BANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANH

BANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANHBANG TINH DAM I33m CẦU ĐƯỜNG TIẾNG ANH

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1.2 Material strength & Stress Limits:

1.2.1 Prestressing steel (low-relaxation)

1.2.2 Reinforcement

1.2.3 Concrete

a) Girder Concrete

Compresive strength at time of initial prestress : f'ci = 0.9f'c = 36 MPa Limit of compresive stress at time of initial prestress: 0.6 f'ci = 21.6 MPa 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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Equivalent diameter of strand = 38.83 (mm)

of fibre

(at)

Area of steel equivalen

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)

Area of steel equivalenR1 1 1311 6864.57 1 1084 6864.57 1 884 6864.57 1 576 6864.57 1 330 6864.57R2 1 1041 6864.57 1 848 6864.57 1 679 6864.57 1 418 6864.57 1 210 6864.57R3 1 770 6864.57 1 613 6864.57 1 474 6864.57 1 261 6864.57 1 90 6864.57R4 1 503 6864.57 1 407 6864.57 1 323 6864.57 1 194 6864.57 1 90 6864.57R5 1 236 6864.57 1 202 6864.57 1 172 6864.57 1 126 6864.57 1 90 6864.57

Yb sv (mm)

463460464040308

Ix sv (mm4)

7531557349

1097.469520584277806

1172

66110946991172634

620658263,122,417 219,345,544,100

Section 4

211928353289

620658Section 4Section 4

Section 5Section 5

Properties

259,451,852259,451,852

213,600,768,818

808

834 268,682,488

280,352,466 235,851,995,578827

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03 Calculation I-Beam_I33m.xls【sectionpro】

SHEET NO : 1 / 1

2.2 Sumary of Section Properties

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

Distance from section to left bearing mm 0 2,013 4,025 8,050 16,100 Distance from section to right bearing mm 32,200 30,188 28,175 24,150 16,100 Moment M N.mm 0 547,014,790 1,021,094,274 1,750,447,327 2,333,929,769

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

Distance from section to left bearing mm 0 2,013 4,025 8,050 16,100 Distance from section to right bearing mm 32,200 30,188 28,175 24,150 16,100 Moment M N.mm 0 451,298,755 842,424,343 1,444,156,017 1,925,541,355

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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= 722000 mm2

W =(SFx0.0000025x9.8066 + 0.5x2)/Nd= 3.740 N/mm

W= 3.740 N/mm

32.20 m

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

Space from section to right bearing mm 32,200 30,188 28,175 24,150 16,100

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

Space from section to right bearing mm 32,200 30,188 28,175 24,150 16,100

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 = 32200.00 mm

Distance between the centers of gravity of beam and slab eg = 923.00 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 = 8.38E+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

VEHICULAR LIVE LOADING DATA

Unit Standard load axle Axle concentrated load P1 N 35,000

Tandem Axle concentrated load P 4 N 110,000

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 2,013 4,025 8,050 16,100

Distance from calculated section to right bearing mm 32,200 30,188 28,175 24,150 16,100

Area of Moment influence line MA mm2 0 30,376,172 56,702,188 97,203,750 129,605,000

Area of Shear influence line VA1 > 0 mm2 16,100 14,150 12,327 9,056 4,025

Area of Shear influence line VA2 < 0 mm 2 0 -63 -252 -1,006 -4,025

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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

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

By P2 0 0 2,013 341,967,773 4,025 638,339,844 8,050 1,094,296,875 16,100 1,459,062,500 Truck P3 4,300 0 6,313 293,256,836 8,325 540,917,969 12,350 899,453,125 20,400 1,069,375,000

P2 0 0 2,013 341,967,773 4,025 638,339,844 8,050 1,094,296,875 16,100 1,459,062,500 P3 4,300 0 6,313 70,786,133 8,325 130,566,406 12,350 217,109,375 20,400 258,125,000

By P4 -0.6 0 2,012 182,080,078 4,024 412,070,313 8,049 768,281,250 16,099 1,065,625,000 Tandem P5 0.6 0 2,013 254,267,578 4,026 473,945,313 8,051 809,531,250 16,101 1,065,625,000

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

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03 Calculation I-Beam_I33m.xls【Prestress_1】

SHEET NO : 1 / 2

3.6 Due to prestressing

3.6.1 Stress Loses (22TCN272-05, 5.9.5)

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

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

Stress in Prestressing steel at jacking fpj = 0.72fpu 1339 MPa

Loss due to Friction and Anchor set Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5

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

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 26.01 MPa

e : Distance from CGS to center of gravity of girder -647 mm

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

Loss due to elastic shortening ∆fpES N/mm2 66.2 66.2 66.2 66.2 66.2

Loss due to Shrinkage

∆ fpSR = (117-1.03*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 = 2,442,443,626 N.mm

Change in concrete stress at CGS ∆fcdp N/mm2 -6.98 -6.98 -6.98 -6.98 -6.98

Friction and anchor set:

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03 Calculation I-Beam_I33m.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 = 0.75*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%

Unit Sec - 1 Sec - 2 Sec - 3 Sec - 4 Sec - 5Time estimated in day from stressing to transfer (t) Day 14 14 14 14 14Loss due to relaxation at transfer ∆fpR1 N/mm2 25.0 25.0 25.0 25.0 25.0Loss due to relaxation after transfer ∆fpR2 N/mm2 15.6 15.6 15.6 15.6 15.6

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

Area of bottom fiber strands A ps1 mm2

Total of Losses due to relaxation + ES+ FR+AS N/mm2 340 323 308 277 225

Distance from CGS at bottom fibre to neutral axles d1 mm 69 206 319 498 647Angle in vertical plan between tendon and reinforecement rad 0.09 0.08 0.07 0.05 0

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

Distance from CGS at bottom fibre to neutral axles d1 mm 325 500 666 874 1025Angle in vertical plan between tendon and reinforecement rad 0.09 0.08 0.07 0.05 0

Where : CGS : Central gravity of strand

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03 Calculation I-Beam_I33m.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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03 Calculation I-Beam_I33m.xls【Checking 1_1】

SHEET NO : 1 / 2

4 Checking for initial stage at transfer

4.1 Summary of Sectional forces

W , A : Bending modulus and Area of transform section

PS, DL1, DL2 checking with noncomposite section

Series1 Series2

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if stress value is negative is fibre compress

if stress value is positive is fibre tension

Series1 Series2

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SHEET NO : 1 / 3

5 Checking for final stage at service

a For girder

b Deck slab

c For prestressing tendon

5.1 Summary of Sectional forces at service

DL3, DW checking with composite section

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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

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DL3, DW checking with composite section

fpt : stress in prestress tendon after total loss

if stress value is negative is fibre compress

if stress value is positive is fibre tension

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SHEET NO : 1 / 2

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

Distance from extreme compressive fibre to centroid of

Average stress in Prestress steel at nominal bending

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Checking Maximum

-20,000 -10,000 0 10,000 20,000

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SHEET NO : 1 / 2

5.5 Checking Shear Resistance (22TCN272-05, 5.8.3.3)

Distance from extreme compressive fibre to centroid of

Angle of inclination of transverse reinforcement to longitudinal

Factor indicating ability of diagonally cracked concrete to

Component of effective prestresed force in the direction of the

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SHEET NO : 2 / 2

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03 Calculation I-Beam_I33m.xls【Deflection】

SHEET NO : 1 / 2

6 Checking deflection and camber (22TCN272-05, 2.5.2.6.2)

g : Distribution of live loads per Lane for Moment in exterior beam 1.25

fpt : Stress in Prestressing steel immediately prior to transfer 1100 MPa

fpe : Stress in Prestressing steel after total losses 731 Mpa

* Deflection due to S.W of girder

∆G : Deflection due to self - weight of gider

* Camber due to prestressing at transfer

∆c : Camber due to prestressing

Nut : Prestressing force at transfer (included losses)

ee : Eccentricity from of prestress force from neutral axle at end of gider 69 mm

ec : Eccentricity from of prestress force from neutral axle at middle of gider 647 mm

* Deflection due to S.W of deck slab

∆D : Deflection due to self - weight of deck slab

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

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

W : Uniform self - weight of railing, parapet and barrier 3.74 N/mm

* Deflection due to S.W of surface

Where : ∆S= (5*W*Ltt

4

∆S : Deflection due to self - weight of surface

* Deflection due to Live Load

- Deflection due to Design truck

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03 Calculation I-Beam_I33m.xls【Deflection】

SHEET NO : 2 / 2

Where : DDT : Deflection due to Design truck

Y1 : Value of influential line due to P1 at the middle of span = 6.14E+11 Y2 : Value of influential line due to P2 at the middle of span 6.96E+11 Y3 : Value of influential line due to P3 at the middle of span 6.14E+11

Yi = If (a>0 and a<Ltt / 2 , b*x/(12*Ltt)*(Ltt2 - b2 - x2))

Yi = If (a>Ltt / 2 and a<Ltt , a*x/(12*Ltt)*(Ltt

Suggested muntipliers to be Used as a Guide in Estimating Long-time cambers and deflections

(In PCI table 4.6.2 from PCI design handbook)

without composite topping

with composite topping

Using the multipliers in tble 1 to approximate the creep effect

The net upward deflection at the time the deck is placed is

4 Deflection (downward) - apply to the elastic

deflection cause by composite topping

Final

1 Deflection (downward) component - apply to the elastic

deflection due the member weight at release of Prestress

2 Camber(upward) component - apply to the elastic

camber due to prestress at the release of Prestress

3 Deflection (downward) - apply to the elastic

deflection due to superrimposed dead load only

At erection

1 Deflection (downward) component - apply to the elastic

deflection due the member weight at release of Prestress

2 Camber(upward) component - apply to the elastic

camber due to prestress at the release of Prestress

X3 X2 X1

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