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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)
7/29/2019 46947288 Post Tensioned Design1
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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)
7/29/2019 46947288 Post Tensioned Design1
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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 :
Filename : W:\SCB Spreadsheet\Post-Tensioned-Design.xls
(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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SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Consulting Engineers
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
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 - 1.200 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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SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Consulting Engineers
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 -
Support Beam Beam & Services
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 -
Support Beam Beam & Services
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
Due to Dead Load Due to Superimposed Dead Load
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)
Due to Dead Load Due to Superimposed Dead Load
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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
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
Dead Load Superimposed Dead Load
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
Dead Load Superimposed Dead Load
NOMINAL - MOMENT NOMINAL CO-EXISITING MOMENT (kNm)
7/29/2019 46947288 Post Tensioned Design1
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SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Consulting Engineers
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
Filename : W:\SCB Spreadsheet\Post-Tensioned-Design.xls
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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
(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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
Prestress Losses
(1) Immediate Losses
1(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)
(i) Force Gradient
Cable Mark A B C D Total
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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
1(b) Prestressing Force Loss due to Draw-in Wedges (VSL Prestressing System)
(i) Distance affected by Draw-in Wedges from Live End
Cable Mark A B C D Total
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
As a percentage of PUTS % of PUTS 9.5 9.3 9.1 8.8 9.18
(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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
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)
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
(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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 37478
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
2) (kN) (% of Pj1) (% of PUTS)
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
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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
(kN) (kN) (kN) (kN) (% of PUTS) (% of PUTS) (% of PUTS) (% of PUTS)
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)
Lx e Cable Force After Moment Due to
(m) All Loss Beam Selfweight ft fb ftendon Allowable
(mm) (kN) (kNm) (N/mm2) (N/mm
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
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Prestress Losses
(3) Immediate Losses
3(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)
(i) Force Gradient
Cable Mark A B C D Total
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
As a percentage of PUTS % of PUTS 60.5 61.1 61.6 62.2 61.36
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
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3(b) Prestressing Force Loss due to Draw-in Wedges (VSL Prestressing System)
(i) Distance affected by Draw-in Wedges from Live End
Cable Mark A B C D Total
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
As a percentage of PUTS % of PUTS 11.5 11.2 11.0 10.7 11.10
(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)
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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
2) (kN) (% of Pj2) (% of PUTS)
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)
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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
(kN) (kN) (kN) (kN) (% of PUTS) (% of PUTS) (% of PUTS) (% of PUTS)
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)
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 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
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(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
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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
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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
(m) Relaxation Loss Shrinkage Loss Creep Loss Total Relaxation Loss Shrinkage Loss Creep Loss Total
(kN) (kN) (kN) (kN) (% of PUTS) (% of PUTS) (% of PUTS) (% of PUTS)
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
Lx Jacking Force Total Total Total Stage 2 Allowable
(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
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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
(m) Relaxation Loss Shrinkage Loss Creep Loss Total Relaxation Loss Shrinkage Loss Creep Loss Total
(kN) (kN) (kN) (kN) (% of PUTS) (% of PUTS) (% of PUTS) (% of PUTS)
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
Lx Jacking Force Total Total Total Stage 2 Allowable
(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
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Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS Job No. : 3
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
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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
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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
Cable NOS. HT. ABOVE
Mark OF STRANDS SOFFIT (mm)
D 19 803.20
C 19 1146.28
B 19 1489.36
A 19 1832.45 N.B. e = distance between centroid of precast beam
to centroid of tendon
TOTAL : 76.000 1317.82 e = -155.52 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 16.07 %
FINAL TOTAL PRESTRESS LOSSES 25.36 %
ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN
EFFECTIVE FORCE @ TRANSFER PER STRAND 113.95 kN
EFFECTIVE FINAL FORCE PER STRAND 101.35 kN
TOP OF BOTT OF TOP OF BOTT OF
INSITU INSITU PRECAST PRECAST
TRANSFER PRESTRESS - - 12.43 6.98
SELF WT - - 0.00 0.00
TOTAL @ TRANSFER - - 12.43 6.98
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
7/29/2019 46947288 Post Tensioned Design1
30/40
SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Consulting Engineers
Prestress Checking at Serviceability Limit State For Post-Tensioned Beam
(2) 2nd SECTION, DISTANCE FROM SUPPORT 1 4.88 m
Cable NOS. HT. ABOVE
Mark OF STRANDS SOFFIT (mm)
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
INITIAL PRESTRESS LOSSES @ TRANSFER 14.20 %
FINAL TOTAL PRESTRESS LOSSES 23.67 %
ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN
73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN
EFFECTIVE FORCE @ TRANSFER PER STRAND 116.49 kN
EFFECTIVE FINAL FORCE PER STRAND 103.64 kN
TOP OF BOTT OF TOP OF BOTT OF
INSITU INSITU PRECAST PRECAST
TRANSFER PRESTRESS - - 5.35 16.02
SELF WT - - 3.18 -3.83
TOTAL @ TRANSFER - - 8.52 12.19
FINAL PRESTRESS - - 4.76 14.25
SELF WT + DEAD INSITU - - 4.53 -5.47
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
Cable NOS. HT. ABOVE
Mark OF STRANDS SOFFIT (mm)
D 19 275.80
C 19 451.57
B 19 627.34
A 19 803.11 N.B. e = distance between centroid of precast beam
to centroid of tendon
TOTAL : 76.000 539.46 e = 622.84 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 12.62 %
FINAL TOTAL PRESTRESS LOSSES 23.46 %
ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN
73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN
EFFECTIVE FORCE @ TRANSFER PER STRAND 118.65 kN
EFFECTIVE FINAL FORCE PER STRAND 103.93 kN
TOP OF BOTT OF TOP OF BOTT OFINSITU INSITU PRECAST PRECAST
TRANSFER PRESTRESS - - 0.09 22.78
SELF WT - - 5.45 -6.57
TOTAL @ TRANSFER - - 5.54 16.20
FINAL PRESTRESS 0.08 19.95
SELF WT + DEAD INSITU 7.77 -9.38
SUPER. DEAD + LIVE HB45 -SLS 5.23 4.16 5.06 -10.170 (SECTION 2)
DIFF. SHRINKAGE -0.438 -0.532 0.540 -0.209
TOTAL @ WORKING 4.79 3.63 13.45 0.20
7/29/2019 46947288 Post Tensioned Design1
31/40
SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Consulting Engineers
Prestress Checking at Serviceability Limit State For Post-Tensioned Beam
(4) 4th SECTION, DISTANCE FROM SUPPORT 1 14.63 m
Cable NOS. HT. ABOVE
Mark OF STRANDS SOFFIT (mm)
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
INITIAL PRESTRESS LOSSES @ TRANSFER 11.03 %
FINAL TOTAL PRESTRESS LOSSES 23.30 %
ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN
73 % OF U.T.S. INITIAL PRESTRESS 135.78 kN
EFFECTIVE FORCE @ TRANSFER PER STRAND 120.81 kN
EFFECTIVE FINAL FORCE PER STRAND 104.14 kN
TOP OF BOTT OF TOP OF BOTT OF
INSITU INSITU PRECAST PRECAST
TRANSFER PRESTRESS - - -3.17 27.14
SELF WT - - 6.81 -8.22
TOTAL @ TRANSFER - - 3.63 18.92
FINAL PRESTRESS - - -2.74 23.40
SELF WT + DEAD INSITU - - 9.71 -11.72
SUPER. DEAD + LIVE HB45 -SLS 6.46 5.14 6.25 -12.560 (SECTION 3)
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
Cable NOS. HT. ABOVE
Mark OF STRANDS SOFFIT (mm)
D 19 100.00C 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 OFINSITU 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 -SLS 6.82 5.43 6.60 -13.270 (MIDSPAN)
DIFF. SHRINKAGE -1.177 -1.122 1.239 -0.477
TOTAL