BANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANH

BANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I25 7m CẦU ĐƯỜNG TIẾNG ANH

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02 Calculation I-Beam_I25.7m.xls【Input_material】

SHEET NO : 1 / 1

1.4 Material strength & Stress Limits:

1.4.1 Prestressing steel (low-relaxation)

1.4.2 Reinforcement

1.4.3 Concrete

a) Girder Concrete

Limit of tensile stress at time of initial prestress : 0.58(f'ci)0.5 = 3.48 MPa Limit of compresive stress at service

b) Slab Concrete

Limit of compresive stress at service

1.MATERIAL DATA

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SHEET NO : 1 / 1

2 SECTION PROPERTIES

2.1 Section Input

Section Properties (Origin)

(mm)

SEC-1 1450

SEC-2 1449

SEC-3 1450

SEC-4 1450

SEC-5 1450

Cross Section Properties (PS steel included)

Equivalent diameter of strand = 29.66 (mm)

No of

cable

(No)

Distance

from bottom

of fibre

(at)

Area of steel equivale n

No of cable (No)

Distance from bottom

of fibre (at)

No of cable (No)

of fibre (at)

No of cable (No)

of fibre (at)

No of cable (No)

of fibre (at)

Included Oval holes

Included PS steel

Sevice stage

Iy

Section 4

(mm 3 )

204,870,204 152,060,058,145

151694336504

(mm)

197,302,365 197,302,365

742 215,146,747

(mm 3 )

725

704 707

706 745

575571

Section 4

575571

723

Section

743

Extreme fibre

Section 1

Properties

732

Area (mm 2 )

Bending Modulus

(mm 4 )

Inertia Ix

738 203,304,088 196,303,312 144,813,222,748

141,714,366,383 193,667,610 141,714,366,383 193,667,610

Nslap/con =

Ns/c =

Section 5

Row of

cable

743

709

1049716

Ix inc holes (mm4) 160070283812

Yb inc holes (mm)

area inc holes (mm2)

982655

Ix inc st (mm4) 162326736074 153828298534 146974772379 145393896405 147499185357

311896727716

583 982655

Yt inc st (mm) 708

725

144372240969

314303438731

Ix sv (mm4)

657 1313355

992.598 346976886001

1050

1066

584

Yt sv (mm)

Ytslab sv (mm)

1067 1018

Yb sv (mm)

384

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02 Calculation I-Beam_I25.7m.xls【sectionpro】

SHEET NO : 1 / 1

2.2.1. Cross Section Properties (Oval holes included)

Cross section

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

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

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SHEET NO : 1 / 4

3 Internal forces

3.1 Due to S.W of Girder (DL1)

W = Σ (FsecixLix0.0000025x9.8066)/ Σ Li = 15.700 N/mm

W= 15.700 N/mm

25.00 m

Bending Moment and Shear forces due to S.W of Girder (DL1)

Distance from section to right bearing mm 25,000 23,438 21,875 18,750 12,500

3.2 Due to S.W of Deck Slab and S.W of longitudinal gider (DL2)

Wdr= (2.65*0.2*2*0+2.52*0.2*2)x25/23.3 1.008 N/mm

W= 15.963 N/mm

25.00 m

Bending Moment and Shear forces due to S.W of deck slab (DL2)

Distance from section to right bearing mm 25,000 23,438 21,875 18,750 12,500

Ltt=

12850

350

12500

110 690

A

B

1 0 0 6 0 0 1 0 0

8 0 0

6 0 0

2 0 0 2 0 0 2 0 0

6 0 0

A - A

1 0 0 6 0 0 1 0 0

8 0 0

B - B

Bb

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SHEET NO : 2 / 4

3.3 Due to S.W of Railing, Parapet and Barrier (DL3)

Flc= 361000 mm2

SF=(2*Flc+Fpc)= 722000 mm2

W =(SFx0.0000025x9.8066)/Nd= 3.540 N/mm

W= 3.540 N/mm

25.00 m

Bending Moment and Shear forces due to S.W of Railing , Parapet and Barrier (DL3)

Space from section to right bearing mm 25,000 23,438 21,875 18,750 12,500

3.4 Due to S.W of surface (DW)

25.00 m

B deck = 11000 mm

W = (Bdesk xTlp * 0.0000023*9.8066)/Nd = 2.481 N / mm

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

Space from section to right bearing mm 25,000 23,438 21,875 18,750 12,500

Bending Moment and Shear forces due to S.W of Railing , Parapet and Barrier (DL3)

Ltt=

500 12000

CROSS SECTION

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SHEET NO : 3 / 4

3.5 Due to Live Load plus Impact (LL+IM)

3.5.1 Calculation distribution of live load on cross beam

Calculation span length (6000mm~73000mm) L = 25000.00 mm

Distance between the centers of gravity of beam and slab eg = 818.00 mm

thickness of concrete slab (450mm~1700mm) t= 200.00 mm

Distance from exterior web of exterior beam

and the interior edge of curb or traffic barrier de = 810.00 mm

Longitudinal stiffness parameter factor Kg = 6.15E+11 mm4

Correction factors for load distribution factors for support shear of the obtuse corner 1.00

Distribution of live loads per Lane for Moment in

Distribution of live loads per Lane for Shear in

VEHICULAR LIVE LOADING DATA

Unit Standard load Distance from axle to front axle Axle concentrated load P1 N 35,000

Lane Load Uniform distributed load W N / mm 9.30

3.6.2 Calculation value of influence line

Distance from calculated section to left bearing mm 0 1,563 3,125 6,250 12,500

Distance from calculated section to right bearing mm 25,000 23,438 21,875 18,750 12,500

Area of Moment influence line MA mm2 0 18,310,547 34,179,688 58,593,750 78,125,000

Area of Shear influence line VA1 > 0 mm2 12,500 10,986 9,570 7,031 3,125

4.3

P4

MY5

Ltt

4.3

MY1

P5

MY4

1.2

2 P3

4.3

P4

VY5

Ltt

4.3

VY2 VY3

VY1

P5

VY4 1.2

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SHEET NO : 4 / 4

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

Truck P3 4,300 0 5,863 216,791,992 7,425 398,183,594 10,550 654,765,625 16,800 743,125,000

P2 0 0 1,563 265,502,930 3,125 495,605,469 6,250 849,609,375 12,500 1,132,812,500 P3 4,300 0 5,863 52,329,102 7,425 96,113,281 10,550 158,046,875 16,800 179,375,000

Tandem P5 0.6 0 1,563 196,259,766 3,126 365,664,063 6,251 623,906,250 12,501 818,125,000

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

0

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02 Calculation I-Beam_I25.7m.xls【Prestress_1】

SHEET NO : 1 / 2

3.6 Due to prestressing

3.6.1 Stress Loses (22TCN272-05, 5.9.5)

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

Specified compressive strength of Concrete at time of stress transferf'ci = 0.9f'c 36 MPa

Loss due to Elastic shortening

∆f pES =(n-1)*E p *f cgp /(2*n*E ci )

E ci Modulus of elasticity of concrete at transfer

E ci = 0.043*y c (1.5) *(f ci ') (0.5) = 32250 MPa

n is the number of identical tendon 5

f cgp Sum of concrete stresses at the center of gravity of prestressing tendons due to prestressing force at trasfer and the self-weight

of the member at the section of maximum moment

fo due to self - weight of girder

Mo Moment due to self-weight of girder

fp due to prestressing steel : fp = N/ A + N*e*e/Ix 17.79 MPa

e : Distance from CGS to center of gravity of girder -572 mm

Loss due to Shrinkage

∆ fpSR = (93-0.85*H)

Loss due to Creep

∆f pCR = 12.0 *f cgp - 7.0*∆f cdp ≥ 0

∆f cdp change 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

Msw : Moment due to self - weight of deck slab , surface, railing and parapet

Msw = 1,717,524,797 N.mm

Friction and anchor set:

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02 Calculation I-Beam_I25.7m.xls【Prestress_1】

SHEET NO : 2 / 2

Loss due to relaxation

Loss due to relaxation at transfer (Initial stage)

∆f pR1 = log(24.0*t) / 40.0*[f pj / f py - 0.55]*f pj

f pj : initial stress in strand at the end of prestressing = 0.72*f pu

Loss due to relaxation at after transfer (final stage)

∆f pR2 = (138 - 0.4*∆f pES - 0.2*(∆f pSR + ∆f pCR ))*30%

3.6.2 Internal forces due to prestressing

Bending moment, shear force and normal force due to prestressing

INITIAL STAGE AT TRANSFER

Initial prestress σi = Jacking stress σj - (prestress losses due to relaxation at transfer and Elastic shortening)

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

σj = fpt

Normal force N = σi1*Aps1 (A'ps1) + σi2*Aps2

Shear force V = 0

Moment M = σi1*Aps1(A'ps1)*d1 - σi2*Aps2*d2

d1 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

FINAL STAGE AT SERVICE

Prestress σi = Jacking stress σj - (total losses of prestress)

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

σj = fpe

Normal force N = σi1*Aps1 (A'ps1) + σi2*Aps2

Shear force V = 0

Moment M = σi1*Aps1(A'ps1)*d1 - σi2*Aps2*d2

d1 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

Where : CGS : Central gravity of strand

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02 Calculation I-Beam_I25.7m.xls【Summary】

SHEET NO : 1 / 1

3.7 Summary of sectional forces

3.7.1 Summary of sectional forces for initial stage(at tranfer)

3.7.2 Summary of sectional forces for final stage(service stage)

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SHEET NO : 1 / 1

4 Checking for initial stage at transfer

Specified compressive strength of Concrete f' c 40 Mpa = 40.0 N / mm2

at time of initial prestressing f' ci = 0.9*f' c 36 Mpa = 36.0 N / mm2

Compressive stress limit [ f 1 ] = 0.6*f' ci 21.6 Mpa = 21.60 N / mm2

Tensile stresses limit [ f 2 ] = 0.25*(f' ci ) 0.5

<=1.38 1.38 Mpa = 1.38 N / mm2

4.1 Summary of Sectional forces

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

M N.mm 0 287,467,534 536,606,064 919,896,110 1,226,528,146

N N 3,719,456 3,787,916 3,824,016 3,892,251 4,043,399

M N.mm 0 -666,166,502 -1,068,146,202 -1,709,098,460 -2,313,198,546

N N 3,719,456 3,787,916 3,824,016 3,892,251 4,043,399

M N.mm 0 -378,698,967 -531,540,138 -789,202,350 -1,086,670,400

M N.mm 0 292,292,450 545,612,573 935,335,840 1,247,114,453

5.2 Calculating of Sectional stress at top, bottom of girder and top slab

f b = M / W - N / A

f t = -M / W - N / A

W , A : Bending modulus and Area of transform section

PS, DL1, DL2 checking with noncomposite section

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

Stress by PS

Stress by DL1

f b N / mm 2

Stress by DL2

f t N / mm 2

4.2 Checking sectional stress for initial stage at transfer (22TCN272-05, 5.9.4.1)

if f b, f t <0 then |f b | or |F t |< [ f 1 ] ⇒ OK

if f b, f t > 0 then |f b |, |F t |< [f 2 ] ⇒ OK

f b N / mm 2

Checking sectional stress f t N / mm 2

4.3 Checking sectional stress for stage pure slab concrete (22TCN272-05, 5.9.4.1)

f b N / mm 2

-25

-15

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000

Leng of girder(mm) Stress on girder

Series1 Series2

-25

-15

0

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000

Stress on girder

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02 Calculation I-Beam_I25.7m.xls【Checking 2_1】

SHEET NO : 1 / 3

5 Checking for final stage at service

a For girder

Compressive stress limit due to Ps + DL [ f1 ] = 0.45*f'c 18 Mpa = 18.0 N / mm2 Compressive stress limit due to LL + 1/2 (Ps + DL) [ f2 ] = 0.4*f'c 16.0 Mpa = 16.0 N / mm2 Compressive stress limit due to Ps + (DL + LL) [ f3 ] = 0.6*f'c 24 Mpa = 24.0 N / mm2 Tensile stresses limit at service stage [ f4 ] = 0.5*(f'c )0.5 3.16 Mpa = 3.16 N / mm2

b Deck slab

Compressive stress limit due to Ps + DL [ f1 ] = 0.45*f'c 18 Mpa = 18.0 N / mm2 Compressive stress limit due to LL + 1/2 (Ps + DL) [ f2 ] = 0.4*f'c 16.0 Mpa = 16.0 N / mm2 Compressive stress limit due to Ps + (DL + LL) [ f3 ] = 0.6*f'c 24 Mpa = 24.0 N / mm2 Tensile stresses limit at service stage [ f4 ] = 0.5*(f'c )0.5 3.16 Mpa = 3.16 N / mm2

c For prestressing tendon

Tensile stresses limit at service stage [ f5 ] = 0.8*f'py 1339.20 Mpa = 1339.20 N / mm2

5.1 Summary of Sectional forces at service

M N.mm 0 -1,291,905,757 -1,717,762,640 -2,304,503,700 -2,837,707,680

5.2 Calculating of Sectional stress at top, bottom of girder and top slab

f b = M / W - N / A

f t = -M / W - N / A

DL3, DW checking with composite section

ft slab= (-M / W - N / A) * modular ratio between slab and girder

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

Stress by PS

Stress by DL1

Stress by DL2

Stress by DL3

Stress by DW

Stress by LL

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

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SHEET NO : 2 / 3

5.3 Checking sectional stress (22TCN272-05, 5.9.4.2)

1.Checking stress due to : Ps + DL1 + DL2 + DL3 + DW + LL

2.Checking stress due to: Ps + DL1 + DL2 + DL3 + DW

3.Checking stress due to: 1/2 (DL1 + DL2 + DL3 + DL4 +Ps) + LL

-30.00

-20.00

-10.00

0.00

10.00

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000

Length of girder

-20.00

-15.00

-10.00

-5.00

0.00

5.00

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000

Length of girder

Stress sevice II

Seri es1 Seri es2

-20.00

-15.00

-10.00-5.00

0.00

5.00

10.00

15.00

20.00

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 24000 26000 28000 30000 32000 34000

Stress sevice III

Seri es1 Seri es2 Seri es3

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SHEET NO : 3 / 3

4.Checking stress in prestessing tendon due to: DL1 + DL2 + DL3 + DL4 +Ps + LL

If f s < [ f 5 ] ⇒ OK

f s = f pt + n t *M/W

DL3, DW checking with composite section

fpt : stress in prestress tendon after total loss

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

Note:

if stress value is negative is fibre compress

if stress value is positive is fibre tension

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SHEET NO : 1 / 2

5.3 Checking Flexural Resistance (22TCN272-05, 5.7.3.2.2)

η*Mu < Mr ⇒ OK

M r = ϕ*M n

M n = A ps *f ps *(d p - a/2) + A s *f y *(d s - a/2) - A' s *f' y *(d' s - a/2) + 0.85*f' c (b - b w )* β 1 *h f *(a/2 - h f /2)

a = c* β 1

c = (A ps *f pu + A s *f y - A' s *f' y ) / (0.85*f' c * β 1 *b + k*A ps *f pu /d p )

f ps = f pu *(1 - k*c/d p )

k=2*(1.04-f py /f pu )

Unit Section 1 Section 2 Section3 Section 4 Section 5 Load combination 1.25*(DL1 + DL2 + DL3) + 1.5*DW + 1.75*LL Mu N.mm 0 1,708,126,547 3,180,200,031 5,497,984,599 7,284,837,267

Distance from extreme compressive fibre to centroid of

Distance from extreme compressive fibre to the Neutral

Average stress in Prestress steel at nominal bending

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