Source: https://ru.scribd.com/doc/46947288/Post-Tensioned-Design1
Timestamp: 2019-07-21 04:51:03
Document Index: 131580218

Matched Legal Cases: ['art 4', 'art 4', 'art4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art4', 'art 4', 'art4', 'ART4', 'ART 4', 'art 4', 'art 4', 'ART4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art 4', 'art4']

saveSave Post Tensioned Design1 For Later
I-Beam Girder Computions.xls
CEB FIP DesignOfPost-TensionedSlabsAndFoundations
Beam_Design_Spreadsheet
Post Tension Ing Design
SEPAKAT SETIA PERUNDING SDN BHD (14142-M)
PROJECT : PROJECT TITLE
DETAIL : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH
JOB NUMBER : 37478
Designed : KKL Date : 16-Jan-2011
Checked : LTC Date : 16-Jan-2011
File name : W:\SCB Spreadsheet\Post-Tensioned-Design.xls
S37T1 - EDGE BEAM (T1)
(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 Elasticity Ec2 = 34 kN/mm2
(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 φs = 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 µ = 0.2 /rad
(f) Wobble Factor K= 0 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 εc = 0 per N/mm2
(c) Shrinkage per unit Length εs = 2.00E-004
(d) Creep reduction Coefficient k= 0.43
SEPAKAT SETIA PERUNDING (14142-M)
POST-TENSIONED BEAM DESIGN - Calculation of Post-Tensioning Cable Profile JOB NO : 37478
Project : PROJECT TITLE Designed : KKL Date : 16-Jan-2011
Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 16-Jan-2011
Filename : W:\SCB Spreadsheet\Post-Tensioned-Design.xls
(1) CALCULATION OF POST-TENSIONED CABLES PROFILE
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
Height of centre-line of cable Cable angle Total Nos of
Cable from soffit of beam Drape at anghorage Strands
Mark (mm) Ye - Ym per Cable
Ye Ym (mm) (degree) (nos)
Cable A 1875.00 460.00 1415.00 8.134 19
Cable B 1525.00 340.00 1185.00 6.826 19
Cable C 1175.00 220.00 955.00 5.510 19
Cable D 825.00 100.00 725.00 4.188 19
(3) CALCULATION OF CABLE PROFILE
Height of centre-line of cable
Distance from from soffit of beam
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 6.000 590 449 308 167
Section 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
Section 19 1.500 18.000 1629 1319 1009 699
Section 20 0.500 19.000 1763 1431 1099 768
Section 21 -0.300 19.800 1875 1525 1175 825
Section 22 -0.300 19.800 1875 1525 1175 825
SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M)
Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. : 37478
Summary of Computer Analysis Output for Post-tensioned Beam Design
(i) Beam Type = S37T1 (SAG)
(ii) Beam Position = ELE 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
NOMINAL - MOMENT NOMINAL MAXIMUM MOMENT (KNm)
Distance Nominal Moment Due to Nominal Moment Due to NOMINAL LIVE LOADING MOMENT (kNm)
from Dead Load Superimposed Dead Load HA1003 - HAHB4503 -
Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total COMPUTER ANALYSIS OUTPUT
Section Lx (m) Beam Beam & Services Unfactored Unfactored Unfactored Unfactored
Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -393.80 2812.00 1606.80 511.50 0.00 694.60 0.00
1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 433.60 0.00 601.60 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 3170.00 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 4387.00 0.00
Mid Span 19.50 3967.53 1692.11 5659.64 0.00 492.20 283.20 1406.50 2181.90 3050.00 0.00 4885.00 0.00
5/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 2903.00 0.00 4749.00 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 4290.00 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 2204.00 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 -329.50 0.00
(1b) SUMMARY OF THE NOMINAL CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING
NOMINAL - SHEAR NOMINAL CO-EXISITING SHEAR FORCE (kN) FOR MAXIMUM MOMENT
Distance Nominal Shear Force Due to Nominal Shear Force Due to NOMINAL LIVE LOADING SHEAR (kN)
Support 1 0.00 406.93 173.55 580.48 70.00 135.00 62.24 123.65 390.89 -22.75 0.00 -33.26 0.00
1/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 15.81 0.00 165.80 0.00
2/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 149.50 0.00 203.80 0.00
3/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 123.70 0.00 109.20 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 -82.27 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 -102.50 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 -459.90 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 -542.50 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 -468.80 0.00
KKHONG (DEC 1998) Page 3
(2a) SUMMARY OF THE SLS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING
S.L.S - MOMENT SERVICEABILITY LIMIT STATE MOMENT (KNm)
Distance Due to Dead Load Due to Superimposed Dead Load Due to Live Loading
from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 - HAHB4503 -
Support Beam Beam & Services
SLS 1 SLS 1 SLS SLS 1 SLS 1 SLS 1 SLS1 SLS SLS 1 SLS 1 SLS 2 SLS 2
Section Lx (m) 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.20 1.20 1.00 1.00
Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -472.56 2812.00 1528.04 613.80 0.00 694.60 0.00
1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -165.48 2460.62 2019.84 520.32 0.00 601.60 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 3170.00 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 4387.00 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 4885.00 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 4749.00 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 4290.00 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 2204.00 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 -329.50 0.00
(2b) SUMMARY OF THE SLS BOTTOM STRESS FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING
S.L.S - STRESS (fb) SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)
Section Lx (m) 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.200 1.200 1.000 1.000
Support 1 0.00 0.00 0.00 0.00 0.00 -1.51 -0.88 5.24 2.85 1.14 0.00 1.29 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 1.12 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 5.90 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 8.17 0.00
Mid Span 19.50 8.77 3.74 12.50 0.00 0.92 0.63 2.62 4.17 6.82 0.00 9.10 0.00
5/8 24.38 8.22 3.50 11.72 0.00 0.97 0.68 1.97 3.62 6.49 0.00 8.84 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 7.99 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 4.10 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 -0.61 0.00
(2c) SUMMARY OF THE SLS BOTTOM STRESS FOR SUPERIMPOSED DEAD LOAD + LIVE LOADING
S.L.S - fb(SDL+LL) SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)
Distance SDL + Live Loading
Support SDL + HA1003 SDL + - SDL + HAHB4503 SDL + -
Section Lx (m)
Support 1 0.00 3.99 0.00 4.14 0.00
1/8 4.88 4.73 0.00 4.88 0.00
2/8 9.75 7.87 0.00 10.17 0.00
3/8 14.63 9.95 0.00 12.56 0.00
Mid Span 19.50 10.99 0.00 13.27 0.00
5/8 24.38 10.11 0.00 12.46 0.00
6/8 29.25 8.22 0.00 10.73 0.00
7/8 34.13 4.64 0.00 5.61 0.00
Support 2 39.00 -0.53 0.00 -0.72 0.00
KKHONG (DEC 1998) Page 4
(3a) SUMMARY OF THE ULS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING
U.L.S-DESIGN Moment ULTIMATE LIMIT STATE MOMENT (KNm)
Distance Due to Dead Load Due to Superimposed Dead Load ULS LIVE LOADING MOMENT (kNm)
ULS 1 ULS 1 ULS ULS 1 ULS 1 ULS 1 ULS1 ULS ULS 1 ULS 1 ULS 1 ULS 1
Section Lx (m) 1.265 1.265 1.320 1.320 1.925 1.320 1.65 1.65 1.43 1.43
Support 1 0.00 0.00 0.00 0.00 0.00 -1071.05 -758.07 3711.84 1882.73 843.98 0.00 993.28 0.00
1/8 4.88 2195.78 936.48 3132.26 0.00 -363.40 -265.46 3248.02 2619.16 715.44 0.00 860.29 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 4533.10 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 6273.41 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 6985.55 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 6791.07 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 6134.70 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 3151.72 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 -471.19 0.00
(3b) SUMMARY OF THE ULS CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING
U.L.S-DESIGN Shear ULTIMATE LIMIT STATE CO-EXISTING SHEAR FORCE (KN)
Distance Due to Dead Load Due to Superimposed Dead Load ULS LIVE LOADING SHEAR (kN)
Support 1 0.00 514.76 219.54 734.30 92.40 178.20 119.81 163.22 553.63 -37.54 0.00 -47.56 0.00
1/8 4.88 386.07 164.66 550.73 0.00 133.58 95.92 155.46 384.97 26.09 0.00 237.09 0.00
2/8 9.75 257.38 109.77 367.15 0.00 95.32 71.28 147.71 314.31 246.68 0.00 291.43 0.00
3/8 14.63 128.69 54.89 183.58 0.00 62.04 46.05 139.95 248.04 204.11 0.00 156.16 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 -117.65 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 -146.58 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 -657.66 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 -775.78 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 -670.38 0.00
(3c) SUMMARY OF THE ULS TOTAL MOMENT AND TOTAL CO-EXISTING SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING
U.L.S-DESIGN TOTAL MOMENT & SHEAR FOR U.L.S-DESIGN
Distance DL + SDL + LIVE LOAD
HA1003 - HAHB4503 -
Moment 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
KKHONG (DEC 1998) Page 5
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 LOADING
NOMINAL - MOMENT NOMINAL CO-EXISITING MOMENT (kNm)
from Dead Load Superimposed Dead Load - - HAHB4513 HAHB4514
Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix CR,DS,DSETTL Total COMPUTER ANALYSIS OUTPUT
Support 1 0.00 0.00 0.00 0.00 0.00 -811.40 -393.80 2812.00 1606.80 0.00 0.00 -2510.00 654.40
1/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 0.00 0.00 -893.30 508.10
2/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 61.42 2109.25 2276.87 0.00 0.00 1828.00 2076.00
3/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 202.30 1757.87 2316.27 0.00 0.00 1771.00 1658.00
Mid Span 19.50 3967.53 1692.11 5659.64 0.00 492.20 283.20 1406.50 2181.90 0.00 0.00 3481.00 4532.00
5/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 0.00 0.00 1088.00 3706.00
6/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 263.30 703.75 1416.25 0.00 0.00 -515.50 4182.00
7/8 34.13 1735.79 740.30 2476.09 0.00 261.20 163.20 352.37 776.77 0.00 0.00 -185.30 2100.00
Support 2 39.00 0.00 0.00 0.00 0.00 -62.73 5.03 0.00 -57.71 0.00 0.00 -210.90 163.00
(4b) SUMMARY OF THE NOMINAL MAXIMUM SHEAR FORCE FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING
NOMINAL - SHEAR NOMINAL MAXIMUM SHEAR FORCE (kN)
Support 1 0.00 406.93 173.55 580.48 70.00 135.00 62.24 123.65 390.89 0.00 0.00 629.60 -32.06
1/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 0.00 0.00 598.50 -27.81
2/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 0.00 0.00 411.20 -91.74
3/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 0.00 0.00 375.50 -88.68
Mid Span 19.50 0.00 0.00 0.00 0.00 23.70 10.66 -100.15 -65.79 0.00 0.00 162.20 -269.70
5/8 24.38 -101.73 -43.39 -145.12 0.00 0.41 -2.60 -94.28 -96.46 0.00 0.00 125.20 -296.30
6/8 29.25 -203.46 -86.78 -290.24 0.00 -24.79 -15.70 -88.40 -128.89 0.00 0.00 74.09 -492.30
7/8 34.13 -305.19 -130.16 -435.36 0.00 -53.93 -28.49 -82.53 -164.95 0.00 0.00 76.36 -506.40
Support 2 39.00 -406.93 -173.55 -580.48 -70.00 -88.08 -40.86 -76.65 -275.59 0.00 0.00 -506.40 76.36
(4c) ULTIMATE LIMIT STATE FACTORS FOR SHEAR REINFORCEMENT DESIGN
ULS FACTORS DEAD LOAD & SUPERIMPOSED DEAD LOAD ULS FACTORS LIVE LOADING ULS FACTORS
Precast Insitu Slab - Diaphragm Parapet, Kerb Premix CR,DS,DSETTL - - - HAHB4513 HAHB4514
Beam Beam & Services
Load Combinations ULS 1 ULS 1 - ULS 1 ULS 1 ULS 1 ULS1 - - - ULS 1 ULS 1
γf3*γfL 1.265 1.265 - 1.320 1.320 1.925 1.320 - - - 1.43 1.43
(4d) SUMMARY OF THE ULS TOTAL CO-EXSITING MOMENT AND TOTAL MAXIMUM SHEAR FORCE FOR SHEAR DESIGN
SHEAR DESIGN (ULS) TOTAL CO-EXISITING MOMENT & MAXIMUM SHEAR FOR SHEAR DESIGN
- - HAHB4513 HAHB4514
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
KKHONG (DEC 1998) Page 6
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
Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/WChecked
WIDTH : LTC Date : 16-Jan-2011
Design Data : Lbeam
S40T1 BEAM
(1) Spanning Length & Cable Length
(i) Total Beam Length Lbeam = 39.600 m
(ii) Edge of Precast Beam to Centreline of Bearing Pads Leff = Lbeam - 2x x = 0.300 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 γcon = 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 µ = 0.2 /rad
(ii) Wobble Factor K = 0 /m
(iii) Average Anchorage Draw in draw-in = 10 mm
(iv) Strand Diameter φs = 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 Sequence
STAGE 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) Jacking Force Jacking Force , Pj (kN) = n(%of PUTS)
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
KKHONG (OCT 1998) 7 of 21
(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 Soffit 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 εc = 0 per N/mm2
(iii) Shrinkage per Unit Length εs = 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 :
% of Total Final Losses During Stage 1 Stressing
Assumed Losses
During Stage 1 Stressing Occured During Stage 1 but Before Stage 2 Stressing
Friction Losses Draw-In Wegdes Elast. Shrt. - Steel Relaxation Shrinkage Creep
At Stage 1 Transfer
100 100 100 - 0 33 33
% of Total Final Losses During Stage 2 Stressing % of Total Final Losses @ Stage 1 Stressing
During Stage 2 Stressing Remaining from Stage 1
At Stage 2 Transfer 100 100 100 - 100 67 67
At Stage 2 Service 100 100 100 - 100 67 67
Total (%) of Loss From Stage 1 and Stage 2 100 100 100
(11) Post-Tensioning Cable Profile
Height of Centre-Line of Cables From Soffit of Beam
Distance of Section from (m)
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 1317.8
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 θsum = θsupport1 θmidspan+ θsupport2 = 2 * artanh [4(Drape)/Lbeam]
Cable Mark A B C D
Drape = Ye - Ym (mm) 1415.00 1185.00 955.00 725.00
θsum (rad) 0.2839 0.2383 0.1923 0.1462
Sum of Cable Angular Deviations (in radian),
KKHONG (OCT 1998) 8 of 21
Stage 1 Post Tensioning
(1) Immediate Losses
1(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)
(i) Force Gradient
θsum 0.2839 0.2383 0.1923 0.1462
µθsum + KLcable 0.1875 0.1783 0.1691 0.1599
e-(µθ + KLcable) 0.8291 0.8367 0.8444 0.8522
Total Loss of Prestr. Force due to Friction Losses
pfrict.Loss = (1 - e-(µθ+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 15.94
As 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
Distance of the section from A
Cable Mark B C D
Suppport Midpsan -1 *
Incre/decre. 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
KKHONG (OCT 1998) 9 of 21
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
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 From pdraw-inLoss (kN)
Total, Pdraw-inLoss
Suppport Cable Mark
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 Cable Mark 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!
KKHONG (OCT 1998) 10 of 21
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 δεp caused by elastic shortening of the concrete
is equal to the strain in the concrete at the steel level, εcp. The loss of prestress in the steel, δfLoss is therefore :
δfLoss = 0.5(Es/Ec1)*ftendon for post-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/mm2) (mm) (N/mm2)
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 -5.780
29.250 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/mm2) (N/mm2)
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 Stress at Tendon Level (ftendon) Loss of Prestress = 0.5*ftendon(Es/Ec1)
(m) Selfweight Prestress Total (Stage 1)
(N/mm2) (N/mm2) (N/mm2) (N/mm2) (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
KKHONG (OCT 1998) 11 of 21
1(d) Summary of Immediate Losses (Friction Loss, Draw-in Loss And Elastic Shortening Loss)
Lx Immediate Losses % of Immediate Loss from PUTS
(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 Cable Force After Allowable
(m) Pj1 Immediate Loss 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 Concrete Stresses
(m) Immediate Loss Beam Selfweight ft fb ftendon Allowable
(mm) (kN) (kNm) (N/mm2) (N/mm2) (N/mm2) 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!
KKHONG (OCT 1998) 12 of 21
(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
Nos. 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,
Shrinkage per unit length
System Humid exposure Normal exposure
(90% r.h) (70% r.h)
Post-tensioning : transfer at
between 7 days and 14 days εs 70 x 10-6 200 x 10-6
(ii) Shrinkage Strain used in the Design, εs = 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 = εs x Es x (% During Stage 1 Transfer)
(During Stage 1 Transfer) = 200.0E-6 x 195000 x 0.33
= 12.999 N/mm2 per strand
(iv) Shrinkage of Concrete Losses in all Cables (During Stage 1 Transfer), pshrink.Loss
Total Shrinkage Loss in Force pshrink.Loss (kN) 24.7 24.7 24.7 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
KKHONG (OCT 1998) 13 of 21
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 10-5 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 εc = 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 .
Stress in the concrete adjacent to tendons level, ftendon Creep Loss
Lx After After Steel Maximum (During Stage 1 Transfer/ Before Stage 2 Stressing)
(m) Immediate Loss Relaxation Loss Stress
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 1.12
39.000 6.785 6.785 21.167 160.871 2.28 1.14
(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 (εc) * Es * Increased Factor * % occured @ Stage 1 Transfer
KKHONG (OCT 1998) 14 of 21
2(d) Summary of Deferred Losses (Steel Relaxation Loss, Concrete Shrinkage Loss and Creep of Concrete Loss)
Lx Deferred Losses % of Deferred Loss from PUTS
(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 1.82
9.750 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 Cable Force After Allowable
(m) Pj1 Immediate Loss Deferred Loss Losses Immediate Loss Immediate & Deferred Losses (% 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
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/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)
(m) All Loss Beam Selfweight ft fb ftendon Allowable
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!
- END OF STAGE 1 CALCULATIONS -
KKHONG (OCT 1998) 15 of 21
Stage 2 Post Tensioning
(3) Immediate Losses
3(a) Friction Loss (BS 5400 : Part 4 : 1990 : CL. 6.7.3)
pfrict.Loss = (1 - e-(µθ+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 15.94
As a percentage of PUTS % of PUTS 12.5 11.9 11.4 10.8 11.64
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
dp = (pfrict.Loss/Lcable) dp (kN/m) 11.136 10.641 10.138 9.628 41.543
Distance of the Section from Cable MarkA B C D
Lx (m) X0 (m) dp (kN/m) -11.136 10.641 -10.138 9.628
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
Note : * = " -1 " for Dead End of Cable is in the Far End and " 1 " for Dead End of Cable is in the Near End.
KKHONG (OCT 1998) 16 of 21
3(b) Prestressing Force Loss due to Draw-in Wedges (VSL Prestressing System)
w = (draw-in * Es * As * n /dp)1/2 w (m) 18.240 18.660 19.117 19.617 -
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
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
Lx >= w pdraw-inLoss = 0 (Lcable - Lx)>= w, pdraw-inLoss = 0
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 2342.2 9342.80 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!
KKHONG (OCT 1998) 17 of 21
3(c) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2)
δfLoss = 0.5(Es/Ec2)*ftendon for post-tensioned beam (ref. BS 5400:Part 4:Cl. 6.7.2.3)
Ec2 is modulus of elasticity of the precast concrete at Stage 2 Service
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
Lx Stress at Tendon Level (ftendon) Net Stress at tendon Loss of Prestress = 0.5*ftendon(Es/Ec2)
(m) Selfweight Prestress Total (Stage 2) (Stage 2 - Stage 1)
(N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (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 1.28
24.375 -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
KKHONG (OCT 1998) 18 of 21
3(d) Summary of Immediate Losses (Friction Loss, Draw-in Loss And Elastic Shortening Loss)
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
(m) Pj2 Immediate Loss 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!
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)
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!
KKHONG (OCT 1998) 19 of 21
(4) Deferred Losses During Stage 2 Stressing
4(a) Relaxation of Steel (BS 5400 : Part 4 : 1990 : C.L. 6.7.2.2)
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)
(ii) Shrinkage Strain used in the Design, εs = 200.0E-6
(iii) Shrinkage Strain Loss as Stress, fshrink.Loss = εs 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
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
KKHONG (OCT 1998) 20 of 21
4(c) Creep of Concrete Losses (BS 5400:Part 4:1990: Cl. 6.7.2.5)
- Creep Strain εc = 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
From Stage 1 Stressing From Stage 2 Stressing For Creep Loss Calculation
Lx Stress in the concrete adjacent to tendons level, ftendon Stress in the concrete adjacent to tendons level, ftendon During Stage 2
(m) After After Steel Maximum After After Steel Maximum After Steel Relaxation Loss
Immediate Loss Relaxation Loss Stress Immediate Loss Relaxation Loss Stress ftendon(Stage2)-ftendon(Stage1)
(N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2)
0.000 6.798 6.798 10.359 10.100 3.301
4.875 6.701 6.701 10.697 10.430 3.729
9.750 7.676 7.676 13.497 13.159 5.483
14.625 8.830 8.830 16.442 16.031 7.201
19.500 9.305 9.305 9.305 17.844 17.398 17.398 8.093
24.375 8.804 8.804 16.393 15.983 7.180
29.250 7.656 7.656 13.458 13.122 5.466
34.125 6.686 6.686 10.670 10.403 3.717
39.000 6.785 6.785 10.334 10.076 3.291
For Creep Loss Calculation Creep Loss During Stage 2 Remaining
Lx During Stage 2 (Final Loss) Creep Loss
(m) After Steel Relaxation Loss fromStage1
ftendon(Stage2)-ftendon(Stage1)
(N/mm2) (N/mm2) (kN) (% of Pj2) (% of PUTS) (kN)
0.000 3.301 23.683 179.987 1.74 1.27 322.423
4.875 3.729 26.752 203.312 1.97 1.44 317.789
9.750 5.483 39.336 298.955 2.90 2.11 364.056
14.625 7.201 51.662 392.631 3.80 2.78 418.757
19.500 8.093 58.057 441.235 4.28 3.12 441.295
24.375 7.180 51.506 391.442 3.79 2.77 417.518
29.250 5.466 39.215 298.033 2.89 2.11 363.075
34.125 3.717 26.667 202.673 1.96 1.43 317.092
39.000 3.291 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 (εc) * Es * Increased Factor
KKHONG (OCT 1998) 21 of 21
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 Deferred Losses During Stage 2 Transfer % of Deferred Loss from 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 Cable Force After Allowable
(m) Pj2 Immediate Loss Deferred Loss Transfer Losses Immediate Loss Immediate & Deferred Losses (% 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 <70%, OK!
4.875 10319.3 14.20 9.46 23.67 8853.5 7876.8 55.72 <70%, OK!
9.750 10319.3 12.62 10.84 23.46 9017.2 7898.6 55.88 <70%, OK!
14.625 10319.3 11.03 12.28 23.30 9181.6 7914.6 55.99 <70%, OK!
19.500 10319.3 9.73 12.97 22.70 9315.4 7977.3 56.43 <70%, OK!
24.375 10319.3 11.22 12.25 23.48 9161.2 7896.7 55.86 <70%, OK!
29.250 10319.3 12.82 10.82 23.64 8996.7 7880.0 55.74 <70%, OK!
34.125 10319.3 14.40 9.45 23.85 8833.0 7857.6 55.59 <70%, OK!
39.000 10319.3 16.27 9.27 25.55 8640.0 7683.2 54.35 <70%, OK!
NOTE: Maximum Initial Prestressing Force for Post-Tensioning Tendon Immediately after anchoring = 70% of PUTS
4(f) Summary of Concrete Stress After Immediate & Deferred Losses And Allowable Stress Checks in Concrete
During Stage 2 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)
0.000 -155.5 7702.5 0.00 11.051 6.212 9.213 OK!
4.875 298.5 7876.8 1735.79 7.932 10.419 9.408 OK!
9.750 622.8 7898.6 2975.65 5.527 13.379 11.385 OK!
14.625 817.4 7914.6 3719.56 4.070 15.178 13.376 OK!
19.500 882.3 7977.3 3967.53 3.555 15.959 14.325 OK!
24.375 817.4 7896.7 3719.56 4.076 15.126 13.332 OK!
29.250 622.8 7880.0 2975.65 5.527 13.332 11.351 OK!
34.125 298.5 7857.6 1735.79 7.921 10.384 9.383 OK!
39.000 -155.5 7683.2 0.00 11.023 6.196 9.190 OK!
KKHONG (OCT 1998) 22 of 21
4(g) Summary of Deferred Losses During Stage 2 Service
(iii) Creep (S1) = 66.67 % of Stage 1 Creep Loss (Remaining from Stage 1 Stressing)
Lx Deferred Losses During Stage 2 Service % of Deferred Loss from PUTS
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 Immediate & Deferred Losses (% of PUTS)
- END OF STAGE 2 LOSSES CALCULATIONS -
KKHONG (OCT 1998) 23 of 21
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 = Φ2EcIpxx where , Ec = Young's modulus of the precast beam concrete
Ipxx = Second moment of area of the precast beam
Φ2 = 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 its centroid; these forces (F) are of such magnitude that the
elongation of the slabs equals the differential shrinkage, i.e.
F = δEin-situA1 where, δ = 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.
δ = 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
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,
M c' = 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
centroid of flange t F -F
e1 y1 f3
y2 centroid of f2
yt composite sbt
centroid of section Mc' = Fe-Mb
yb y4 Mb
sbb f4
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 beam Ein-situ= Modulus of elasticity of the in-situ concrete
yb = distance from centroid of the precast beam to soffit of precast beam 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
KKHONG (OCT 1998) 24 of 21
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 fibre 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 δ = 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 σt
Lx @ Stage 2 Transfer M (N/mm2)
(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 σb
(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 15.405
34.125 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
KKHONG (OCT 1998) 25 of 21
(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 εc = 1.80E-05 per N/mm2
increased creep factor = 1.022
and F= δEin-situA1 = 9.83E+02 kN
(sbb - sbt) = (creep strain when casting of insitu slab)*(increased creep factor)(sb - st)
Mb = Φ2Eci2Ipxx
Mc = Fe1
Mc' = Mc - Mb
Lx (sbb - sbt) Φ2 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+09
14.625 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
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
KKHONG (OCT 1998) 26 of 21
(iii) Determination of stresses at Top of Precast Beam , f3
Lx F/Ac Mc' y2/Icxx Mb yt/Ipxx (k) f3
0.000 0.848 1.483 -1.499 0.430 -0.358
4.875 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
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 Slab
9.750 0.848 2.108 -0.773 0.430 0.209 f3 = Stresses @ Top of Precast Beam
14.625 0.848 0.179 1.515 0.430 0.364 f4 = Stresses @ Bottom of Precast Beam
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/mm2) (N/mm2) (N/mm2)
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
KKHONG (OCT 1998) 27 of 21
Prestress Checking at Serviceability Limit State For Post-Tensioned Beam Job No. : 37478
Prestress Checking at Deflected Sections At Serviceability Limit State For
Precast Prestressed Post-Tensioned Beam Design
Prestressing System Post-tensioned = Post -Tensioned ; Class 2 member
Tensile stress permitted, but no visible cracking Crack = 0 mm
Precast Beam Section = S40T1 BEAM Precast Beam
(1) SECTION PROPERTIES OF PRECAST BEAM :
TOTAL HEIGHT OF THE PRECAST SECTION
AREA OF PRECAST BEAM
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 39 m Eff. Span
(vi) SELFWEIGHT OF PRECAST BEAM w = 20.868 kN/m
(2) SECTION MODULI OF COMPOSITE SECTION :
Zt,c =
HB45 -SLS2
(i) TOP FIBRE OF COMPOSITE SECTION 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 CLASS 2
(3) DEAD WT OF INSITU CONCRETE winsitu = 8.900 kN/m
(4) CONCRETE STRENGTH: CRACK WIDTH (mm) 0.00
(i) Presstress Concrete : @ TRANSFER fci2 = 50 N/mm2
@ 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
ALLOWABLE CONCRETE STRESSES @ TRANSFER :
MEMBER TENSION COMPRESSION
CLASS 1 -1.000 20.000
CLASS 2 -1.000 20.000
CLASS 3 -1.000 20.000
ALLOWABLE CONCRETE STRESSES @ SERVICE/WORKING:
CLASS 1 0.000 20.000
CLASS 2 -2.546 20.000
CRACK WIDTH fcu = 40 N/mm fcu = >=50 N/mm
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:
(i) TENSILE STRESS (BS5400:P4:1990:CL.7.4.3.3) -3.60 N/mm2
(ii) COMPRESSIVE STRESS (BS5400:P4:1990:CL.7.4.3.2) 15.00 N/mm2
(7) EFFECTIVE SPAN OF PRECAST BEAM Leff = 39.000 m
(8) MODULAR RATIO (Einsitu/Ecu) m = 0.824
KKHONG (NOV 1998) 28
KKHONG (NOV 1998) 29
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
A 19 1832.45 N.B. e = distance between centroid of precast beam
TOTAL : 76.000 1317.82 e = -155.52 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 16.07 %
FINAL TOTAL PRESTRESS LOSSES 25.36 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 113.95 kN
EFFECTIVE FINAL FORCE PER STRAND 101.35 kN
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 -SLS2 2.13 1.70 2.06 -4.140 (SUPPORT 1)
DIFF. SHRINKAGE -0.245 -0.378 0.358 -0.139
TOTAL @ WORKING 0.88 1.32 13.47 2.93
KKHONG (NOV 1998) 30
(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 beam
TOTAL : 76.000 863.77 e = 298.53 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 14.20 %
FINAL TOTAL PRESTRESS LOSSES 23.67 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 116.49 kN
EFFECTIVE FINAL FORCE PER STRAND 103.64 kN
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 -SLS2 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
A 19 803.11 N.B. e = distance between centroid of precast beam
TOTAL : 76.000 539.46 e = 622.84 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 12.62 %
FINAL TOTAL PRESTRESS LOSSES 23.46 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 118.65 kN
EFFECTIVE FINAL FORCE PER STRAND 103.93 kN
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 -SLS2 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
KKHONG (NOV 1998) 31
(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 beam
TOTAL : 76.000 344.86 e = 817.44 mm
INITIAL PRESTRESS LOSSES @ TRANSFER 11.03 %
FINAL TOTAL PRESTRESS LOSSES 23.30 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 120.81 kN
EFFECTIVE FINAL FORCE PER STRAND 104.14 kN
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 -SLS2 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
KKHONG (NOV 1998) 32
(6) 6th SECTION, DISTANCE FROM SUPPORT 1 24.38 m
INITIAL PRESTRESS LOSSES @ TRANSFER 11.22 %
FINAL TOTAL PRESTRESS LOSSES 23.48 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 120.54 kN
EFFECTIVE FINAL FORCE PER STRAND 103.90 kN
TRANSFER PRESTRESS - - -3.17 27.08
TOTAL @ TRANSFER - - 3.64 18.86
FINAL PRESTRESS - - -2.73 23.34
SUPER. DEAD + LIVE HB45 -SLS2 6.40 5.10 6.20 -12.460 (SECTION 5)
DIFF. SHRINKAGE -1.339 -1.251 1.391 -0.536
TOTAL @ WORKING 5.06 3.85 14.57 -1.38
(7) 7th SECTION, DISTANCE FROM SUPPORT 1 29.25 m
INITIAL PRESTRESS LOSSES @ TRANSFER 12.82 %
FINAL TOTAL PRESTRESS LOSSES 23.64 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 118.38 kN
EFFECTIVE FINAL FORCE PER STRAND 103.68 kN
TRANSFER PRESTRESS - - 0.09 22.73
TOTAL @ TRANSFER - - 5.54 16.15
FINAL PRESTRESS - - 0.08 19.91
SELF WT + DEAD INSITU - - 7.77 -9.38
SUPER. DEAD + LIVE HB45 -SLS2 5.51 4.39 5.34 -10.730 (SECTION 6)
DIFF. SHRINKAGE -1.390 -1.291 1.440 -0.554
TOTAL @ WORKING 4.12 3.10 14.62 -0.76
KKHONG (NOV 1998) 33
(8) 8th SECTION, DISTANCE FROM SUPPORT 1 34.13 m
INITIAL PRESTRESS LOSSES @ TRANSFER 14.40 %
FINAL TOTAL PRESTRESS LOSSES 23.85 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 116.22 kN
EFFECTIVE FINAL FORCE PER STRAND 103.39 kN
TRANSFER PRESTRESS - - 5.33 15.98
TOTAL @ TRANSFER - - 8.51 12.15
FINAL PRESTRESS 4.74 14.22
SELF WT + DEAD INSITU 4.53 -5.47
SUPER. DEAD + LIVE HB45 -SLS2 2.88 2.30 2.79 -5.610 (SECTION 7)
DIFF. SHRINKAGE -1.318 -1.234 1.372 -0.529
TOTAL @ WORKING 1.56 1.06 13.44 2.61
(9) At SUPPORT 2 SECTION, DISTANCE FROM SUPPORT 1 39.00 m
INITIAL PRESTRESS LOSSES @ TRANSFER 16.27 %
FINAL TOTAL PRESTRESS LOSSES 25.55 %
EFFECTIVE FORCE @ TRANSFER PER STRAND 113.68 kN
EFFECTIVE FINAL FORCE PER STRAND 101.09 kN
TRANSFER PRESTRESS - - 12.40 6.97
TOTAL @ TRANSFER - - 12.40 6.97
FINAL PRESTRESS - - 11.02 6.20
SUPER. DEAD + LIVE HB45 -SLS2 -0.37 -0.29 -0.36 0.720 (SUPPORT 2)
DIFF. SHRINKAGE -1.117 -1.073 1.181 -0.455
TOTAL @ WORKING -2.49 -1.37 11.85 7.46
KKHONG (NOV 1998) 34
Ultimate Moment Capacity Checks for Post-Tensioned Beam Job No. : 37478
ULTIMATE MOMENT CAPACITY CHECKS AT MIDSPAN & OTHER SECTIONS
FOR PRECAST POST-TENSIONED BEAM USING STRAIN COMPATIBILITY METHOD
(BS5400:PART4:1990:CL.6.3.3.1)
Project : PROJECT TITLE Designed: KKL Date : 16-Jan-2011
Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked: LTC Date : 16-Jan-2011
(A) Checking Section : 4"/8 SPAN (19.500 M FROM SUPP.) ; S40T1 BEAM ; 39.00 m Effective Span
(B) Design Ultimate Moment : = 16307.98 kNm
(C) Require Ultimate Moment Capacity At Mid Span = 18754.18 kNm
(D) Depth of Neutral Axis from Top Fibre (N.A) = 490.53 mm
(E) Calculation of Ultimate Moment Capacity
39.00 m Eff. Span
(1) Concrete Section
(i) Characteristic Strength of Precast Concrete at Service fcu = 50.00 N/mm2
(ii) Characteristic Strength of In-situ Concrete at Service fcu = 30.00 N/mm2
4/8 SPAN
(iii) Material Safety Factor for Concrete γm= 1.50
(iv) Assumed Concrete Maximum Compressive Strain εu= 0.0035
Table 1 : Ultimate Moment Capacity From Concrete Section
Concrete Section Dimension Measure Depth To Section Section Centroid Centroid Concrete Compressive Moment
Section Width Height Top Fibre Bot. Fibre Area fcu Sect. fr. Top Sect. to N.A Strain Force about N.A
(mm) (mm) (mm) (mm) (mm ) 2
(N/mm ) 2
(mm) (mm) ε (kN) (kNm)
1 In-situ slab 0 0.00 0 0 0 30 0 490.5 0.00350 0.00 0.0
2 In-situ slab 1950 180.00 0 180 351000 30 90 400.5 0.00286 4703.40 1883.9
3 Top Flange 1920 120.00 180 300 230400 50 240 250.5 0.00179 5145.60 1289.1
4 Top Flange 660 70.00 300 370 46200 50 335 155.5 0.00111 985.32 153.2
5 Top Flange 220 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.0
6 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.0
7 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.0
8 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.0
9 Top Flange 220 120.53 370 491 26517 50 415 75.3 0.00054 365.70 27.5
10 Web 0 0.00 491 491 0 50 491 0.0 0.00000 0.00 0.0
490.53 O.K! 654117 11200 3354
Note : (I) Parabolic centroid = 3/8 w from start of parabolic curve, where w = depth of parabolic curve on the Stress the diagram
(II) Total depth of the section in parabolic curve (mm) = 197.44 for fcu = 50.0 N/mm2
(measure from Neutral Axis) (mm) = 152.93 for fcu = 30.0 N/mm2
(2) Prestressing Tendons
(i) Tendon Diameter φ = 12.9 mm (v) Material Safety Factor for Concrete γm = 1.15
(ii) Nominal Cross Section Area of Tendon As = 100.0 mm2 (vi) Percentage of Jacking Force % = 75 %
(ii) Ultimate Characteristic Strength (UTS) PUTS = 186 kN (vii) Final Prestress Losses Lossfinal = 25 %
(iii) Modulus of Elasticity of Tendon Es = 195000 N/mm 2
(viii) Total Effective Jacking Force per Strand Peff = 139.5 kN
(iv) Characteristic Strength of Tendon fpu = 1860 N/mm 2
(ix) Total Final Prestress Force per Strand after all losses Pfinal = 104.63 kN
Table 2 : Ultimate Moment Capacity From Prestressing Tendons
Prestress Number Total Cross Depth from Prestressing Tendon Strain, ε Tension Tension Moment About
Tendon Layer of Tendon Section Area Tob Fiber Strain Prestrain Total Strain Stress Force N.A Axis
From Bot. Fibre (nos) (mm2) (mm) (N/mm2) (kN) (kNm)
1 Layer 1 18 1800 2205 0.01223 0.00537 0.01760 1617.39 2911.30 4991.34
2 Layer 2 18 1800 2085 0.01138 0.00537 0.01674 1617.39 2911.30 4641.99
3 Layer 3 17 1700 1965 0.01052 0.00537 0.01589 1617.39 2749.57 4054.15
4 Layer 4 17 1700 1845 0.00966 0.00537 0.01503 1617.39 2749.57 3724.20
5 Layer 5 0 0 0 0.00000 0.00000 0.00000 0.00 0.00 0.00
70 7000 11321.74 17411.69
(i) Strain = εu/x*(Depth of Tendon from Top Fibre - N.A Depth from Top Fibre ) (ii) Prestrain = Pfinal /As/Es
(iii) Moment of Tendon Above the N.A shall be negative and Below the N.A shall be positive.
(3) Reinforcement Bars
(i) Characteristic Strength of Steel Reinforcement fy = 460 N/mm2 (iii) Material Safety Factor for Steel Reinforcement γm = 1.15
(ii) Modulus of Elasticity of Steel Reinforcement Es = 200000 N/mm2 (iv) Maximum Compressive Strain = 0
Table 2 : Ultimate Moment Capacity From Steel Reinforcement
Steel Steel Depth from Strain Stress Force Moment About
Reinforcement Reinfor. Top Fibre ε Compressive Tension Compressive Tension N.A. Axis
from. Top (mm2) (mm) (N/mm2) (N/mm2) (kN) (kN) (kNm)
1 Layer 1 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
2 Layer 2 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
3 Layer 3 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
4 Layer 4 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
5 Layer 5 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
6 Layer 6 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
7 Layer 7 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
8 Layer 8 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
9 Layer 9 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
10 Layer 10 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.00
Note : (i) Force in the steel Reinforcement Above N.A shall be Compressive Force and Below N.A shall be Tension Force.
(F) Summary of Forces and Stresses
Force Moment Abt.
Compressive Tension N.A. Axis
(kN) (kN) (kNm)
Concrete Section 11200 - 3354
Prestressing Tendon - 11322 17412
Reinforcement 0 0 0
Total 11200 11322 20765
Difference -121.7
(I) PERMISSIBLE TOLERANCE FOR FORCES EQUIVALENT = 10 kN
(II) PLEASE INCREACE NEUTRAL AXIS DEPTH.........
(III) DESIGN ULTIMATE MOMENT = 16307.98 kNm
(IV) ULTIMATE MOMENT CAPACITY/DESIGN ULTIMATE MOMENT =
HENCE, CHANGE NEUTRAL AXIS PLEASE.......AND TRY AGAIN.....!!!
KKHONG (DEC 1998) Page 35
Shear Design for Post-Tensioned Beam JOB NO. : 37478
DETAILS : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 16-Jan-2011
Design Of Precast Post-Tensioned Beam At Ultimate Limit State - Shear Reinforcement Design
(BS 5400 : PART 4 : 1990 ; CL. 5.3.3 , CL. 6.3.4 & CL. 7.4.2.3)
(1) Precast Beam Section Properties 39 m Effective Span
(i) Total Height of Precast Section H = 2125 mm
(ii) Cross Section Area of Precast Section Ap = 0.869500 m2
(iii) Precast Section Centroid above Bottom Fibre yb = 1162.30 mm
Definations, Symbols and Notes
(iv) Second Moment Of Area of Precast Section Ipre = 5.2608E-01 m4 fpt = Stress due to prestress only at tensile fibre (bottom fibre)
(v) Section Modulus of Precast Section : @ Top Fibre Zt = 5.4646E-01 m3 γfL = 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3)
(vi) @ Bottom Fibre Zb = 4.5262E-01 m3 e = Eccentricity from centroid of tendon to centroid of precast beam
(vii) @ Composite Beam Centroid Zcentroid = 2.0472E+00 m3 Mcr = Cracking Moment at Section considered
(viii) Rib/Web Breadth of Precast Section @ Beam Ends (Supports) bend = 660 mm Vcr-i = Ultimate Cracking Shear Capacity (Equation 29 BS5400)
(ix) @ Middle of Beams bmiddle = 220 mm 0.037bdt(fcu)1/2+ (Mcr/M)(V) but not less than 0.1bd(fcu)1/2
(x) Concrete Strength @ 28 days of Precast Section fcu2 = 50 N/mm2 b = Breadth of member/breadth of rib/web,bw
dt = Eff. depth of Centroid of tendons to Extreme Compression Fibre
(2) Composite Section Properties V & M = The shear force and bending moment (both taken as +ve) at section
(i) Total Height of Composite Section Hc = 2305 mm considered due to ultimate load
(ii) Cross Section Area of Composite Section Ac = 1.15 m2 yb,c = Distance of tensile fibre to centroid composite beam
(iii) Composite Section Centroid above Bottom Fibre yb,c = 1419.28 mm
(iv) Second moment of area of the transformed Composite Section Icomposite = 7.6205E-01 m4
(v) Modular Ratio m = 0.824 fcp = Comp. stress due to prestress at the composite centroid axis (+ve)
(3) Prestress Strand Properties γfL = 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3)
(i) Strand Description : Ipre = = 0.52608 m4
(ii) Nominal Cross Section Area per Strand, As = 100.00 mm2 Y = yb,c - yb = 0.26 m
(iii) Ultimate Tensile Strength per Strand PUTS = 186.00 kN Zcentroid = Ipre /Y = 2.0472 m3
(iv) 70 % of U.T.S. per Strand Peff = 130.20 kN Vco = Ultimate shear resistance of a section uncracked in flexure
(v) Cable Length/Beam Length Lcable/beam = 39.60 m = 0.67bHc(ft2+fcpft)1/2 (Equation 28 BS5400:PART4:1990)
(4) Link Rebars Properties = Hc-(yb-e)
(i) Characteristic Strength of Links Rebars fyv = 460 N/mm2
(ii) Shear Reinforcement diameter provided φv = 12 mm V1 = Horizontal Interface Shear Force
(iii) Total Leg x-Section Area per Links Asv = 226 mm2 Sc = First moment of area, about the neutral axis of the transformed
(iv) Characteristic Strength of Strands (max 460) fstrand = 460 N/mm2 composite section, of the insitu concrete to one side of the interface
(v) Characteristic Strength of Longitudinal Steel Reinforcement provided fyL = 460 N/mm2 Ae = area of fully anchoraged reinforcement per unit length crossing the
(vi) Longitudinal Steel Reinforcement diameter provided (max 12 mm) φL = 12 mm shear plane under consideration
(vii) @ Support : R.C. Shear Resistance vc = (0.27/γm)*(100As(pre)/benddt)1/3*(fcu)1/3 vc = 0.7776 N/mm2
(viii) Depth Factor §s = greater of (500/dt)1/4 or 0.7 §s = 0.8436
(5) Data To Calculate Longitudinal Shear Note :
(i) First moment of area, about the neutral axis of the transformed (1) Max. Spacing of the links : Spacing of the links along the beam should not exceeded
Composite sect., of the concrete to one side of the interface Sc = 0.23001 m3 0.75dt, nor four times the web thickness for flanged beams. When V' exceeds 1.8 Vc,
(ii) Ult. long. stress in the sect. for shear plane under considered (Table 31:BS 5400:P4) v1 = 0.45 N/mm2 the max. spacing should be reduced to 0.5 dt. The lateral spacing of the individual
(iii) Constant depending on the conc. bonding across the shear plane (Table 31:BS 5400:P4) k1 = 0.09 (Surface Type 2) legs of the links provided at a cross section should not exceed 0.75dt.(V'=V-Vprtestress)
(iv) Length of Shear plane under consideration Ls = 660 mm (2) For longitudinal shear reinforcements : a minimum area of fully anchored reinf. of
(v) Embedment of The Insitu Slab = 0 mm 0.15% of the area of the contact should cross this surface; the spacing of this reinf.
(vi) Minimum thickness of the insitu top slab tslab = 180 mm should not exceed the lesser of ;
(vii) Insitu slab Width lf = 1950 mm (i) 4 times of minimum thickness of the in situ concrete flange ;
Concrete strength of insitu top slab @ 28 days fc = 30 N/mm2 (ii) 600 mm.
KKHONG (DEC 1998) Page 36
CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR
Section Support 1 Section 1 Section 2 Section 3 Mid Span Section 5 Section 6 Section 7 Support 2
Distance From Support Lx (m) 0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000
Distance From MidSpan Xo (m) 19.500 14.625 9.750 4.875 0.000 4.875 9.750 14.625 19.500
(1) Summary Of The Max V : VV
max (From Grillage Analysis) (kN) 2141.19 1756.25 1245.94 956.81 466.06 724.42 1227.24 1474.54 1799.88
Ultimate Design M (From Grillage Analysis) (kNm) -1706.57 4085.30 10359.91 11591.45 15803.19 13846.44 12712.25 6870.63 374.72
Shear Forces and Max M : V (From Grillage Analysis) (kN) 1894.07 1137.49 949.36 623.95 198.04 462.88 1180.91 1526.16 1746.11
Moment Bending MMmax
max (From Grillage Analysis) (kNm) 8143.62 6223.01 12278.97 13160.82 16307.98 13336.81 12866.69 7019.35 544.32
(2) Prestressing Strands n = Effective No. of Strands (Nos) 76 76 76 76 76 76 76 76 76
Information e = Eccentricity @ Centroid of Precast Beam = yb-e' (mm) -155.52 298.53 622.84 817.44 882.30 817.44 622.84 298.53 -155.52
Loss = Total % of Prestress Losses at Service (%) 25.36 23.67 23.46 23.30 22.70 23.48 23.64 23.85 25.55
Pfinal = Effective prestress Force = (n*Peff(1-%Loss)) (kN) 7385.994 7553.120 7573.954 7589.322 7649.451 7572.172 7556.196 7534.710 7367.441
(3) Vertical Component Shear e' = Combined Cables Centroid from Botttom Fibre of Beam (mm) 1317.82 863.77 539.46 344.86 280.00 344.86 539.46 863.77 1317.82
Force From Deflected Ye - Ym ==Drape = (1350 - 280) = 1070 mm (mm) 1070 1070 1070 1070 1070 1070 1070 1070 1070
Tendons, Vprestress θο = Combined Deflection Angle = Atan((Ye - Ym)*(2X0/(Lbeam/2)2)) (o) 6.0759 4.5644 3.0465 1.5243 0.0000 1.5243 3.0465 4.5644 6.0759
Vprestress = γm * Pfinal * Sin(θo), where γm = 0.8 (L.A. Clark) (kN) 625.418 480.857 322.023 161.509 0.000 161.144 321.268 479.685 623.847
(4) Allowable Maximum dt = Effective depth of Tendons = Hc-(yb-e) (mm) 987.18 1441.23 1765.54 1960.14 2025.00 1960.14 1765.54 1441.23 987.18
Ultimate Applied v = Max Applied Ult.Shear Stress = [Vmaxor V-Vprestress]/bdt (N/mm2) 2.33 4.02 2.38 1.84 1.05 1.31 2.33 3.30 1.81
Shear Stress Checks Checks = Allowable Shear Stress = 0.75fcu1/2 or 5.8 N/mm2 (N/mm2) 5.30 5.30 5.30 5.30 5.30 5.30 5.30 5.30 5.30
(BS 5400:Part 4:1990:CL.5.3.3.1) Checks = Applied Ultimate Shear Stress Check : Compliance within allowable within allowable within allowable within allowable within allowable within allowable within allowable within allowable within allowable
(5) Design Of Flexure Shears :
(5a) Assume Sections fpt = γfL*(Pfinal/Ap + Pfinal*e/Zb), where γfL = 0.87 (N/mm ) 2
- 11.89 16.65 19.52 20.63 19.47 16.61 11.86 -
Cracked in Flexure Mcr = [0.37(fcu)1/2 + fpt] * Icomposite/yb,c (kNm) - 7789.63 10342.35 11884.64 12479.74 11860.96 10321.40 7774.07 -
- For Class 1 and Class 2 member d = (H-yb+e) (mm) - 1261 1586 1780 1845 1780 1586 1261 -
(BS 5400:Part 4:1990:CL 6..3.4.3) Vcr(min) = min. required by code 0.1bdt(fcu) 1/2
(kN) - 224 275 305 315 305 275 224 -
Vcr1 = 0.037bdt(fcu)1/2+ (Mcr/M)(Vmax) (kN) - 3432 1345 1094 485 733 1098 1751 -
Vcr2 = 0.037bdt(fcu)1/2+ (Mcr/Mmax)(V) (kN) - 1507 901 676 268 524 1049 1773 -
(5b) Assume Sections fcp = γfL*(Pfinal/Ap - Pfinal*e/Zcentroid) taken as positive (N/mm2) 7.878 6.599 5.574 4.957 4.786 4.946 5.560 6.583 7.859
UnCracked in Flexure ft = 0.24(fcu)1/2 taken as positive (N/mm2) 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70 1.70
(BS 5400 : Part 4:1990 : CL 6.3.4.2) Vco = 0.67bHc(ft2+fcpft)1/2 (kN) 4109 1275 1193 1142 1127 1141 1192 1274 4105
(5c) Calculations of (V - Vc) (Vmax - Max(Vcr1,Vcr(min)) - Vprestress) (kN) - -2156 -422 -299 -19 -170 -192 -757 -
and determination of (V - Max(Vcr2,Vcr(min) - Vprestress) (kN) - -850 -274 -214 -117 -223 -189 -727 -
(V - Vc) Max (Vmax - Vco -Vprestress) (kN) -2593 1 -270 -346 -661 -578 -286 -279 -2929
(V - Vco -Vprestress) (kN) -2840 -618 -566 -679 -929 -839 -333 -227 -2982
(V - Vc - Vprestress) Max (kN) -2593 1 -270 -214 -19 -170 -189 -227 -2929
(V - Vc - Vprestress) Max (Double Check) (kN) -2593 1 -270 -214 -19 -170 -189 -227 -2929
(5d) Flexure Shear Asv/Sv(Min) = V+0.4bdt-(Vc+Vprestress)/(0.87fyvdt) or 0.4b/(0.87fyv) (mm) 3.4145 0.2208 0.2199 0.2199 0.2199 0.2199 0.2199 0.2199 2.5546
Reinforcement Design Sv(min) Calculated (mm) 66 1024 1029 1029 1029 1029 1029 1029 89
(BS 5400:Part 4:1990:CL 6.3.4.4)
(5e) Minimum Area of EXCESS AsLong(pre) : (i) Bonded Prestressing Strands EXCESS in resist bending nos 0 0 0 0 0 0 0 0 0
Long. Bars/Strand Checks Total Effective area of the above Prestressing Tendons (mm2) 0 0 0 0 0 0 0 0 0
( Note : The AsLong shall be the area AsLong(Bar): (ii) No. of Longitudinal reinforcement EXCESS in resist bending nos 17 15 11 9 6 7 11 12 14
of strands/rebars which are NOT Total Effective area of the above Longitudinal Bars (mm2) 1923 1696 1244 1018 679 792 1244 1357 1583
Used in the bending/ others designs.)AsLongTotal = AsLong(pre) + AsLong(Bar) (mm2) 1923 1696 1244 1018 679 792 1244 1357 1583
(In Tension Zone Only) AsLong(Min) = V /(2*0.87*fyL) (mm2) 1894 1593 1154 994 582 704 1132 1307 1469
(BS 5400:Part 4:1990:CL 6..3.4.4) Checks = Minimum AsLong Checks Compliance 'As' is Complied 'As' is Complied 'As' is Complied 'As' is Complied'As' is Complied'As' is Complied 'As' is Complied 'As' is Complied 'As' is Complied
KKHONG (DEC 1998) Page 37
CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR (Continue)
(6) Design Of Longitudinal Shears :
(6a) Longditudinal Shear V1 = Max(V,Vmax)*Sc/Icomposite (kN/m) 646 530 376 289 141 219 370 461 543
Reinforcement Design k1*fc*Ls (kN/m) 1782 1782 1782 1782 1782 1782 1782 1782 1782
Checks = Checking of allowable V1 Compliance O.K. O.K. O.K. O.K. O.K. O.K. O.K. O.K. O.K.
Checks The Longitudinal Shear force (V1) are not exceeded the allowable value specified in Code (BS 5400:Part 4:1990:C.L. 7.4.2.3).
(BS 5400 : Part 4:1990 : CL 7.4.2.3) Ae = the larger of (V1 - v1Ls)/(0.7fyv) and (0.15/100)*(Ls*1000) (mm2/m) 1085 990 990 990 990 990 990 990 990
Sv Calculated = Asv*1000/Ae (mm) 209 228 228 228 228 228 228 228 228
(7) Shear Reinforcement
Design Minimum of Sv Calculated (From Item (5d) & (6a)) & (mm) 66 228 228 228 228 228 228 228 89
(BS 5400:Part 4:1990:CL 6..3.4.4) Required by The Code.
No of Links required per m length = (1000/Sv) + 1 (nos) 16.1 5.4 5.4 5.4 5.4 5.4 5.4 5.4 12.3
Average No. of Links provided per m (nos) 17 6 6 6 6 6 6 6 13
-------- END OF SHEAR DESIGN ---------
KKHONG (DEC 1998) Page 38
Post-Tensioning Losses :
(a) Friction Loss Along Prestressing Tendon
(b) Friction Loss In The Anchorage
(c) Losses Due to Wedges Draw-in
(d) Elastic Shortening of Concrete
(2) Deferred Losses
(a) Relaxation Loss of Prestressing Tendon
(b) Shrinkage Loss of Concrete
(c) Creep Loss in Concrete
(1)(a) Friction Loss Along Prestressing Tendon
Losses due to frinction in a cable can be calculated to a relatively high degree of accuracy
by Coulomb's formula:
P(x) = Pj * e-(µθ + Kx)
P(x) = Post-tensioning force at a distance x from the stressing anchorage (Live end)
Pj = Post-tensioning force at the stressing anchorage
e = Base of Napierian logarithms
θ = Sum of angular deviations (in radian) of tendon in all planes over the distance x
K = Wobble factor (inaccuracies in placing per unit length
(1)(b) Friction Loss In The Anchorage
Not Consider in the design
(1)(c) Losses Due to Wedges Draw-in
By assuming a linear loss of prestressing force due to frincion, loss of prestressing force of
tendon per meter length/ Force Gradient,
δp = (1 - e-(µθ + Kx) )Pj /Lcable
δp = Loss of prestressing force in tendon per meter length/ Force Gradient
(1 - e-(µθ + Kx) )Pj = Loss
of prestressing force in tendon
Lcable = Total Cable length
and the diatance affected by the draw-in of wedges,
w = (Draw-in * Es * As * n)1/2
Draw-in = Draw-in of Wedges in mm
Es = Modulus of Elasticity og post-tensioning cable in kN/m2
As = Cable cross Section Area in mm2
n = Total number of prestressing cables
w = Distance affected by the draw-in of wedges (< Lcable)
Forces Along Prestressing Cable After Friction and Wedges Draw-in Losses
(i) For w < Lcable /2
Loss of force due to draw-in of wedges
Pj-Dp PL
Length of Tendon Lcable
(ii) For w >= Lcable /2
Pj-Dp
(1)(d) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2)
Immediately after transfer, the change in strain in the prestressing steel δεp caused by elastic shortening
of the concrete is equal to the strain in the concrete at the steel level, εcp. The loss of prestress in the steel,
δfLoss is therefore :
δfLoss = 0.5(Es/Ec)*ftendon for post-tensioned beam
(ref. BS5400:Part4:Cl. 6.7.2.3)
ftendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons.
Ec is modulus of elasticity of the precast concrete at transfer
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.
Relaxation Loss as Stress,
Steel Jacking Force per strand
frelax.Loss = Relaxation (%) x Strand Cross Section Area x Assumed % Occured
At 1000h
- Shrinkage Strain used in the Design, εs = per unit length
- Shrinkage Strain Loss as Stress,
fshrink.Loss = εs x Es x Assumed % Occured
- 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.
- Creep Strain εc = per N/mm2
- Modulus of Elasticity of Strand Es = kN/mm2
(I) Total Creep Loss At Stage 1
= (Stress at tendon level during Stage 1) * Creep Strain (εc) * Es * Increased Factor * Assumed % Occured
= (σStage1) * εc * Es * Increased Factor * Assumed % occured
= (σStage2 - σStage1) * εc * Es * Increased Factor * Assumed % occured
Stress in the concrete adjacent to tendons at transfer after Steel Relaxation Loss
Documents Similar To Post Tensioned Design1
Mark Christopher Del Rosario
46947288 Post Tensioned Design1
Convergence Confinement Method
construction sequence.xlsx
ULS Design of Tunnel Segment