Psc Box Girder Bridge Design In Irc

Structural Design of Pre Stressed Concrete (PSC) Box Girder Bridges in IRC Standard with IRC 6 Loadings by ASTRA Pro

Foreword: The procedure starts with Analysis for DL, SIDL, Live Load (Multi lane vehicle moving load), then stepwise design considering temperature, creep shrinkage etc. for Flexure, Shear including Blister Blocks etc. and finally producing editable CAD drawings with relevant structural & construction details.

The detail step wise calculations are provided in MS-Excel Worksheet.

Input for Live Loads by IRC 6 Class Combinations is very simple in ASTRA Pro

The Design of Deck Slab with Transverse Analysis by Effective Width Method,

LONGITUDINAL ANALYSIS & DESIGN OF BOX GIRDER

Basic Design Data Overall Span (C/C spacing of exp. joint) Effective Span (C/C spacing of Bearing) Distance between C/L of Brg. and C/L of Exp. Joint Girder end to bearing centre line Expansion gap Width of deck Depth of Box Girder Grade of Concrete of Girder Age of concrete for at transfer Maturity of concrete for at transfer Strength concrete at the time of transfer Age of girder at the time of casting of SIDL Maturity of girder at the time of casting of SIDL

Extra time dependent loss to be considered Wearing coat thickness

= = = = = = = = = = = = = = =

48.750 47.750 0.500 0.240 0.040 9.750 2.500 40 14 87 34.8 56 100 20.0 0.065

m m m m m m m Mpa days % Mpa days % % m

CALCULATION OF SECTION PROPERTIES OF SINGLE CELL BOX GIRDER DW HW2

HW1

Td

CH1 HH1

5

HH2

6

1

Tf

3

Tw C2

Ttip

2

4

C1

11

7

HW3

D1

D

K2

HH3

10

Angle q

D2 K1

Ts

IW

NOTE :

8

9

SW

1. ALL DIMENSIONS ARE TO BE GIVEN IN METERS 2. CELLS SHADED ARE NOT BE GIVEN ANY INPUT

SECTION

Support

D away from support

L/8

L/4

3L/8

L/2

Web Inclination, θ(deg)

17.6501

17.6501

17.6501

17.6501

17.6501

17.6501

D

2.500

2.200

1.900

1.600

1.300

1.000

DW Td C1 C2 Ttip

9.750 0.225 1.500 0.000 0.200

9.750 0.225 1.500 0.000 0.200

9.750 0.225 1.500 0.000 0.200

9.750 0.225 1.500 0.000 0.200

9.750 0.225 1.500 0.000 0.200

9.750 0.225 1.500 0.000 0.200

Tf

0.300

0.300

0.300

0.300

0.300

0.300

IW D1 Tw SW Ts D2 K1 K2

0.700 2.200 0.600 4.500 0.550 0.000 0.0000 0.1750 0.409 0.083

0.700 2.200 0.579 4.500 0.260 -0.300 -0.0955 0.0827 0.485 0.097

0.700 2.200 0.480 4.500 0.260 -0.600 -0.1909 0.0827 0.582 0.116

0.700 2.200 0.310 4.500 0.260 -0.900 -0.2864 0.0827 0.750 0.150

0.700 2.200 0.310 4.500 0.260 -1.200 -0.3818 0.0827 0.750 0.150

0.700 2.200 0.310 4.500 0.260 -1.500 -0.4773 0.0827 0.750 0.150

1.850 0.000 0.000 0.000 0.000

1.850 0.000 0.000 0.000 0.000

1.850 0.000 0.000 0.088 0.044

1.850 0.000 0.000 0.300 0.150

1.850 0.000 0.000 0.300 0.150

1.850 0.000 0.000 0.300 0.150

Total Depth Top Flange

cantilever

Web

soffit Slab

HW1

t. hnch1

HH1

CH1 t. hnch2 bot. hnch

HW2 HH2

HW3 HH3

1

2

Area Yt

1.5188 0.1125

1.5188 0.1125

1.5188 0.1125

1.5188 0.1125

1.5188 0.1125

1.5188 0.1125

A.Yt

0.1709

0.1709

0.1709

0.1709

0.1709

0.1709

A.Yt2

0.0192

0.0192

0.0192

0.0192

0.0192

0.0192

Iself-xx

0.0064

0.0064

0.0064

0.0064

0.0064

0.0064

Iself+A.Yt2

0.0256

0.0256

0.0256

0.0256

0.0256

0.0256

IY-Y Area Yt

5.7665 0.6000 0.1000

5.7665 0.6000 0.1000

5.7665 0.6000 0.1000

5.7665 0.6000 0.1000

5.7665 0.6000 0.1000

5.7665 0.6000 0.1000

A.Yt

0.0600

0.0600

0.0600

0.0600

0.0600

0.0600

A.Yt2

0.0060

0.0060

0.0060

0.0060

0.0060

0.0060

0.0020

0.0020

0.0020

0.0020

0.0020

0.0020

0.0080

0.0080

0.0080

0.0080

0.0080

0.0080

IY-Y Area Yt

10.3219 0.1500 0.2333

10.3219 0.1500 0.2333

10.3219 0.1500 0.2333

10.3219 0.1500 0.2333

10.3219 0.1500 0.2333

10.3219 0.1500 0.2333

A.Yt

0.0350

0.0350

0.0350

0.0350

0.0350

0.0350

A.Yt2

0.0082

0.0082

0.0082

0.0082

0.0082

0.0082

Iself

0.0001

0.0001

0.00008

0.0001

0.0001

0.0001

Iself+A.Yt2

0.0083

0.0083

0.0083

0.0083

0.0083

0.0083

IY-Y Area Yt

2.2711 0.1259 0.2500

2.2711 0.1215 0.2500

2.2711 0.1007 0.2500

2.2711 0.0651 0.2500

2.2711 0.0651 0.2500

2.2711 0.0651 0.2500

A.Yt

0.0315

0.0304

0.0252

0.0163

0.0163

0.0163

A.Yt2

0.0079

0.0076

0.0063

0.0041

0.0041

0.0041

0.0001

0.0001

0.0001

0.0001

0.0001

0.0001

0.0080

0.0077

0.0064

0.0041

0.0041

0.0041

1.18344 0.0339636 0.2527

1.14995 0.0470644 0.2573

0.98477 0.0675352 0.2637

0.67197 0.11253 0.2750

0.67197 0.11253 0.2750

0.67197 0.11253 0.2750

Iself Iself+A.Yt

3

4

2

Iself Iself+A.Yt

2

IY-Y Area Yt A.Yt 5

0.0086

0.0121

0.0178

0.0309

0.0309

0.0309

0.00217

0.00312

0.00470

0.00851

0.00851

0.00851

0.000013

0.000025

0.000050

0.000141

0.000141

0.000141

0.00218

0.00314

0.00475

0.00865

0.00865

0.00865

IY-Y Area Yt

0.153355587 0.00000 0.30803

0.222931747 0.00000 0.32203

0.339551023 0.00000 0.34103

0.624999216 0.00000 0.37503

0.624999216 0.00000 0.37503

0.624999216 0.00000 0.37503

A.Yt

0.00000

0.00000

0.00000

0.00000

0.00000

0.00000

A.Yt2

0.00000

0.00000

0.00000

0.00000

0.00000

0.00000

0.000000

0.000000

0.000000

0.000000

0.000000

0.000000

A.Yt2 Iself Iself+A.Yt2

6

Iself Iself+A.Yt2

7

0.00000

0.00000

0.00000

0.00000

0.00000

0.00000

IY-Y Area Yt

5.10338E-08 2.07781 1.12500

5.45254E-08 1.99294 1.12000

5.91495E-08 1.34995 0.97000

6.76035E-08 0.67665 0.82000

6.76035E-08 0.48146 0.67000

6.76035E-08 0.28628 0.52000

A.Yt

2.33754

2.23209

1.30945

0.55486

0.32258

0.14886

A.Yt2

2.62973

2.49994

1.27017

0.45498

0.21613

0.07741

0.471403

0.446683

0.201997

0.060989

0.021971

0.004619

Iself Iself+A.Yt

2

IY-Y Area Yt A.Yt 8

0.23810

0.08203

4.615062213 1.36855 1.17000

2.82930776 1.41818 0.87000 1.23382

2.52465

2.24661

1.93880

1.60120

5.22602

3.97650

2.85003

1.87340

1.07342

Iself

0.062391

0.006871

0.007150

0.007430

0.007709

0.007989

12.31519

5.23289

3.98365

2.85746

1.88111

1.08141

IY-Y Area Yt

4.1765625 0 2.5

2.236470383 0.028636364 2.3

2.520791371 0.114545455 2.1

2.828242494 0.257727273 1.9

3.159728283 0.458181818 1.7

3.516153268 0.715909091 1.5

A.Yt

0.00000

0.06586

0.24055

0.48968

0.77891

1.07386

A.Yt2

0.00000

0.15149

0.50515

0.93040

1.32415

1.61080

0.000000

0.000143

0.002291

0.011598

0.036655

0.089489

2

0.00000

0.15163

0.50744

0.94199

1.36080

1.70028

IY-Y Area Yt

0 0.09625 2.13333

0.149115285 0.02151 2.02667

0.613383809 0.02151 1.72667

1.418972347 0.02151 1.42667

2.59309136 0.02151 1.12667

4.163994999 0.02151 0.82667

A.Yt

0.20533

0.04359

0.03714

0.03069

0.02423

0.01778

A.Yt2

0.43804

0.08835

0.06413

0.04378

0.02730

0.01470

Iself

0.00162

0.00008

0.00008

0.00008

0.00008

0.00008

Iself+A.Yt2

0.43966

0.08843

0.06421

0.04386

0.02738

0.01478

IY-Y Area Yt

0.513022526 0.00000 1.95000

0.121131737 0.00000 1.94000

0.131072048 0.00387 1.62533

0.141404322 0.04500 1.29000

0.152128559 0.04500 0.99000

0.163244759 0.04500 0.69000

A.Yt

0.00000

0.00000

0.00629

0.05805

0.04455

0.03105

A.Yt2

0.00000

0.00000

0.01023

0.07488

0.04410

0.02142

0.00000

0.00000

0.00000

0.00006

0.00006

0.00006

0.00000

0.00000

0.01023

0.07494

0.04416

0.02148

0

0

0.015344285

0.216794591

0.23605115

0.256127751

7.078 8.356 15.908 1.181 1.319 6.044 40.718 5.119 4.580

5.700 5.175 8.472 0.908 1.292 3.775 38.040 4.158 2.921

5.1962 4.1489 6.0907 0.798 1.102 2.778 34.424 3.479 2.522

4.766 3.385 4.489 0.710 0.890 2.085 30.550 2.935 2.343

4.821 3.085 3.606 0.640 0.660 1.633 30.412 2.552 2.473

4.933 2.818 2.955 0.571 0.429 1.344 30.585 2.353 3.136

Iself Iself+A.Yt IY-Y AREA, A ΣΑ.Y ΣΑ. t ΣIself+A.Yt2 Yt Yb Ix-x IY-Y Zt Zb

0.51597 6.287694741 1.31891 1.47000

5.50688

Iself+A.Yt

11

1.47216 11.45973895 1.26927 1.77000

12.25280

Iself

10

2.94662 15.80097891 1.21964 2.07000

A.Yt2 Iself+A.Yt2

9

3.10113 16.33170343 2.47500 2.22500

m2 m3 m4 m m m4 m4 m3 m3

2

Summary of Bending Moments & Shear Forces at Various Sections Selfweight of Box Girder:

2.25

10.19

11.935

C.L of Span

w2 w1

w3

0.5

23.875

w1 w2 w3 Support Reaction

= = = =

18.58 15.78 12.95 342.7

t/m t/m t/m t

Five % extra taken for blister, deviator & future prestressing

B.M & S.F Component

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

0.0 336.0

779.0 291.0

1695.0 239.0

2865.0 156.0

3563.0 78.0

3795.0 0.0

B.M (t.m) S.F (t)

Due to SIDL

C.L of Span w 23.875

0.5

w Support Reaction Component

= =

3.60 t/m 87.8 t

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

0.0 87.8

203.2 77.0

448.4 64.5

769.1 43.0

961.5 21.5

1026 0.0

Design B. Moment Design S.F

Carriageway Live Load Impact Factor =

1.084

5%

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

Governing Live Load

0.0

184.7

494.2

820.6

1009.6

1042.8

Carriageway Live Load (incl. impact) & distortion

0.0

210.2

562.4

933.8

1148.9

1186.6

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

Governing Live Load

99.4

86.0

70.8

61.4

27.2

9.0

Ecc of Live Load

1.325

1.780

1.780

1.325

1.325

1.325

Carriageway Live Load (incl. impact) & distortion

113.1

97.9

80.6

69.9

31.0

10.2

Component

Bending Moment

Distorsion taken =

Component

Shear Force

Summary of Design Forces A. Bending Moments at various sections (in T.m) Component Self Wt. Of Box Girder Superimposed Dead Load Carriageway Live Load TOTAL DESIGN B.M (t.m)

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

0.0 0.0 0.0 0

779.0 203.2 210.2 1192

1695.0 448.4 562.4 2706

2865.0 769.1 933.8 4568

3563.0 961.5 1148.9 5673

3795.0 1025.6 1186.6 6007

B. Summary of Shear Forces at various sections (in T) Ultimate Load Factor : DL = 1.25 Ecc of DeadLoad wrt c/l of box = SIDL = 2 Ecc of SIDL wrt c/l of box = LL = 2.5

0 0

m m

Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

Self Wt. Of Box Girder Superimposed Dead Load Carriageway Live Load

336.0 87.8 113.1

291.0 77.0 97.9

239.0 64.5 80.6

156.0 43.0 69.9

78.0 21.5 31.0

0.0 0.0 10.2

TOTAL ULT. DESIGN S.F (t)

878

762

629

456

218

26

CORRESPONDING MULT. (t.m)

0

1906

4422

7454

9249

9761

CORRESPONDING TULT. (t.m)

375

435

359

231

103

34

Component

Calculation of Prestressing Force & Its Effects at Various Sections A. CONSTRUCTION PROGRAM & PRESTRESSING STAGES

i) ii) iii)

ACTIVITY Completion of casting of Box Girder 1st Stage prestress Completion of wearing coat, crash barrier

DAY AFTER CASTING 0 day 14 day 56 day

fcj (MPa) 34.80 40.00

B. TENDON PARTICULARS 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

Nominal Diameter Nominal Area Nominal Mass Yield Strength Tensile Strength Minimum Breaking Load Young's Modulus of Elasticity Jacking Force at Transfer (% of Breaking Load) Slip at Jacking end Coefficient of Friction Wobble Friction Coefficient Relaxation of prestressing steel at 70% uts Relaxation of prestressing steel at 50% uts Age of concrete for 1st Stage prestressing Dia of Prestressing Duct Concrete Grade

D A Pu Fy Fu Pn Eps Pj s m k Re1 Re2 td1 qd Fcu

15.2 140 1.1 1670 1860 260.7 195 76.5 6 0.17 0.002 35.0 0 14 110 40

mm sq.mm Kg/m MPa MPa KN Gpa % mm per radian per metre Mpa MPa days mm MPa

17)

Modulus of Elasticity of Concrete (28 days)

Ec

31622.8

Mpa

C. FORCES AFTER FRICTION SLIP (For Friction & Slip calculation refer next few sheets) Support Section

Daway from support

1/8th span section

1/4th span section

3/8th span section

Mid span

0.00

2.50

5.97

5.97

5.97

5.97

m

1.672

1.505

1.274

0.876

0.478

0.130

t

326.6

335.9

342.6

345.5

348.3

345.4

m

1.104

0.970

0.783

0.462

0.147

0.130

t

326.5

335.8

343.1

347.4

350.7

333.6

m

0.000

0.000

0.000

0.000

0.167

0.130

t

0.0

0.0

0.0

0.0

316.9

334.2

m

0.000

0.000

0.000

0.279

0.130

0.130

t

0.0

0.0

0.0

307.3

338.6

339.5

m

0.522

0.312

0.130

0.130

0.130

0.130

t

328.7

330.6

338.4

341.4

339.7

335.6

m

0.248

0.130

0.130

0.130

0.130

0.130

t

317.0

325.0

336.5

343.1

342.0

340.9

m

0.248

0.130

0.130

0.130

0.130

0.130

t

338.2

345.3

347.0

350.0

353.0

356.0

9.1

9.1

9.1

11.1

12.1

12.1

Section Distance from Left support

UNIT

1

No. of Cables

2

Ecc. From sofit

Px (per Cable) 2

No. of Cables

2

Ecc. From sofit

Px (per Cable)

3

No. of Cables

1.052

Ecc. From sofit

Px (per Cable)

4

No. of Cables

2

Ecc. From sofit

Px (per Cable)

5

No. of Cables

2

Ecc. From sofit

Px (per Cable)

6

No. of Cables

2

Ecc. From sofit

Px (per Cable) No. of

7

Cable No.

Cable No.

Cable No.

Cable No.

Cable No.

Cable No. Cable No.

COMPONENT

Cables

1.052

Ecc. From

Px (per Cable)

sofit

TOTAL NO. OF CABLE TOTAL Px (STAGE-1)

t

2954

3018

3086

3738

4143

4116

Cg from Bottom

m

0.812

0.660

0.527

0.352

0.193

0.130

Ecc. From cg

m

0.507

0.635

0.577

0.540

0.468

0.300

t.m

1498

1916

1780

2017

1941

1235

TOTAL PRIMARY BM

CALCULATION OF LOAD DUE TO TEMPERATURE GRADIENT Total Height of the girder C.G. of Girder from bottom

h Y

= =

2.5 0.430

m m

M.O.I. of the Section

I

=

1.3465

m4

Area of the Section

A

=

4.9545

m2

Modulus of Elasticity of Concrete

Ec

=

3.16E+07

Coefficient of thermal expansion of concrete

α

=

0.0000117

oC

Section Modulus at the top

ZT

=

0.6505

m3

Section Modulus at the bottom of top slab

ZBS

=

0.7298

m3

Section Modulus at the bottom

ZB

=

3.1312

m3

KN/m2

T1

=

17.8

o

C

h1

=

0.15

m

T2

=

4.0

o

C

h2

=

0.25

m

T3

=

2.1

o

C

h3

=

0.15

m

1.0 COMPUTATION OF STRESSES DUE TO RISE IN TEMPERATURE

1.1 STRESSES AT SPAN SECTION

2.0 COMPUTATION OF STRESSES DUE TO FALL IN TEMPERATURE

h

=

2.500

m

h1

=

0.250

m

T1

=

10.6

o

C

h2

=

0.200

m

T2

=

0.7

o

C

h3

=

0.200

m

T3

=

0.8

o

C

h4

=

0.250

m

T4

=

6.6

o

C

Check for Longitudinal Flexural Stresses Concrete Grade

40

Allowable stresses in concrete : Temporary compressive stress after 14 days Temporary tensile stress after 14 days Temporary compressive stress after 28 days Temporary tensile stress after 28 days Service Stage compressive stress Modulus of rupture Factor for extra time dependent loss considered :

S. No.

1 2 3 4 5 6 7 8

SECTION Length of Segment Section Properties, Box Girder

Unit

17.40 1.74 20.00 2.00 13.46 2.95 1.2

MPa

MPa MPa MPa MPa MPa MPa (Should be 1.0 as well as 1.2)

Support 1/8th span 1/4th span 3/8th span Mid span Section section section section

m

5.969

5.969

5.969

5.969

4.8423 0.6619 1.6358 2.5635 2.4715

4.9545 0.4300 1.3465 2.3625 3.1312

Area, A c.g from soffit, Yb M.O.I Zt Zb

m2 m m4 m3 m3

7.0777 1.3194 6.0436 5.1193 4.5805

5.2174 1.1038 2.7843 3.4968 2.5225

4.7874 0.8918 2.0890 2.9496 2.3425

tm

0.0

1695.0

2865.0

3563.0

3795.0

9

top stress due to DL

t/m2

0.0

484.7

971.3

1389.9

1606.3

10 11 12 13

bottom stress due to DL Stage 1 Prestressing at Stage 1 P. Force after friction & slip Eccentricty of cables from bottom

t/m2

-1223.0

-1441.6

-1212.0

3737.5 0.3521

4143.4 0.1935

4116.2 0.1300

14

top stress due to P

t/m2

125

83

97

99

308

bottom stressdue to P

t/m2

744

1297

1642

1641

1225

top stress

t/m2

125

567

1068

1488

1914

bottom stress

t/m2

744

625

419

199

13

Stress at C.G of Cables

t/m2

542.9

612.9

510.1

299.1

112.1

Av. Stress at c.g of Tendon

2

4100.0 371.0 0.75

4072.7 336.5 0.68

15 16

B.M due to self wt

18

21 22 23 24 25 26 27 28 29

0.0 -671.9 days after casting 2953.5 3086.3 0.8124 0.5271

Total Stress after prestress

17

19 20

14 t m

Immediate Losses in Cables t/m

Elastic Shortening Loss (Total in t)

t

Force in Prestressing Cables after ES

t

Avg force per cable % of UTF Av. Force in Cables after Elastic Short. Loss

2910.1 321.5 0.65

3042.9 336.2 0.68

t

% of Av. Force in Cables wrt UTF Relaxation Loss (Total in t)

t

% of Relxation Loss in 4 hours

%

437.4 43.42 3694.1 408.1 0.82 3582.1 0.729 386.94 7.51

Stress due to Losses in Prestress on account of E.

30

Shortening & Immediate Relaxation "P"

31

top stress

t/m2

-3.06

-1.94

-1.88

-1.72

-5.42

32 33

bottom stress

t/m2

-18.26

-30.46

-31.83

-28.70

-21.57

Stress at C.G of Cables due to loss

t/m2

-13.3

-24.4

-20.7

t/m2

-27.6 -23.9

-26.6

Av. Stress at c.g of Tendon due to loss

34 35

Stress at Transfer after Prestress

36

top stress

t/m2

122

565

1066

1487

1909

37 38

bottom stress

t/m2

726 OK

595 OK

387 OK

171 OK

-8 OK

Av. Stress at c.g of Tendon after Immediate Loss

t/m2

39

413.5

40 41 42 43 44 45 46 47

Losses in Stage 1 Cables,14-56 days % of Relxation Loss in 14-56 days

Shrinkage Loss (14-56 days)

52 53 54

164.16

t

Creep Strain at 14 day / 10 Mpa Creep Strain at 56 day / 10 Mpa Losses due to Creep (14-56 days) days

48

50 51

t

Residual Shrinkage Strain at 56 days

Total Loss (Shrinkage+Creep+Relaxation), 14-56

49

t

28.60 0.00025 0.00019 37.67 0.00046 0.00040 15.84

%

Residual Shrinkage Strain at 14 days

top stress : losses due to creep + shrinkage + Relaxation bottom stress : losses due to creep + shrinkage + Relaxation

t/m2

-6.94

-4.39

-4.26

-3.91

-12.29

t/m2

-41.36

-68.99

-72.11

-65.01

-48.86

-30.2

-55.4

-62.5 -54.2 236.6

-60.3

-47.0

2

Stress at C.G of Cables due to loss

t/m

Av. Stress at c.g of Tendon due to loss

t/m

Total Losses in Prestress at 56 days

t

2

Total Stress before SIDL at 56 days top stress

t/m2

115

561

1062

1483

1897

bottom stress

t/m2

685 OK

526 OK

315 OK

106 OK

-57 OK

tm

0.0

448.4

769.1

961.5

1025.6

60

top stress due to SIDL

t/m2

0.0

128.2

260.7

375.0

434.1

61 62

bottom stress due to SIDL

t/m2

0.0

-177.8

-328.3

-389.0

-327.5

2

115

689

1323

1858

2331

2

685 OK 499.4

348 OK 419.9

-14 OK 174.6 151.2

-283 OK -117.7

-385 OK -243.5

55 56 57 59

SIDL Bending Moment

Total Stress after SIDL

63

top stress

t/m

64 65 66

bottom stress

t/m

67 68 69 70 71 72 73 74

Stress at C.G of cables after SIDL

t/m2

Av. Stress at c.g of cables

t/m2

Losses in prestress,56days to infinity % Residual Relaxation Loss Relaxation Loss ,56days to infinity

63.90 247.24 0.00015 94.18 0.00040 37.97

t

Residual Shrinkage Strain at 56 days Shrinkage Loss,56days to infinity

t

Creep Strain at 56 day / 10 Mpa Creep Loss,56days to infinity

t

Stress due to Losses in Prestress on account of

75

CR+SH+RL

76

top stress

t/m2

-16.0

-10.2

-9.8

-9.0

-28.4

bottom stress

t/m2

-95.6

-159.4

-166.6

-150.3

-112.9

80

top stress

t/m2

81 82 83 84

bottom stress

77 78 79

Total Stress after SIDL & all Losses

LL Bending Moment

98.8

679.1

1313.0

1848.8

2302.4

t/m

589.0 OK

188.5 OK

-180.2 OK

-433.7 OK

-497.7 OK

562.4

933.8

1148.9

1186.6

2

tm

0.0

85

top stress due to LL

t/m2

0.0

160.8

316.6

448.2

502.3

86 87 88

bottom stress due to LL

t/m2

0.0

-222.9

-398.6

-464.8

-379.0

top stress due to temp-rise

t/m2

-1585.4

-1585.4

-1585.4

-1585.4

-1585.4

bottom stress due to temp-rise

t/m2

369.1

369.1

369.1

369.1

369.1

2

1192.0

1192.0

1192.0

1192.0

1192.0

2

190.2

190.2

190.2

190.2

190.2

89 90 91 92

STRESS DUE TO TEMP RISE

STRESS DUE TO TEMP FALL

93

top stress due to temp-fall

t/m

94

bottom stress due to temp-fall

t/m

96

Service stage checks without extra time dependent loss without temperature

97

top stress

t/m2

99

840

1630

2297

2805

98 99 100 101

bottom stress

t/m2

589 OK

-34 OK

-579 OK

-899 OK

-877 OK

Service stage checks without extra time dependent loss with temperature rise& 50% Liveload

102

top stress

t/m2

-1487

-826

-114

488

968

103 104 105 106

bottom stress

t/m2

958 OK

446 OK

-10 OK

-297 OK

-318 OK

107 108 109 110 111 112 113 114 115 116 117

Service stage checks without extra time dependent loss with temperature fall & 50% Liveload top stress bottom stress

Extra Time Dependent Loss ( 20%) Relaxation Loss Creep Loss Shrinkage Loss

130 131 132

3265

3746

-189 OK

-476 OK

-497 OK

77.4 10.8 26.4

t t t

2

-4.84

-3.06

-2.97

-2.72

-8.57

t/m2

-27.52

-40.83

-44.87

-44.57

-37.66

837

1627

2294

2796

561 -75 -624 OK OK OK Service stage checks with extra time dependent loss with temperature rise and 50% Live load

-943 OK

-914 OK

-117

485

960

931 405 -55 OK OK OK Service stage checks with extra time dependent loss with temperature fall and 50% Live load

-342 OK

-356 OK

3262

3737

-520 OK

-535 OK

bottom stress

127 128 129

2663

267 OK

t/m

119 120 121

126

1952

779 OK

Stress due to extra Losses in Prestress

top stress

123 124 125

1291

t/m2

NOTE : TENSION IS ALLOWED IN TEMP. CASE IN DECK SLAB, (STRESS<MODULUS OF RUPTURE) FOR WHICH UNTENSIONED STEEL IS PROVIDED

118

122

2

t/m

Service stage checks with extra time dependent loss without temperature load top stress

t/m2

bottom stress

t/m2

top stress

t/m2

bottom stress

t/m2

top stress

t/m2

94

-1491

1286

-829

1948

2

2660

752 226 -234 OK OK OK NOTE : TENSION IS ALLOWED IN TEMP. CASE IN DECK SLAB, (STRESS<MODULUS OF RUPTURE) FOR WHICH UNTENSIONED STEEL IS PROVIDED bottom stress

t/m

SUMMARY OF LOSSES Elastic Shortening Loss Relaxation Loss Creep Loss Shrinkage Loss TOTAL LOSS Initial Force after Friction & Slip loss % LOSS

43.42 386.94 53.80 131.85 616.01 3625.52 17.0

Check for Ultimate Shear Grade of Concrete

40

Mpa

Perm. direct shear stress ; τv

4.70

Mpa

(Table 6 of IRC 18 - 2000)

Perm. direct shear stress ; τtv

0.42

Mpa

(Table 6 of IRC 18 - 2000)

Perm. shear stress in combined shear & torsion; τtu

4.75

Mpa

(Table 6 of IRC 18 - 2000)

Section "d" away from Support

COMPONENT

L/8

L/4

3L/8

L/2

UNIT Ultimate Shear Capacity of Section uncracked in Flexure (Cl. 14.1.2, IRC:18-2000)

Overall Width, bo Overall Depth, d Area of Section Dia of duct, φ Effective Width, b = bo-2/3φ Maximum Principal Tensile Stress, ft = 0.24(fck)0.5 Horizontal Component of prestress after all losses Cg of cable from sofit, Yord Comp. Stress due to prestress, fcp Effect of Vertical Prestress, Vpr Shear Capacity, Vco = 0.67*b.d.(ft2+.8fcp*ft)0.5 Vc = Vco + Vpr

m m m2 m m

1.215 2.500 5.721 0.110 1.142

1.007 2.500 5.217 0.110 0.934

0.651 2.500 4.787 0.110 0.577

0.651 2.500 4.842 0.110 0.577

0.651 2.500 4.954 0.110 0.577

Mpa

1.52

1.52

1.52

1.52

1.52

KN

2505.2

2561.9

3102.5

3439.4

3416.8

m Mpa KN KN KN

0.660 0.438 0.0 3220.8 3220.8

0.527 0.491 0.0 2664.5 2664.5

0.352 0.648 0.0 1700.0 1700.0

0.193 0.710 0.0 1720.7 1720.7

0.130 0.690 0.0 1713.9 1713.9

Ultimate Shear Capacity of Section cracked in Flexure (Cl. 14.1.3, IRC:18-2000)

Effective Width, b (m) D1 = (D - Yord) D2 = 0.8*D Depth , db Stress due to prestress. fpt Distance of extreme fibre from centroid, yb Second Moment of Area, I

m4

1.142 1.840 2.000 2.000 982.0 1.295 3.784

0.934 1.973 2.000 2.000 1076.7 1.104 2.784

0.577 2.148 2.000 2.148 1362.8 0.892 2.089

0.577 2.307 2.000 2.307 1362.1 0.662 1.636

0.577 2.370 2.000 2.370 1017.0 0.430 1.347

KNm

9135.7

8075.7

8035.5

8476.7

9874.9

KN

7623

6291

4556

2179

256

Knm

19055

44216

74538

92488

97614

Shear Capacity, Vcr = 0.037*b*db*(fck)0.5+Mt/M*V

KN

4189.1

1586.1

781.3

511.3

346.1

Design Shear Capacity, Vc

KN

3220.8

1586.1

781.3

511.3

346.1

Cracking Moment, Mt = (0.37*(fck)0.5+0.8*fpt).I/y Ult. Applied Shear Force, Vult B. Moment corresponding to Ult. Shear Force, Mult

m m m m KN/m2 m

Check for Limiting Shear for Outer Girder (As per Cl. 14.1.5 of IRC: 18-2000)

Ultimate Shear, Vu Vu -Vpr Depth , db

KN KN m MPa

τ=Vu/(b.db)/1000

7623.0 7623.0 2.000 3.338 OK

6290.8 6290.8 2.000 3.367 OK

4556.2 4556.2 2.148 3.675 OK

2178.5 2178.5 2.307 1.636 OK

256.0 256.0 2.370 0.187 OK

KN

No 4402.2

No 4704.7

No 3774.9

No 1667.3

No -90.0

mm2/m

1346.3

1116.1

720.8

720.8

720.8

mm2/m

5080

5429

4356

1924

0

mm2/m

5080.3

5429.4

4356.3

1924.1

720.8

Status Provision of Shear Reinforcement (Cl. 14.1.4, IRC:18-2000)

Is V less than Vc/2 ? V-Vc (in KN) Minimum reift.,

Asv / Sv =

0.4*b/(.87*fyv)

Shear Reinft. Due to ultimate loads, Asv/Sv = (VVc)/(0.87*fyv*dt)

Design Shear Reinforcement

REINFORCEMENT REQUIRED FOR TORSION

Ult. Applied Torsional Moment, Tult Area enclosed on C/L of Box, Ao Perimeter of Ao Deck Thickness Sofit thickness Total Shear Stress due to torsion : Web Total Shear Stress due to torsion : deck Total Shear Stress due to torsion: sofit Status Asv/Sv for torsion/web Tot Asl for torsion Asl for deck Asl for web Asl for sofit

Knm m2 m m m MPa MPa MPa mm2/m

4354.77 10.70 13.90 0.225 0.260 0.34 0.90 0.78 R/F Reqd. 563.9

3585.09 10.70 13.90 0.225 0.260 0.33 0.74 0.64 R/F Reqd. 464.2

2314.36 10.70 13.90 0.225 0.260 0.33 0.48 0.42 R/F Reqd. 299.7

1025.25 10.70 13.90 0.225 0.260 0.15 0.21 0.18 OK 0.0

339.24 10.70 13.90 0.225 0.260 0.05 0.07 0.06 OK 0.0

mm2/m mm2/m mm2/m

563.9 563.9 563.9

464.2 464.2 464.2

299.7 299.7 299.7

0.0 0.0 0.0

0.0 0.0 0.0

MPa

3.67 OK 3104 673 3104

3.70 OK 3178.9 558 3179

4.01 OK 2477.8 360 2478

1.78 OK 962.0 360 962

0.24 OK 0.0 360 360

EFFECT OF COMBINED TORSION & SHEAR

Total Shear Stress : Web Status Total Asv/Sv/web due to torsion & shear Minimum Asv/Sv/web Asv/Sv/web required

2

mm /m 2 mm /m 2 mm /m

Check for Ultimate Moment of Midspan Section (Which is more critical) I) Failure by Yield of Steel Area of high tensile steel, As, (mm2) Distance of cg of tendons from compression fibre, db, (mm) Ultimate tensile strength of steel, fp, MPa

32196.64 2370.0 1860

Ultimate Moment capacity of steel, Msult, kNm = 0.9*db*As*fp

127736.3

II) Failure by Crushing of Concrete Width of web, b, (mm) Width of flange, Bf, (mm) Thickness of flange, t, (mm) Ultimate Moment capacity of concrete, Mcult, (kNm) = 0.176*b*db2*fck + 2/3*0.8*(Bf-b)*(db-t/2)*t*fck

III) Ultimate Moment Capacity of Section IV) Applied Ultimate Moment Status

651 9750 225 124328.6 124328.6 97614 OK

Calculation of Transverse steel in Web SL.NO.

1

Units

Outer Face cm2/m Inner Face cm2/m

ZONE I : Support to L/8 For Torsion & For TOTAL Shear Flexure AST (I+II) I II

15.52 15.52

ZONE II : L/8 to L/4 For Torsion & For TOTAL Shear Flexure AST (I+II) I II

14.84 30.4 12.57 28.1

15.89 15.89

Provided

25T @ 200 +20T @ 200c/c in both face of Zone I

Provided

20T @ 100c/c in both face of Zone II

Provided

16T @ 200c/c + 20T @ 200c/c in both face of Zone III

14.84 30.7 12.57 28.5

ZONE III : L/4 to L/2 For Torsion & For TOTAL Shear Flexure AST (I+II) I II

4.81 4.81

14.84 12.57

Shear Parameters of Concrete: Grade of Concrete Vu Vtc Vtu

30 4.1 0.37 4.1

Table -2 : Creep of Concrete

35 4.4 0.4 4.45

40 4.7 0.42 4.75

45 5 0.42 5.03

50 5.3 0.42 5.3

55 5.5 0.42 5.56

60 5.8 0.42 5.81

19.7 17.4