Maximum Live Load + Impact

9 LL_MIN Minimum Live Load + Impact

10 IM_MAX Maximum Impact of Live Load

11 IM_MIN Minimum Impact of Live Load

12 PS Prestress after losses


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10. Checking Nominal Flexural Resistance of Section

COMBINATIONS TO BE UTILIZED FOR CHECKING

LOADINGSDC DW (LL+IM)_MAX (LL+IM)_MIN PS CR_D SH_D TG CR

STRENGTH-I1 1.25 1.50 1.002 1.25 1.50 1.00 0.50 0.50 0.503 1.25 1.50 1.75 1.00 0.50 0.50 0.504 0.90 0.65 1.75 1.00 0.50 0.50 0.50

STRENGTH-IV5 1.50 1.50 1.006 1.50 1.50 1.00 0.50 0.50 0.507 0.90 0.65 1.00 0.50 0.50 0.50

SERVICE III8 1.00 1.00 0.80 1.00 1.00 1.00 0.50 1.009 1.00 1.00 0.80 1.00 1.00 1.00 0.50 1.0010 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Notes: *For checking tensile stress, SERVICE III Combinations will be used.

*For checking Nominal Resistances of Sections, all Combinations will be used.

COMBINATION


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INPUT DATA FOR CALCULATION

Thickness of Slab (mm) TS = 100 mmWidth of Slab (mm) BS = 990 mm

1.4. Material strength & Stress Limits:1.4.1. Prestressing steel (low-relaxation)

Ultimate strength of prestressing steel : f'pu = 1860 MPa

Yield strength : f py=0.9f'pu 1674 MPa

Elastic Modulus : Ep ####### MPa

Limit of tensile stress after immediate losses : 0.9f'py 1506.6 MPa

Limit of tensile stress at service state : f'pe=0.8f'py = 1339.2 MPa

1.4.2. Reinforcement

Yield strength : f'sy = 400 MPa

Limit of tensile stress at service : f'sa=0.6fsy = 240 MPa

Elastic Modulus : Es = ####### MPa

1.4.3. Concrete

Density gc = 2500 kg/m3Thermal coefficient EXP = ####### 1/ C

a) Girder Concrete

Compresive strength at 28 days : f'c = 50 MPa

Compresive strength at time of initial prestress : f'ci = 0.9f'c = 45 MPa

Limit of compresive stress at time of initial prestres : 0.6 f'ci = 27 MPa

Limit of tensile stress at time of initial prestress : 0.58(f'ci).

= 3.89076 MPa

Limit of compresive stress at service

* Prestress + permanent load : 0.45 f'c 22.5 MPa

* Live load +1/2(prestress + permanent l : 0.4 f'c 20 MPa

Limit of tensile stress at service : 0.5(f'c).

= 3.54 MPa

Elastic Modulus : 0.043gc.(f'c)

.: Ec1 = 38010 MPa

b) Slab Concrete

Compresive strength at 28 days : f'c = 30 MPa

Limit of compresive stress at service

* Prestress + permanent load : 0.45 f'c 13.5 MPa

* Live load +1/2(prestress + permanent l : 0.4 f'c 12 MPa

Limit of tensile stress at service : 0.5(f'c).

= 2.74 MPa

Elastic Modulus : 0.043gc.(f'c)

.: Ec2 = 29440 MPa

Creep Coeff. : (at t= 120 days) Fti = 1.2

Infinity Creep Coeff. : (infinitive time t= 75years) Finf = 2.2

Stress Coeff. Due to Creep at t=120 days: K = 0.375

Stress Coeff. Due to Creep at t=120 days: K' 0.6875

1.5.4 Differential Shrinkage : (at time t= days) SHDIF = #######

1.5.7 Differential Temperature:

Page 3 1-Condition


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Delta T TDIF = 5 C

Page 4 1-Condition


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2. Section Properties

2.1. Cross Section Properties (Oval holes included)

Cross section

Section Area Extreme fibre Bending Modulus Ine

mm2 Top y' Bottom y Top W' Bottom W Ix

mm mm mm3

mm3

mm4

SEC-1 713,025 382 368 87,731,257 91,068,859 33,513,340,000

SEC-2 511,653 385 365 81,612,832 85,972,276 31,400,944,531

SEC-3 511,653 385 365 81,612,832 85,972,276 31,400,944,531

SEC-4 511,653 385 365 81,612,832 85,972,276 31,400,944,531

SEC-5 511,653 385 365 81,612,832 85,972,276 31,400,944,531

2.2. Tranformed Section Properties for initial stage at tranfer (Prestressing steel included)

Area Extreme fibre Bending Modulus Ine

Section mm2

Top y2' Bottom y2 Top W2' Bottom W2 Ix

mm mm mm3

mm3

mm4

SEC-1 730,342 388 362 90,456,833 96,870,829 35,082,759,403

SEC-2 528,971 393 357 83,872,816 92,196,292 32,939,179,778

SEC-3 528,971 393 357 83,872,816 92,196,292 32,939,179,778

SEC-4 528,971 393 357 83,872,816 92,196,292 32,939,179,778

SEC-5 528,971 393 357 83,872,816 92,196,292 32,939,179,778

2.3. Composite Section Properties for final stage (service stage)

Area Extreme fibre Bending Modulus Ine

Section mm2

Top y3' Bottom y3 Top W3' Bottom W3 Ix

mm mm mm3

mm3

mm4

SEC-1 830,747 334 416 159,420,322 127,798,476 53,200,750,670

SEC-2 629,375 321 429 158,748,483 118,463,316 50,879,521,983

SEC-3 629,375 321 429 158,748,483 118,463,316 50,879,521,983

SEC-4 629,375 321 429 158,748,483 118,463,316 50,879,521,983

SEC-5 629,375 321 429 158,748,483 118,463,316 50,879,521,983


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rtia

Iy

mm4

54,012,959,000

42,573,303,073

42,573,303,073

42,573,303,073

42,573,303,073

rtia

Iy

mm4

56,907,377,220

45,467,721,293

45,467,721,293

45,467,721,293

45,467,721,293

rtia

Iy

mm4

65,107,900,503

53,668,244,575

53,668,244,575

53,668,244,575

53,668,244,575


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3 Internal forces

3.1. Due to S.W of Girder

w = (A1x2+A2x18)x2.5/20 = (0.03351x1.2+0.03225x18.8) x 2.5 / 20 = 13.04 kg/cm

Where : A1 : Area of Section 1

A2 : Area of Section 2 , 3 , 4

Length of Section 1 : 2 m

Length of Section 1+2+3 : 18 m

Bending Moment and Shear forces due to S.W of Girder

Component Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5

Distance from section to left bearing mm 0 375 3,300 4,850 9,700

Distance from section to right bearing mm 19,400 19,025 16,100 14,550 9,700

Moment M N.mm 0 46,526,827 346,487,295 460,205,951 613,607,935

Shear V N 126,517 121,626 83,475 63,259 0

3.2. Due to S.W of Deck Slab

w = 2.913 + 0.723 = 3.64 N / mm

Bending Moment and Shear forces due to S.W of deck slab


Distance from section to left bearing mm 0 375 3,300 4,850 9,700

Distance from section to right bearing mm 19,400 19,025 16,100 14,550 9,700

Moment M N.mm 0 12,970,294 96,590,340 128,291,715 171,055,620

Shear V N 35,269 33,906 23,270 17,635 0

Ltt

Ltt = 19.4m

w = 3.64 N / mm

A - A

BA

B - B

BA

HOLLOW SLAB

DEAD LOAD(DC)


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3.3. Due to S.W of Railing, Parapet and Barrier

w = 0.968 N / MM

Bending Moment and Shear forces due to S.W of Railing , Parapet and Barrier


Space from section to left bearing mm 0 375 3,300 4,850 9,700

Space from section to right bearing mm 19,400 19,025 16,100 14,550 9,700

Moment M N.mm 0 3,453,038 25,714,920 34,154,670 45,539,560

Shear V N 9,390 9,027 6,195 4,695 0

3.4. Due to S.W of surface

w = 990 *50 * 0.0000023*9.8066 = 1.116 N / mm

Ltt = 19.4m

w = 0.968 N / MM

Ltt = 19.4m

w = 1.116 N/mm

A B

DETAIL "A" DETAIL "B"

SUPERSTRUCTURE

DEAD LOAD (DC)


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Bending Moment and Shear forces due to S.W of Surface


Space from section to left bearing m 0 375 3,300 4,850 9,700

Space from section to right bearing m 19,400 19,025 16,100 14,550 9,700

Moment M T.m 0 3,982,699 29,659,329 39,393,651 52,524,868

Shear V T 10,830 10,411 7,145 5,415 0

3.5. Due to Live Load plus Impact

3.5.1. Calculation of transverse distribution of live load (AASHTO 98 4.6.2.2.2)

Calculation span length L = 19400.00 mm

With of beam b = 990.00 mm

Moment of inertia of beam I = 5.09E+10 mm4

St. Venant's torsional inertia J = A4

/ (40*(Ix+Iy)) 3.75E+10 mm4

Number of beams Nb = 18.00 Nos

Distance from exterior web of exterior beam

and the interior edge of curb or traffic barrier de = -200.00 mm

Correction factor for Moment e = 1.01

Correction factor for Shear e = 1.01

Impact factor IM = 1.33

Factor used in calculation of distribution factor k = 1.50

Distribution of live loads per Lane for Moment in

+ Interior beams g = 0.2480

+ Exterior beams g = 0.2514

Distribution of live loads per Lane for Shear in

+ Interior beams g = 0.4313

+ Exterior beams g = 0.4342

VEHICULAR LIVE LOADING DATA

Unit

Standard

load

Distance from axle to front

axle

Axle concentrated load P1 N 35,000

Truck Axle concentrated load P2 N 145,000 4300

Axle concentrated load P3 N 145,000 4300

Tandem Axle concentrated load P4 N 110,000

Axle concentrated load P5 N 110,000 1200Lane Load Uniform distributed load W N / mm 9.30

3.5.2. Calculation value of influence line

P1 P2 P3

4.3

P4

MY5LttLtt

4.3

MY2 MY3MY1

P5

MY4

1.2

P1 P2 P3

4.3P4

VY5LttLtt

4.3

VY2 VY3VY1

P5

VY4

1.2

Xi Xi


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Iterm Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5

Distance from calculated section to left bearing mm 0 375 3,300 4,850 9,700

Distance from calculated section to right bearin mm 19,400 19,025 16,100 14,550 9,700

Area of Moment influence line MA mm2

0 3,567,188 26,565,000 35,283,750 47,045,000

Area of Shear influence line VA1 > 0 mm2

9,700 9,329 6,681 5,456 2,425

Area of Shear influence line VA2 < 0 mm2

0 -4 -281 -606 -2,425

Value of Moment influence line MY1 0.00 0 0 413 2700


Value of Moment influence line MY3 0.00 285 2007 2563 2700Value of Moment influence line MY4 0.00 0 2241 3188 4550


Value of Shear influence line VY1 1.00 0.98 0.83 0.75 0.50





Bending Moment due to Live Load plus Impact

M = IM*g*MY(i)*P(i) for concentrated load or M = g*MA*W for uniform load

Forces Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec

0 375 3300 4850 97

X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) X(mm) M(N.mm) X(mm)

P1 -3,925 0 -1,000 0 550 4,827,630 5,400

By P2 375 17,830,528 3,300 132,784,716 4,850 176,365,245 9,700

Truck P3 4,675 13,800,501 7,600 97,320,475 9,150 124,243,557 14,000

Total 31,631,029 230,105,191 305,436,432

By P4 374 0 3,299 82,418,100 4,849 117,242,449 9,699

Tandem P5 376 13,100,013 3,301 96,979,199 4,851 128,277,032 9,701

Total 13,100,013 179,397,299 245,519,480

By lane load W 8,340,637 62,113,089 82,498,879

Total 0 39,971,666 292,218,280 387,935,311

Shear forces due to Live Load plus Impact

V = IM*g*VY(i)*P(i) for concentrated load or V = g*VA(i)*W for uniform load

Forces Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec

0 375 3300 4850 97X(mm) V(N) X(mm) V(N) X(mm) V(N) X(mm) V(N) X(mm)

P1 8,600 20,204 8,975 19,813 11,900 16,766 13,450 15,151 18,300

By P2 4,300 83,721 4,675 82,103 7,600 69,477 9,150 62,786 14,000

Truck P3 0 83,740 375 82,121 3,300 69,496 4,850 62,805 9,700

Total 187,665 184,037 155,738 140,742

By P4 0 63,527 375 62,299 3,300 52,721 4,850 47,645 9,700

Tandem P5 1,200 63,523 1,575 62,295 4,500 52,717 6,050 47,641 10,900

Total 127,050 124,594 105,438 95,286

By lane load W 119,979 115,386 82,633 67,488

Total 307,645 299,423 238,372 208,231


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3.6. Due to prestressing

3.6.1 Stress Loses (AASHTO LRFD 5.9.5)Specified strength of Prestressing steel fpu 1860 MPa

Yield strength of Prestressing steel fpy = 0.9fpu 1674 MPa

Stress in Prestressing steel immediately prior to transfer fpt = 0.75fpu 1395 MPa

Stress in Prestressing steel at service limit state after all losses fpe = 0.8fpy 1339 MPa

Area of strand at bottom fibre (at section 3,4,5) (32 strands) Aps1 3158.7 mm

Area of strand at top fibre (3 strands) Aps2 296.1 mm

Area of strand at bottom fibre (at section 1,2) (10 strands) A'ps1 987.1 mm

Density of concrete yc 2400 Kg/m

Specified compressive strength of Concrete f'c 42 MPa

Specified compressive strength of Concrete at time of stress transfer f'ci = 0.9f'c 37.8 MPa

Elastic modulus of Prestressing Steel Ep 197000 MPa

Elastic modulus of Concrete Ec 32765 MPa

Stress in Prestressing steel at jacking fpj = 0.75fpu 1395 MPa

Jacking force (for one strand) 14 Ton

Loss due to Elastic shorteningfpES =Ep*fcgp/Eci

ci Modulus of elasticity of concrete at transfer

Eci = 0.043*yc.

*(fci').

= 31084 MPa

fcgpSum of concrete stresses at the center of gravity of prestressing tendons due to prestressing force at trasfer and the self-wei

of the member at the section of maximum moment

fcgp = fo + fp 11.67 MPa

fo due to self - weight of girderfo = Mo*e / Ix -4.38 MPa

Mo Moment due to self-weight of girder

fp due to prestressing steel : fp = N/ A + N*e*e/Ix 16.05 MPa

N = 0.7*fpu*(Aps1 + Aps2) = 4498215 N

e : Distance from CGS to center of gravity of girder -235 mm

Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5

Sum of concrete stress at CGS fcgp N/mm2 11.67 11.67 11.67 11.67 11.67

Loss due to elastic shortening DfpES N/mm2 73.9 73.9 73.9 73.9 73.9

Loss due to Shrinkage

fpSR = (117-1.03*H)

Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5The average annual ambient relative humidity H % 85 85 85 85 85

Loss due to Shrinkage DfpSR N/mm2 29.5 29.5 29.5 29.5 29.5

Loss due to Creep

fpCR = 12.0 *fcgp - 7.0* fcdp

fcdpchange in concrete stress at center of gravity of prestressing steel due to permanent loads, with the

exception of the load acting at the time the prestressing force is applied

fcdp = Msw *e/Ix -1.92 MPaMsw : Moment due to self - weight of deck slab , surface, railing and parapet

Msw = 2.69E+08 N.mm


Sum of concrete stress at CGS fcgp N/mm

2

11.7 11.7 11.7 11.7 11.7Change in concrete stress at CGS Dfcdp N/mm

2 -1.9 -1.9 -1.9 -1.9 -1.9

Loss due to Creep DfpCR N/mm2 126.6 126.6 126.6 126.6 126.6


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Loss due to relaxation

Loss due to relaxation at transfer (Initial stage)

fpR1 = log(24.0*t) / 40.0*[fpj / fpy - 0.55]*fpjfpj : initial stress in strand at the end of prestressing = 0.75*fpu

Loss due to relaxation at after transfer (final stage)

fpR2 = (138 - 0.4* fpES - 0.2*( fpSR + fpCR))*30%


Time estimated in day from stressing to transfer (t) Day 5 5 5 5 5

Loss due to relaxation at transferDfpR1 N/mm2 20.5 20.5 20.5 20.5 20.5

Loss due to relaxation after transferDfpR2 N/mm2 23.2 23.2 23.2 23.2 23.2

3.6.2 Internal forces due to prestressing

Bending moment, shear force and normal force due to prestressing


INITIAL STAGE AT TRANSFERInitial prestress i = Jacking stress j - (prestress losses due to relaxation at transfer and Elastic shortening)

Jacking stress j = stress in prestressing steel immidiately prior to transfer fpt

j = fptNormal force N =si1*Aps1 (A'ps1) + si2*Aps2

Shear force V = 0Moment M = si1*Aps1(A'ps1)*d1 - si2*Aps2*d2d1 Distance from CGS at bottom fibre to neutral axles

d2 Distance from CGS at top fibre to neutral axles

A'ps1 for Section 1 and Section 2 750

Total of Losses due to relaxation and elastic shortening N/mm2 94 94 94 94 94Jacking stress at bottom fibre j1 N/mm

2 1395 1395 1395 1395 1395

Jacking stress at top fibre j2 N/mm2 1395 1395 1395 1395 1395

Initial stress at bottom fibre i1 N/mm2 1301 1301 1301 1301 1301

Initial stress at top fibre i2 N/mm2 1301 1301 1301 1301 1301

Distance from CGS at bottom fibre to neutral axles d1 mm 295 290 290 290 290

Distance from CGS at top fibre to neutral axles d2 mm 338 343 343 343 343

Normal force N N 1.67E+06 1.67E+06 4.49E+06 4.49E+06 4.49E+06

Shear force V N 0 0 0 0 0

Moment M N.mm 0.00E+00 -2.40E+08 -1.06E+09 -1.06E+09 -1.06E+09

FINAL STAGE AT SERVICEPrestress i = Jacking stress j - (total losses of prestress)

Jacking stress sj = Stress in Prestressing steel at service limit state after all losses fpe

j = fpeNormal force N =si1*Aps1 (A'ps1) + si2*Aps2

Shear force V = 0Moment M = si1*Aps1(A'ps1)*d1 - si2*Aps2*d2d1 Distance from CGS at bottom fibre to neutral axles

d2 Distance from CGS at top fibre to neutral axles

A'ps1 for Section 1 and Section 2

Total of Losses N/mm2

274 274 274 274 274Jacking stress at bottom fibre j1 N/mm

2 1339 1339 1339 1339 1339

Jacking stress at top fibre j2 N/mm2 1339 1339 1339 1339 1339

Stress at bottom fibre i1 N/mm2 1066 1066 1066 1066 1066

Stress at top fibre i2 N/mm2 1066 1066 1066 1066 1066

Distance from CGS at bottom fibre to neutral axles d1 mm 349 362 362 362 362

Distance from CGS at top fibre to neutral axles d2 mm 164 151 151 151 151

Normal force N N 1.37E+06 1.37E+06 3.68E+06 3.68E+06 3.68E+06

Shear force V N 0 0 0 0 0

Moment M N.mm 0.00E+00 -3.33E+08 -1.17E+09 -1.17E+09 -1.17E+09

Where : CGS : Central gravity of strand


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Summary of sectional forces for initial stage(at tranfer)

Unit Section - 1 Section - 2 Section - 3 Section - 4 Section -

N N 0 0 0 0 0

Self - Weight of Girder (DL1) V N 126,517 121,626 83,475 63,259 0

M N.mm 0 46,526,827 346,487,295 460,205,951 613,607,93

N N 1,668,852 1,668,852 4,493,063 4,493,063 4,493,063Initial prestress (Ps) V N 0 0 0 0 0

M N.mm 0 -239,998,824 ########### ########### #########

Summary of sectional forces for final stage(service stage)

Unit Section - 1 Section - 2 Section - 3 Section - 4 Section -

N N 0 0 0 0 0

Self - Weight of Girder (DL1) V N 126,517 121,626 83,475 63,259 0

M N.mm 0 46,526,827 346,487,295 460,205,951 613,607,93

N N 0 0 0 0 0

Self - Weight of deck (DL2) V N 35,269 33,906 23,270 17,635 0

M N.mm 0 12,970,294 96,590,340 128,291,715 171,055,62

N N 0 0 0 0 0Self-Weight of railing, parapet, Barrier(DL3) V N 9,390 9,027 6,195 4,695 0

M N.mm 0 3,453,038 25,714,920 34,154,670 45,539,56

N N 0 0 0 0 0

Self - Weight of surface (DL4) V N 10,830 10,411 7,145 5,415 0

M N.mm 0 3,982,699 29,659,329 39,393,651 52,524,86

N N 0 0 0 0 0

Live load plus impact (LL) V N 307,645 299,423 238,372 208,231 123,814

M N.mm 0 39,971,666 292,218,280 387,935,311 507,661,48

N N 1,367,310 1,367,310 3,681,220 3,681,220 3,681,220

Prestress (Ps) V N 0 0 0 0 0

M N.mm 0 -333,250,123 ########### ########### #########


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4. Checking for initial stage at transfer

Specified compressive strength of Concrete f'c 42 Mpa = 42.0 N / mm

at time of initial prestressing f'ci = 0.9*f'c 37.8 Mpa = 37.8 N / mm

Compressive stress limit [ f 1 ] = 0.6*f'ci 22.68 Mpa = 22.68 N / mmTensile stresses limit [ f 2 ] = 0.58*(f'ci )

0.53.57 Mpa = 3.57 N / mm

4.1. Summary of Sectional forcesUnit Section - 1 Section - 2 Section - 3 Section - 4 Section - 5

N N 0 0 0 0 0Self - Weight of Girder (DL1) V N 126,517 121,626 83,475 63,259 0

M N.mm 0 46,526,827 346,487,295 460,205,951 613,607,935N N 1,668,852 1,668,852 4,493,063 4,493,063 4,493,063

Initial prestress (Ps) V N 0 0 0 0 0M N.mm 0 -239,998,824 ########### ########### ###########N N 1,668,852 1,668,852 4,493,063 4,493,063 4,493,063

Total (DL1 + Ps) V N 126,517 121,626 83,475 63,259 0M N.mm 0 -193,471,998 -711,889,542 -598,170,886 -444,768,902

4.2. Checking sectional stress (AASHTO' 98 5.9.4.1)

fb < [ f1 ] OKif ( ft < 0, ft < [ f2 ] , ft < [ f1 ] ) OK

fb = M / W + N / A

ft = -M / W + N / AW , A : Bending modulus and Area of transform section

Unit Section - 1 Section - 2 Section - 3 Section - 4 Section - 5

fb N / mm 2.29 5.25 16.22 14.98 13.32

Checking OK OK OK OK OK

Checking sectional stress f t N / mm 2.29 0.85 0.01 1.36 3.19

Checking OK OK OK OK OK

TRANSFORM SECTION 3,4,5TRANSFORM SECTION 1 , 2


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4.3. Checking Flexural Resistance (AASHTO 98 5.7.3.2.2)Specified strength of Prestressing steel fpu 1860 MPa


Yield strength of tension reinforcement fy 400 MPa

Yield strength of compression reinforcement f'y 400 MPa

Area of strand at bottom fibre (at section 3,4,5) (32 strands) Aps1 3.16E+03 mm2

Area of strand at bottom fibre (at section 1,2) (10 strands) A'ps1 9.87E+02 mm2

Density of concrete yc 2500 Kg/m3


Specified compressive strength of Concrete at time of initial prestressing f'ci = 0.9f'c 37.8 MPa

*Mu < Mr OKMr = *MnMn = Aps*fps*(dp - a/2) + As*fy*(ds - a/2) - A's*f'y*(d's-a/2) + 0.85*f'c(b - bw)* 1*hf*(a/2 - hf/2)

a = c* 1c = (Aps*fpu + As*fy - A's*f'y) / (0.85*f'c* 1*b + k*Aps*fpu/dp)

fps = fpu*(1 - k*c/dp)Unit Section 1 Sect

Sectional Properties Depth of Girder H mm 750Width of compression flange b mm 990Width of web bw mm 920

Compression flange depth hf mm 0

Total Area of Prestressing Cables Aps mm2

987Distance from extreme compressive fibre to

centroid of Prestressing Cables dp mm 700

Area of Tensile Reinforcement As mm2

0

Distance from extreme compressive fibre to

centroid of Tensile Reinforcement ds mm 0

Area of Compressive Reinforcement A's mm2

0

Distance from extreme compressive fibre to

centroid of Compressive Reinforcement d's mm 0

Calculation of Mr Stress block factor b1 0.69

Distance from extreme compressive fibre to the

Neutral Axis c mm 73Depth of equivalent stress block a mm 50

Average stress in Prestress steel at nominal

bending resistance fps MPa 1806Nominal Resistance Mn N.mm 1,202,830,392 1,202,830Flexural Resistance factor j 1.0Factored Resistance Mr N.mm 1,202,830,392 1,202,830

Checking Factored Bending Moment due to

External Loads Mu N.mm 0 193,47OK


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4.4. Checking Shear Resistance (ASSHTO 98 5.8.3.3)

Specified strength of Prestressing steel fpu 1860

Yield strength of Prestressing steel fpy = 0.9fpu 1674

Yield strength of tension reinforcement fy 400

Yield strength of compression reinforcement f'y 400

Area of strand at bottom fibre (at section 3,4,5) (32 strands) Aps1 3.16E+03

Area of strand at bottom fibre (at section 1,2) (10 strands) A'ps1 9.87E+02

Specified compressive strength of Concrete f'c 42

Specified compressive strength of Concrete at time of initial prestressing f'ci = 0.9f'c 37.8

Elastic modulus of Prestressing Steel Ep 197000

Elastic modulus of reinfocing bars Es 200000

Elastic modulus of Concrete Ec 32765

Vu < Vr OKVr = *VnVn = Vc + Vs + V

Unit Section 1

Sectional Properties Depth of Girder H mm 750

Width of compression flange b mm 990

Effective web width bw mm 920

Total Area of Prestressing Cables Aps mm 987

s ance rom ex reme compress ve re o cen ro oPrestressing Cables dp mm 67500

Area of Tensile Reinforcement As mm2

0

Calculation of Vr Effective shear Depth dv mm 540

Effective web width bv mm 920

Spacing of stirrups s mm 150Angle of inclination of transverse reinforcement to longitudinal

axis of girder a degrees 90Factor indicating ability of diagonally cracked concrete to

transmit tension b #NAME?

Area of shear reinf. within a distance s Av mm2

616

Strain in the tensile reinforcement ex 0.002000

Inclination angle of diagonal compressive stress q degrees #NAME?

Calculate b & q Shear stress on the concrete v N/mm2

0.283

v/f'c 0.0057Assumed Inclination angle ssumed degrees 27.00#NAME?

Effective stress of P/S after all losses fpe MPa 13

ex1 0.002

Area of Conc. on flexural tensile side of section Act mm2

345000Fe 1

omponen o e ec ve pres rese orce n e rec on o e

applied shear Vp N 0

Nominal Resistance of Concrete Vc N #NAME?

Nominal Resistance of Reinforcement Vs N #NAME?

Nominal Resistance Vn N #NAME?Resistance factor for shear j 0.9Factored Resistance Vr N #NAME?

Checkin Factored Moment due to External Loads Mu N.mm 0

Factored Axial Force due to External Loads Nu N 16,688,518,466Factored Shear Force due to External Loads Vu N 126,517

#NAME?


17/62

5. Checking for final stage at service

Specified compressive strength of Concrete f'c 42 Mpa = 42.00 N / mm

Compressive stress limit due to Ps + DL [ f 1 ] = 0.45*f'c 18.9 Mpa = 18.90 N / mm

Compressive stress limit due to LL + 1/2 (Ps + DL) [ f2 ] = 0.4*f'c 17 Mpa = 16.80 N / mm

Compressive stress limit due to Ps + (DL + LL) [ f 3 ] = 0.6*f'c 25.2 Mpa = 25.20 N / mm

Tensile stresses limit at service stage [ f 4 ] = 0.5*(f'c )0.5

3.24 Mpa = 3.24 N / mm

5.1. Summary of Sectional forcesUnit Section - 1 Section - 2 Section - 3 Section - 4 Section - 5

N N 0 0 0 0 0Self - Weight of Girder (DL1) V N 126,517 121,626 83,475 63,259 0

M N.mm 0 46,526,827 346,487,295 460,205,951 613,607,935N N 0 0 0 0 0

Self - Weight of deck (DL2) V N 35,269 33,906 23,270 17,635 0M N.mm 0 12,970,294 96,590,340 128,291,715 171,055,620N N 0 0 0 0 0

Self-Weight of railing, parapet, Barrier (DL3) V N 9,390 9,027 6,195 4,695 0M N.mm 0 3,453,038 25,714,920 34,154,670 45,539,560N N 0 0 0 0 0

Self - Weight of surface (DL4) V N 10,830 10,411 7,145 5,415 0M N.mm 0 3,982,699 29,659,329 39,393,651 52,524,868N N 0 0 0 0 0

Live load plus impact (LL) V N 307,645 299,423 238,372 208,231 123,814M N.mm 0 39,971,666 292,218,280 387,935,311 507,661,483N N 1,367,310 1,367,310 3,681,220 3,681,220 3,681,220

Prestress (Ps) V N 0 0 0 0 0M N.mm 0 ########## -1,170,876,183 -1,170,876,183 -1,170,876,183N N 1,367,310 1,367,310 3,681,220 3,681,220 3,681,220

I. Ps + (DL1 + DL2 + DL3 + DL4) V N 182,006 174,969 120,086 91,003 0M N.mm 0 ########## -672,424,299 -508,830,195 -288,148,200N N 683,655 683,655 1,840,610 1,840,610 1,840,610

II. LL*1.25 + 1/2 * (DL1+DL2+DL3+DL4+Ps) V N 475,559 461,764 358,008 305,790 154,767M N.mm 0 -83,194,051 29,060,701 230,504,041 490,502,754N N 1,367,310 1,367,310 3,681,220 3,681,220 3,681,220

III. Ps + (DL1 + DL2 + DL3 + DL4 + LL*1.25) V N 566,562 549,248 418,051 351,291 154,767M N.mm 0 ########## -307,151,449 -23,911,057 346,428,654

COMPOSITE SECTION 3,4,COMPOSITE SECTION 1 , 2


18/62

5.2. Checking sectional stress (AASHTO' 98 5.9.4.2)

Checking stress due to Ps + (DL1 + DL2 + DL3 + DL4)

fb < [ f1 ] OK

if ( ft < 0, abs(ft)< [ f4 ] , ft < [ f1 ] ) OK

fb = M / W + N / A

ft

= -M / W + N / A

W , A : Bending modulus and Area of transform sectionUnit Section - 1 Section - 2 Section - 3 Section - 4 Section - 5

fb N / mm 1.65 4.42 11.53 10.14 8.28

Checking OK OK OK OK OKChecking sectional stress f t N / mm 1.65 0.49 1.61 2.64 4.03

Checking OK OK OK OK OKChecking stress due to LL*1.25 + 1/2 * (DL1 + DL2 + DL3 + DL4 + Ps)

fb < [ f2 ] OK

if ( ft < 0, abs(ft)< [ f4 ] , ft < [ f2 ] ) OK

fb = M / W + N / A

ft = -M / W + N / A

W , A : Bending modulus and Area of transform sectionUnit Section - 1 Section - 2 Section - 3 Section - 4 Section - 5

fb N / mm 0.82 1.79 2.68 0.98 -1.22

Checking OK OK OK OK OKChecking sectional stress f t N / mm 0.82 1.61 3.11 4.38 6.01

Checking OK OK OK OK OKChecking stress due to Ps + (DL1 + DL2 + DL3 + DL4 + LL * 1.25)

if (fb


19/62

5.3. Checking Flexural Resistance (AASHTO 98 5.7.3.2.2)Specified strength of Prestressing steel fpu 1860 MPa


Yield strength of tension reinforcement fy 400 MPa

Yield strength of compression reinforcement f'y 400 MPa

Area of strand at bottom fibre (at section 3,4,5) (32 strands) Aps1 3.16E+03 mm2

Area of strand at bottom fibre (at section 1,2) (10 strands) A'ps1 9.87E+02 mm2

Density of concrete yc 2500 Kg/m


Specified compressive strength of Concrete at time of initial prestressing f'ci = 0.9f'c 37.8 MPa

*Mu < Mr OK

Mr = *MnMn = Aps*fps*(dp - a/2) + As*fy*(ds - a/2) - A's*f'y*(d's - a/2) + 0.85*f'c(b - bw )* 1*hf*(a/2 - hf /2)

a = c* 1c = (Aps*fpu + As*fy - A's*f'y) / (0.85*f'c* 1*b + k*Aps*fpu/dp)

fps = fpu*(1 - k*c/dp)Unit Section 1

Load combination Ps*1+DL1*1.25+DL2*1.25+DL3*1.25+DL4*1.5+LL*1.75 Mu N.mm 0 17

Sectional Properties Depth of Girder H mm 870

Width of compression flange b mm 990Width of web bw mm 990

Compression flange depth hf mm 120

Total Area of Prestressing Cables Aps mm2

987

Distance from extreme compressive fibre to centroid of

Prestressing Cables dp mm 820

Area of Tensile Reinforcement As mm 0


Tensile Reinforcement ds mm 0

Area of Compressive Reinforcement A's mm 0


Compressive Reinforcement d's mm 0

Calculation of Mr Stress block factor b1 0.69

Distance from extreme compressive fibre to the Neutral

Axis c mm 73

Depth of equivalent stress block a mm 51Average stress in Prestress steel at nominal bending

resistance fps MPa 1814

Nominal Resistance Mn N.mm 1,422,605,420 1,42Flexural Resistance factor j 1.0Factored Resistance Mr N.mm 1,422,605,420 1,42

Checking Factored Bending Moment due to External Loads Mu N.mm 0 17

OK

Checking Limit for reinforcement (AASHTO 98 5.7.3.3)

Maximum reinforcement

C/de 0.42 OK

c = (Aps*fpu + As*fy - A's*f'y) / (0.85*f'c* 1*b + k*Aps*fpu/dp)

de = (Aps*fps*dp + As*fy*ds) / (Aps*fps + As*fy)

Minimum reinforcement

Mr 1.2*Mcr OK


20/62

Mcr = fr* Wtfr = 0.63*f'c^0.5

Unit Section 1

Checking Maximum

reinforcement

The corresponding effective depth from extreme

compression fibre to centroid of the tensile force in the

tensile reinforcement

de mm 820

C/de 0.09OK

Checking Maximum

reinforcementModulus of rupture fr MPa 4.08

Bending modulus for top fibre of section Wt mm3 159,420,322 15

Factored Resistance Mr N.mm 1,422,605,420 1,42

Cracking moment Mcr N.mm 650,891,916 64

OK


21/62

5.4. Checking Shear Resistance (ASSHTO 98 5.8.3.3)Specified strength of Prestressing steel fpu 1860 M

Yield strength of Prestressing steel fpy = 0.9fpu 1674 M

Yield strength of tension reinforcement fy 400 M

Yield strength of compression reinforcement f'y 400 M

Area of strand at bottom fibre (at section 3,4,5) (32 strands) Aps1 3.16E+03 mArea of strand at bottom fibre (at section 1,2) (10 strands) A'ps1 9.87E+02 m

Specified compressive strength of Concrete f'c 42 MSpecified compressive strength of Concrete at time of initial prestressing f'ci = 0.9f'c 37.8 M

Elastic modulus of Prestressing Steel Ep 197000 M

Elastic modulus of reinfocing bars Es 200000 M

Elastic modulus of Concrete Ec 33990 M

Vu < Vr OK

Vr = *Vn

Vn = Vc + Vs + VpUnit Section 1

Load combination Ps*1+DL1*1.25+DL2*1.25+DL3*1.25+DL4*1.5+LL*1.75 Mu N.mm 0Nu N 1,367,310Vu N 768,593

Sectional Properties Depth of Girder H mm 870Width of compression flange b mm 990

Effective web width bw mm 990

Total Area of Prestressing Cables Aps mm2 987,000,000s ance rom ex reme compress ve re o cen ro o

Prestressing Cables dp mm 67500

Area of Tensile Reinforcement As mm2 0

Calculation of Vr Effective shear Depth dv mm 626Effective web width bv mm 990

Spacing of stirrups s mm 150Angle of inclination of transverse reinforcement to longitudinal

axis of girder a degrees 90Factor indicating ability of diagonally cracked concrete to

transmit tension b #NAME?Area of shear reinf. within a distance s Av mm

2 616

Strain in the tensile reinforcement ex -0.000065

Inclination angle of diagonal compressive stress q degrees #NAME?Component of effective prestresed force in the direction of the

applied shear Vp N 0omna es s ance o oncre e Vc N #NAME?

Nominal Resistance of Reinforcement Vs N #NAME?

Nominal Resistance Vn N #NAME?

Resistance factor for shear j 0.9

Factored Resistance Vr N #NAME?

Checking Factored Moment due to External Loads Mu N.mm 0Factored Axial Force due to External Loads Nu N 1,367,310

Factored Shear Force due to External Loads Vu N 768,593#NAME?


22/62

6. Checking deflection and camber (AASHTO 98 2.5.2.6.2)

[D] : Deflection limits = Ltt / 800 24.25 mm

Ltt : Span length for calculation 19400 mm

g : Distribution of live loads per Lane for Moment in exterior beam 0.25

I : Impact factor 1.33

Ec : Elastic modulus of concrete 32765 MPa

fpt : Stress in Prestressing steel immediately prior to transfer 1395 MPa

It : Transform moment of inertia 3.294E+10 mm4

Ic : Composite moment of inertia 5.088E+10 mm4

Asp1 : Area of strand at bottom fibre 3.16E+03 mm2

Asp2 : Area of strand at top fibre 9.87E+02 mm2

* Deflection due to S.W of girder

Where : G = 1.85*(5*W*Ltt4)/(384*Ec*It) = 41.2 mm

DG : Deflection due to self - weight of gider

W : Uniform self - weight of girder 13.04 N/mm

1.85 : Long - term deflection component due to creep effect* Camber due to prestressing

c = 1.8*(Nu*e*Ltt2) / 8*B1 = -68.1 mm

Where : B1 = Ec*It = 1.08E+15 N.mm2

Dc : Camber due to prestressing

Nu : Prestressing force at transfer (not included losses)

Nu = fpt*Asp1 - fpt*Asp2 = 2397226 N

B1 : Stiffness of girder

e : Eccentricity from of prestress force from neutral axle of girder 362 mm

1.8 : Long - term camber component

* Deflection due to S.W of deck slab

Where : D = (5*W*Ltt4)/(384*Ec*Ic) = 4.0 mm

DD : Deflection due to self - weight of deck slab

W : Uniform self - weight of deck slab 3.64 N/mm

* Deflection due to S.W of railing, parapet and barrier

Where : R = (5*W*Ltt4)/(384*Ec*Ic) = 1.1 mm

DR : Deflection due to self - weight of railing, parapet and barrier

W : Uniform self - weight of railing, parapet and barrier 0.97 N/mm

* Deflection due to S.W of surface

Where : S = (5*W*Ltt )/(384*Ec*Ic) = 1.2 mm

DS : Deflection due to self - weight of surface

W : Uniform self - weight of surface 1.12 N/mm

* Deflection due to Live Load

- Deflection due to Design truck

P1 = 35000 N X1 = 5400 mm

P2 = 145000 N X2 = 9700 mm

P3 = 145000 N X3 = 14000 mm


23/62

DT = (P1*Y1 + P2*Y2 + P3*Y3)*1.25*g*I / (Ec*Ic) = 10.1 mm

Where : DDT : Deflection due to Design truck

Y1 : Value of influential line due to P1 at the middle of span = 1.01E+11

Y2 : Value of influential line due to P2 at the middle of span 1.52E+11

Y3 : Value of influential line due to P3 at the middle of span 1.01E+11

Yi = If (a>0 and aLtt / 2 and a


24/62

5. Checking Norminal Flexural Resistance of Sections5.1 Load Combinations for Checking Nominal Resistance (LRFD)

COMBINATION 1 MAXIMUMLoad type Factor

Girder Selfweight G_DC 1.25

Prestress PS 1.00

Section N(T) V(T) M(T.m) N(T) V(T) M(T.m)

SEC-1 1668851.85 158146.38 0.00 1668851.85 158146.38 0.00

SEC-2 1668851.85 152032.47 ######### 1668851.85 152032.47 0.00

SEC-3 4493062.66 104344.00 ######### 4493062.66 104344.00 0.00

SEC-4 4493062.66 79073.19 ######### 4493062.66 79073.19 0.00

SEC-5 4493062.66 0.00 ######### 4493062.66 0.00 0.00


25/62

1 2 3 4 5 6 7 8Section S.W of girder S.W of Deck Slab S.W

N (tf) V (tf) M (tf.m) N (tf) V (tf) M (tf.m) N (tf)SEC-1 0.00 ######## 0.00 0.00 35269.20 0.00 0.00SEC-2 0.00 ######## 46526826.56 0.00 33905.70 12970293.75 0.00SEC-3 0.00 83475.20 ########### 0.00 23270.40 96590340.00 0.00SEC-4 0.00 63258.55 ########### 0.00 17634.60 ########### 0.00SEC-5 0.00 0.00 ########### 0.00 0.00 ########### 0.00

R R

0.23255 0.58138


26/62

9 10 11 12 13 35 36of Surface (g = 1) LiveLoad max + Impact Prestre

V (tf) M (tf.m) N (tf) V (tf) M (tf.m) N (tf) V (tf)10829.87 0.00 0.00 ######## 0.00 1668851.85 0.0010411.19 3982698.53 0.00 ######## 39971666.35 1668851.85 0.00

7145.48 ########## 0.00 ######## ########### 4493062.66 0.005414.93 ########## 0.00 ######## ########### 4493062.66 0.00

0.00 ########## 0.00 ######## ########### 4493062.66 0.00


27/62

37s

M (tf.m)0.00

-239998824.35-1058376836.77-1058376836.77-1058376836.77


28/62

4 Summary of sectional Forces:

Section S.W of girder S.W of Deck Slab

. o ur ace +

+ Parapet + Railing(g

N (tf) V (tf) M (tf.m) N (tf) V (tf) M (tf.m) N (tf) V (tf)SEC-1 0.00 ######## 0.00 0.00 35269.20 0.00 0.00 0.00

SEC-2 0.00 ######## 46526826.56 0.00 33905.70 12970293.75 0.00 0.00SEC-3 0.00 83475.20 346487295.00 0.00 23270.40 96590340.00 0.00 0.00SEC-4 0.00 63258.55 460205951.25 0.00 17634.60 128291715.00 0.00 0.00SEC-5 0.00 0.00 613607935.00 0.00 0.00 171055620.00 0.00 0.00

Section

. o ur ace + arre r +

Parapet + Railing (g= 1) Live Load + Impact Prestress

N (tf) V (tf) M (tf.m) N (tf) V (tf) M (tf.m) N (tf) V (tf)SEC-1 0.00 10829.87 0.00 0.00 ######## 0.00 ######## 0.00SEC-2 0.00 10411.19 3982698.53 0.00 ######## 39971666.35 ######## 0.00SEC-3 0.00 7145.48 29659328.66 0.00 ######## 292218280.35 ######## 0.00SEC-4 0.00 5414.93 39393650.95 0.00 ######## 387935310.77 ######## 0.00SEC-5 0.00 0.00 52524867.93 0.00 ######## 507661483.34 ######## 0.00


29/62

M (tf.m)0.00

0.000.000.000.00

M (tf.m)0.00

################################


30/62

6. Checking Nominal Shear Resistance of Sections6.1. Load Combinations for Checking Nominal Resistance (See Section 5.1 above)6.2. Nominal Shear Strength of Girder (Article 5.8.3.3 AASHTO)

Section 1Sectional Properties

Depth of Girder H 750 mmWidth of Deck Slab bd 920 mmDepth of Deck Slab hd 120 mm

Total width of Webs bw 920 mm

Width of Soffit Slab bs 990 mmDepth of Soffit Slab hs 0 mm

Total Area of Prestressing Cables Ap 987 mms ance rom ex reme compress ve re o

centroid of Prestressing Cables dp -66750 mm

Area of Tensile Reinforcement Ast 0 mms ance rom ex reme compress ve re o

centroid of Tensile Reinforcement dst 0 mm

Area of Compressive Reinforcement Asc 0 mms ance rom ex reme compress ve re o

centroid of Compressive Reinforcement dsc 0 mm

Calculation of Vr Effective shear Depth dv 540 mm

Effective web width bv 920 mm

Spacing of stirrups s 150 mmAngle of inclination of transverse

reinforcement to longitudinal axis of girder a 90 degrees

Factor indicating ability of diagonallycracked concrete to transmit tension b #NAME?

Area of shear reinf. within a distance s Av 616 mm


Inclination angle of diagonal compressive strq #NAME? degrees

Calculate b & q Shear stress on the concrete v 3537.001 N/mm2

v/f'c #DIV/0!Assumed Inclination angle qassu 27.00 degrees

#NAME?Effective stress of P/S after all losses fpe 16,906,614 MPa

ex1 -34.92957912

Area of Conc. on flexural tensile side of sectiAct 345000 mm2

Fe 0.016312269omponen o e ec ve pres rese orce n

the direction of the applied shear Vp 0 N

Nominal Resistance of Concrete Vc #NAME? N

Nominal Resistance of Reinforcement Vs #NAME? N

Nominal Resistance Vn #NAME? NResistance factor for shear j 0.9Factored Resistance Vr #NAME? N

Checkin Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu ############ NFactored Shear Force due to External Vu 1,581,463,750 N

#NAME?


31/62

6. Checking Nomin6.1. Load Combin6.2. Nominal She

Sectional Properties

Calculation of Vr

Calculate b & q

Checkin

Section 2










Effective shear Depth dv 540 mm








Shear stress on the concrete v 3400.261 N/mm2



ex1 -35.23810779







Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu ############ NFactored Shear Force due to External Vu 1,520,324,688 N

#NAME?


32/62



Calculation of Vr

Calculate b & q

Checkin

Section 3





















ex1 -34.4568348







Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu ############ NFactored Shear Force due to External Vu 1,043,440,000 N

#NAME?


33/62



Calculation of Vr

Calculate b & q

Checkin

Section 4














Factor indicating ability of diagonallycracked concrete to transmit tension b 0.0


Strain in the tensile reinforcement ex #NAME?

Inclination angle of diagonal compressive str q 0.00 degrees


v/f'c #DIV/0!Assumed Inclination angle qassu #NAME? degrees


ex1 #NAME?


Fe #NAME?omponen o e ec ve presrese orce n





Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu ############ NFactored Shear Force due to External Vu 790,731,875 N

#NAME?

#DIV/0!


34/62



Calculation of Vr

Calculate b & q

Checkin

Section 5





















ex1 #NAME?


Fe #NAME?omponen o e ec ve pres rese orce n





Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu ############ NFactored Shear Force due to External Vu 0 N

#NAME?


35/62



Calculation of Vr

Calculate b & q

Checkin

Section 6




















#NAME?Effective stress of P/S after all losses fpe 0 MPa

ex1 #NAME?







Factored Moment due to External Loads Mu 0 N.mmFactored Axial Force due to External Loads Nu 0 NFactored Shear Force due to External Vu 0 N

#NAME?


36/62



Calculation of Vr

Calculate b & q

Checkin

Section 7


















Shear stress on the concrete v -0.263 N/mm2


#NAME?Effective stress of P/S after all losses fpe 1,246 MPa

ex1 #NAME?



the direction of the applied shear Vp 130,900 N





#NAME?


37/62



Calculation of Vr

Calculate b & q

Checkin

Section 8





















ex1 #NAME?








#NAME?


38/62



Calculation of Vr

Calculate b & q

Checkin

Section 9





















ex1 #NAME?








#NAME?


39/62



Calculation of Vr

Calculate b & q

Checkin

Section 10





















ex1 #NAME?








#NAME?


40/62



Calculation of Vr

Calculate b & q

Checkin

Section 11





















ex1 #NAME?








#NAME?


41/62

SECTION PROPERTIES FOR CHECKING NORMINAL RESISTANCEFor Initial stageSection 1 2 3 4 5

Depth of Girder H 750 750 750 750 750Width of Deck Slab bd 920 920 920 920 920

Depth of Deck Slab hd 120 120 120 120 120

Total width of Webs bw 920 920 920 920 920Width of Bottom Slab bs 990 990 990 990 990

Depth of Bottom Slab hs 0 0 0 0 0

Total Area of Prestressing Cables Ap 987.1 987.1 3158.72 3158.72 3158.72Distance from extreme top fibre to

centroid of Prestressing Cables dp -66750 -66750 -66750 -66750 -66750

Area of bottom Reinforcement Asts ance rom ex reme compress ve

fibre to centroid of bottom Reinforcement dst 850

Area of Top Reinforcement AscDistance from extreme compressive

fibre to centroid of Top Reinforcement dsc 850

For final stageSection 1 2 3 4 5

Depth of Girder H 750 750 750 750 750Width of Deck Slab bd 920 920 920 920 920

Depth of Deck Slab hd 120 120 120 120 120

Total width of Webs bw 920 920 920 920 920

Width of Bottom Slab bs 990 990 990 990 990

Depth of Bottom Slab hs 0 0 0 0 0

Total Area of Prestressing Cables Ap 987.1 987.1 3158.72 3158.72 3158.72Distance from extreme top fibre to

centroid of Prestressing Cables dp -66750 -66750 -66750 -66750 -66750

Area of bottom Reinforcement AstDistance from extreme compressive

fibre to centroid of bottom Reinforcement dst 850

Area of Top Reinforcement Ascs ance rom ex reme compress ve

fibre to centroid of Top Reinforcement dsc 850

Material Properties

Specified strength of Prestressing steel fpu 1860 MPa

Yield strength of Prestressing steel f py 1674 MPa

Yield strength of Tensile Reinforcement fy 400 MPa


42/62

Specified compressive strength of Concr f'c 42 MPa

Elastic modulus of Prestressing Steel Ep 197000 MPaElastic modulus of Reinforcement Es 200000 MPaElastic modulus of Concrete Ec 33900 MPa

Stress Limits of concrete (tf/m2)

f'c 40 30Compressive 1835.50 1376.62Tensile -161.23 -139.63

Stress (-) tensile(+) Compress


43/62

8. Horizontal Shear at the interface between girder and deck slab (AASHTO 5.8.4):

Horizontal Shear per unit length of girder V h due to Vertical Shear Vu Vh = Vu/de

Distance from the centroid of tensile steel to the midthickness of the deck deRequired area of reinforcement: Avf

Avf>= max {0.35 bv / fy ; (Vh - c bv - m Pc) / m fy}

Width of the interface between the girder and the deck: bv= 920 mm

Yield strength of reinforcement f y= 400 MPa

Cohesion factor c = 0.17 MPaFriction factor m = 0.7Permanent net compressive force normal to the shear plan Pc= 2475 N

Section SEC-1 SEC-2 SEC-3 SEC-4 SEC-5

de (mm) -66800 -66800 -66800 -66800 -66800

Interface Shear(N):Girder Selfweight G_DC ######## ######## ######## ######## 0Slab+Dia. Selfweight S_DC ######## ######## ######## ######## 0Surface + Railings DW ######## ######## 70072874 53102100 0Max. Live Load LL_MAX ######## ######## ######## ######## ########Creep CR 0 0 0 0 0Shrinkage SH 0 0 0 0 0

Temperature TG 0 0 0 0 0Total ######## ######## ######## ######## ########

Avf required (mm2) 16820447 16298773 12337488 10315790 4336395

Area of Stirrups (mm2) 5881 2714 2714 1357 679

(D12@75) (D12@150) (D12@150) (D12@300) (D14@300)

Total Connector Area Avf (mm2) 5881 2714 2714 1357 4448

Checking FAILURE FAILURE FAILURE FAILURE FAILURE


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Section P/S

N (T) V (T) M(T.m) Vp (T) Np (T) Nmax(T) Nmin(T) Vmax(T)

1 ####### ###### 0.000 0.00 ###### ###### 0.00 158146.38

2 ####### ###### 0.000 0.00 ###### ###### 0.00 152032.47

3 ####### ###### 0.000 0.00 ###### ###### 0.00 104344.00

4 ####### 79073.19 0.000 0.00 ###### ###### 0.00 79073.19

5 ####### 0.00 0.000 0.00 ###### ###### 0.00 0.00

6 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00

7 0.00 0.00 0.000 13.09 393.64 0.00 0.00 0.00

8 0.00 0.00 0.000 21.38 388.39 0.00 0.00 0.00

9 0.00 0.00 0.000 29.29 381.16 0.00 0.00 0.00

10 0.00 0.00 0.000 36.34 374.55 0.00 0.00 0.00

11 0.00 0.00 0.000 38.75 374.55 0.00 0.00 0.00

12 0.00 0.00 0.000 0.00 0.00 0.00 0.00 0.00

External Forces


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Vmin(T) Mmax(T.mMmin(T.mNode

0.00 0.00 0.00 1

0.00 0.00 0.00 2

0.00 0.00 0.00 3

0.00 0.00 0.00 4

0.00 0.00 0.00 5

0.00 0.00 0.00 6

0.00 0.00 0.00 7

0.00 0.00 0.00 8

0.00 0.00 0.00 9

0.00 0.00 0.00 10

0.00 0.00 0.00 11

0.00 0.00 0.00 12


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1 2 3 4 5 6 7 8

Shrinkage Stress due to Differential Shrinkage

Diff. Top of Slab Top of Girder Bottom of G. Ns(N) Ms(N*mm) m

1 SEC- 1 -0.37 0.00 0.00 3.64E+04 1.82E+06 549034784630674.02 SEC- 2 -0.37 0.00 0.00 3.64E+04 1.82E+06 515488398941595.0

3 SEC- 3 -0.37 0.00 0.00 3.64E+04 1.82E+06 515488398941595.0

4 SEC- 4 -0.37 0.00 0.00 3.64E+04 1.82E+06 515488398941595.0

Creep Stress due to Creep Diff.Diff. Top of Slab Top of Girder Bottom of G. NCr(N) Cr(N*mm P(N)

SEC- 1 0.01 0.00 0.00 -5.480E+02 -2.740E+04 1.669E+10

SEC- 2 0.01 0.00 0.00 -1.292E+03 -6.460E+04 1.669E+10

SEC- 3 0.05 0.00 0.00 -5.081E+03 -2.540E+05 4.493E+10

SEC- 4 0.06 0.00 0.00 -5.904E+03 -2.952E+05 4.493E+10

Temp. Stress due to Differential Temp.

Diff. Top of Slab Top of Girder Bottom of G. Nt(N) Mt(N*mm) m

1 SEC- 1 -0.50 0.00 0.00 4.92E+04 2.46E+06 549034784630674.0

2 SEC- 2 -0.50 0.00 0.00 4.92E+04 2.46E+06 515488398941595.0

3 SEC- 3 -0.50 0.00 0.00 4.92E+04 2.46E+06 515488398941595.0

4 SEC- 4 -0.50 0.00 0.00 4.92E+04 2.46E+06 515488398941595.0


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9 10 11 12 13 14 15 16

Ic1(mm4) Ic2(mm4) Ac1(mm2) y1' y1 R2c1 R2c2 B C

3.51E+22 8.25E+07 7.30E+11 387839.8 -362160.2 ###### 833.3 ###### ######3.29E+22 8.25E+07 5.29E+11 392727.7 -357272.3 ###### 833.3 ###### ######

3.29E+22 8.25E+07 5.29E+11 392727.7 -357272.3 ###### 833.3 ###### ######

3.29E+22 8.25E+07 5.29E+11 392727.7 -357272.3 ###### 833.3 ###### ######

Md0 Md1(N*mm) (N*mm) B C(mm) F mm2 y1'(mm) y1(mm) ep1(mm) c12 mm2

0.000E+00 0.000E+00 ####### ####### ####### 387839.8 -362160.2 67500.0 ######

4.653E+14 1.297E+14 ####### ####### ####### 392727.7 -357272.3 67500.0 ######

3.465E+15 9.659E+14 ####### ####### ####### 392727.7 -357272.3 67500.0 ######

4.602E+15 1.283E+15 ####### ####### ####### 392727.7 -357272.3 67500.0 ######

Ic1(mm4) Ic2(mm4) Ac1(mm2) y1' y1 R2c1 R2c2 B C

3.51E+22 8.25E+07 7.30E+11 3.88E+05 -3.62E+05 4.80E+10 8.33E+02 5.49E+14 ######

3.29E+22 8.25E+07 5.29E+11 3.93E+05 -3.57E+05 6.23E+10 8.33E+02 5.15E+14 ######

3.29E+22 8.25E+07 5.29E+11 3.93E+05 -3.57E+05 6.23E+10 8.33E+02 5.15E+14 ######

3.29E+22 8.25E+07 5.29E+11 3.93E+05 -3.57E+05 6.23E+10 8.33E+02 5.15E+14 ######


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17

F

############

######

######

F

1.83E+18

1.72E+18

1.72E+18

1.72E+18


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51 51 0 0 -51.265 300.594 0

52 374.547 0 -48.857 221.35 0

53 381.155 0 -41.761 93.307 0

54 388.39 0 -33.781 -38.495 0

55 393.642 0 -25.414 -63.722 0

56 395.958 0 -12.316 -148.056 0

57 393.642 0 0.72 -165.955 0

58 388.39 0 9.014 -161.73 0

59 381.155 0 16.925 -117.844 0

60 374.547 0 23.966 -58.788 0

61 0 0 26.378 0 0


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Secondary Moment due to Creep (tf.m)

Section Mgirder1 Mslab1 Mps1 Mgirder0 Mslab0 Mps0 M0-M1

SEC-1 0.000 0.000 0.000 -111.599 -87.734 300.594 101.261

SEC-2 46526826.563 12970293.750 -239998824.350 -91.897 -72.808 221.350 180501760.683

SEC-3 346487295.000 96590340.000 -1058376836.774 -35.777 -28.767 93.307 615299230.537

SEC-4 460205951.250 128291715.000 -1058376836.774 17.025 13.724 -38.495 469879162.778

SEC-5 613607935.000 171055620.000 -1058376836.774 26.830 21.591 -63.722 273713266.473

SEC-6 114.756 91.065 -298.353 58.956 47.198 -148.056 50.630

SEC-7 101.688 80.441 -264.915 64.948 51.558 -165.955 33.337

SEC-8 95.787 75.643 -250.176 62.951 49.829 -161.730 29.796

SEC-9 59.290 45.970 -162.376 42.756 32.972 -117.844 15.000

SEC-10 15.914 11.948 -68.993 12.125 8.969 -58.788 3.437

SEC-11 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Secondary Shear due to Creep (tf)

Section Vgirder1 Vslab1 Vps1 Vgirder0 Vslab0 Vps0 V0-V1

SEC-1 126517.100 35269.200 0.000 24.883 18.601 -51.265 -161794.082SEC-2 121625.975 33905.700 0.000 22.880 17.583 -48.857 -155540.069

SEC-3 83475.200 23270.400 0.000 17.568 14.159 -41.761 -106755.634

SEC-4 63258.550 17634.600 0.000 12.180 9.779 -33.781 -80904.972

SEC-5 0.000 0.000 0.000 10.891 8.731 -25.414 -5.793

SEC-6 0.000 0.000 0.000 4.593 3.611 -12.316 -4.113

SEC-7 -6.298 -5.120 13.090 -1.705 -1.510 0.720 -4.167

SEC-8 -7.588 -6.169 21.384 -2.995 -2.558 9.014 -4.167

SEC-9 -12.975 -10.549 29.294 -8.382 -6.938 16.925 -4.166

SEC-10 -18.287 -13.972 36.336 -13.695 -10.362 23.966 -4.167

SEC-11 -20.290 -14.990 38.748 -15.698 -11.380 26.378 -4.167


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M0-M1)x(1-e-f)

70.762

126135675.125

429974663.705

328354278.651

191272414.888

35.381

23.296

20.822

10.482

2.402

0.000

`

(V0-V1)x(1-e-f)

-113062.641-108692.301

-74601.455

-56536.863

-4.048

-2.874

-2.912

-2.912

-2.911

-2.912

-2.912


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Secondary Moment due to DeadLoad Creep (tf.m)

Section Mgirder1 Mslab1 Mgirder0 Mslab0 M0-M1 M0-M1)x(1-e-f)

SEC-1 0.000 0.000 0.000 0.000 0.000 0.000

SEC-2 46526826.563 12970293.750 17.792 11.157 -59497091.364 -41576911.819

SEC-3 ########## 96590340.000 77.206 50.653 ########## ##########SEC-4 ########## 128291715.000 115.096 77.857 ########## ##########

SEC-5 ########## 171055620.000 116.327 78.796 ########## ##########

SEC-6 114.756 91.065 104.248 71.230 -30.343 -21.204

SEC-7 101.688 80.441 47.822 32.820 -101.487 -70.920

SEC-8 95.787 75.643 39.740 27.283 -104.407 -72.960

SEC-9 59.290 45.970 -68.025 -46.817 -220.102 -153.808

SEC-10 15.914 11.948 -177.790 -120.105 -325.757 -227.641

SEC-11 0.000 0.000 -206.885 -138.848 -345.733 -241.600

Secondary Shear due to DeadLoad Creep (tf)

Section Vgirder1 Vslab1 Vgirder0 Vslab0 V0-V1 (V0-V1)x(1-e-f)

SEC-1 126517.100 35269.200 22.750 14.032 -161749.518 -113031.500

SEC-2 121625.975 33905.700 20.381 13.014 -155498.280 -108663.098

SEC-3 83475.200 23270.400 11.953 8.480 -106725.168 -74580.165

SEC-4 63258.550 17634.600 2.906 2.188 -80888.056 -56525.042

SEC-5 0.000 0.000 2.019 1.571 3.590 2.509

SEC-6 0.000 0.000 -6.851 -4.598 -11.448 -8.000

SEC-7 -6.298 -5.120 -15.720 -10.766 -15.069 -10.530

SEC-8 -7.588 -6.169 -16.607 -11.383 -14.234 -9.947

SEC-9 -12.975 -10.549 -25.654 -17.675 -19.806 -13.840

SEC-10 -18.287 -13.972 -34.082 -22.209 -24.031 -16.793SEC-11 -20.290 -14.990 -36.451 -23.227 -24.397 -17.049

Secondary Moment due to PC Creep (tf.m)

Section Mpc1 Mpc0 M0-M1 M0-M1)x(1-e-f)

SEC-1 0.000 0.000 0.000 0.000 0.000

SEC-2 ########## -149.469 ####### 167712463.141 ######

SEC-3 ########## -319.638 ####### 739599636.151 ######

SEC-4 ########## -437.016 ####### 739599554.127 ######

SEC-5 ########## -439.310 ####### 739599552.524 ######

SEC-6 -298.353 -332.567 -34.214 -23.909 -45.113

SEC-7 -264.915 -171.335 93.580 65.394 -5.526

SEC-8 -250.176 -142.295 107.881 75.388 2.428

SEC-9 -162.376 246.964 409.340 286.049 132.241

SEC-10 -68.993 612.154 681.147 475.989 248.349

SEC-11 0.000 805.523 805.523 562.904 321.304


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Secondary Shear due to PC Creep (tf)

Section Vpc1 Vpc0 V0-V1 (V0-V1)x(1-e-f)

SEC-1 0.000 -37.228 -37.228 -26.015

SEC-2 0.000 -33.772 -33.772 -23.600

SEC-3 0.000 -15.863 -15.863 -11.085

SEC-4 0.000 -7.459 -7.459 -5.213SEC-5 0.000 4.081 4.081 2.852

SEC-6 0.000 13.432 13.432 9.386

SEC-7 13.090 22.861 9.771 6.828

SEC-8 21.384 34.159 12.775 8.927

SEC-9 29.294 45.642 16.347 11.424

SEC-10 36.336 53.405 17.069 11.928

SEC-11 38.748 63.746 24.998 17.469


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SURFACE LLMAX

Node Sec N V M N V M N

1 1 0.000 12.298 -1.361 0.000 9.012 2.144 0.000

6 2 0.000 10.862 9.350 0.000 8.569 6.477 0.000

11 3 0.000 5.311 38.258 0.000 6.937 28.640 0.000

16 4 0.000 -1.828 48.863 0.000 5.452 49.910 0.000

21 5 0.000 -2.605 47.755 0.000 5.244 51.238 0.000

26 6 0.000 -2.437 54.923 0.000 2.594 49.296 0.000

31 7 0.000 -9.888 24.917 0.000 1.323 36.206 0.000

36 8 0.000 -3.705 23.372 0.000 2.607 33.904 0.000

41 9 0.000 -11.624 -15.718 0.000 1.487 13.495 0.000

46 10 0.000 -16.760 -65.472 0.000 1.123 12.128 0.000

51 11 0.000 -18.196 -81.640 0.000 1.120 12.906 0.000

56 12 0.000 1.474 -80.709 0.000 8.091 14.838 0.000


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LLMIN DECK

V M N V M

-0.719 -2.092 0.000 -18.629 0.000

-0.726 -0.549 0.000 17.611 14.950

-1.149 -2.616 0.000 13.078 71.342

-3.336 -6.579 0.000 6.786 121.994

-3.589 -6.999 0.000 6.169 125.232

-5.098 -9.366 0.000 0.000 140.654

-6.979 -12.070 0.000 -6.169 125.232

-8.605 -12.285 0.000 -6.786 121.994

-10.489 -19.659 0.000 -13.078 71.342

-11.305 -46.049 0.000 -17.611 14.950

-11.551 -54.291 0.000 -18.629 0.000

-6.664 -53.123


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Table 5.8.3.4.2-1 - Values of and for Sections with Transverse Reinforcement

1 - Values of

v/f'c x x 1000

-0.200 -0.150 -0.100 0.000 0.125 0.250 0.500 0.750 1.000 1.500

0.050 6.78 6.17 5.63 4.88 3.99 3.49 2.51 2.37 2.33 1.950.075 6.78 6.17 5.63 4.88 3.65 3.01 2.47 2.33 2.16 1.900.100 6.50 5.87 5.31 3.26 2.61 2.54 2.41 2.28 2.09 1.720.125 2.71 2.71 2.71 2.60 2.57 2.50 2.37 2.18 2.01 1.600.150 2.66 2.61 2.61 2.55 2.50 2.45 2.28 2.06 1.93 1.500.175 2.59 2.58 2.54 2.50 2.41 2.39 2.20 1.95 1.74 1.350.200 2.55 2.49 2.48 2.45 2.37 2.33 2.10 1.82 1.58 1.210.225 2.45 2.44 2.43 2.37 2.33 2.27 1.92 1.67 1.43 1.180.250 2.36 2.36 2.32 2.30 2.28 2.01 1.64 1.52 1.40 1.30

2 - Values of

v/f'c x x 1000

-0.200 -0.150 -0.100 0.000 0.125 0.250 0.500 0.750 1.000 1.5000.050 27.00 27.00 27.00 27.00 27.00 28.50 29.00 33.00 36.00 41.000.075 27.00 27.00 27.00 27.00 27.00 27.50 30.00 33.50 36.00 40.000.100 23.50 23.50 23.50 23.50 24.00 26.50 30.50 34.00 36.00 38.000.125 20.00 21.00 22.00 23.50 26.00 28.00 31.50 34.00 36.00 37.000.150 22.00 22.50 23.50 25.00 27.00 29.00 32.00 34.00 36.00 36.500.175 23.50 24.00 25.00 26.50 28.00 30.00 32.50 34.00 35.00 35.500.200 25.00 25.50 26.50 27.50 29.00 31.00 33.00 34.00 34.50 35.000.225 26.50 27.00 27.50 29.00 30.50 32.00 33.00 34.00 34.50 36.500.250 28.00 28.50 29.00 30.00 31.00 32.00 33.00 34.00 35.50 38.50

Chu y khi nhap so lieu:

* Cac o ch mau o la so can nhap* Cac hang co nen mau xam ghi la cac hang can an (Hide) trc khi in.


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2.000

1.721.651.451.351.241.111.001.141.25

2.00043.0042.0039.0038.0037.0036.0036.0039.0041.50


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11. Design of Deck Slab

11.1 Sumary of Bending Moment:

Bending Moment due to Live Load:

(a) Continuous Slab

1) Effective Span Length 1.700 m

2) Load 10.000 T

3) Impact Factor IM 33%

4) Positive Moment M=0.8*(1+IM)*(0.12S+0.07) 2.92 T.m/m

5) Negative Moment M=-(1+IM)*(0.15S+0.125)*P -5.05 T.m/m

(2) Cantilever Slab

1) Effective Span Length 0.100 m < 0.5m --> ignore

2) Load 10.000 T

3) Impact Factor IM 33%

4) Negative Moment M= 0.00 T.m/m

Bending Moment due to Self-weight of Slab:

Section A B C

Bending Moment (T.m) -0.152 0.152 -0.150

Bending Moment due to Asphalt Concrete:

Section A B C

Bending Moment (T.m) -0.050 0.050 -0.030

Bending Moment due to Parapet & Railings:

Section A B C

Bending Moment (T.m) 0.000 0.000 -0.424


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Sectional forces of deck slab

Self Surface Parapet ive load with impac ERVICE-II STRENGTH-ISection weight load & Railings (LF=1.0)

M(tfm) M(tfm) M(tfm) M(tfm) M(tfm) M(tfm) M(tfm)Section-A -0.152 -0.050 0.000 -5.054 -0.202 -4.245 -9.109

Section-B 0.152 0.050 0.000 2.915 0.202 2.534 5.366Section-C -0.150 -0.030 -0.424 0.000 -0.603 -0.603 -0.762

Dead load


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Combination of Bending Stress

Top Bottom Upper Lower Top Bottom Top Bottom Top

fibre fibre edge edge fibre fibre fibre fibre fibre

Section A #REF! #REF! -3.01 3.01 -0.99 0.99 -100.24 100.24 #REF!

Section B #REF! #REF! 3.01 -3.01 0.99 -0.99 57.83 -57.83 #REF!

Section C #REF! #REF! -14.37 14.37 -2.90 2.90 0.00 0.00 #REF!

Section D #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Section E #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF! #REF!

Stress Notations: (+): Compressive

(-): Tensile

Live

Prestress Self-weight Surface load Live Load


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Unit: T/m2

Bottom

fibre

#REF!

#REF!

#REF!

#REF!

#REF!

Load

Date post:	04-Apr-2018
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Calculation of L20-H0.75m_new

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