46947288 Post Tensioned Design1

7/29/2019 46947288 Post Tensioned Design1

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SEPAKAT SETIA PERUNDING SDN BHD (14142-M)

CONSULTING ENGINNERS

PROJECT : PROJECT TITLE

DETAIL : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH

JOB NUMBER : 37478

Designed : KKL Date : 19-Mar-2013

Checked : LTC Date : 19-Mar-2013

File name : W:\SCB Spreadsheet\Post-Tensioned-Design.xls

DESIGN DATA :

(I) Number Of Stage For Stressing = 2 Stages

(II) Concrete Properties for Precast Beam:

(a) 1st Stage : (i) Concrete Cube Strength fci1 = 30 N/mm2

(ii) Modulus of Elasticity Ec1 = 28 kN/mm2

(b) 2nd Stage : (i) Concrete Cube Strength fci2 = 50 N/mm2

(ii) Modulus of ElasticityE

c2=

34 kN/mm

2

(c) 28 days (i) Concrete Cube Strength fcu = 50 N/mm2

(ii) Modulus of Elasticity Ecu = 34 kN/mm2

(III) Prestressing Strands Properties :

(a) Strand Diameter fs = 12.9 mm

(b) Cross Section Area As = 100 mm2

(c) Mudulus of Elasticity Es = 195 kN/mm2

(d) U.T.S per Strand PUTS = 186 kN

(e) Co-efficient of Friction m = 0.2 /rad

(f) Wobble Factor K = 0.0033 rad/m

(g) Average Anchorage Draw in draw-in = 10 mm

(IV) Prestressing Losses Data:

(a) Relaxation of Strand Cable (At 1000 hours) = 2.5 % of Jacking Force

(b) Creep of Concrete per unit Length ec = 0.000036 per N/mm2

(c) Shrinkage per unit Length es = 0.0002

(d) Creep reduction Coefficient k = 0.43

S37T1 - EDGE BEAM (T1)


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SEPAKAT SETIA PERUNDING (14142-M)

POST-TENSIONED BEAM DESIGN - Calculation of Post-Tensioning Cable Profile JOB NO :

Project : PROJECT TITLE Designed : KKL Date : 19

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 19

Filename : W:\SCB Spreadsheet\Post-Tensioned-Design.xls

(1) CALCULATION OF POST-TENSIONED CABLES PROFILE

(a) Input Data

Effective Span Leff = 39.00 m

Beam Length Lbeam = 39.60 m

Cable Length Lcable = 39.60 m

Nos. of Cables = 4 nos

(b) Cable Profile Formula

(i) Formulae used for computing cable profile :

Y0 = Ym + (Ye - Ym) * (X0/Half beam length)2

(ii) Formulae used for computing cable angle at anchorage :

Angle = arctan(2 * Drape / Half beam length)

Drape = Ye - Ym

where, Y0 = Height of centre-line of cable from soffit at distance X0 from midspan.

Ye = Height of centre-line of cable from soffit at beam end.

Ym = Height of centre-line of cable from soffit at midspan.

(2) CABLE INFO

Cable angle Total Nos of

Drape at anghorage Strands

Ye - Ym per Cable

(mm) (degree) (nos)

Cable A 1875.00 460.00 1415.00 8.134 19Cable B 1525.00 340.00 1185.00 6.826 19Cable C 1175.00 220.00 955.00 5.510 19

Cable D 825.00 100.00 725.00 4.188 19

76

(3) CALCULATION OF CABLE PROFILE

Cable angle 8.134 6.826 5.510 4.188

Support Midspan at anchorage

X (m) X0 (m) Cable Mark A B C D

Nos. Of Strands 19 19 19 19

Section 1 19.500 0.000 460 340 220 100

Section 2 18.500 1.000 464 343 222 102

Section 3 17.500 2.000 474 352 230 107

Section 4 16.500 3.000 492 367 242 117

Section 5 15.500 4.000 518 388 259 130

Section 6 14.500 5.000 550 416 281 146

Section 7 13.500 6.000 590 449 308 167Section 8 12.500 7.000 637 488 339 191

Section 9 11.500 8.000 691 533 376 218

Section 10 10.500 9.000 752 585 417 250

Section 11 9.500 10.000 821 642 464 285

Section 12 8.500 11.000 897 706 515 324

Section 13 7.500 12.000 980 775 571 366

Section 14 6.500 13.000 1070 851 632 413

Section 15 5.500 14.000 1167 932 697 462

Section 16 4.500 15.000 1272 1020 768 516

Section 17 3.500 16.000 1384 1114 844 573

Section 18 2 500 17 000 1503 1214 924 634

Height of centre-line of cable

from soffit of beam

(mm)

Distance from

Ye Ym

Height of centre-line of cable

Cable from soffit of beam

Mark (mm)


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SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)

Consulting Engineers

Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. :

Summary of Computer Analysis Output for Post-tensioned Beam Design

Project : PROJECT TITLE Designed : KKL Date :

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date :


(i) Beam Type = S37T1 (SAG)

(ii) Beam Position = LE 89 TO 96

(iii) Effective Span /Length Between Centreline of Bearings Leff = 39.000 m

(iv) Section Modulus : @ Bottom Fibre of Precast Beam Zb = 4.526E+08 mm3

(v) Section Modulus : @ Bottom Fibre of Composite Beam Zb,p = 5.369E+08 mm3

(vi) Precast Beam Selfweight wpre = 20.868 kN/m

(vii) Deck Slab Selfweight wslab = 8.900 kN/m

NOTE : UDLMoment w/2(Lx) (Leff-Lx)

UDL Shear w (Leff/2-Lx)

MAXIMUM BENDING MOMENT WITH CO-EXISTING SHEAR FOR PRESTRESSING DESIGN(1a) SUMMARY OF THE NOMINAL MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

Distance

from HA1003 -

Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total

Section Lx (m) Beam Beam & Services Unfactored Unfactored

Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -393.80 2812.00 1606.80 511.50 0.00

1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 433.60 0.00

2/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 61.42 2109.25 2276.87 1614.00 0.00

3/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 202.30 1757.87 2316.27 2486.00 0.00

Mid Span 19.50 3967.53 1692.11 5659.64 0.00 492.20 283.20 1406.50 2181.90 3050.00 0.005/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 2903.00 0.00

6/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 263.30 703.75 1416.25 2456.00 0.00

7/8 34.13 1735.79 740.30 2476.09 0.00 261.20 163.20 352.37 776.77 1403.00 0.00

Support 2 39.00 0.00 0.00 0.00 0.00 -62.73 5.03 0.00 -57.71 -188.30 0.00

(1b) SUMMARY OF THE NOMINAL CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

Distance

from HA1003 -

Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total

Section Lx (m) Beam Beam & Services Unfactored Unfactored

Support 1 0.00 406.93 173.55 580.48 70.00 135.00 62.24 123.65 390.89 -22.75 0.00

1/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 15.81 0.00

2/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 149.50 0.00

3/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 123.70 0.00

Mid Span 19.50 0.00 0.00 0.00 0.00 23.70 10.66 -100.15 -65.79 -36.25 0.00

5/8 24.38 -101.73 -43.39 -145.12 0.00 0.41 -2.60 -94.28 -96.46 -98.29 0.00

6/8 29.25 -203.46 -86.78 -290.24 0.00 -24.79 -15.70 -88.40 -128.89 -231.30 0.00

7/8 34.13 -305.19 -130.16 -435.36 0.00 -53.93 -28.49 -82.53 -164.95 -319.40 0.00

Support 2 39.00 -406.93 -173.55 -580.48 -70.00 -88.08 -40.86 -76.65 -275.59 -239.50 0.00

Nominal Shear Force Due to NOMINAL LIVE LO

COMPUTER AN

Dead Load Superimposed Dead Load

COMPUTER AN

NOMINAL CO-EXISITING SHEAR FORCE (kN) FOR MAXIMUM MOMENT

Nominal Shear Force Due to

NOMINAL MAXIMUM MOMENT (KNm)NOMINAL - MOMENT

NOMINAL LIVE LOANominal Moment Due to

Dead Load

Nominal Moment Due to

Superimposed Dead Load

NOMINAL - SHEAR


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Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. :

(2a) SUMMARY OF THE SLS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

Distance

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 - H

Support Beam Beam & Services

SLS 1 SLS 1 SLS SLS 1 SLS 1 SLS 1 SLS1 SLS SLS 1 SLS 1

Section Lx (m) 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.20 1.20

Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -472.56 2812.00 1528.04 613.80 0.00

1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -165.48 2460.62 2019.84 520.32 0.00

2/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 73.70 2109.25 2289.15 1936.80 0.00

3/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 242.76 1757.87 2356.73 2983.20 0.00

Mid Span 19.50 3967.53 1692.11 5659.64 0.00 492.20 339.84 1406.50 2238.54 3660.00 0.00

5/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 364.32 1055.12 1942.64 3483.60 0.00

6/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 315.96 703.75 1468.91 2947.20 0.00

7/8 34.13 1735.79 740.30 2476.09 0.00 261.20 195.84 352.37 809.41 1683.60 0.00

Support 2 39.00 0.00 0.00 0.00 0.00 -62.73 6.03 0.00 -56.70 -225.96 0.00

(2b) SUMMARY OF THE SLS BOTTOM STRESS FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

Distance

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 - H


SLS 1 SLS 1 SLS SLS 1 SLS 1 SLS 1 SLS1 SLS SLS 1 SLS 1

Section Lx (m) 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.200 1.200

Support 1 0.00 0.00 0.00 0.00 0.00 -1.51 -0.88 5.24 2.85 1.14 0.00

1/8 4.88 3.83 1.64 5.47 0.00 -0.51 -0.31 4.58 3.76 0.97 0.00

2/8 9.75 6.57 2.80 9.38 0.00 0.20 0.14 3.93 4.26 3.61 0.00

3/8 14.63 8.22 3.50 11.72 0.00 0.66 0.45 3.27 4.39 5.56 0.00

Mid Span19.50 8.77 3.74 12.50 0.00 0.92 0.63 2.62 4.17 6.82 0.005/8 24.38 8.22 3.50 11.72 0.00 0.97 0.68 1.97 3.62 6.49 0.00

6/8 29.25 6.57 2.80 9.38 0.00 0.84 0.59 1.31 2.74 5.49 0.00

7/8 34.13 3.83 1.64 5.47 0.00 0.49 0.36 0.66 1.51 3.14 0.00

Support 2 39.00 0.00 0.00 0.00 0.00 -0.12 0.01 0.00 -0.11 -0.42 0.00

(2c) SUMMARY OF THE SLS BOTTOM STRESS FOR SUPERIMPOSED DEAD LOAD + LIVE LOADING

Distance

from

Support

Section Lx (m)

Support 1 0.00

1/8 4.88

2/8 9.75

3/8 14.63

Mid Span 19.50

5/8 24.38

6/8 29.25

7/8 34.13

Support 2 39.00

8.22

4.64

-0.53

0.00 10.73 0.00

SDL + HA1003 SDL + - SDL + HAHB4503

10.11

Due to Live

Due to Live

0.00 4.14 0.00

10.99

3.99

SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)

Due to Superimposed Dead Load

Due to Dead Load Due to Superimposed Dead Load

SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)

SERVICEABILITY LIMIT STATE MOMENT (KNm)

7.87

9.95

SDL + -

0.00 4.88 0.004.73

S.L.S - MOMENT

S.L.S - STRESS (fb)

S.L.S - fb(SDL+LL)

Due to Dead Load

SDL + Live Loading

0.00 10.17 0.00

0.00 12.56 0.00

-0.72 0.00

0.00 13.27 0.00

0.00 12.46 0.00

0.00 5.61 0.00

0.00


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Summary of Computer Analysis Output for Post-tensioned Beam Design Job No.

(3a) SUMMARY OF THE ULS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING

Distance

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 -


ULS 1 ULS 1 ULS ULS 1 ULS 1 ULS 1 ULS1 ULS ULS 1 ULS 1

Section Lx (m) 1.265 1.265 1.320 1.320 1.925 1.320 1.65 1.65

Support 1 0.00 0.00 0.00 0.00 0.00 -1071.05 -758.07 3711.84 1882.73 843.98 0.00

1/8 4.88 2195.78 936.48 3132.26 0.00 -363.40 -265.46 3248.02 2619.16 715.44 0.00

2/8 9.75 3764.19 1605.39 5369.58 0.00 140.18 118.23 2784.21 3042.63 2663.10 0.00

3/8 14.63 4705.24 2006.74 6711.98 0.00 470.05 389.43 2320.39 3179.87 4101.90 0.00

Mid Span 19.50 5018.92 2140.52 7159.45 0.00 649.70 545.16 1856.58 3051.44 5032.50 0.00

5/8 24.38 4705.24 2006.74 6711.98 0.00 690.62 584.43 1392.76 2667.81 4789.95 0.00

6/8 29.25 3764.19 1605.39 5369.58 0.00 592.94 506.85 928.95 2028.75 4052.40 0.00

7/8 34.13 2195.78 936.48 3132.26 0.00 344.78 314.16 465.13 1124.07 2314.95 0.00

Support 2 39.00 0.00 0.00 0.00 0.00 -82.80 9.67 0.00 -73.13 -310.70 0.00

(3b) SUMMARY OF THE ULS CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING

Distance

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 -


ULS 1 ULS 1 ULS ULS 1 ULS 1 ULS 1 ULS1 ULS ULS 1 ULS 1

Section Lx (m) 1.265 1.265 1.320 1.320 1.925 1.320 1.65 1.65

Support 1 0.00 514.76 219.54 734.30 92.40 178.20 119.81 163.22 553.63 -37.54 0.00

1/8 4.88 386.07 164.66 550.73 0.00 133.58 95.92 155.46 384.97 26.09 0.00

2/8 9.75 257.38 109.77 367.15 0.00 95.32 71.28 147.71 314.31 246.68 0.00

3/8 14.63 128.69 54.89 183.58 0.00 62.04 46.05 139.95 248.04 204.11 0.00

Mid Span 19.50 0.00 0.00 0.00 0.00 31.28 20.52 -132.20 -80.39 -59.81 0.00

5/8 24.38 -128.69 -54.89 -183.58 0.00 0.55 -5.00 -124.44 -128.90 -162.18 0.00

6/8 29.25 -257.38 -109.77 -367.15 0.00 -32.72 -30.22 -116.69 -179.63 -381.65 0.00

7/8 34.13 -386.07 -164.66 -550.73 0.00 -71.19 -54.84 -108.93 -234.96 -527.01 0.00

Support 2 39.00 -514.76 -219.54 -734.30 -92.40 -116.27 -78.66 -101.18 -388.50 -395.18 0.00

(3c) SUMMARY OF THE ULS TOTAL MOMENT AND TOTAL CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE L

Distance

from

SupportMoment Shear Moment Shear Moment Shear Moment Shear

Section Lx (m) (kNm) (kN) (kNm) (kN) (kNm) (kN) (kNm) (kN)

Support 1 0.00 2726.70 1250.39 0.00 0.00 2876.01 1240.37 0.00 0.00

1/8 4.88 6466.86 961.78 0.00 0.00 6611.71 1172.79 0.00 0.00

2/8 9.75 11075.31 928.13 0.00 0.00 12945.31 972.89 0.00 0.00

3/8 14.63 13993.75 635.72 0.00 0.00 16165.26 587.77 0.00 0.00

Mid Span 19.50 15243.39 -140.21 0.00 0.00 17196.44 -198.04 0.00 0.00

5/8 24.38 14169.74 -474.65 0.00 0.00 16170.86 -459.05 0.00 0.00

6/8 29.25 11450.73 -928.43 0.00 0.00 13533.03 -1204.44 0.00 0.00

7/8 34.13 6571.28 -1312.70 0.00 0.00 7408.05 -1561.47 0.00 0.00

Support 2 39.00 -383.83 -1517.98 0.00 0.00 -544.32 -1793.19 0.00 0.00


DL + SDL + LIVE LOAD

HA1003 - HAHB4503 -

ULS LIVE LOA

U.L.S-DESIGN TOTAL MOMENT & SHEAR FOR U.L.S-DESIGN

U.L.S-DESIGN Shear ULTIMATE LIMIT STATE CO-EXISTING SHEAR FORCE (KN)

U.L.S-DESIGN Moment

ULS LIVE LOADI

ULTIMATE LIMIT STATE MOMENT (KNm)



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Summary of Computer Analysis Output for Post-tensioned Beam Design Job No

MAXIMUM SHEAR FORCE WITH CO-EXISTING MOMENT FOR SHEAR REINFORCEMENT DESIGN

(4a) SUMMARY OF THE NOMINAL CO-EXSITING MOMENT WITH MAXIMUM SHEAR FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOA

Distancefrom - -

Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix CR,DS,DSETTL Total

Section Lx (m) Beam Beam & Services Unfactored Unfactor

Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -393.80 2812.00 1606.80 0.00 0.00

1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 0.00 0.00

2/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 61.42 2109.25 2276.87 0.00 0.00

3/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 202.30 1757.87 2316.27 0.00 0.00

Mid Span 19.50 3967.53 1692.11 5659.64 0.00 492.20 283.20 1406.50 2181.90 0.00 0.00

5/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 0.00 0.00

6/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 263.30 703.75 1416.25 0.00 0.00

7/8 34.13 1735.79 740.30 2476.09 0.00 261.20 163.20 352.37 776.77 0.00 0.00

Support 2 39.00 0.00 0.00 0.00 0.00 -62.73 5.03 0.00 -57.71 0.00 0.00

(4b) SUMMARY OF THE NOMINAL MAXIMUM SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

Distance

from - -

Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix CR,DS,DSETTL Total

Section Lx (m) Beam Beam & Services Unfactored Unfactor

Support 1 0.00 406.93 173.55 580.48 70.00 135.00 62.24 123.65 390.89 0.00 0.00

1/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 0.00 0.00

2/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 0.00 0.00

3/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 0.00 0.00

Mid Span 19.50 0.00 0.00 0.00 0.00 23.70 10.66 -100.15 -65.79 0.00 0.00

5/8 24.38 -101.73 -43.39 -145.12 0.00 0.41 -2.60 -94.28 -96.46 0.00 0.00

6/8 29.25 -203.46 -86.78 -290.24 0.00 -24.79 -15.70 -88.40 -128.89 0.00 0.00

7/8 34.13 -305.19 -130.16 -435.36 0.00 -53.93 -28.49 -82.53 -164.95 0.00 0.00

Support 2 39.00 -406.93 -173.55 -580.48 -70.00 -88.08 -40.86 -76.65 -275.59 0.00 0.00

(4c) ULTIMATE LIMIT STATE FACTORS FOR SHEAR REINFORCEMENT DESIGN

Precast Insitu Slab - Diaphragm Parapet, Kerb Premix CR,DS,DSETTL - - -

Beam Beam & Services

ULS 1 ULS 1 - ULS 1 ULS 1 ULS 1 ULS1 - - -

1.265 1.265 - 1.320 1.320 1.925 1.320 - - -

(4d) SUMMARY OF THE ULS TOTAL CO-EXSITING MOMENT AND TOTAL MAXIMUM SHEAR FORCE FOR SHEAR DESIGN

Distance

from

Support

Moment Shear Moment Shear Moment Shear Moment Shear

Section Lx (m) (kNm) (kN) (kNm) (kN) (kNm) (kN) (kNm) (kN)

Support 1 0.00 0.00 0.00 0.00 0.00 -1706.57 2188.26 2818.52 1242.09

1/8 4.88 0.00 0.00 0.00 0.00 4474.00 1791.55 6478.01 895.93

2/8 9.75 0.00 0.00 0.00 0.00 11026.25 1269.48 11380.89 550.27

3/8 14.63 0.00 0.00 0.00 0.00 12424.38 968.58 12262.79 304.80

Mid Span 19.50 0.00 0.00 0.00 0.00 15188.72 151.55 16691.65 -466.06

5/8 24.38 0.00 0.00 0.00 0.00 10935.63 -133.44 14679.37 -736.18

6/8 29.25 0.00 0.00 0.00 0.00 6661.17 -440.84 13378.59 -1250.77

7/8 34.13 0.00 0.00 0.00 0.00 3991.35 -676.50 7259.33 -1509.84

Support 2 39.00 0.00 0.00 0.00 0.00 -374.72 -1846.95 159.96 -1013.61

TOTAL CO-EXISITING MOMENT & MAXIMUM SHEAR FOR SHEAR DESIGN


COMPUTER

Nominal Moment Due to Nominal Moment Due to NOMINAL LIVE L

Elements

Load Combinations

gf3*gfL

SHEAR DESIGN (ULS)

DL + SDL + LIVE LOAD

- - HAHB4513 HAHB4514

ULS FACTORS DEAD LOAD & SUPERIMPOSED DEAD LOAD ULS FACTORS LIVE LOADI

COMPUTER

NOMINAL - SHEAR NOMINAL MAXIMUM SHEAR FORCE (kN)

Nominal Shear Force Due to Nominal Shear Force Due to NOMINAL LIVE


NOMINAL - MOMENT NOMINAL CO-EXISITING MOMENT (kNm)


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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478

Calculation of Prestress Losses & Differential Shrinkage At SLS

For PRECAST POST-TENSIONED PRESTRESSED BEAM Design

Project : PROJECT TITLE Designed : KKL Date : 19-Mar-2013

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/ Checked : LTC Date : 19-Mar-2013


Design Data :

x

(1) Spanning Length & Cable Length

(i) Total Beam Length Lbeam = 39.600 m

(ii) Edge of Precast Beam to Centreline of Bearing Pad x = 0.300 m

(iii) Effective Span /Length Between Centreline of Bearings Leff = 39.000 m

(iv) Total Cable Length/Beam Length Lcable = 39.600 m

(2) Precast Beam Concrete Properties

(i) Number of Stage of Stressing (Max. = 2) Number of Stage = 2 Stages O.K.!

(ii) Concrete Cube Strength : @ 28 Days fcu = 50 N/mm2

@ Stage 1 Stressing fci1 = 30 N/mm2 O.K.!

@ Stage 2 Stressing fci2 = 50 N/mm2

(iii) Modulus Of Elasticity of Concrete : @ 28 Days Ecu = 34.0 kN/mm2

@ Stage 1 Stressing Ec1 = 28.0 kN/mm2 O.K.!

@ Stage 2 Stressing Ec2 = 34.0 kN/mm2 O.K.!

(iv) Concrete Density gcon = 24.0 kN/mm3

(3) Section Properties Of Precast Beam

(i) Cross Sectional Area Ap = 869500 mm2

(ii) Total Height H = 2125 mm

(iii) Centriod of Precast Beam To Bottom Fibre yb = 1162.3 mm

(iv) Centriod of Precast Beam To Top Fibre yt = 962.7 mm

(v) Moment of Inertia Ipxx = 5.26080E+11 mm4

(vi) Section Modulus : @ Top Fibre of Precast Beam Zt = 5.4646E+08 mm3

(vii) Section Modulus : @ Bottom Fibre of Precast Beam Zb = 4.5262E+08 mm3

(viii) Selfweight of Precast Beam wpre = 20.868 kN/m

(4) Stressing Cable Properties

(i) Coefficient of Friction m = 0.2 /rad

(ii) Wobble Factor K = 0.0033 /m

(iii) Average Anchorage Draw in draw-in = 10 mm

(iv) Strand Diameter fs = 12.9 mm

(v) Ultimate Tensile Strength per Strand PUTS = 186.0 kN

(vi) Cross Sectional Area per Strand As = 100 mm2

(vii) Modulus of Elasticity of Strand Es = 195.0 kN/mm2

(5) Proposed Stressing SequenceSTAGE 1 : Stress Cable "A" to = 50 % of PUTS O.K.!

Stress Cable "B" to = 50 % of PUTS O.K.!

Stress Cable "C" to = 50 % of PUTS O.K.!

Stress Cable "D" to = 50 % of PUTS O.K.!

STAGE 2 : Stress Cable "A" to = 73 % of PUTS O.K.!

Stress Cable "B" to = 73 % of PUTS O.K.!

Stress Cable "C" to = 73 % of PUTS O.K.!

Stress Cable "D" to = 73 % of PUTS O.K.!

(6)

Cable Mark A B C D Total

Nos. Of Strands 19 19 19 19 76

pj1 Stage 1 1767.0 1767.0 1767.0 1767.0 7068.0

pj2 Stage 2 2579.8 2579.8 2579.8 2579.8 10319.3

S40T1 BEAM

Jacking Force Jacking Force , Pj (kN) = n(%of PUTS)

Lbeam

Leff= Lbeam - 2x

KKHONG (OCT 1998)7 of 21


8/40




(7) In-Situ Slab/Flange Properties

(i) Embedment of The Insitu Slab = 0 mm

(ii) Thickness of The In-situ Slab t = 180 mm

(iii) Width of the Top in-situ Slab lf= 1950 mm

(iv) Area of in-situ flange/slab Af = 351000 mm2

(v) Concrete Grade fc = 30 N/mm2

(vi) Modulus Elasticity of In-situ Ein-situ = 28.0 kN/mm2

(vii) SelfWeight Of In-Situ Slab wslab = 8.900 kN/m

(8) Composite Beam Section Properties

(a) Total Height of The Composite Hc = 2305 mm

(b) Cross Section Area Ac = 1150300 mm2

(c) Centroid from Soffi t yb,c = 1419.28 mm

(d) Second Moment of Area Icxx = 7.6205E+11 mm4

(e) Section Moduli : @ Top of Composite section Zt,c = 8.6037E+08 mm3

(f) Section Moduli : @ Top of Precast Beam Zt,p = 1.0798E+09 mm3

(g) Section Moduli : @ Bottom of Top In-situ Slab Zb,s = 1.0798E+09 mm3

(h) Section Moduli : @ Bottom of Precast Beam Zb,p = 5.3693E+08 mm3

(9) Modular Ratio (Einsitu/Ecu2) m = 0.824

(10) Prestress Losses Calculation Data

(i) Maximum Relaxation of Strands after 1000 h durations % = 2.5 %

(ii) Creep of Concrete per Unit Length ec = 0.000036 per N/mm2

(iii) Shrinkage per Unit Length es = 2.00E-04

(iv) No. of weeks of Stage 2 Prestressing after Stage 1 = 2 weeks

(v) Allowed % of Final Losses at Stage 1 Transfer, Stage 2 Transfer and Stage 2 Service :

Friction Losses Draw-In Wegdes Elast. Shrt. - Steel Relaxation Shrinkage Creep

100 100 100 - 0 33 33

Friction Losses Draw-In Wegdes Elast. Shrt. - Steel Relaxation Shrinkage Creep

At Stage 2 Transfer 100 100 100 - 100 67 67At Stage 2 Service 100 100 100 - 100 67 67

100 100 100

(11) Post-Tensioning Cable Profile

End Conditions -1 * 1 * -1 * 1 *

Support Midspan Cable Mark A B C D Total

Lx (m) X0 (m) Nos. Of Strands 19 19 19 19 76

Near End Live End Dead End Live End Dead End e'

Beam Ends 19.800 Ye 1875.0 1525.0 1175.0 825.0 1350.0

0.000 19.500 1832.4 1489.4 1146.3 803.2 1317.8

4.875 14.625 1232.0 986.5 741.0 495.5 863.8

9.750 9.750 803.1 627.3 451.6 275.8 539.5

14.625 4.875 545.8 411.8 277.9 143.9 344.9

19.500 0.000 Ym 460.0 340.0 220.0 100.0 280.0

24.375 4.875 545.8 411.8 277.9 143.9 344.9

29.250 9.750 803.1 627.3 451.6 275.8 539.5

34.125 14.625 1232.0 986.5 741.0 495.5 863.8

39.000 19.500 1832.4 1489.4 1146.3 803.2 1317.8Beam Ends 19.800 Ye 1875.0 1525.0 1175.0 825.0 1350.0

Far End Dead End Live End Dead End Live End

Note : * = Please Type " -1 " for Dead End of Cable is in the Far End and Type " 1 " for Dead End of Cable is in the Near End.

(12) Sum Of Cable Deviation Angle qsum = qsupport1 qmidspan+ qsupport2 = 2 * artanh [4(Drape)/Lbeam]

Cable Mark A B C D

Nos. Of Strands 19 19 19 19 76

Drape = Ye - Ym (mm) 1415.00 1185.00 955.00 725.00

qsum (rad) 0.2839 0.2383 0.1923 0.1462

Sum of Cable Angular Deviations (in radian)

% of Total Final Losses @ Stage 1 Stressing

% of Total Final Losses During Stage 1 Stressing

During Stage 1 Stressing

% of Total Final Losses During Stage 2 Stressing

During Stage 2 Stressing

Total (%) of Loss From Stage 1 and Stage 2

Assumed Losses

Distance of Section from

Height of Centre-Line of Cables From Soffit of Beam

(m)

Occured During Stage 1 but Before Stage 2 Stressing

At Stage 1 Transfer

Assumed LossesRemaining from Stage 1


9/40




Prestress Losses

(1) Immediate Losses

1(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)

(i) Force Gradient


qsum 0.2839 0.2383 0.1923 0.1462

mqsum + KLcable 0.1875 0.1783 0.1691 0.1599

e-(mq + KLcable) 0.8291 0.8367 0.8444 0.8522

Total Loss of Prestr. Force due to Friction Losses

pfrict.Loss = (1 - e-(mq+KLcable))*pj1 pfrict.Loss (kN) 302.1 288.6 275.0 261.1 1126.79

As a percentage of pj1 % of pj1 17.1 16.3 15.6 14.8 15.94As a percentage of PUTS % of PUTS 8.5 8.2 7.8 7.4 7.97

Cable Force @ Dead End after Frict. Losses

pd = pj1 - pfrict.Loss pd (kN) 1464.9 1478.4 1492.0 1505.9 5941.21

As a percentage of PUTS % of PUTS 41.5 41.8 42.2 42.6 42.03

Loss of Pres. Force per unit length/Force Gradient

dp = (pfrict.Loss/Lcable) dp (kN/m) 7.628 7.288 6.944 6.595 28.454

(ii) Cable Force Along Beam Length After Friction Losses

Cable Mark A B C D

Suppport Midpsan Incre/decre. -1 * 1 * -1 * 1 * Total

Lx (m) X0 (m) dp (kN/m) -7.628 7.288 -6.944 6.595

Near End Live End Dead End Live End Dead End

Beam Ends 19.800 1767.0 1478.4 1767.0 1505.9 6518.2

0.000 19.500 SUPPORT 1 1764.7 1480.6 1764.9 1507.8 6518.0

4.875 14.625 1727.5 1516.1 1731.1 1540.0 6514.7

9.750 9.750 1690.3 1551.6 1697.2 1572.1 6511.3

14.625 4.875 1653.2 1587.2 1663.4 1604.3 6508.0

19.500 0.000 MIDSPAN 1616.0 1622.7 1629.5 1636.4 6504.6

24.375 4.875 1578.8 1658.2 1595.7 1668.6 6501.2

29.250 9.750 1541.6 1693.8 1561.8 1700.7 6497.9

34.125 14.625 1504.4 1729.3 1528.0 1732.9 6494.5

39.000 19.500 SUPPORT 2 1467.2 1764.8 1494.1 1765.0 6491.2

Beam Ends 19.800 1464.9 1767.0 1492.0 1767.0 6491.0

Far End Dead End Live End Dead End Live EndNote : * = Please Type " -1 " for Dead End of Cable is in the Far End and Type " 1 " for Dead End of Cable is in the Near End.

Stage 1 Post Tensioning

Distance of the section from



10/40




1(b) Prestressing Force Loss due to Draw-in Wedges (VSL Prestressing System)

(i) Distance affected by Draw-in Wedges from Live End


Distance affected by Draw-in Wedges from Live End,

w = (draw-in * Es * As * n /dp)1/2 w (m) 22.039 22.547 23.099 23.703 -

w < Lcable

Loss of Force @ Live Ends Due to Wedges Draw-in

pdraw-inLoss = 2 * w * dp pdraw-inLoss (kN) 336.22 328.65 320.79 312.62 1298.28

As a percentage of pj1 % of pj1 19.0 18.6 18.2 17.7 18.37


(ii) Draw-in Wedges Losses Along Beam Length

Distance FromSuppport

Lx (m) A B C D (kN) (% of Pj1) (% of PUTS)

0.000 331.64 0.00 316.62 0.00 648.27 9.17 4.59

4.875 257.27 0.00 248.92 0.00 506.19 7.16 3.58

9.750 182.90 0.00 181.22 0.00 364.12 5.15 2.58

14.625 108.53 0.00 113.52 0.00 222.05 3.14 1.57

19.500 34.16 40.04 45.82 51.48 171.49 2.43 1.21

24.375 0.00 111.10 0.00 115.77 226.87 3.21 1.60

29.250 0.00 182.16 0.00 180.07 362.23 5.12 2.56

34.125 0.00 253.22 0.00 244.37 497.58 7.04 3.52

39.000 0.00 324.28 0.00 308.66 632.94 8.96 4.48

For -ve Force Gradient, For +ve Force Gradient,

Lx < w pdraw-inLoss = 2 * dp * (w - Lx) (Lcable - Lx) < w, pdraw-inLoss = 2 * dp * ( w - (Lcable - Lx))

Lx >= w pdraw-inLoss = 0 (Lcable - Lx)>=w, pdraw-inLoss = 0

(iii) Cable Force Along Beam Length After Friction & Wedges Draw-in Losses

Distance From Allowable

Suppport A B C D (% of PUTS)

Lx (m) (kN) (% of PUTS) Checks

0.000 1433.1 1480.6 1448.3 1507.8 5869.77 41.52 < 70% OK!

4.875 1470.3 1516.1 1482.1 1540.0 6008.49 42.50 < 70% OK!

9.750 1507.4 1551.6 1516.0 1572.1 6147.20 43.49 < 70% OK!

14.625 1544.6 1587.2 1549.8 1604.3 6285.91 44.47 < 70% OK!19.500 1581.8 1582.7 1583.7 1585.0 6333.11 44.80 < 70% OK!

24.375 1578.8 1547.1 1595.7 1552.8 6274.38 44.39 < 70% OK!

29.250 1541.6 1511.6 1561.8 1520.7 6135.67 43.40 < 70% OK!

34.125 1504.4 1476.1 1528.0 1488.5 5996.95 42.42 < 70% OK!

39.000 1467.2 1440.5 1494.1 1456.4 5858.24 41.44 < 70% OK!

Cable Mark

Total

pdraw-inLoss

(kN)

Cable Mark

Total, Pdraw-inLoss

10 of


11/40




1(c) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2)

Immediately after transfer, the change in strain in the prestressing steel dep caused by elastic shortening of the concrete

is equal to the strain in the concrete at the steel level, ecp. The loss of prestress in the steel, dfLoss is therefore :

dfLoss = 0.5(Es/Ec1)*ftendon forpost-tensioned beam (ref. BS5400:Part4:Cl. 6.7.2.3)

N.B. ftendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons.ES is modulus of elasticity of the prestressing tendon

Ec1 is modulus of elasticity of the precast concrete at Stage1

(i) Moment & Concrete Stress Due To Selfweight of Precast Beam

Lx M ft fb e' ftendon

(m) (kNm) (N/mm2) (N/mm

2) (mm) (N/mm

2)

0.000 0.00 0.000 0.000 1317.8 0.000

4.875 1735.79 3.176 -3.835 863.8 -0.985

9.750 2975.65 5.445 -6.574 539.5 -3.523

14.625 3719.56 6.807 -8.218 344.9 -5.780

19.500 3967.53 7.260 -8.766 280.0 -6.654

24.375 3719.56 6.807 -8.218 344.9 -5.78029.250 2975.65 5.445 -6.574 539.5 -3.523

34.125 1735.79 3.176 -3.835 863.8 -0.985

39.000 0.00 0.000 0.000 1317.8 0.000

Moment, M = w(Lx/2)(Leff-L x) H = Total Height of Precast Beam.

ft = M/Zt e' = Distance from centroid of tendon to soffit.

fb = -M/Zb ftendon = fb + [(-fb+ft)x(e'/H)]

(ii) Concrete Stress Due To Prestressing Force After Friction & Wedges Draw-in Losses

Lx e = yb - e' Pi ft fb ftendon

(m) (mm) (kN) (N/mm2) (N/mm

2) (N/mm

2)

0.000 -155.5 5869.77 8.421 4.734 7.021

4.875 298.5 6008.49 3.628 10.873 7.928

9.750 622.8 6147.20 0.063 15.529 11.603

14.625 817.4 6285.91 -2.174 18.582 15.213

19.500 882.3 6333.11 -2.942 19.629 16.655

24.375 817.4 6274.38 -2.170 18.548 15.185

29.250 622.8 6135.67 0.063 15.500 11.581

34.125 298.5 5996.95 3.621 10.852 7.913

39.000 -155.5 5858.24 8.405 4.725 7.007

e' = distance from centroid of tendon to soffit of Precast Beam

e = distance from centroid of tendon to neutral axis of Precast Beam

Ap = Cross Section Area of Precast Beam

Pi = Total Initial Prestress Forces after Friction and Wedge Draw-in Losses

ft = Pi/Ap - Pie/Zt fb = Pi/Ap + Pie/Zb ftendon = fb + [(-fb+ft)x(e'/H)]

(iii) Calculation of Prestress Loss Due To Elastic Shortening of Concrete Along Beam Length

Lx

(m) Selfweight Prestress Total (Stage 1)

(N/mm2) (N/mm

2) (N/mm

2) (N/mm

2) (kN) (% of Pj1) (% of PUTS)

0.000 0.000 7.021 7.021 24.447 185.795 2.629 1.31

4.875 -0.985 7.928 6.943 24.177 183.745 2.600 1.30

9.750 -3.523 11.603 8.080 28.135 213.827 3.025 1.51

14.625 -5.780 15.213 9.434 32.850 249.661 3.532 1.77

19.500 -6.654 16.655 10.001 34.824 264.666 3.745 1.87

24.375 -5.780 15.185 9.406 32.753 248.922 3.522 1.76

29.250 -3.523 11.581 8.058 28.059 213.251 3.017 1.51

34.125 -0.985 7.913 6.928 24.124 183.342 2.594 1.30

39.000 0.000 7.007 7.007 24.399 185.430 2.624 1.31

Loss of Prestress = 0.5*ftendon(Es/Ec1)Stress at Tendon Level (ftendon)



12/40




1(d) Summary of Immediate Losses (Friction Loss, Draw-in Loss And Elastic Shortening Loss)

Lx

(m) Friction Loss Draw-in Loss Elastic Loss Total Friction Loss Draw-in Loss Elastic Loss Total

(kN) (kN) (kN) (kN) (% of PUTS) (% of PUTS) (% of PUTS) (% of PUTS)

0.000 550.0 648.27 185.795 1384.0 3.89 4.59 1.31 9.79

4.875 553.3 506.19 183.745 1243.3 3.91 3.58 1.30 8.79

9.750 556.7 364.12 213.827 1134.6 3.94 2.58 1.51 8.03

14.625 560.0 222.05 249.661 1031.7 3.96 1.57 1.77 7.30

19.500 563.4 171.49 264.666 999.6 3.99 1.21 1.87 7.07

24.375 566.8 226.87 248.922 1042.5 4.01 1.60 1.76 7.38

29.250 570.1 362.23 213.251 1145.6 4.03 2.56 1.51 8.10

34.125 573.5 497.58 183.342 1254.4 4.06 3.52 1.30 8.87

39.000 576.8 632.94 185.430 1395.2 4.08 4.48 1.31 9.87

1(e) Summary of Cable Force After Immediate Losses and Allowable Prestressing Force Checks In Cables

Lx Jacking Force Total Allowable

(m) Pj1 Immediate Loss (% of PUTS)

(kN) (% of Pj1) (kN) (% of PUTS) Checks

0.000 7068.0 19.58 5684.0 40.21 < 70% OK!

4.875 7068.0 17.59 5824.7 41.21 < 70% OK!

9.750 7068.0 16.05 5933.4 41.97 < 70% OK!

14.625 7068.0 14.60 6036.3 42.70 < 70% OK!

19.500 7068.0 14.14 6068.4 42.93 < 70% OK!

24.375 7068.0 14.75 6025.5 42.62 < 70% OK!

29.250 7068.0 16.21 5922.4 41.90 < 70% OK!

34.125 7068.0 17.75 5813.6 41.13 < 70% OK!

39.000 7068.0 19.74 5672.8 40.13 < 70% OK!

NOTE : Maximum Initial Prestressing Force for Post-Tensioning Tendon Immediately after anchoring = 70% of PUTS.(BS 5400 : Part 4 : 1990 : CL. 6.7.1)

1(f) Summary of Concrete Stress After Immediate Losses And Allowable Stress Checks in Concrete at Transfer

Allowable Tensile Stress @ Stage 1 Transfer = -1.00 (N/mm2) (BS 5400 :Part 4 :1990 : CL. 6.3.2.4b)

Allowable Compressive Stress @ Stage 1 Transfer = 15.00 (N/mm2) (BS 5400 :Part 4 :1990 : Table 23)

Lx e Cable Force After Moment Due to

(m) Immediate Loss Beam Selfweight ft fb ftendon Allowable

(mm) (kN) (kNm) (N/mm2) (N/mm

2) (N/mm

2) Checks

0.000 -155.5 5684.0 0.00 8.155 4.584 6.798 OK!

4.875 298.5 5824.7 1735.79 6.693 6.706 6.701 OK!9.750 622.8 5933.4 2975.65 5.506 8.414 7.676 OK!

14.625 817.4 6036.3 3719.56 4.719 9.626 8.830 OK!

19.500 882.3 6068.4 3967.53 4.442 10.043 9.305 OK!

24.375 817.4 6025.5 3719.56 4.723 9.594 8.804 OK!

29.250 622.8 5922.4 2975.65 5.506 8.387 7.656 OK!

34.125 298.5 5813.6 1735.79 6.687 6.686 6.686 OK!

39.000 -155.5 5672.8 0.00 8.139 4.575 6.785 OK!

Cable Force After

Immediate Loss

Concrete Stresses

% of Immediate Loss from PUTSImmediate Losses



13/40




(2) Deferred Losses Before Stage 2 Stressing

2(a) Relaxation of Steel (BS 5400 : Part 4 : 1990 : C.L. 6.7.2.2)

The Loss of force in the tendon allowed for in the design should be the maximum relaxation after 1000 h duration, for a jacking force

equal to that imposed at transfer.

No reduction in the value of relaxation loss should be made for a tendon when a load equal to or greater that the relevant jacking force

has applied for time proir to anchoring of tendon.

(i) At 1000 hours, Relaxation of Steel of Cable = 2.5 % of Jacking Force

(ii) Assumed Percentage Occurred During Stage 1 Transfer = 0.0 % of final

Cable Mark A B C D TOTALNos. Of Strands n (nos) 19 19 19 19 76

Jacking Force pj1 (kN) 1767.0 1767.0 1767.0 1767.0 7068

Total Relaxation Loss in Force prelaxLoss (kN) 0.00 0.00 0.00 0.00 0.00

Relaxation Loss as percentage of pj1 % of pj1 0.00 0.00 0.00 0.00 0.00

Relaxation Loss as percentage of PUTS % of PUTS 0.00 0.00 0.00 0.00 0.00

2(b) Shrinkage of Concrete Losses (BS 5400 : Part 4 : 1990 : C.L. 6.7.2.2)

(i) From BS 5400:Part 4:1990:Table 29,

System

Post-tensioning : transfer at

between 7 days and 14 days esafter concreting

(ii) Shrinkage Strain used in the Design, es = 200.0E-6 per unit length

(iii) Assumed Percentage Occurred,

during Stage 1 Transfer. % = 33 % of final

(iii) Shrinkage Strain Loss as Stress, fshrink.Loss = es x Es x (% During Stage 1 Transfer)

(During Stage 1 Transfer) = 200.0E-6 x 195000 x 0.3333

= 12.999 N/mm2

per strand

(iv) Shrinkage of Concrete Losses in all Cables (During Stage 1 Transfer), pshrink.Loss

Cable Mark A B C D TOTALNos. Of Strands 19 19 19 19 76

Total Shrinkage Loss in Force pshrink.Loss (kN) 24.69753 24.69753 24.69753 24.698 98.790

As Loss in percentage of pi1 % of pj1 1.40 1.40 1.40 1.40 1.40

As Loss in percentage of PUTS % of PUTS 0.70 0.70 0.70 0.70 0.70

(70% r.h)(90% r.h)

Shrinkage per unit length

Humid exposure Normal exposure

70 x 10-6

200 x 10-6



14/40




2(c) Creep of Concrete Losses (BS 5400:Part 4:1990: Cl. 6.7.2.5)

- The loss of prestress in the tendons due to creep of the concrete should be calculated on the assumption that creep is proportional to

stress in the concrete for stress of up to one-third of the cube strength at transfer.

- For Post-tensioning System :

(i) If the required cube strength at transfer is greater than 40.0 N/mm2, the creep per unit length should be taken as 3.60 x 10-5 per N/mm2.(ii) For lower values of the cube strength at transfer (fci), the creep per unit length should be taken as 3.60 x 10

-5x (40.0/fci) per N/mm

2.

(iii) Where the maximum stress anywhere in the section at transfer exceeds one-third of the cube strength, the value of the

creep should be increased with the factor as below:

Increased factor = 1 + (Max stress @ Transfer - fci/3)*0.25

(fci/2- fci/3)

(iv) Calculation of Stress in the concrete adjacent to the tendon after elastic deformation losses

- Creep Strain ec = 4.80E-05 per N/mm2

- Assumed Concrete Creep Loss During Stage 1 Transfer % = 33.33 % of final

- Modulus of Elasticity of Strand Es = 195.0 kN/mm2

- Increased factor = 1.000

- One -third (1/3) of Concrete cube Strength at Stage 1, fci1 fci1/3 = 10.00 N/mm2

.

Lx After After Steel Maximum

(m) Immediate Loss Relaxation Loss Stress

(N/mm2) (N/mm

2) (N/mm

2) (N/mm


0.000 6.798 6.798 21.209 161.187 2.28 1.14

4.875 6.701 6.701 20.904 158.871 2.25 1.12

9.750 7.676 7.676 23.947 182.001 2.57 1.29

14.625 8.830 8.830 27.546 209.347 2.96 1.48

19.500 9.305 9.305 9.305 29.028 220.614 3.12 1.56

24.375 8.804 8.804 27.464 208.728 2.95 1.48

29.250 7.656 7.656 23.883 181.510 2.57 1.28

34.125 6.686 6.686 20.858 158.522 2.24 1.1239.000 6.785 6.785 21.167 160.871 2.28 1.14

Where,

(i) Stress in the concrete adjacent to tendons at transfer after Steel Relaxation Losses

= Stress at Tendon level after Immediate Losses - The Steel Relaxation Loss at Stage 1 transfer

(ii) Creep Loss = Stress at tendon level * Creep Strain (ec) * Es * Increased Factor * % occured @ Stage 1 Transfer

(During Stage 1 Transfer/ Before Stage 2 Stressing)

Stress in the concrete adjacent to tendons level, ftendon Creep Loss



15/40




2(d) Summary of Deferred Losses (Steel Relaxation Loss, Concrete Shrinkage Loss and Creep of Concrete Loss)

Lx

(m) Relaxation Loss Shrinkage Loss Creep Loss Total Relaxation Loss Shrinkage Loss Creep Loss Total


0.000 0.0 98.79 161.187 260.0 0.00 0.70 1.14 1.84

4.875 0.0 98.79 158.871 257.7 0.00 0.70 1.12 1.829.750 0.0 98.79 182.001 280.8 0.00 0.70 1.29 1.99

14.625 0.0 98.79 209.347 308.1 0.00 0.70 1.48 2.18

19.500 0.0 98.79 220.614 319.4 0.00 0.70 1.56 2.26

24.375 0.0 98.79 208.728 307.5 0.00 0.70 1.48 2.18

29.250 0.0 98.79 181.510 280.3 0.00 0.70 1.28 1.98

34.125 0.0 98.79 158.522 257.3 0.00 0.70 1.12 1.82

39.000 0.0 98.79 160.871 259.7 0.00 0.70 1.14 1.84

2(e) Summary of Cable Force After Immediate & Deferred Losses and Allowable Prestressing Force Checks

Lx Jacking Force Total Total Total Stage 1 Allowable

(m) Pj1 Immediate Loss Deferred Loss Losses Immediate Loss (% of PUTS)(kN) (% of Pj1) (% of Pj1) (% of Pj1) (kN) (kN) (% of PUTS) Checks

0.000 7068.0 19.58 3.68 23.26 5684.0 5424.0 38.37 < 70% OK!

4.875 7068.0 17.59 3.65 21.24 5824.7 5567.1 39.38 < 70% OK!

9.750 7068.0 16.05 3.97 20.03 5933.4 5652.6 39.99 < 70% OK!

14.625 7068.0 14.60 4.36 18.96 6036.3 5728.1 40.52 < 70% OK!

19.500 7068.0 14.14 4.52 18.66 6068.4 5749.0 40.67 < 70% OK!

24.375 7068.0 14.75 4.35 19.10 6025.5 5717.9 40.45 < 70% OK!

29.250 7068.0 16.21 3.97 20.17 5922.4 5642.1 39.91 < 70% OK!

34.125 7068.0 17.75 3.64 21.39 5813.6 5556.3 39.31 < 70% OK!

39.000 7068.0 19.74 3.67 23.41 5672.8 5413.1 38.29 < 70% OK!

NOTE : Maximum Initial Prestressing Force for Post-Tensioning Tendon Immediately after anchoring = 70% of PUTS

(BS 5400 : Part 4 : 1990 : CL. 6.7.1)

2(f) Summary of Concrete Stress After Immediate & Deferred Losses And Allowable Stress Checks in Concrete

at Transfer(Not Required to Check - Can Be Ommited)Allowable Tensile Stress @ Stage 1 Transfer = -1.00 N/mm

2 (BS 5400 :Part 4 :1990 : CL. 6.3.2.4b)

Allowable Compressive Stress @ Stage 1 Transfer = 15.00 N/mm2 (BS 5400 :Part 4 :1990 : Table 23)


(m) All Loss Beam Selfweight ft fb ftendon Allowable


2) (N/mm

2) Checks

0.000 -155.5 5424.0 0.00 7.782 4.374 6.487 OK!

4.875 298.5 5567.1 1735.79 6.538 6.239 6.361 OK!9.750 622.8 5652.6 2975.65 5.504 7.705 7.146 OK!

14.625 817.4 5728.1 3719.56 4.826 8.715 8.084 OK!

19.500 882.3 5749.0 3967.53 4.590 9.053 8.465 OK!

24.375 817.4 5717.9 3719.56 4.829 8.685 8.059 OK!

29.250 622.8 5642.1 2975.65 5.503 7.679 7.126 OK!

34.125 298.5 5556.3 1735.79 6.531 6.220 6.346 OK!

39.000 -155.5 5413.1 0.00 7.766 4.366 6.474 OK!

Immediate & Deferred Losses

Concrete Stresses

Deferred Losses % of Deferred Loss from PUTS

- END OF STAGE 1 CALCULATIONS -

Cable Force After



16/40




Prestress Losses

(3) Immediate Losses

3(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)

(i) Force Gradient


qsum 0.2839 0.2383 0.1923 0.1462

mqsum + KLcable 0.1875 0.1783 0.1691 0.1599

e-(mq + KLcable) 0.8291 0.8367 0.8444 0.8522

Total Loss of Prestr. Force due to Friction Losses

pfrict.Loss = (1 - e-(mq+KLcable))*pj2 pfrict.Loss (kN) 441.0 421.4 401.5 381.3 1645.11

As a percentage of pj2 % of pj2 17.1 16.3 15.6 14.8 15.94As a percentage of PUTS % of PUTS 12.5 11.9 11.4 10.8 11.64

Cable Force @ Dead End after Frict. Losses

pd = pj2 - pfrict.Loss pd (kN) 2138.8 2158.4 2178.4 2198.6 8674.17


Loss of Pres. Force per unit length/Force Gradient

dp = (pfrict.Loss/Lcable) dp (kN/m) 11.136 10.641 10.138 9.628 41.543

(ii) Cable Force Along Beam Length After Friction Losses

Cable Mark A B C D

Suppport Midpsan Incre/decre. -1 * 1 * -1 * 1 * Total

Lx (m) X0 (m) dp (kN/m) -11.136 10.641 -10.138 9.628

Near End Live End Dead End Live End Dead End

Beam Ends 19.800 2579.8 2158.4 2579.8 2198.6 9516.6

0.000 19.500 SUPPORT 1 2576.5 2161.6 2576.8 2201.4 9516.3

4.875 14.625 2522.2 2213.5 2527.4 2248.4 9511.4

9.750 9.750 2467.9 2265.4 2477.9 2295.3 9506.5

14.625 4.875 2413.6 2317.3 2428.5 2342.2 9501.6

19.500 0.000 MIDSPAN 2359.3 2369.1 2379.1 2389.2 9496.7

24.375 4.875 2305.0 2421.0 2329.7 2436.1 9491.8

29.250 9.750 2250.7 2472.9 2280.2 2483.1 9486.9

34.125 14.625 2196.4 2524.8 2230.8 2530.0 9482.0

39.000 19.500 SUPPORT 2 2142.2 2576.6 2181.4 2576.9 9477.1

Beam Ends 19.800 2138.8 2579.8 2178.4 2579.8 9476.8

Far End Dead End Live End Dead End Live EndNote : * = " -1 " for Dead End of Cable is in the Far End and " 1 " for Dead End of Cable is in the Near End.

Distance of the Section from

Stage 2 Post Tensioning



17/40




3(b) Prestressing Force Loss due to Draw-in Wedges (VSL Prestressing System)

(i) Distance affected by Draw-in Wedges from Live End


Distance affected by Draw-in Wedges from Live End,

w = (draw-in * Es * As * n /dp)1/2 w (m) 18.240 18.660 19.117 19.617 -

w < Lcable

Loss of Force @ Live Ends Due to Wedges Draw-in

pdraw-inLoss = 2 * w * dp pdraw-inLoss (kN) 406.25 397.11 387.61 377.74 1568.72

As a percentage of pj2 % of pj2 15.7 15.4 15.0 14.6 15.20


(ii) Draw-in Wedges Losses Along Beam Length

Distance From

Suppport

Lx (m) A B C D (kN) (% of Pj2) (% of PUTS)

0.000 399.57 0.00 381.53 0.00 781.10 7.57 5.53

4.875 290.99 0.00 282.69 0.00 573.68 5.56 4.06

9.750 182.41 0.00 183.84 0.00 366.25 3.55 2.59

14.625 73.83 0.00 85.00 0.00 158.83 1.54 1.12

19.500 0.00 0.00 0.00 0.00 0.00 0.00 0.00

24.375 0.00 79.48 0.00 90.34 169.83 1.65 1.20

29.250 0.00 183.23 0.00 184.22 367.45 3.56 2.60

34.125 0.00 286.98 0.00 278.09 565.07 5.48 4.00

39.000 0.00 390.73 0.00 371.96 762.69 7.39 5.40

For -ve Force Gradient, For +ve Force Gradient,Lx < w pdraw-inLoss = 2 * dp * (w - Lx) (Lcable - Lx) < w, pdraw-inLoss = 2 * dp * ( w - (Lcable - Lx))

Lx >= w pdraw-inLoss = 0 (Lcable - Lx)>= w, pdraw-inLoss = 0

(iii) Cable Force Along Beam Length After Friction & Wedges Draw-in Losses

Distance From Allowable

Suppport A B C D (% of PUTS)

Lx (m) (kN) (% of PUTS) Checks

0.000 2176.9 2161.6 2195.2 2201.4 8735.23 61.79 < 70% OK!

4.875 2231.2 2213.5 2244.7 2248.4 8937.76 63.23 < 70% OK!

9.750 2285.5 2265.4 2294.1 2295.3 9140.28 64.66 < 70% OK!

14.625 2339.8 2317.3 2343.5 2342.29342.80

66.09 < 70% OK!

19.500 2359.3 2369.1 2379.1 2389.2 9496.73 67.18 < 70% OK!

24.375 2305.0 2341.5 2329.7 2345.8 9322.00 65.95 < 70% OK!

29.250 2250.7 2289.6 2280.2 2298.8 9119.48 64.51 < 70% OK!

34.125 2196.4 2237.8 2230.8 2251.9 8916.95 63.08 < 70% OK!

39.000 2142.2 2185.9 2181.4 2205.0 8714.43 61.65 < 70% OK!

Cable Mark

Cable MarkTotal

Total, Pdraw-inLoss

pdraw-inLoss (kN)

17 of


18/40




3(c) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2)

Immediately after transfer, the change in strain in the prestressing steel dep caused by elastic shortening of the concrete

is equal to the strain in the concrete at the steel level, ecp. The loss of prestress in the steel, dfLoss is therefore :

dfLoss = 0.5(Es/Ec2)*ftendon forpost-tensioned beam (ref. BS 5400:Part 4:Cl. 6.7.2.3)

N.B. ftendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons.ES is modulus of elasticity of the prestressing tendon

Ec2 is modulus of elasticity of the precast concrete at Stage 2 Service

(i) Moment & Concrete Stress Due To Selfweight of Precast Beam

Lx M ft fb e' ftendon

(m) (kNm) (N/mm2) (N/mm

2) (mm) (N/mm

2)

0.000 0.00 0.000 0.000 1317.8 0.000

4.875 1735.79 3.176 -3.835 863.8 -0.985

9.750 2975.65 5.445 -6.574 539.5 -3.523

14.625 3719.56 6.807 -8.218 344.9 -5.780

19.500 3967.53 7.260 -8.766 280.0 -6.654

24.375 3719.56 6.807 -8.218 344.9 -5.78029.250 2975.65 5.445 -6.574 539.5 -3.523

34.125 1735.79 3.176 -3.835 863.8 -0.985

39.000 0.00 0.000 0.000 1317.8 0.000

Moment, M = w(Lx/2)(Leff-L x) H = Total Height of Precast Beam.

ft = M/Zt e' = Distance from centroid of tendon to soffit.

fb = -M/Zb ftendon = fb + [(-fb+ft)x(e'/H)]

(ii) Concrete Stress Due To Prestressing Force After Friction & Wedges Draw-in Losses

Lx e = yb - e' Pi ft fb ftendon

(m) (mm) (kN) (N/mm2) (N/mm

2) (N/mm

2)

0.000 -155.5 8735.23 12.532 7.045 10.448

4.875 298.5 8937.76 5.397 16.174 11.793

9.750 622.8 9140.28 0.094 23.090 17.252

14.625 817.4 9342.80 -3.231 27.618 22.612

19.500 882.3 9496.73 -4.411 29.434 24.975

24.375 817.4 9322.00 -3.223 27.557 22.561

29.250 622.8 9119.48 0.094 23.037 17.213

34.125 298.5 8916.95 5.384 16.136 11.766

39.000 -155.5 8714.43 12.502 7.028 10.423

e' = distance from centroid of tendon to soffit

e = distance from centroid of tendon to neutral axis of Precast

Ap = Cross Section Area of Precast Beam

Pi = Total Initial Prestress Forces after Friction and Wedge Draw-in Losses

ft = Pi/Ap - Pie/Zt fb = Pi/Ap + Pie/Zb ftendon = fb + [(-fb+ft)x(e'/H)]

(iii) Calculation of Prestress Loss Due To Elastic Shortening of Concrete Along Beam Length

Lx Net Stress at tendon

(m) Selfweight Prestress Total (Stage 2) (Stage 2 - Stage 1)

(N/mm2) (N/mm

2) (N/mm

2) (N/mm

2) (N/mm


0.000 0.000 10.448 10.448 3.427 9.828 74.694 0.724 0.53

4.875 -0.985 11.793 10.808 3.865 11.084 84.237 0.816 0.60

9.750 -3.523 17.252 13.729 5.649 16.201 123.124 1.193 0.87

14.625 -5.780 22.612 16.832 7.398 21.216 161.242 1.563 1.14

19.500 -6.654 24.975 18.321 8.320 23.858 181.321 1.757 1.2824.375 -5.780 22.561 16.782 7.376 21.152 160.753 1.558 1.14

29.250 -3.523 17.213 13.690 5.632 16.150 122.743 1.189 0.87

34.125 -0.985 11.766 10.781 3.853 11.049 83.971 0.814 0.59

39.000 0.000 10.423 10.423 3.416 9.796 74.453 0.721 0.53

Stress at Tendon Level (ftendon) Loss of Prestress = 0.5*f tendon(Es/Ec2)



19/40




3(d) Summary of Immediate Losses (Friction Loss, Draw-in Loss And Elastic Shortening Loss)

Lx

(m) Friction Loss Draw-in Loss Elastic Loss Total Friction Loss Draw-in Loss Elastic Loss Total


0.000 802.9 781.10 74.694 1658.7 5.68 5.53 0.53 11.73

4.875 807.8 573.68 84.237 1465.8 5.71 4.06 0.60 10.37

9.750 812.7 366.25 123.124 1302.1 5.75 2.59 0.87 9.21

14.625 817.7 158.83 161.242 1137.7 5.78 1.12 1.14 8.05

19.500 822.6 0.00 181.321 1003.9 5.82 0.00 1.28 7.10

24.375 827.5 169.83 160.753 1158.0 5.85 1.20 1.14 8.19

29.250 832.4 367.45 122.743 1322.5 5.89 2.60 0.87 9.36

34.125 837.3 565.07 83.971 1486.3 5.92 4.00 0.59 10.51

39.000 842.2 762.69 74.453 1679.3 5.96 5.40 0.53 11.88

3(e) Summary of Cable Force After Immediate Losses and Allowable Prestressing Force Checks In Cables

Lx Jacking Force Total Allowable

(m) Pj2 Immediate Loss (% of PUTS)

(kN) (% of Pj2) (kN) (% of PUTS) Checks

0.000 10319.3 16.07 8660.5 61.27 < 70% OK!

4.875 10319.3 14.20 8853.5 62.63 < 70% OK!

9.750 10319.3 12.62 9017.2 63.79 < 70% OK!

14.625 10319.3 11.03 9181.6 64.95 < 70% OK!

19.500 10319.3 9.73 9315.4 65.90 < 70% OK!

24.375 10319.3 11.22 9161.2 64.81 < 70% OK!

29.250 10319.3 12.82 8996.7 63.64 < 70% OK!

34.125 10319.3 14.40 8833.0 62.49 < 70% OK!

39.000 10319.3 16.27 8640.0 61.12 < 70% OK!

NOTE : Maximum Initial Prestressing Force for Post-Tensioning Tendon Immediately after anchoring = 70% of PUTS(BS 5400 : Part 4 : 1990 : CL. 6.7.1)

3(f) Summary of Concrete Stress After Immediate Losses And Allowable Stress Checks in Concrete at Transfer

Allowable Tensile Stress @ Stage 2 Transfer = -1.00 (N/mm2) (BS 5400 :Part 4 :1990 : CL. 6.3.2.4b)

Allowable Compressive Stress @ Stage 2 Transfer = 20.00 (N/mm2) (BS 5400 :Part 4 :1990 : Table 23)


(m) Immediate Loss Beam Selfweight ft fb ftendon Allowable


2) (N/mm

2) Checks

0.000 -155.5 8660.5 0.00 12.425 6.985 10.359 OK!

4.875 298.5 8853.5 1735.79 8.522 12.187 10.697 OK!

9.750 622.8 9017.2 2975.65 5.538 16.205 13.497 OK!

14.625 817.4 9181.6 3719.56 3.632 18.924 16.442 OK!

19.500 882.3 9315.4 3967.53 2.934 20.107 17.844 NOT OK!

24.375 817.4 9161.2 3719.56 3.639 18.864 16.393 OK!

29.250 622.8 8996.7 2975.65 5.538 16.153 13.458 OK!

34.125 298.5 8833.0 1735.79 8.510 12.149 10.670 OK!

39.000 -155.5 8640.0 0.00 12.396 6.968 10.334 OK!

Immediate Loss

% of Immediate Loss from PUTS

Cable Force After

Concrete Stresses

Immediate Losses



20/40




(4) Deferred Losses During Stage 2 Stressing

4(a) Relaxation of Steel (BS 5400 : Part 4 : 1990 : C.L. 6.7.2.2)

The Loss of force in the tendon allowed for in the design should be the maximum relaxation after 1000 h duration, for a jacking force

equal to that imposed at transfer.

No reduction in the value of relaxation loss should be made for a tendon when a load equal to or greater that the relevant jacking force

has applied for time proir to anchoring of tendon.

(i) At 1000 hours, Relaxation of Steel of Cable = 2.5 % of Jacking Force

Cable Mark A B C D TOTALNos. Of Strands n (nos) 19 19 19 19 76

Jacking Force pj2 (kN) 2579.8 2579.8 2579.8 2579.8 10319.28

Total Final Relaxation Loss in Force prelaxLoss (kN) 64.50 64.50 64.50 64.50 257.98

Relaxation Loss as percentage of pj2 % of pj2 2.50 2.50 2.50 2.50 2.50

Relaxation Loss as percentage of PUTS % of PUTS 1.83 1.83 1.83 1.83 1.83

4(b) Shrinkage of Concrete Losses (BS 5400 : Part 4 : 1990 : C.L. 6.7.2.2)

(i) From BS 5400:Part 4:1990:Table 29,

System

Post-tensioning : transfer at

between 7 days and 14 days esafter concreting

(ii) Shrinkage Strain used in the Design, es = 200.0E-6

(iii) Shrinkage Strain Loss as Stress, fshrink.Loss = es x Es

(Final Loss) = 200.0E-6 x 195000

= 39.000 N/mm2

per strand

(iv) Shrinkage of Concrete Final Losses in all Cables, pshrink.Loss

Cable Mark A B C D TOTALNos. Of Strands 19 19 19 19 76

Total Shrinkage Loss in Force pshrink.Loss (kN) 74.1 74.1 74.1 74.100 296.400

As Loss in percentage of pi2 % of pj2 2.87 2.87 2.87 2.87 2.87

As Loss in percentage of PUTS % of PUTS 2.10 2.10 2.10 2.10 2.10

200 x 10-6

(70% r.h)

Shrinkage per unit length

(90% r.h)

Humid exposure Normal exposure

70 x 10-6



21/40




4(c) Creep of Concrete Losses (BS 5400:Part 4:1990: Cl. 6.7.2.5)

- The loss of prestress in the tendons due to creep of the concrete should be calculated on the assumption that creep is proportional to

stress in the concrete for stress of up to one-third of the cube strength at transfer.

- For Post-tensioning System :

(i) If the required cube strength at transfer is greater than 40.0 N/mm 2, the creep per unit length should be taken as 3.60 x 10-5 per N/mm2.

(ii) For lower values of the cube strength at transfer (fci), the creep per unit length should be taken as 3.60 x 10-5

x (40.0/fci) per N/mm2.

(iii) Where the maximum stress anywhere in the section at transfer exceeds one-third of the cube strength, the value of the

creep should be increased with the factor as below:

Increased factor = 1 + (Max stress @ Transfer - fci/3)*0.25

(fci/2- fci/3)

(iv) Calculation of Stress in the concrete adjacent to the tendon after elastic deformation losses

- Creep Strain ec = 3.60E-05 per N/mm2

- Modulus of Elasticity of Strand Es = 195 kN/mm2

- Increased factor = 1.022

- One -third (1/3) of Concrete cube Strength at Stage 2 fci2/3 = 16.67 N/mm2 .- Assumed Steel Relaxation Loss During Stage 2 Transfer % = 100.00 % of final

Lx

(m) After After Steel Maximum After After Steel Maximum

Immediate Loss Relaxation Loss Stress Immediate Loss Relaxation Loss Stress

(N/mm2) (N/mm

2) (N/mm

2) (N/mm

2) (N/mm

2) (N/mm

2)

0.000 6.798 6.798 10.359 10.100

4.875 6.701 6.701 10.697 10.430

9.750 7.676 7.676 13.497 13.159

14.625 8.830 8.830 16.442 16.031

19.500 9.305 9.305 9.305 17.844 17.398 17.39824.375 8.804 8.804 16.393 15.983

29.250 7.656 7.656 13.458 13.122

34.125 6.686 6.686 10.670 10.403

39.000 6.785 6.785 10.334 10.076

Remaining

Lx Creep Loss

(m) fromStage1

(N/mm2) (kN) (% of Pj2) (% of PUTS) (kN)

0.000 23.683 179.987 1.74 1.27 322.423

4.875 26.752 203.312 1.97 1.44 317.789

9.750 39.336 298.955 2.90 2.11 364.056

14.625 51.662 392.631 3.80 2.78 418.757

19.500 58.057 441.235 4.28 3.12 441.295

24.375 51.506 391.442 3.79 2.77 417.518

29.250 39.215 298.033 2.89 2.11 363.075

34.125 26.667 202.673 1.96 1.43 317.092

39.000 23.606 179.408 1.74 1.27 321.789

Where, (Only for 2 stages Stressing)

(i) Stress in the concrete adjacent to tendons at transfer after Steel Relaxation Loss

= Stress at Tendon level after Immediate Losses - the Steel Relaxation Losses at Stage 2 Transfer

(ii) Total Creep Loss At Stage 2 ( due to additional prestressing in Stage 2 compared to Stage 1)= (Stress at tendon level during Stage 2 - Stress at tendon level During Stage 1) * Creep Strain ( ec) * Es * Increased Factor

(N/mm2)

3.729

5.483

8.093

7.180

5.466

3.717

3.301

3.729

5.483

7.201

Stress in the concrete adjacent to tendons level, ftendon

3.291

During Stage 2

After Steel Relaxation Loss

Creep Loss During Stage 2

3.291

For Creep Loss Calculation

5.466

3.717

7.201

8.0937.180

Stress in the concrete adjacent to tendons level, ftendon

From Stage 1 Stressing

ftendon(Stage2)-ftendon(Stage1)

(N/mm2)

For Creep Loss Calculatio

(Final Loss)

From Stage 2 Stressing

3.301

During Stage 2

After Steel Relaxation Los

ftendon(Stage2)-ftendon(Stag

21 of 2


22/40




4(d) Summary of Deferred Losses During Stage 2 Transfer(Steel Relaxation Loss, Concrete Shrinkage Loss and Creep of Concrete Loss)

Assumed Percentage of Losses : (i) Relaxation = 100.00 % of final

(ii) Shrinkage = 66.67 % of final

(iii) Creep (S1) = 66.67 % of Stage 1 final Creep Loss

(iv) Creep (S2) = 100.00 % of Stage 2 final Creep Loss

Lx



0.000 258.0 197.61 502.410 958.0 1.83 1.40 3.55 6.78

4.875 258.0 197.61 521.101 976.7 1.83 1.40 3.69 6.91

9.750 258.0 197.61 663.010 1118.6 1.83 1.40 4.69 7.91

14.625 258.0 197.61 811.389 1267.0 1.83 1.40 5.74 8.96

19.500 258.0 197.61 882.530 1338.1 1.83 1.40 6.24 9.47

24.375 258.0 197.61 808.961 1264.6 1.83 1.40 5.72 8.95

29.250 258.0 197.61 661.108 1116.7 1.83 1.40 4.68 7.90

34.125 258.0 197.61 519.765 975.4 1.83 1.40 3.68 6.90

39.000 258.0 197.61 501.198 956.8 1.83 1.40 3.55 6.77

4(e) Summary of Cable Force After Immediate & Deferred Losses and Allowable Prestressing Force Checks In

Cables During Stage 2 Transfer


(m) Pj2 Immediate Loss Deferred Loss Transfer Losses Immediate Loss (% of PUTS)

(kN) (% of Pj2) (% of Pj2) (% of Pj2) (kN) (kN) (% of PUTS) Checks

0.000 10319.3 16.07 9.28 25.36 8660.5 7702.5 54.49


23/40




4(g) Summary of Deferred Losses During Stage 2 Service(Steel Relaxation Loss, Concrete Shrinkage Loss and Creep of Concrete Loss)

Assumed Percentage of Losses : (i) Relaxation = 100.00 % of final

(ii) Shrinkage = 66.67 % of final

(iii) Creep (S1) = 66.67 % of Stage 1 Creep Loss (Remaining from Stage 1 Stres

(iv) Creep (S2) = 100.00 % of Stage 2 final Creep Loss

Lx



0.000 258.0 197.61 502.410 958.0 1.83 1.40 3.55 6.78

4.875 258.0 197.61 521.101 976.7 1.83 1.40 3.69 6.91

9.750 258.0 197.61 663.010 1118.6 1.83 1.40 4.69 7.91

14.625 258.0 197.61 811.389 1267.0 1.83 1.40 5.74 8.96

19.500 258.0 197.61 882.530 1338.1 1.83 1.40 6.24 9.47

24.375 258.0 197.61 808.961 1264.6 1.83 1.40 5.72 8.95

29.250 258.0 197.61 661.108 1116.7 1.83 1.40 4.68 7.90

34.125 258.0 197.61 519.765 975.4 1.83 1.40 3.68 6.90

39.000 258.0 197.61 501.198 956.8 1.83 1.40 3.55 6.77

4(h) Summary of Cable Force After Immediate & Deferred Losses and Allowable Prestressing Force Checks In

Cables During Stage 2 Service


(m) Pj2 Immediate Loss Deferred Loss Service Losses Immediate Loss (% of PUTS)

(kN) (% of Pj2) (% of Pj2) (% of Pj2) (kN) (kN) (% of PUTS) Checks

0.000 10319.3 16.07 9.28 25.36 8660.5 7702.5 54.49


24/40




DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM AND IN-SITU SLAB(IN ACCORDANCE WITH RESEARCH REPORT NO. 15 : NOVEMBER 1963 - AN INVESTIGATIONOF THE BEHAVIOUR OF

THE COMPOSITE CONCRETE BEAMS FROM C&CA )

(BS 5400:Part4:1990 Cl.7.4.3.4)

Before the two concretes could be jointed together, external forces and moments would have to be applied to the beam to

straighten it. Firstly the moment is to be applied:

Mb = F2EcIpxx where , Ec = Young's modulus of the precast beam concrete

Ipxx= Second moment of area of the precast beam

F2 = Rotation of the beam = 1/H (sbb - sbt)

sbb = free total strain movement of the bottom fibres

sbt = free total strain movement of the top fibres

H = Total depth of precast beam

A pair of tensile forces is now applied to the ends of the slab at i ts centroid; these forces (F) are of such magnitude that the

elongation of the slabs equals the differential shrinkage, i.e.

F = dEin-situA1 where, d = Differential shrinkage coefficient

Ein-situ= Modulus of elasticity of the in-situ concrete

A1= Area of the in-situ flange/slab

Assume deck slab is cast one month after precast beams, so then 50 % of the shrinkage has taken place.

Hence,

d = 0.5 * Differential shrinkage coefficient

The two concrete can now be jointed together and equal and opposite forces and moments applied to cancel F and Mb.

Since the two concrete are now acting as a composite section, the compressive cancelling forces -F will be accompained by

a moment,

Mc = Fe1 where, e1 = Diatance between the centroid of insitu flange

to centroid of composite section

The net value of the cancelling moment is therefore,

Mc'= Mc - Mb = Fe1 - Mb

The resulting stresses in the cross-section due to these external and cancelling forces can now be dertermined, these are, (see Figure 1)

f1 = ( F/A1' - F/Ac - Mc' y1/Icxx)(Einsitu/Ec) * (k) (Top of Insitu Slab)

f2 = ( F/A1' - F/Ac - Mc' y2/Icxx)(Einsitu/Ec) * (k) (Bottom of Insitu Slab)

f3 = ( -F/Ac - Mc' y2/Icxx-Mb yt/Ipxx) * (k) (Top of Precast Beam)

f4 = ( -F/Ac + Mc' y4/Icxx +Mb yb/Ipxx) * (k) (Bottom of Precast Beam)

original length at time of

casting insitu flange sf

f1

centroid of flange t F -F

e1 y1

y2 centroid of f2

yt composite sbt

centroid of section Mc' = Fe-Mbprecast beam

yb y4 Mb

sbb f4

where,

A1 = area of in situ concrete y2 = distance from centroid of the composite beam to top fibre of precast beam

A2 = area of precast concrete section y4 = distance from centroid of the composite beam to soffit fo precast beam

Ac = area of composite concrete section Icxx = moment of inertia/second moment of area of composite section

A1' = transformed area of in situ concrete = (Modular ratio) * A1 k = creep reduction coefficient

yt = distance from centroid of the precast beam to top of precast bea Ein-situ= Modulus of elasticity of the in-situ concrete

yb = distance from centroid of the precast beam to soffit of precast be Ec = Young's modulus of the precast beam concrete

y1 = distance from centroid of the composite beam to top fibre of in-situ flange

FIGURE 1 - Theoretical Approach to Differential Shrinkage


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CALCULATION OF THE DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM

AND IN-SITU SLAB

(1) Design Parameter :

(a) Modular Ratio (Einsitu/Ecu) m = 0.824(b) Area of Insitu Slab A1 = 351000 mm2

(c) Transformed Area of Insitu Slab A1' = 289059 mm2

(d) Area of Precast Section A2 = 869500 mm2

(e) Area of Composite Section Ac = 1158559 mm2

(f) Moment of Inertia of Precast Ipxx= 5.2608E+11 mm4

(g) Moment of Inertia of Composite Icxx= 7.6205E+11 mm4

(h) Total Depth of Precast Beam H = 2125 mm

(I) Thickness of Insitu Slab t = 180 mm

(j) Centroid of Precast to Top f ibre yt = 963 mm

(k) Centroid of Precast to Bottom fibre yb = 1162 mm

Centroid of Composite Beam to :

(l) Top of Insitu Slab y1 = 885.72 mm

(m) Top of Precast Beam y2 = 705.72 mm

(n) Bottom of Precast Beam y4 = 1419.28 mm

(o) Centroid of Top Slab e1 = 795.72 mm

(p) Differential Shrinkage Coefficient d = 1.00E-04 50.0 % has occured during slab Const...)"

(q) Creep Reduction Coefficient k = 0.43 (BS 5400 : Part 4 : 1990: Cl.7.4.3.4)

(r) Modulus of Elasticity of the precast @transfer Eci2 = 34 kN/mm2

(s) Modulus of Elasticity of the precast @service Ecu = 34 kN/mm2

(t) Modulus of Elasticity of the Insitu Ein-situ= 28 kN/mm2

(2) Calculation of The Section Differential Shrinkage Between Precast Beam And Insitu Slab

(a) Previous Calculated Final stresses due to selfweight and prestressing (after short term losses) :

Prestress Force Selfwt. Moment

Lx @ Stage 2 Transfer M

(m) Pfinal (kN) (kNm) DL Pfinal / A Pfinal (e)/Zt Total

0.000 7702.54 0.000 0.000 8.859 2.646 11.504

4.875 7876.83 1735.794 3.176 9.059 2.242 14.477

9.750 7898.55 2975.646 5.445 9.084 -4.315 10.214

14.625 7914.58 3719.558 6.807 9.102 -9.021 6.888

19.500 7977.28 3967.529 7.260 9.175 -11.933 4.502

24.375 7896.69 3719.558 6.807 9.082 -12.750 3.139

29.250 7880.03 2975.646 5.445 9.063 -11.787 2.721

34.125 7857.63 1735.794 3.176 9.037 -8.956 3.257

39.000 7683.19 0.000 0.000 8.836 -4.197 4.639

Prestress Force Selfwt. Moment

Lx @ Stage 2 Transfer M

(m) Pfinal (kN) (kNm) DL Pfinal / A Pfinal (e)/Zb Total

0.000 7702.54 0.000 0.000 8.859 -2.646 6.213

4.875 7876.83 1735.794 -3.176 9.059 -2.242 3.641

9.750 7898.55 2975.646 -5.445 9.084 4.315 7.954

14.625 7914.58 3719.558 -6.807 9.102 9.021 11.317

19.500 7977.28 3967.529 -7.260 9.175 11.933 13.847

24.375 7896.69 3719.558 -6.807 9.082 12.750 15.025

29.250 7880.03 2975.646 -5.445 9.063 11.787 15.40534.125 7857.63 1735.794 -3.176 9.037 8.956 14.816

39.000 7683.19 0.000 0.000 8.836 4.197 13.034

(N/mm2)

sb

(N/mm2)

st



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(b) Now calculate the (sbb - sbt), Mb, Mc, Mc'as following : -

Assuming % of the Creep has occured in the precast beam (short term losses)

when the in-situ slab is cast = 50.00 % of 3.60E-05 per N/mm2

Then, creep strain ec = 1.80E-05 per N/mm2

increased creep factor = 1.022

and F = dEin-situA1 = 9.83E+02 kN

(sbb - sbt) = (creep strain when casting of insitu slab)*(increased creep factor)(sb - st)

F2 = Rotation of the beam = 1/H (sbb - sbt)

Mb = F2Eci2Ipxx

Mc = Fe1

Mc'= Mc - Mb

Lx (sbb - sbt) F2 Mb Mc Mc'

(m) (Nmm) (Nmm) (Nmm)

0.000 -9.73E-05 -4.58E-08 -8.193E+08 7.82E+08 1.60E+09

4.875 -1.99E-04 -9.38E-08 -1.678E+09 7.82E+08 2.46E+09

9.750 -4.16E-05 -1.96E-08 -3.501E+08 7.82E+08 1.13E+0914.625 8.15E-05 3.83E-08 6.857E+08 7.82E+08 9.64E+07

19.500 1.72E-04 8.09E-08 1.447E+09 7.82E+08 -6.65E+08

24.375 2.19E-04 1.03E-07 1.840E+09 7.82E+08 -1.06E+09

29.250 2.33E-04 1.10E-07 1.964E+09 7.82E+08 -1.18E+09

34.125 2.13E-04 1.00E-07 1.790E+09 7.82E+08 -1.01E+09

39.000 1.54E-04 7.27E-08 1.300E+09 7.82E+08 -5.18E+08

(c) Resulting Stresses Due To Differential Shrinkage Between Precast Beam and Insitu Slab

(i) Determination of stresses at Top of Insitu Slab , f1

Lx F/A1' F/Ac Mc' y1/Icxx (m) * (k) f1

(m) (N/mm2)

0.000 3.400 0.848 1.861 0.354 0.245

4.875 3.400 0.848 2.859 0.354 -0.109

9.750 3.400 0.848 1.316 0.354 0.438

14.625 3.400 0.848 0.112 0.354 0.864

19.500 3.400 0.848 -0.773 0.354 1.177

24.375 3.400 0.848 -1.230 0.354 1.339

29.250 3.400 0.848 -1.374 0.354 1.390

34.125 3.400 0.848 -1.171 0.354 1.318

39.000 3.400 0.848 -0.602 0.354 1.117

(ii) Determination of stresses at Bottom of Insitu Slab , f2

Lx F/A1' F/Ac Mc' y2/Icxx (m) * (k) f2

(m) (N/mm2)

0.000 3.400 0.848 1.483 0.354 0.378

4.875 3.400 0.848 2.278 0.354 0.097

9.750 3.400 0.848 1.048 0.354 0.532

14.625 3.400 0.848 0.089 0.354 0.872

19.500 3.400 0.848 -0.616 0.354 1.122

24.375 3.400 0.848 -0.980 0.354 1.251

29.250 3.400 0.848 -1.095 0.354 1.291

34.125 3.400 0.848 -0.933 0.354 1.234

39.000 3.400 0.848 -0.479 0.354 1.073



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(iii) Determination of stresses at Top of Precast Beam , f3

Lx F/Ac Mc' y2/Icxx Mb yt/Ipxx (k) f3

(m) (N/mm2)

0.000 0.848 1.483 -1.499 0.430 -0.3584.875 0.848 2.278 -3.070 0.430 -0.024

9.750 0.848 1.048 -0.641 0.430 -0.540

14.625 0.848 0.089 1.255 0.430 -0.943

19.500 0.848 -0.616 2.648 0.430 -1.239

24.375 0.848 -0.980 3.368 0.430 -1.391

29.250 0.848 -1.095 3.594 0.430 -1.440

34.125 0.848 -0.933 3.275 0.430 -1.372

39.000 0.848 -0.479 2.378 0.430 -1.181

(iv) Determination of stresses at Bottom of Precast Beam , f4

Lx F/Ac Mc' y4/Icxx Mb yb/Ipxx (k) f4(m) (N/mm

2)

0.000 0.848 2.982 -1.810 0.430 0.139 f1 = Stresses @ Top of Insitu Slab

4.875 0.848 4.581 -3.707 0.430 0.011 f2 = Stresses @ Bottom of Insitu Sla

9.750 0.848 2.108 -0.773 0.430 0.209 f3 = Stresses @ Top of Precast Bea

14.625 0.848 0.179 1.515 0.430 0.364 f4 = Stresses @ Bottom of Precast B

19.500 0.848 -1.238 3.197 0.430 0.477

24.375 0.848 -1.971 4.066 0.430 0.536

29.250 0.848 -2.201 4.339 0.430 0.554

34.125 0.848 -1.877 3.954 0.430 0.529

39.000 0.848 -0.964 2.872 0.430 0.455

(3) Summary Of The Resulting Stresses After Losses and Differential Shrinkage

Lx f1 f2 f3 f4

(m) (N/mm2) (N/mm

2) (N/mm

2) (N/mm

2)

f1 = ( F/A1' - F/Ac - Mc' y1/Icxx)(Einsitu/Ec) * (k)

0.000 -0.245 -0.378 0.358 -0.139

4.875 0.109 -0.097 0.024 -0.011 f2 = ( F/A1' - F/Ac - Mc' y2/Icxx)(Einsitu/Ec) * (k)

9.750 -0.438 -0.532 0.540 -0.209

14.625 -0.864 -0.872 0.943 -0.364 f3 = ( -F/Ac - Mc' y2/Icxx -Mb yt/Ipxx) * (k)

19.500 -1.177 -1.122 1.239 -0.477

24.375 -1.339 -1.251 1.391 -0.536 f4 = ( -F/Ac + Mc' y4/Icxx +Mb yb/Ipxx) * (k)

29.250 -1.390 -1.291 1.440 -0.554

34.125 -1.318 -1.234 1.372 -0.529

39.000 -1.117 -1.073 1.181 -0.455

Note : In the above table the sign convention has been amended to give tension as -ve

for consistance with other calculations.

End of Calculation Of Differential Shrinkage

27 of


28/40



Prestress Checking at Serviceability Limit State For Post-Tensioned Beam Jo

Prestress Checking at Deflected Sections At Serviceability Limit State For

Precast Prestressed Post-Tensioned Beam Design

Project : PROJECT TITLE Designed : KKL

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC

File name : W:\SCB Spreadsheet\Post-Tensioned-Design.xls

DESIGN DATA

Prestressing System Post-tensioned = Post -Tensioned ; Class 2

Tensile stress permitted, but no visible cracking Crack = 0

Precast Beam Section = S40T1 BEAM Precast Beam

(1) SECTION PROPERTIES OF PRECAST BEAM :

(i) TOTAL HEIGHT OF THE PRECAST SECTION H = 2125 mm

(ii) AREA OF PRECAST BEAM A = 0.869500 m2

(iii) HEIGHT OF CENTROID ABOVE BOTTOM FIBRE yb = 1162.3 mm

(iv) SECTION MUDULI : TOP FIBRE OF PRECAST Zt = 0.54646 m3

(v) BOTTOM FIBRE OF PRECAST Zb = 0.45262 m3

(vi) SELFWEIGHT OF PRECAST BEAM w = 20.868 kN/m

(2) SECTION MODULI OF COMPOSITE SECTION :

(i) TOP FIBRE OF COMPOSITE SECTION Zt,c = 0.86037 m3

(ii) TOP FIBRE OF PRECAST SECTION Zt,p = 1.07982 m3

(iii) BOTTOM FIBRE OF TOP SLAB Zb,s = 1.07982 m3

(iv) BOTTOM FIBRE OF PRECAST SECTION Zb,p = 0.53693 m3

(3) DEAD WT OF INSITU CONCRETE winsitu = 8.900 kN/m

(4) CONCRETE STRENGTH:(i) Presstress Concrete : @ TRANSFER fci2 = 50 N/mm

2

@ 28 DAYS fcu = 50 N/mm2

(ii) Insitu Concrete : fc = 30 N/mm2

(5) ALLOWABLE CONCRETE STRESSES FOR PRECAST BEAM:(ref. BS5400:Part4:1990:Cl. 6.3.2)

FOR PRESTRESSING CONCRETE

MEMBER TENSION COMPRESSION

N/mm2

CLASS 1 -1.000 20.000

CLASS 2 -1.000 20.000

CLASS 3 -1.000 20.000

ALLOWABLE CONCRETE STRESSES @ SERVICE/WORKING:

MEMBER TENSION COMPRESSION

N/mm2

CLASS 1 0.000 20.000

CLASS 2 -2.546 20.000

CLASS 3 CRACK WIDTH fcu = 40 N/mm2

fcu = >=50 N/mm2

0.10 -2.87 -3.36 20.000

0.15 -3.15 -3.71

0.25 -3.85 -4.41

(a) ALLOWABLE CONCRETE STRESSES @ TRANSFER FOR PRECAST BEAM:

(i) TENSILE STRESS WITH SELF WT (BS5400:P4:90:CL. 6.3.2.4 b(1)) -1.00 N/mm2

(ii) COMPRESSIVE STRESS (BS5400:P4:1990:CL.6.3.2.2 b) 20.00 N/mm2

(b) ALLOWABLE CONCRETE STRESSES UNDER SERVICE/WORKING LOADS FOR PRECAST BEAM :

(i) TENSILE STRESS (BS5400:P4:1990:CL.6.3.2.4a) -2.55 N/mm2

(ii) COMPRESSIVE STRESS (BS5400:P4:1990:CL6.3.2.2a) 20.00 N/mm2

(6) ALLOWABLE CONCRETE STRESSES FOR INSITU SLAB:

N/mm2

ALLOWABLE CONCRETE STRESSES @ TRANSFER :

N/mm2

S40T1

HB45

39 m Ef

CLASS

CRACK WIDTH


29/40



Prestress Checking at Serviceability Limit State For Post-Tensioned Beam

STRESS CHECKS AT MID-SPAN AND VARIES SECTIONS ALONG THE BEAM

(0) AT MIDSPAN, DISTANCE FROM SUPPORT 1 19.50 m

Cable NOS. HT. ABOVE

Mark OF STRANDS SOFFIT (mm)

D 19 100.00

C 19 220.00

B 19 340.00

A 19 460.00 N.B. e = distance between centroid of precast beam

to centroid of tendon

TOTAL : 76.000 280.00 e = 882.30 mm

INITIAL PRESTRESS LOSSES @ TRANSFER 9.73 %

FINAL TOTAL PRESTRESS LOSSES 22.70 %

ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN

73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN

EFFECTIVE FORCE @ TRANSFER PER STRAND 122.57 kN

EFFECTIVE FINAL FORCE PER STRAND 104.96 kN

TOP OF BOTT OF TOP OF BOTT OF

INSITU INSITU PRECAST PRECAST

TRANSFER PRESTRESS - - -4.33 28.87

SELF WT - - 7.26 -8.77

TOTAL @ TRANSFER - - 2.93 20.11

EXCEEDED ALLOWABLE PRESTRESSING STRESSES AT TRANSFER, TRY AGAIN

FINAL PRESTRESS - - -3.71 24.72

SELF WT + DEAD INSITU - - 10.36 -12.50

TEMPERATURE DIFFERENCE 2 - - -1.00

SUPER. DEAD + LIVE HB45 -SLS2 6.82 5.43 6.60 -13.270 (MIDSPAN)

DIFF. SHRINKAGE -1.177 -1.122 1.239 -0.477

TOTAL @ WORKING 7.64 4.31 14.49 -2.53

(1) AT SUPPORT 1, DISTANCE FROM SUPPORT 1 0.00 m



D 19 803.20

C 19 1146.28

B 19 1489.36



TOTAL : 76.000 1317.82 e = -155.52 mm



ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN





TRANSFER PRESTRESS - - 12.43 6.98

SELF WT - - 0.00 0.00


FINAL PRESTRESS - - 11.05 6.21

SELF WT + DEAD INSITU - - 0.00 0.00

TEMPERATURE DIFFERENCE -1 - - 1.00

SUPER. DEAD + LIVE HB45 -SLS 2.13 1.70 2.06 -4.140 (SUPPORT 1)

DIFF. SHRINKAGE -0.245 -0.378 0.358 -0.139TOTAL @ WORKING 0.88 1.32 13.47 2.93


30/40




(2) 2nd SECTION, DISTANCE FROM SUPPORT 1 4.88 m



D 19 495.55

C 19 741.03

B 19 986.52

A 19 1232.00 N.B. e = distance between centroid of precast beamto centroid of tendon

TOTAL : 76.000 863.77 e = 298.53 mm










SELF WT - - 3.18 -3.83


FINAL PRESTRESS - - 4.76 14.25


SUPER. DEAD + LIVE HB45 -SLS 2.51 2.00 2.43 -4.880 (SECTION 1)

DIFF. SHRINKAGE 0.109 -0.097 0.024 -0.011

TOTAL @ WORKING 2.62 1.90 11.74 3.89

(3) 3rd SECTION, DISTANCE FROM SUPPORT 1 9.75 m



D 19 275.80

C 19 451.57

B 19 627.34



TOTAL : 76.000 539.46 e = 622.84 mm







TOP OF BOTT OF TOP OF BOTT OFINSITU INSITU PRECAST PRECAST


SELF WT - - 5.45 -6.57


FINAL PRESTRESS 0.08 19.95

SELF WT + DEAD INSITU 7.77 -9.38


DIFF. SHRINKAGE -0.438 -0.532 0.540 -0.209

TOTAL @ WORKING 4.79 3.63 13.45 0.20


31/40




(4) 4th SECTION, DISTANCE FROM SUPPORT 1 14.63 m



D 19 143.95

C 19 277.89

B 19 411.84

A 19 545.78 N.B. e = distance between centroid of precast beamto centroid of tendon

TOTAL : 76.000 344.86 e = 817.44 mm










SELF WT - - 6.81 -8.22





DIFF. SHRINKAGE -0.864 -0.872 0.943 -0.364

TOTAL @ WORKING 5.59 4.27 14.16 -1.25

(5) AT MID-SPAN, DISTANCE FROM SUPPORT 1 19.50 m



D 19 100.00C 19 220.00

B 19 340.00



TOTAL : 76.000 280.00 e = 882.30 mm







TOP OF BOTT OF TOP OF BOTT OFINSITU INSITU PRECAST PRECAST


SELF WT - - 7.26 -8.77


EXCEEDED ALLOWABLE PRESTRESSING STRESSES AT TRANSFER, TRY AGAIN



TEMPERATURE DIFFERENCE 2 - - -1.00

SUPER. DEAD + LIVE HB45 -SLS 6.82 5.43 6.60 -13.270 (MIDSPAN)

DIFF. SHRINKAGE -1.177 -1.122 1.239 -0.477

TOTAL

Documents

46947288 Post Tensioned Design1