Super T L30m

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Prepared by 2/12/10

Checked by

Approved by

CONTENT

Design Specification - 22TCN-272-05

- AASHTO-LRFD

Scope of project - Permanent bridge

I. DATA

1. General Information

2. Material

2.1.Concrete

2.1.1.Stress Limit

2.1.2.Poission ratio and modulus of rupture

2.2.Strand

2.2.1.Interior Girder

2.2.2.Exterior Girder

2.3.Reinforcment

II. GEOMETRIC PROPERTIES

1. Section Properties

2. Detail of strands

3. Property and position of sections

3.1.Properties of girder

3.2.Properties of composite section

III. DISTRIBUTION FACTOR OF LIVELOAD

1.Distribution factor of moment

2.Distribution factor of shear force

IV. LOADS AND ACTIONS

1. General concept

2. Moment and shear force ( due to DC, DW )

3. Moment and shear force ( due to LL, IM, PL )

V. LOAD COMBINATIONS

1. General concept

2. Load combinations

VII. CHECK INTERIOR GIRDER

1. Loss of prestress

2. Check stress at jack release

3. Check compressive stress at service limit state I

4. Check tensile stress at service limit state III

5. Check stress range in strands at fatigue limit state

6. Strength limit state

7. Check maximum ratio of reinforcement

8. Check minimum ratio of reinforcement

9. Check shear resistance

10. Check tension in longitudinal reinforcement due to shear

11. Check interface shear reinforcement

12. Check composite slab

13. Check the end of girder

14. Camber and deflection

SUPER - T, L=30.00m(in)

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1. General Information

Total of length L = 30.00 m

Effective span length Ls = 29.30 m

Total width of deck B = 12.00 m

Width of wearing surface on the deck W = 10.00 m

Height of girder H = 1750.00 mm

Distance between center of girders S = 2400.00 mm

Average thickness of C.I.P slab hs = 200.00 mm

Thickness of wearing surface hw = 70.00 mm

2. Material

2.1.Concrete

Unit weight of asphant concrete, or wearing concrete c = 22.25 kN/m3

Unit weight of reinforcement c = 24.50 kN/m3

a. Slab Concrete

Concrete strength at 28 days f'cs = 35.00 Mpa

Stress block factor = 0.80

Elastic modulus of concrete at 28 days Ecs = 31750.32 Mpa

b. Girder concrete

Compressive strength of concrete at 28 days f'c = 50.00 Mpa

Tensile strength of concrete at 28 days fr= 4.45 Mpa

Elastic modulus of concrete at 28 days Ec = 37948.89 Mpa

Ratio of elastic modulus between slab and girder n = 0.84 Mpa

Compressive strength of concrete at jack release f'ci 0.80f'c = 40.00 Mpa

Modulus of elasticity of concrete at jack release Ec = 33942.52 Mpa

2.1.1.Stress Limit

Compressive stress before all losses f'c = 0.60f'ci = 24.00 Mpa

Tensile stress before all losses f'ct = 0.5f'ci0.5

= 3.16 Mpa

Compressive stress at service limit state f'c = 0.45f'c= 22.50 Mpa

Tensile stress at service limit state f'ct = 0.5f'c0.5

= 3.54 Mpa

Tensile stress at service limit state (debonding) f'c = 0.00 Mpa

2.1.2.Poission ratio and modulus of rupture

Poission ratio n = 0.20 Mpa

Modulus of rupture Gc = E/(2.(n+1)) = 15812.04 Mpa

2.2.Strand

Strand 15.2 mm, low relaxation strand which complies with : ASTM A416, Grade 270

Cross section area of strand Atps = 140.00 mm2

Unit weight Wps = 1.10 kg/m

Tensile Strength fpu = 1860.00 Mpa

Yield Strength fpy = 0.9fpu = 1674.00 Mpa

Stress Limit before all of losses fpi 0.75 fpu , fpi 1395.00 Mpa

Stress Limit at service limit state fpe 0.80 fpy , fpe 1339.20 Mpa

Modulus of elasticity of strand Eps = 197000.00 Mpa

2.3.Reinforcment

Complying with TCVN

Yield strength fy = 400.00 Mpa

Modulus of elasticity Es = 200000.00 Mpa

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1.Distribution factor of moment

Spacing of girders S = 2400.00 mm

Depth of girder d = 1750.00 mm

Effective length of span L = 29300.00 mm

Number of girder Nb = 5 girders

1.1. Interior girder

Strength limit state, service limit state

1.1.1. For one design lane loaded

Gi = ( S / 910 )0.35

( S.d / L2

)0.25 Gi = 0.371

1.1.2. Two or more design lanes loaded

Gi = ( S / 1900 )0.6

( S.d / L2

)0.125 Gi = 0.592

Conclusion : ( use larger value of 1.1.1 & 1.1.2 ) Gi = 0.592

For fatigue limit state

GF = Gi / 1.2 GF = 0.309

1.2. Exterior girder

1.2.1. For one design lane loaded ( lever rule )

Ge= 1.2(0.5+(S -1800)/2S) Gi = 0.750


Distance from the ex-web of ex-girder to in-edge of curb de = 374.00 mm

Ge = e.Gi = ( 0.97 + de/8700 ).Gi Ge = 0.599


2.Distribution factor of shear force

2.1. Interior girder

Strength limit state, service limit state

2.1.1. For one design lane loaded

Gi = ( S / 3050 )0.6

( d / L )0.1 Gi = 0.653


Gi = ( S / 2250 )0.8

( d / L )0.1 Gi = 0.794


For fatigue limit state

GF = Gi / 1.2 GF = 0.544

2.2. Exterior girder

2.2.1. For one design lane loaded ( lever rule )

Ge= 1.2(0.5+(S -1800)/2S) Gi = 0.750


Ge = e.Gi = ( 0.8 + de/3050 ).Gi Ge =0.733


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Position of check section

3.1.Properties of girder

Section 0 1/8 1/4 1/2 X=1.5 m Unit

A 0.883 0.643 0.643 0.643 1.637 m2

Ix 0.053 0.252 0.252 0.252 0.445 m4

Iy 0.139 0.141 0.141 0.141 0.180 m4

Ixy 0.000 0.050 0.050 0.050 0.030 m4

yb 0.453 0.861 0.861 0.861 0.984 m

yt 0.347 0.889 0.889 0.889 0.766 m

Sb 0.116 0.293 0.293 0.293 0.452 m3

St 0.152 0.284 0.284 0.284 0.581 m3

3.2.Properties of composite section

3.2.1. Effective flange width

Effective span Ls = 29.30 m

Thickness of web hsb = 225.00 mm

Width of flange side bst = 1185.00 mm

Average thickness of deck hs = 200.00 mm Average spacing of girders S = 2400.00 mm

Effective flange width of interior girder bef= 2400.00 mm

Effective flange width of exterior girder bef= 2696.25 mm

3.2.2.Geometric properties of interior girder

Section 0 1/8 1/4 1/2 X=1.5 m Unit

A 1.363 1.123 1.123 1.123 2.117 m2

Ixc 3.2E-01 6.4E-01 6.4E-01 6.4E-01 8.9E-01 m4

Iyc 1.4E-01 1.4E-01 1.4E-01 1.4E-01 1.8E-01 m4

Ixy 0.0E+00 3.1E-01 3.1E-01 3.1E-01 3.1E-01 m4

yb 0.610 1.284 1.284 1.284 1.180 m

yt 0.390 0.666 0.666 0.666 0.770 m

Sbc 0.530 0.496 0.496 0.496 0.755 m3

Stc 0.830 0.955 0.955 0.955 1.157 m3

3.2.3.Geometric properties of exterior girder

Section 0 1/8 1/4 1/2 X=1.5 m Unit

A 1.422 1.182 1.182 1.182 2.177 m2

Ixc 4.2E-01 7.4E-01 7.4E-01 7.4E-01 1.0E+00 m4

Iyc 1.4E-01 1.4E-01 1.4E-01 1.4E-01 1.8E-01 m4

Ixyc 0.0E+00 9.1E-18 9.1E-18 9.1E-18 0.000 m4

ybc 0.622 1.312 1.312 1.312 0.999 m

ytc 0.378 0.638 0.638 0.638 0.751 m

Sbc 0.676 0.560 0.560 0.560 1.002 m3

Stc 1.115 1.152 1.152 1.152 1.332 m3

L

1/21/1/0

xX

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3.1.Dynamic load allowance IM

Joint and slab IM = 75.00 %

Other part

Fatigue and Fracture limit state IM = 15.00 %

Other states IM = 25.00 %

M = 0.5q.x.( L - x ) kNm

V = q.( 0.5L - x ) kN

L = 29.30 m

In the below table, caculation for one design lane loaded, is not composed of distribution factor

With HL-93 : Vz =(145.(L-x)+ 145.(L-x-4.3) + 35(L-x-8.6))/L

With lane load : Vz =9.3(L-x)2/(2L)

If x 4.3 m : My =(145.(L-x)x + 145.(L-x-4.3).x + 35(x-4.3).(L-x))/L

if x < 4.3 m : My =(145.(L-x)x + 145.(L-x-4.3).x + 35(L-x-8.6).x)/L

In fatigue My =(145.(L-x)x + 145.(L-x-9).x + 35(x-4.3).(L-x))/L

Section

x ( m ) LT LT + IM

Vz ( kN ) My ( kNm ) Vz ( kN ) My ( kNm ) Vz ( kN ) My( kNm ) My ( kNm ) My ( kNm )

0.00 293.447 366.809 136.245

2.00 271.263 542.526 339.078 678.157 118.280 253.890 376.326 432.775

3.00 260.171 780.512 325.213 975.640 109.773 366.885 606.462 697.432

4.00 249.078 996.314 311.348 1245.392 101.584 470.580 814.415 936.577

5.00 237.986 1116.480 297.483 1395.599 93.713 564.975 1000.183 1150.210

6.00 226.894 1303.323 283.618 1629.153 86.158 650.070 1163.766 1338.331

7.00 215.802 1467.981 269.753 1834.977 78.921 725.865 1305.166 1500.940

7.33 212.197 1516.719 265.246 1895.898 76.638 748.496 1346.344 1548.295

14.65 130.947 1993.625 163.684 2492.031 34.061 997.995 1652.875 1900.806

HL93 + IM Lane Load Fatigue

HL93 LT=HL93+IM LL

1/21/41/80

x

X

P1 P2

4.3 m 4.3 ~ 9 m

P2

y

x

z

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1. General concept

All limit states shall be considered of equal

( i.Qi ) .Rn = Rr In which

= D.R.I 0.95

State Strength Extreme Service Fatigue

D 1.00 1.00 1.00 1.00

R 1.00 1.00 1.00 1.00

I 1.00 1.05 1.00 1.00

1.00 1.05 1.00 1.00

There are three loaded stages of Super-T girder

Stage 1: Prestress and self weight

Stage 2: Self weight , Prestress, Live load and other action ( wearing,etc )

Stage 3: All action of stage 2 and temperature action

2. Moment and shear force ( due to DC, DW )

Moment and shear force due to Self weight of girder are calculated in appendix 1(on page 9)

Self weight of stay-in-placed concrete formwork(plank) Wsg= 0.93 kN/m

Permanent Weight of deck and weight on the deck are taked as distribution of each girder

if it satifies follow requirements

The width of deck is constant OK

Number of girder Nb= 5 OK

Girder are paralle and approximate rigid OK

The width of lane in overhang part ( mm ) de = 374 OK

Curvature in horizontal plan = 0 OK

Type of transverse section Loi = c OK

Weight of deck Ws= 11.76 kN/m

Weight of wearing surface Ww= 3.12 kN/m

Weight of parapet Wrp1= 8.90 kN/m

Weight of other Item Wrp2= 7.63 kN/m

Weight of parapet and other Item act on this girder Wrp= 7.48 kN/m

Caculated Equation

M = 0.5q.x.( L - x ) kNm

V = q.( 0.5L - x ) kN

L = 29.30 m

Section

x ( m )V ( kN ) M ( kNm ) V ( kN ) M ( kNm ) V ( kN ) M ( kNm ) V ( kN ) M ( kNm )

0.00 321.028 0.000 172.284 0.000 155.206 0.000 648.517 0.000

2.00 252.692 603.842 148.764 321.048 134.017 289.223 535.473 1214.113

3.00 236.010 848.193 137.004 463.932 123.423 417.943 496.437 1730.068

4.00 219.329 1075.863 125.244 595.056 112.829 536.069 457.402 2206.988

5.00 202.648 1286.851 113.484 714.420 102.234 643.600 418.366 2644.872

6.00 185.966 1481.158 101.724 822.024 91.640 740.538 379.330 3043.720

7.00 153.533 1813.078 89.964 917.868 81.046 826.881 324.543 3557.827

7.33 144.032 1898.164 86.142 946.485 77.603 852.661 307.777 3697.310

14.65 -2.010 2520.689 0.000 1261.980 0.000 1136.881 -2.010 4919.551

Total

DC DW ( DC + DW )

Girder Slab Wearing+Parapet

x

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L = 29.30 m

A B

a.Data

Length of head block b1 = 0.80 m

Length of next solid block b2 = 1.20 m

Width of deck b3 = 6.00 m

Width of wearing on the deck b4 = 6.65 m Hight of girder b5 = 6.00 m

Uniform force p1 = 21.62 kN/m



concentric force F = 4.02 kN

b.Equation to calculate

Vertical Reaction Force A = 270.720 kN

if x< =b1 then

Mx = Ax-p1.x2/2

Vx = A - p1.b1 - p2.(x-b1)

if b1 < x

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1. General concept

Load combinations are taked as:

Q = ( i.Qi )

In which

- Load modifier; a factor relating to ductivity, redundancy, and operational importance

i - Load factor

2. Load combinations

Service I : For Checking of compressive stress in prestressed concrete components under service

limit state

Q =1.00( DC + DW ) + 1.00( LL + IM )

Service III : For Checking of tensile stress and crack control in prestressed concrete components

under service limit state

Q =1.00( DC + DW ) + 0.80( LL + IM )

Strength I : For checking of resistance and stability of components under strength limit state

Q =0.90(DC) + 0.65(DW) + 1.75( LL + IM )

Fratigue : For checking of stress due to liveload and impact under fatigue limit state

Q =0.75( LL+IM )

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1. Loss of prestress

Total final loss

fpT =fpES+fpSR+fpCR+fpR2 Mpa

Where

fpES - Loss due to elastic shortening

fpSR - Loss due to shrinkage

fpCR - Loss due to creep of concrete

fpR2 - loss due to relaxation of steel after transfer

1.1.Loss due to elastic shortening

fpES = Ep / Eci . fcpg Mpa

Where

fcpg - Sum of concrete stresses at the center of gravity of prestressing tendons due to the prestressing

force at transfer and the self-weight of the member at the sections of maximum moment

fcgp - be assumed to be 0.75fpu for low-relaxation strands 0.75f pu = 1395 Mpa

pretension force after allowing for the initial losses P = 195.3 kN

Assuming loss of stress after release Loss = 7.977 %

concrete stresses at the center of gravity of the prestressing steel fpi = 1283.7209 Mpa

fcpg = Pi / A + Pi.ec2

/ I - Mg.ec / I

Number of tendon n = 38 b

pretension force after allowing for the initial losses Ppi = 6829.395 kN

Moment due to self weight of girder Mg = 2520.6894 kNm

Average eccentricity of tendon ec = 0.729 m

Area of girder section A = 0.643m

2

Moment of inertia of girder Ix = 0.252 m4

fcpg - Sum of concrete stresses at the center of gravity of tendons f cpg = 17.74 Mpa

Modulus of elasticity of concrete at jack release Eci = 33942.52 Mpa

Modulus of elasticity of strand Ep = 197000.00 Mpa

fpES = 102.95 Mpa

1.2.Loss due to shrinkage

fpSR = 117 - 1.03H Mpa

the average annual ambient relative humidity H = 85.000 %

fpSR = 29.45 Mpa

1.3.Loss due to creep of concrete

fpCR = 12fcpg - 7fcdp 0 Mpa

Where

fcdp

- change of stresses at the center of gravity of the prestressing steel due to

permanent loads except the dead load present at the time the prestress force is applied

Moment due to weight of slab Ms= 1261.98 kNm

Moment due to weight of wearing and parapete Mw+u = 1136.88 kNm

Average eccentricity of prestress tendon ec = 1.171 m

Moment of inertia of composite section Ix = 0.7350 m4

fcdp = 5.46 Mpa

fpCR = 174.63 Mpa

1.4.Loss due to relaxation of steel after transfer

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

loss due to relaxation after transfer fpR2 = 16.80 Mpa

Initial loss finitial = 111.35 Mpa

Sum of loss stress

fpT

=fpES

+fpSR

+fpCR

+fpR2

fpT

= 323.82 Mpa

Initial Prestress loss Loss = 7.982 %

Conclusion

Different from assume and cacualtion of initial loss = -0.061 N.G

Effective initial prestress fpi = 1283.65 Mpa

Check: fpi = 1283.65 1395.00 OK

Effective pretension force after allowing for the initial losses Ppi = 6829.04 kN

Effective final prestress after all of losses fpe = 959.83 Mpa

Check: fpi = 959.83 1339.20 OK

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Total prestressing force after all losses Ppe = 5106.29 kN

H1: Rate of losses

31.79%

9.09%53.93%

5.19%fpES

fpSR

fpCR

fpR2

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For top fiber

ft = Pi/A - Pi.e/St + Mg/St + ftop

ftop = p/A + p.et / St ; p - prestress after initial loss of 2 tendons on top fiber

x n A Pi e St Mg ftop ft Check

(m) strands m2 kN m m

3 kNm Mpa Mpa

2.00 26.00 1.64 4672.50 0.859 0.581 603.84 0.220 -2.798 OK

3.00 28.00 0.64 5031.92 0.733 0.284 848.19 0.559 -1.631 OK

4.00 30.00 0.64 5391.34 0.737 0.284 1075.86 0.559 -1.277 OK

5.00 32.00 0.64 5750.77 0.741 0.284 1286.85 0.559 -0.983 OK

6.00 34.00 0.64 6110.19 0.741 0.284 1481.16 0.559 -0.683 OK

7.00 38.00 0.64 6829.04 0.739 0.284 1813.08 0.559 -0.221 OK

7.33 38.00 0.64 6829.04 0.739 0.284 1898.16 0.559 0.079 OK

14.65 38.00 0.64 6829.04 0.739 0.284 2520.69 0.559 2.274 OK

et : Eccentricity of tendons on top with neutral axis, e : Eccentricity of tendons on bottom with neutral axis

For bottom fiber

fb= Pi/A + Pi.e/Sb - Mg/Sb - fbtop

fbtop=p/A + p.et / Sb ; p - prestress after initial loss of 2 tendons on top fiber

x n A Pi e Sb Mg fbtop fb Check

(m) strands m2 kN m m

3 kNm Mpa Mpa

2.00 26.00 1.64 4672.50 0.859 0.452 603.84 -0.220 10.176 OK

3.00 28.00 0.64 5031.92 0.733 0.293 848.19 -0.559 16.961 OK

4.00 30.00 0.64 5391.34 0.737 0.293 1075.86 -0.559 17.719 OK

5.00 32.00 0.64 5750.77 0.741 0.293 1286.85 -0.559 18.534 OK

6.00 34.00 0.64 6110.19 0.741 0.293 1481.16 -0.559 19.344 OK

7.00 38.00 0.64 6829.04 0.739 0.293 1813.08 -0.559 21.097 OK

7.33 38.00 0.64 6829.04 0.739 0.293 1898.16 -0.559 20.807 OK

14.65 38.00 0.64 6829.04 0.739 0.293 2520.69 -0.559 18.683 OK

et : Eccentricity of tendons on top with neutral axis, e : Eccentricity of tendons on bottom with neutral axis

3. Check compressive stress at service limit state I

Due to effecive prestress and permanent loads

ft = Ppe/A - Ppe.e/St + (Mg+Ms)/St + MSDL/Stc 0.45 f'c

Area of girder section A = 0.64 m2

Check stress of top fiber

x n Ppe e St Stc Mg+Ms MSDL MLT+MLL ft Check

(m) strands kN m m3

1/m3 kNm kNm kNm Mpa

2.00 26.00 3493.78 0.859 0.581 1.157 924.89 289.22 551.44 -1.11 OK

3.00 28.00 3762.53 0.733 0.284 0.955 1312.13 417.94 794.30 1.15 OK

4.00 30.00 4031.28 0.737 0.284 0.955 1670.92 536.07 1015.25 2.19 OK

5.00 32.00 4300.03 0.741 0.284 0.955 2001.27 643.60 1159.97 3.13 OK

6.00 34.00 4568.78 0.741 0.284 0.955 2303.18 740.54 1348.50 3.99 OK

7.00 38.00 5106.29 0.739 0.284 0.955 2730.95 826.88 1515.12 5.06 OK

7.33 38.00 5106.29 0.739 0.284 0.955 2844.65 852.66 1564.55 5.48 OK

14.65 38.00 5106.29 0.739 0.284 0.955 3782.67 1136.88 2064.87 9.06 OK

Due to 1/2.( effecive prestress + permanent loads) and transient loads

ft =0.5(Ppe/A - Ppe.e/St + (Mg+Ms)/St + MSDL.Stc)+ (MLL+MLT)Stc 0.40 f'c

Check stress of the top fiber


(m) strands kN m m3


2.00 26.00 3493.78 0.859 0.581 1.157 924.89 289.22 551.44 0.08 OK

3.00 28.00 3762.53 0.733 0.284 0.955 1312.13 417.94 794.30 1.99 OK

4.00 30.00 4031.28 0.737 0.284 0.955 1670.92 536.07 1015.25 2.74 OK

5.00 32.00 4300.03 0.741 0.284 0.955 2001.27 643.60 1159.97 3.37 OK

6.00 34.00 4568.78 0.741 0.284 0.955 2303.18 740.54 1348.50 4.00 OK

7.00 38.00 5106.29 0.739 0.284 0.955 2730.95 826.88 1515.12 4.71 OK

7.33 38.00 5106.29 0.739 0.284 0.955 2844.65 852.66 1564.55 4.98 OK

14.65 38.00 5106.29 0.739 0.284 0.955 3782.67 1136.88 2064.87 7.30 OK

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Due to effecive prestress and permanent loads and transient loads

ft =Ppe/A - Ppe.e/St + (Mg+Ms)/St + MSDL.Stc + (MLL+MLT)Stc 0.40 f'c

Check stress of the top fiber


(m) strands kN m m3


2.00 26.00 3493.78 0.859 0.581 1.157 924.89 289.22 551.44 2.83 OK

3.00 28.00 3762.53 0.733 0.284 0.955 1312.13 417.94 794.30 1.91 OK

4.00 30.00 4031.28 0.737 0.284 0.955 1670.92 536.07 1015.25 3.16 OK

5.00 32.00 4300.03 0.741 0.284 0.955 2001.27 643.60 1159.97 4.23 OK

6.00 34.00 4568.78 0.741 0.284 0.955 2303.18 740.54 1348.50 5.28 OK

7.00 38.00 5106.29 0.739 0.284 0.955 2730.95 826.88 1515.12 6.50 OK

7.33 38.00 5106.29 0.739 0.284 0.955 2844.65 852.66 1564.55 6.98 OK

14.65 38.00 5106.29 0.739 0.284 0.955 3782.67 1136.88 2064.87 11.03 OK

4. Check tensile stress at service limit state III

For bottom fiber

fb = Ppe/A + Ppe.e/Sb- (Mg+Ms)/Sb - MSDL/Sbc - 0.8(MLL+MLT)/Sbc

Check stress of the bottom fiber

x n Ppe e Sb Sbc Mg+Ms MSDL MLT+MLL fb Check

(m) strands kN m m3

m4 kNm kNm kNm Mpa

2.00 26.00 3493.78 0.859 0.452 0.755 924.89 289.22 551.44 5.76 OK

3.00 28.00 3762.53 0.733 0.293 0.496 1312.13 417.94 794.30 8.66 OK

4.00 30.00 4031.28 0.737 0.293 0.496 1670.92 536.07 1015.25 7.99 OK

5.00 32.00 4300.03 0.741 0.293 0.496 2001.27 643.60 1159.97 7.56 OK

6.00 34.00 4568.78 0.741 0.293 0.496 2303.18 740.54 1348.50 7.13 OK

7.00 38.00 5106.29 0.739 0.293 0.496 2730.95 826.88 1515.12 7.39 OK

7.33 38.00 5106.29 0.739 0.293 0.496 2844.65 852.66 1564.55 6.87 OK

14.65 38.00 5106.29 0.739 0.293 0.496 3782.67 1136.88 2064.87 2.29 OK

5. Check stress range in strands at fatigue l imit state

Compressive stress due to prestress and permanent load

fb = Ppe/A + Ppe.e/Sb - (Mg+Ms)/Sb - MSDL/Sbc

Tensile stress due to frague

ft

= - Mf

/ Sbc

x n Ppe e Sbc Mg+Ms MSDL Mf fb ft Check

(m) strands kN m m4 kNm kNm kNm Mpa Mpa

2.00 26.00 3493.78 0.859 0.755 924.89 289.22 133.93 6.461 -0.133 OK

3.00 28.00 3762.53 0.733 0.496 1312.13 417.94 215.83 9.944 -0.326 OK

4.00 30.00 4031.28 0.737 0.496 1670.92 536.07 289.83 9.629 -0.438 OK

5.00 32.00 4300.03 0.741 0.496 2001.27 643.60 355.95 9.433 -0.538 OK

6.00 34.00 4568.78 0.741 0.496 2303.18 740.54 414.16 9.309 -0.626 OK

7.00 38.00 5106.29 0.739 0.496 2730.95 826.88 464.48 9.833 -0.702 OK

7.33 38.00 5106.29 0.739 0.496 2844.65 852.66 479.14 9.393 -0.724 OK

6. Strength limit state

Ultimate moment

Mu

= 1.25(DC) + 1.5(DW) + 1.75(LL+IM)

Determine neutral axis, consider section is like as Retangular-shape (R) or T-shape (T)

Effective width of flange with interior girder bef= 2400.00 mm

x n As A's Aps bw k c a hs Check

(m) strands mm2

mm2

mm2 mm mm mm mm

2.00 26 1570.80 5629.73 3640.00 935.63 0.280 88.37 70.70 200.00 R

3.00 28 1570.80 5629.73 3920.00 367.38 0.280 97.17 77.73 200.00 R

4.00 30 1570.80 5629.73 4200.00 367.38 0.280 105.94 84.75 200.00 R

5.00 32 1570.80 5629.73 4480.00 367.38 0.280 114.69 91.75 200.00 R

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6.00 34 1570.80 5629.73 4760.00 367.38 0.280 123.41 98.73 200.00 R

7.00 38 1570.80 5629.73 5320.00 367.38 0.280 140.77 112.62 200.00 R

7.33 38 1570.80 5629.73 5320.00 367.38 0.280 140.77 112.62 200.00 R

14.65 38 1570.80 5629.73 5320.00 367.38 0.280 140.77 112.62 200.00 R

x (m) fps As A's Aps bw dp a Mr Mu Check

Mpa mm2

mm2

mm2 mm mm mm kNm kNm

2.00 1831 1570.80 5629.73 3640.00 935.63 1608.75 70.70 11502 2813.26 OK

3.00 1829 1570.80 5629.73 3920.00 367.38 1608.75 77.73 12271 4029.14 OK

4.00 1826 1570.80 5629.73 4200.00 367.38 1608.75 84.75 13035 5144.97 OK

5.00 1823 1570.80 5629.73 4480.00 367.38 1608.75 91.75 13793 6040.24 OK

6.00 1820 1570.80 5629.73 4760.00 367.38 1608.75 98.73 14545 6981.26 OK

7.00 1814 1570.80 5629.73 5320.00 367.38 1608.75 112.62 16032 8015.11 OK

7.33 1814 1570.80 5629.73 5320.00 367.38 1608.75 112.62 16032 8305.6 OK

14.65 1814 1570.80 5629.73 5320.00 367.38 1608.75 112.62 16032 11014.3 OK

7. Check maximum ratio of reinforcement

Distance from extreme compressive fiber to neutral axis c = 638.08 mm

Depth from to Steel Centroid de = 1614.33 mm

Ratio of maximum reinforcement c/de = 0.40

Check : c/de = 0.40 0.42 OK

8. Check minimum ratio of reinforcement

Check : Mr min( 1.2Mcr, 1.33Mu )

Caculation Mcr

Mcr= ( fr+ fpe )Sbc - Md-nc(Sbc/Sb -1)

Where

Tensile strength of concrete at 28 days fr= 4.45 Mpa

Moment due to weight of girder and slab Md-nc

Effective prestress in concrete

fpe = Ppe/A + Ppe.e/Sb

x Md-nc Ppe e Sbc Sb fpe 1.2Mcr 1.33Mu Mr Check

(m) kNm kN m m3

m3 Mpa kNm kNm kNm

2.00 924.89 3493.78 0.859 0.755 0.452 8.24 10757.4 3741.63 11501.7 OK

3.00 1312.13 3762.53 0.733 0.496 0.293 15.26 10646.6 5358.75 12271.4 OK

4.00 1670.92 4031.28 0.737 0.496 0.293 16.41 11031.6 6842.80 13035.2 OK

5.00 2001.27 4300.03 0.741 0.496 0.293 17.56 11440.2 8033.52 13793.2 OK

6.00 2303.18 4568.78 0.741 0.496 0.293 18.66 11845.1 9285.08 14545.3 OK

7.00 2730.95 5106.29 0.739 0.496 0.293 20.82 12773.9 10660.1 16032.3 OK

7.33 2844.65 5106.29 0.739 0.496 0.293 20.82 12679.4 11046.4 16032.3 OK

14.65 3782.67 5106.29 0.739 0.496 0.293 20.82 11900.0 14649.0 16032.3 OK

9. Check shear resistance

Shear Reinforcement Spacing s mm

Area of one stirrup leg Av mm2

Max. Spacing of Reinf. According to Av s1 mm

Max. Spacing of Reinf. According to Vu s2 mm

minimum transverse reinforcement Avmin mm

Vu = 1.25(DC) + 1.5(DW) + 1.75(LL+IM) Vu kN

Check: Av, s

x bv Vu dv Av s s1 s2 Avmins

min(s1,s2)Av Avmin

(m) mm kN mm mm2 mm mm mm mm

2 kNm mm2

2.00 935.63 1194.16 1260.0 402.12 150.0 292.9 600.0 205.92 OK OK

3.00 367.38 1122.19 1260.0 402.12 150.0 746 600.0 80.86 OK OK

4.00 367.38 1050.67 1260.0 402.12 150.0 746 600.0 80.86 OK OK

5.00 367.38 979.58 1260.0 402.12 150.0 746 600.0 80.86 OK OK

6.00 367.38 908.94 1260.0 402.12 150.0 746 600.0 80.86 OK OK

7.00 367.38 823.10 1260.0 402.12 150.0 746 600.0 80.86 OK OK

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7.33 367.38 796.32 1260.0 402.12 150.0 746 600.0 80.86 OK OK

14.65 367.38 272.91 1260.0 402.12 300.0 746 600.0 161.71 OK OK

Assumption angle of inclination 1 deg

Choose angle of inclination deg

Factor

Shear stress in concrete v kN/m2

v = (Vu - .VP)/(.bv.dv)

Shear resistance factor = 0.90

Shear Resistance due to prestress Vp = 0.00 kN

Strain in the tensile reinforcement

x= ( Mu/dv+0.5Nu+0.5Vu.cot-Aps.fpo)/(Es.As + Ep.Aps ) 0.002

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Distance from reinforcment to slab dv= 1.552 m

Shear force act on 1m in length Vh= 769.22 kN / m

Check : Vh.Vn 769.22 1331.35 kN OK

12. Check composite slab

Stress in top fiber of slab

fbs = Ms/St + MSDL/Ic+ 0.8MLT+LL/Ic f'ct =0.45f'c= 15.750 Mpa

x yt ytc hs St Ms MSDL MLT+LL Ic fbs Check

(m) m m m m3 kNm kNm kNm m

4 Mpa

2.00 0.766 0.770 200.00 0.581 240.79 216.92 699.04 1.001 1.19 OK

3.00 0.889 0.638 200.00 0.284 347.95 313.46 1006.89 0.735 2.75 OK

4.00 0.889 0.638 200.00 0.284 446.29 402.05 1286.98 0.735 3.52 OK

5.00 0.889 0.638 200.00 0.284 535.82 482.70 1470.43 0.735 4.15 OK

6.00 0.889 0.638 200.00 0.284 616.52 555.40 1709.42 0.735 4.79 OK

7.00 0.889 0.638 200.00 0.284 688.40 620.16 1920.63 0.735 5.36 OK

7.33 0.889 0.638 200.00 0.284 709.86 639.50 1983.30 0.735 5.53 OK

14.65 0.889 0.638 200.00 0.284 946.49 852.66 2617.52 0.735 7.35 OK

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14.1.At Jack Release

14.1.1. Camber

Prestress load for one tendon after jack release ppe= 179.72 kN

Moment of inertia of girder section Ix = 0.252 m4

Effective span length Ls= 29.300 m

Elastic modulus of concrete at jack release Ec = 33942.519 Mpa

Number ofDebondingb

i (m)Distance e

Ppe(kN)

Camber

(m)1 (rad) 2 (rad)

2 0.034 0.829 359 -0.004 -0.00053 0.00053

2.00 0.085 0.796 359 0.003 0.00042 -0.00042

2.00 0.119 0.746 359 0.003 0.00035 -0.00035

2.00 0.154 0.796 359 0.003 0.00028 -0.00028

2.00 0.188 0.746 359 0.003 0.00022 -0.00022

4.00 0.222 0.696 719 0.005 0.00032 -0.00032

26.00 0.017 0.707 4673 0.059 0.00800 -0.00800

Sum 7189 C=0.073 0.009 -0.009

14.1.2. Defelection

Self weight of girder Wg= 18.24 kN/m

Deflection due to self weight of girder De=5Wg.Ls4/(384.E.Ix) De = -0.020 m

14.1.3. Camber at release

Camber at release = C - De = 0.052 m

14.1.4. Camber at erection due to creep and shrinkage effect

Long term deflection = 1.7C - 1.75De = 0.088 m

14.2.At final stage

14.2.1. Camber and defleclection at release time

Moment of inertia of composite section Ix = 0.735 m4

Effective length Ls= 29.300 m

Elastic modulus of concrete at 28 days Ec = 37948.890 Mpa

Deflection due to self weight of girder De=5Wg.Ls4/(384.E.Ix) De = -0.020 m

Camber due to prestressing C = 0.073 m

14.2.2. Defelection

Self weight of slab Ws= 11.76 kN/m

Deflection due to self weight of slab Dslab=5Wg.Ls4/(384.E.Ix) Dslab = -0.004 m

Self weight of parapet Ws= 7.48 kN/m

Deflection due to self weight of parapet Dp=5Wg.Ls4/(384.E.Ix) Dp = -0.003 m

Self weight of wearing Ww= 3.12 kN/m

Deflection due to self weight of girder Dw=5Wg.Ls4/(384.E.Ix) Dw= -0.001 m

14.2.3. Camber at final time

Camber at final = C - De-Dslab-Dp-Dw = 0.045 m

14.2.4. Camber at final time due to creep effect

Long term deflection = 2.1C - 2.2De-2.15Dslab-2.75(Dp+Dw) = 0.089 m

14.3.Live Load Deflection

Uniform load due to lane load is : w= 9.300 kN/m

Deflection due to lane load is:

lane =5.w.L4/(384.E.I) lane = 0.003 m

Deflection due to truck is:

P (kN) a (m) b (m) x (m) D (m)

145 14.65 14.65 14.65 0.005

145 10.35 18.95 14.65 0.004

35 18.95 10.35 14.65 0.001

Sum truck = 0.011

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Deflection due to live load is:

LL=( lane + truck).DFM = 0.008 m

Limited Deflection due to live load is: Limit = 0.037 m

Check : 0.008 0.037 m OK

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Super T L30m