Post Tensioned Design1

SEPAKAT SETIA PERUNDING SDN BHD (14142-M)CONSULTING ENGINNERS

PROJECT : PROJECT TITLEDETAIL : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTHJOB NUMBER : 37478

Designed : KKL Date : 8-Apr-2023Checked : LTC Date : 8-Apr-2023

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

S37T1 - EDGE BEAM (T1)

DESIGN DATA :

(I) Number Of Stage For Stressing = 2 Stages

(II) Concrete Properties for Precast Beam:

(a) 1st Stage : (i) Concrete Cube Strength 30

(ii) Modulus of Elasticity 28

(b) 2nd Stage : (i) Concrete Cube Strength 50


(c) 28 days (i) Concrete Cube Strength 50


(III) Prestressing Strands Properties :

(a) Strand Diameter 12.9 mm

(b) Cross Section Area 100

(c) Mudulus of Elasticity 195

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

(e) Co-efficient of Friction 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 0.000036

(c) Shrinkage per unit Length 0.0002

(d) Creep reduction Coefficient k = 0.43

fci1 = N/mm2

Ec1 = kN/mm2

fci2 = N/mm2

Ec2 = kN/mm2

fcu = N/mm2

Ecu = kN/mm2

fs =

As = mm2

Es = kN/mm2

PUTS =

m =

ec = per N/mm2

es =

SEPAKAT SETIA PERUNDING (14142-M)

POST-TENSIONED BEAM DESIGN - Calculation of Post-Tensioning Cable Profile JOB NO : 37478

Project : PROJECT TITLE Designed : KKL Date : 8-Apr-2023Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 8-Apr-2023Filename : W:\SCB Spreadsheet\Post-Tensioned-Design.xls

(1) CALCULATION OF POST-TENSIONED CABLES PROFILE

(a) Input Data

Effective Span 39.00 m

Beam Length 39.60 m

Cable Length 39.60 m

Nos. of Cables = 4 nos

(b) Cable Profile Formula

(i) Formulae used for computing cable profile :

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

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

Drape =

where,

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

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) per Cable

(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

76

(3) CALCULATION OF CABLE PROFILE

Height of centre-line of cable

Distance from from soffit of beam

(mm)

Cable angle 8.134 6.826 5.510 4.188 Support Midspan at anchorage

Cable Mark A B C DNos. 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

Leff =

Lbeam =

Lcable =

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

Ye - Ym

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

Ye =

Ym =

Ye - Ym

Ye Ym

X (m) X0 (m)

KKHONG (DEC 1998) Page 3

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

Consulting Engineers

Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. : 37478

Summary of Computer Analysis Output for Post-tensioned Beam Design

Project : PROJECT TITLE Designed : KKL Date : 8-Apr-2023

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 8-Apr-2023

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

(i) Beam Type = S37T1 (SAG)(ii) Beam Position = ELE 89 TO 96

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

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

(v) Section Modulus : @ Bottom Fibre of Composite Beam 5.369E+08

(vi) Precast Beam Selfweight 20.868 kN/m

(vii) Deck Slab Selfweight 8.900 kN/m

NOTE : UDLMoment =UDL Shear

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

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 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 0.001/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 433.60 0.00 601.60 0.002/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 61.42 2109.25 2276.87 1614.00 0.00 3170.00 0.003/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 202.30 1757.87 2316.27 2486.00 0.00 4387.00 0.00Mid 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 0.005/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 2903.00 0.00 4749.00 0.006/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 263.30 703.75 1416.25 2456.00 0.00 4290.00 0.007/8 34.13 1735.79 740.30 2476.09 0.00 261.20 163.20 352.37 776.77 1403.00 0.00 2204.00 0.00Support 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)

from Dead Load Superimposed Dead Load HA1003 - HAHB4503 -Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total COMPUTER ANALYSIS OUTPUT


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 0.001/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 15.81 0.00 165.80 0.002/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 149.50 0.00 203.80 0.003/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 123.70 0.00 109.20 0.00Mid 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 0.005/8 24.38 -101.73 -43.39 -145.12 0.00 0.41 -2.60 -94.28 -96.46 -98.29 0.00 -102.50 0.006/8 29.25 -203.46 -86.78 -290.24 0.00 -24.79 -15.70 -88.40 -128.89 -231.30 0.00 -459.90 0.007/8 34.13 -305.19 -130.16 -435.36 0.00 -53.93 -28.49 -82.53 -164.95 -319.40 0.00 -542.50 0.00Support 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

Leff =

Zb = mm3

Zb,p = mm3

wpre =

wslab =

w/2(Lx) (Leff-Lx)

w (Leff/2-Lx)

NOMINAL MAXIMUM MOMENT (KNm)

Lx (m)

Lx (m)




Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. : 37478(2a) SUMMARY OF THE SLS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

S.L.S - MOMENT

Distance Due to Dead Load Due to Superimposed Dead Load Due to Live Loadingfrom 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 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.20 1.20 1.00 1.00


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

Distance Due to Dead Load Due to Superimposed Dead Load Due to Live Loadingfrom 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 1.000 1.000 - 1.000 1.000 1.200 1.000 - 1.200 1.200 1.000 1.000


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

Distance SDL + Live Loadingfrom

SDL + HA1003 SDL + - SDL + HAHB4503 SDL + -Support

Section

Support 1 0.00 3.99 0.00 4.14 0.001/8 4.88 4.73 0.00 4.88 0.002/8 9.75 7.87 0.00 10.17 0.003/8 14.63 9.95 0.00 12.56 0.00Mid Span 19.50 10.99 0.00 13.27 0.005/8 24.38 10.11 0.00 12.46 0.006/8 29.25 8.22 0.00 10.73 0.007/8 34.13 4.64 0.00 5.61 0.00Support 2 39.00 -0.53 0.00 -0.72 0.00

SERVICEABILITY LIMIT STATE MOMENT (KNm)

Lx (m)

S.L.S - STRESS (fb) SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)

Lx (m)

S.L.S - fb(SDL+LL) SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2)

Lx (m)




Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. : 37478(3a) SUMMARY OF THE ULS MOMENT FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD + LIVE LOADING

U.L.S-DESIGN Moment

Distance Due to Dead Load Due to Superimposed Dead Load ULS LIVE LOADING MOMENT (kNm)

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 - HAHB4503 -Support Beam Beam & Services

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

Section 1.265 1.265 1.320 1.320 1.925 1.320 1.65 1.65 1.43 1.43


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

U.L.S-DESIGN Shear

Distance Due to Dead Load Due to Superimposed Dead Load ULS LIVE LOADING SHEAR (kN)

from Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix DS.CR,DSETT Total HA1003 - HAHB4503 -Support Beam Beam & Services

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

Section 1.265 1.265 1.320 1.320 1.925 1.320 1.65 1.65 1.43 1.43

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 0.001/8 4.88 386.07 164.66 550.73 0.00 133.58 95.92 155.46 384.97 26.09 0.00 237.09 0.002/8 9.75 257.38 109.77 367.15 0.00 95.32 71.28 147.71 314.31 246.67 0.00 291.43 0.003/8 14.63 128.69 54.89 183.58 0.00 62.04 46.05 139.95 248.04 204.11 0.00 156.16 0.00Mid 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 0.005/8 24.38 -128.69 -54.89 -183.58 0.00 0.55 -5.00 -124.44 -128.90 -162.18 0.00 -146.58 0.006/8 29.25 -257.38 -109.77 -367.15 0.00 -32.72 -30.22 -116.69 -179.63 -381.65 0.00 -657.66 0.007/8 34.13 -386.07 -164.66 -550.73 0.00 -71.19 -54.84 -108.93 -234.96 -527.01 0.00 -775.78 0.00Support 2 39.00 -514.76 -219.54 -734.30 -92.40 -116.27 -78.66 -101.18 -388.50 -395.17 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 LOADfrom

HA1003 - HAHB4503 -Support

Moment Shear Moment Shear Moment Shear Moment Shear

Section (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 0.001/8 4.88 6466.86 961.78 0.00 0.00 6611.71 1172.79 0.00 0.002/8 9.75 11075.31 928.13 0.00 0.00 12945.31 972.89 0.00 0.003/8 14.63 13993.75 635.72 0.00 0.00 16165.26 587.77 0.00 0.00Mid Span 19.50 15243.39 -140.21 0.00 0.00 17196.44 -198.04 0.00 0.005/8 24.38 14169.74 -474.65 0.00 0.00 16170.86 -459.05 0.00 0.006/8 29.25 11450.73 -928.43 0.00 0.00 13533.03 -1204.44 0.00 0.007/8 34.13 6571.28 -1312.70 0.00 0.00 7408.05 -1561.47 0.00 0.00Support 2 39.00 -383.83 -1517.98 0.00 0.00 -544.32 -1793.19 0.00 0.00

ULTIMATE LIMIT STATE MOMENT (KNm)

Lx (m)

ULTIMATE LIMIT STATE CO-EXISTING SHEAR FORCE (KN)

Lx (m)

Lx (m)




Summary of Computer Analysis Output for Post-tensioned Beam Design Job No. : 37478

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

Distance Nominal Moment Due to Nominal Moment Due to NOMINAL LIVE LOADING MOMENT (kNm)

from Dead Load Superimposed Dead Load - - HAHB4513 HAHB4514Support 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 -2510.00 654.401/8 4.88 1735.79 740.30 2476.09 0.00 -275.30 -137.90 2460.62 2047.42 0.00 0.00 -893.30 508.102/8 9.75 2975.65 1269.08 4244.73 0.00 106.20 61.42 2109.25 2276.87 0.00 0.00 1828.00 2076.003/8 14.63 3719.56 1586.36 5305.91 0.00 356.10 202.30 1757.87 2316.27 0.00 0.00 1771.00 1658.00Mid 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 4532.005/8 24.38 3719.56 1586.36 5305.91 0.00 523.20 303.60 1055.12 1881.92 0.00 0.00 1088.00 3706.006/8 29.25 2975.65 1269.08 4244.73 0.00 449.20 263.30 703.75 1416.25 0.00 0.00 -515.50 4182.007/8 34.13 1735.79 740.30 2476.09 0.00 261.20 163.20 352.37 776.77 0.00 0.00 -185.30 2100.00Support 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)

Distance Nominal Shear Force Due to Nominal Shear Force Due to NOMINAL LIVE LOADING SHEAR (kN)

from Dead Load Superimposed Dead Load - - HAHB4513 HAHB4514Support Precast Insitu Slab Total Diaphragm Parapet, Kerb Premix CR,DS,DSETTL Total COMPUTER ANALYSIS OUTPUT


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 -32.061/8 4.88 305.19 130.16 435.36 0.00 101.20 49.83 117.78 268.81 0.00 0.00 598.50 -27.812/8 9.75 203.46 86.78 290.24 0.00 72.21 37.03 111.90 221.14 0.00 0.00 411.20 -91.743/8 14.63 101.73 43.39 145.12 0.00 47.00 23.92 106.03 176.95 0.00 0.00 375.50 -88.68Mid 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 -269.705/8 24.38 -101.73 -43.39 -145.12 0.00 0.41 -2.60 -94.28 -96.46 0.00 0.00 125.20 -296.306/8 29.25 -203.46 -86.78 -290.24 0.00 -24.79 -15.70 -88.40 -128.89 0.00 0.00 74.09 -492.307/8 34.13 -305.19 -130.16 -435.36 0.00 -53.93 -28.49 -82.53 -164.95 0.00 0.00 76.36 -506.40Support 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

ElementsPrecast Insitu Slab - Diaphragm Parapet, Kerb Premix CR,DS,DSETTL - - - HAHB4513 HAHB4514Beam Beam & Services

Load Combinations ULS 1 ULS 1 - ULS 1 ULS 1 ULS 1 ULS1 - - - ULS 1 ULS 1

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

Distance DL + SDL + LIVE LOADfrom

- - HAHB4513 HAHB4514Support

Moment Shear Moment Shear Moment Shear Moment Shear

Section (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 1242.091/8 4.88 0.00 0.00 0.00 0.00 4474.00 1791.55 6478.01 895.932/8 9.75 0.00 0.00 0.00 0.00 11026.25 1269.48 11380.89 550.273/8 14.63 0.00 0.00 0.00 0.00 12424.38 968.58 12262.79 304.80Mid Span 19.50 0.00 0.00 0.00 0.00 15188.72 151.55 16691.65 -466.065/8 24.38 0.00 0.00 0.00 0.00 10935.63 -133.44 14679.37 -736.186/8 29.25 0.00 0.00 0.00 0.00 6661.17 -440.84 13378.59 -1250.777/8 34.13 0.00 0.00 0.00 0.00 3991.35 -676.50 7259.33 -1509.84Support 2 39.00 0.00 0.00 0.00 0.00 -374.72 -1846.95 159.96 -1013.61

NOMINAL CO-EXISITING MOMENT (kNm)

Lx (m)

Lx (m)

gf3*gfL

Lx (m)

KKHONG (OCT 1998) 7 of 21



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

Calculation of Prestress Losses & Differential Shrinkage At SLSFor PRECAST POST-TENSIONED PRESTRESSED BEAM Design


Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/ Checked : LTC Date : 8-Apr-2023

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

Design Data :S40T1 BEAM

x

(1) Spanning Length & Cable Length

(i) Total Beam Length 39.600 m

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

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

(iv) Total Cable Length/Beam Length 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 50@ Stage 1 Stressing 30 O.K.!

@ Stage 2 Stressing 50(iii) Modulus Of Elasticity of Concrete : @ 28 Days 34.0

@ Stage 1 Stressing 28.0 O.K.!

@ Stage 2 Stressing 34.0 O.K.!

(iv) Concrete Density 24.0

(3) Section Properties Of Precast Beam

(i) Cross Sectional Area 869500(ii) Total Height H = 2125 mm

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

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

(v) Moment of Inertia 5.26080E+11

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

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

(viii) Selfweight of Precast Beam 20.868 kN/m

(4) Stressing Cable Properties

(i) Coefficient of Friction 0.2 /rad

(ii) Wobble Factor K = 0.0033 /m

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

(iv) Strand Diameter 12.9 mm

(v) Ultimate Tensile Strength per Strand 186.0 kN

(vi) Cross Sectional Area per Strand 100(vii) Modulus of Elasticity of Strand 195.0

(5) Proposed Stressing Sequence

STAGE 1 : Stress Cable "A" to = 50 O.K.!

Stress Cable "B" to = 50 O.K.!

Stress Cable "C" to = 50 O.K.!

Stress Cable "D" to = 50 O.K.!

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

Stress Cable "B" to = 73 O.K.!

Stress Cable "C" to = 73 O.K.!

Stress Cable "D" to = 73 O.K.!

(6) Jacking Force

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

Stage 1 1767.0 1767.0 1767.0 1767.0 7068.0

Stage 2 2579.8 2579.8 2579.8 2579.8 10319.3

Lbeam

Lbeam =

Leff = Lbeam - 2x

Leff =

Lcable =

fcu = N/mm2

fci1 = N/mm2

fci2 = N/mm2

Ecu = kN/mm2

Ec1 = kN/mm2

Ec2 = kN/mm2

gcon = kN/mm3

Ap = mm2

yb =

yt =

Ipxx = mm4

Zt = mm3

Zb = mm3

wpre =

m =

fs =

PUTS =

As = mm2

Es = kN/mm2

% of PUTS

% of PUTS

% of PUTS

% of PUTS

% of PUTS

% of PUTS

% of PUTS

% of PUTS

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

pj1

pj2





(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 1950 mm

(iv) Area of in-situ flange/slab 351000(v) Concrete Grade 30(vi) Modulus Elasticity of In-situ 28.0(vii) SelfWeight Of In-Situ Slab 8.900 kN/m

(8) Composite Beam Section Properties

(a) Total Height of The Composite 2305 mm

(b) Cross Section Area 1150300(c) Centroid from Soffit 1419.28 mm

(d) Second Moment of Area 7.6205E+11

(e) Section Moduli : @ Top of Composite section 8.6037E+08

(f) Section Moduli : @ Top of Precast Beam 1.0798E+09

(g) Section Moduli : @ Bottom of Top In-situ Slab 1.0798E+09

(h) Section Moduli : @ Bottom of Precast Beam 5.3693E+08

(9) Modular Ratio 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 0.000036

(iii) Shrinkage per Unit Length 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 :

Assumed Losses% of Total Final Losses During Stage 1 Stressing

During Stage 1 Stressing Occured During Stage 1 but Before Stage 2 Stressing

At Stage 1 Transfer Friction Losses Draw-In Wegdes Elast. Shrt. - Steel Relaxation Shrinkage Creep

100 100 100 - 0 33 33

Assumed Losses% of Total Final Losses During Stage 2 Stressing % of Total Final Losses @ Stage 1 Stressing

During Stage 2 Stressing Remaining from Stage 1

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

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

Nos. Of Strands 19 19 19 19 76Near End Live End Dead End Live End Dead End e'

Beam Ends 19.800 1875.0 1525.0 1175.0 825.0 1350.0

0.000 19.500 1832.4 1489.4 1146.3 803.2 1317.84.875 14.625 1232.0 986.5 741.0 495.5 863.89.750 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 0.000 460.0 340.0 220.0 100.0 280.0

24.375 4.875 545.8 411.8 277.9 143.9 344.929.250 9.750 803.1 627.3 451.6 275.8 539.534.125 14.625 1232.0 986.5 741.0 495.5 863.839.000 19.500 1832.4 1489.4 1146.3 803.2 1317.8

Beam Ends 19.800 1875.0 1525.0 1175.0 825.0 1350.0

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.

(12) Sum Of Cable Deviation Angle

Cable Mark A B C DNos. Of Strands 19 19 19 19 76

(mm) 1415.00 1185.00 955.00 725.00

(rad) 0.2839 0.2383 0.1923 0.1462

Sum of Cable Angular Deviations (in radian),

lf =

Af = mm2

fc = N/mm2

Ein-situ = kN/mm2

wslab =

Hc =

Ac = mm2

yb,c =

Icxx = mm4

Zt,c = mm3

Zt,p = mm3

Zb,s = mm3

Zb,p = mm3

(Einsitu/Ecu2)

ec = per N/mm2

es =

Lx (m) X0 (m)

Ye

Ym

Ye

qsum = qsupport1 qmidspan+ qsupport2 = 2 * artanh [4(Drape)/Lbeam]

Drape = Ye - Ym

qsum





Stage 1 Post Tensioning

Prestress Losses

(1) Immediate Losses

1(a)

(i) Force Gradient

Cable Mark A B C D Total

0.2839 0.2383 0.1923 0.1462

0.1875 0.1783 0.1691 0.1599

0.8291 0.8367 0.8444 0.8522

Total Loss of Prestr. Force due to Friction Losses

302.1 288.6 275.0 261.1 1126.79

17.1 16.3 15.6 14.8 15.94

8.5 8.2 7.8 7.4 7.97

Cable Force @ Dead End after Frict. Losses

1464.9 1478.4 1492.0 1505.9 5941.21

41.5 41.8 42.2 42.6 42.03

Loss of Pres. Force per unit length/Force Gradient

7.628 7.288 6.944 6.595 28.454

(ii) Cable Force Along Beam Length After Friction Losses

Distance of the section from Cable Mark A B C DSuppport Midpsan Incre/decre. -1 * 1 * -1 * 1 * Total

-7.628 7.288 -6.944 6.595Near End Live End Dead End Live End Dead End

Beam Ends 19.800 1767.0 1478.4 1767.0 1505.9 6518.20.000 19.500 SUPPORT 1 1764.7 1480.6 1764.9 1507.8 6518.04.875 14.625 1727.5 1516.1 1731.1 1540.0 6514.79.750 9.750 1690.3 1551.6 1697.2 1572.1 6511.3

14.625 4.875 1653.2 1587.2 1663.4 1604.3 6508.019.500 0.000 MIDSPAN 1616.0 1622.7 1629.5 1636.4 6504.624.375 4.875 1578.8 1658.2 1595.7 1668.6 6501.229.250 9.750 1541.6 1693.8 1561.8 1700.7 6497.934.125 14.625 1504.4 1729.3 1528.0 1732.9 6494.539.000 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 6491.0Far 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.

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

qsum

mqsum + KLcable

e-(mq + KLcable)

pfrict.Loss = (1 - e-(mq+KLcable))*pj1 pfrict.Loss (kN)

As a percentage of pj1 % of pj1

As a percentage of PUTS % of PUTS

pd = pj1 - pfrict.Loss pd (kN)


dp = (pfrict.Loss/Lcable) dp (kN/m)

Lx (m) X0 (m) dp (kN/m)





1(b)

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


Distance affected by Draw-in Wedges from Live End,

w (m) 22.039 22.547 23.099 23.703 -

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

336.22 328.65 320.79 312.62 1298.28

19.0 18.6 18.2 17.7 18.37

9.5 9.3 9.1 8.8 9.18

(ii) Draw-in Wedges Losses Along Beam Length

Distance From

Suppport Cable Mark

A B C D (kN)

0.000 331.64 0.00 316.62 0.00 648.27 9.17 4.594.875 257.27 0.00 248.92 0.00 506.19 7.16 3.589.750 182.90 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 1.5719.500 34.16 40.04 45.82 51.48 171.49 2.43 1.2124.375 0.00 111.10 0.00 115.77 226.87 3.21 1.6029.250 0.00 182.16 0.00 180.07 362.23 5.12 2.5634.125 0.00 253.22 0.00 244.37 497.58 7.04 3.5239.000 0.00 324.28 0.00 308.66 632.94 8.96 4.48

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

0 0

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

Distance From Cable MarkTotal

Allowable

Suppport A B C D

(kN) 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!

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

w = (draw-in * Es * As * n /dp)1/2

w < Lcable

pdraw-inLoss = 2 * w * dp pdraw-inLoss (kN)



pdraw-inLoss (kN)Total, Pdraw-inLoss

Lx (m) (% of Pj1) (% of PUTS)

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

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

(% of PUTS)

Lx (m) (% of PUTS)





1(c)

= (ref. BS5400:Part4:Cl. 6.7.2.3)

N.B.

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

M e'

(m) (kNm) (mm)

0.000 0.00 0.000 0.000 1317.8 0.0004.875 1735.79 3.176 -3.835 863.8 -0.9859.750 2975.65 5.445 -6.574 539.5 -3.523

14.625 3719.56 6.807 -8.218 344.9 -5.78019.500 3967.53 7.260 -8.766 280.0 -6.65424.375 3719.56 6.807 -8.218 344.9 -5.78029.250 2975.65 5.445 -6.574 539.5 -3.52334.125 1735.79 3.176 -3.835 863.8 -0.98539.000 0.00 0.000 0.000 1317.8 0.000

Moment, M = H = Total Height of Precast Beam.

e' = Distance from centroid of tendon to soffit.

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

(m) (mm) (kN)

0.000 -155.5 5869.77 8.421 4.734 7.0214.875 298.5 6008.49 3.628 10.873 7.9289.750 622.8 6147.20 0.063 15.529 11.603

14.625 817.4 6285.91 -2.174 18.582 15.21319.500 882.3 6333.11 -2.942 19.629 16.65524.375 817.4 6274.38 -2.170 18.548 15.18529.250 622.8 6135.67 0.063 15.500 11.58134.125 298.5 5996.95 3.621 10.852 7.91339.000 -155.5 5858.24 8.405 4.725 7.007

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

Cross Section Area of Precast Beam

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

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

(m) Selfweight Prestress Total (Stage 1)

(kN)

0.000 0.000 7.021 7.021 24.447 185.795 2.629 1.314.875 -0.985 7.928 6.943 24.177 183.745 2.600 1.309.750 -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 1.7719.500 -6.654 16.655 10.001 34.824 264.666 3.745 1.8724.375 -5.780 15.185 9.406 32.753 248.922 3.522 1.7629.250 -3.523 11.581 8.058 28.059 213.251 3.017 1.5134.125 -0.985 7.913 6.928 24.124 183.342 2.594 1.3039.000 0.000 7.007 7.007 24.399 185.430 2.624 1.31

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 for post-tensioned beam

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

Lx ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)

w(Lx/2)(Leff -L x)

ft = M/Zt

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

Lx e = yb - e' Pi ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)

Ap =

Pi =

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

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

(N/mm2) (N/mm2) (N/mm2) (N/mm2) (% of Pj1) (% of PUTS)





1(d)

Immediate Losses

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

0.000 550.0 648.27 185.795 1384.0 3.89 4.59 1.31 9.794.875 553.3 506.19 183.745 1243.3 3.91 3.58 1.30 8.799.750 556.7 364.12 213.827 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 7.3019.500 563.4 171.49 264.666 999.6 3.99 1.21 1.87 7.0724.375 566.8 226.87 248.922 1042.5 4.01 1.60 1.76 7.3829.250 570.1 362.23 213.251 1145.6 4.03 2.56 1.51 8.1034.125 573.5 497.58 183.342 1254.4 4.06 3.52 1.30 8.8739.000 576.8 632.94 185.430 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

Jacking Force Total Cable Force After Allowable

(m) Immediate Loss Immediate Loss

(kN) (kN) 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!

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

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

e Cable Force After Moment Due to Concrete Stresses

(m) Immediate Loss Beam Selfweight Allowable

(mm) (kN) (kNm) 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!

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

Lx % of Immediate Loss from PUTS

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

Lx

Pj1 (% of PUTS)

(% of Pj1) (% of PUTS)

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

(N/mm2)

(N/mm2)

Lx

ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)





(2) Deferred Losses Before Stage 2 Stressing

2(a)

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 forcehas 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 1767.0 1767.0 1767.0 1767.0 7068

Total Relaxation Loss in Force 0.00 0.00 0.00 0.00 0.00

Relaxation Loss as percentage of pj1 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00

2(b)

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

Shrinkage per unit lengthSystem Humid exposure Normal exposure

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

between 7 days and 14 days

after concreting

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

(iii) Assumed Percentage Occurred,during Stage 1 Transfer. % = 33 % of final

(iii) Shrinkage Strain Loss as Stress, x x (% During Stage 1 Transfer)

(During Stage 1 Transfer) = 200.0E-6 x 195000 x 0.3333= 12.999

(iv)

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

Total Shrinkage Loss in Force 24.69753 24.69753 24.69753 24.698 98.790

1.40 1.40 1.40 1.40 1.40

0.70 0.70 0.70 0.70 0.70

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

pj1 (kN)

prelaxLoss (kN)

% of pj1

Relaxation Loss as percentage of PUTS % of PUTS

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

Post-tensioning : transfer at

es 70 x 10-6 200 x 10-6

es =

fshrink.Loss = es Es

N/mm2 per strand

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

pshrink.Loss (kN)

As Loss in percentage of pi1 % of pj1

As Loss in percentage of PUTS % of PUTS





2(c)

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

- For Post-tensioning System :

(i)

(ii)

(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 +

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

- Creep Strain 4.80E-05

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

- Modulus of Elasticity of Strand 195.0

- Increased factor = 1.000

- 10.00

Creep Loss

After After Steel Maximum (During Stage 1 Transfer/ Before Stage 2 Stressing)

(m) Immediate Loss Relaxation Loss Stress

(kN)

0.000 6.798 6.798 21.209 161.187 2.28 1.144.875 6.701 6.701 20.904 158.871 2.25 1.129.750 7.676 7.676 23.947 182.001 2.57 1.29

14.625 8.830 8.830 27.546 209.347 2.96 1.4819.500 9.305 9.305 9.305 29.028 220.614 3.12 1.5624.375 8.804 8.804 27.464 208.728 2.95 1.4829.250 7.656 7.656 23.883 181.510 2.57 1.2834.125 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 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

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/mm 2.

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/f ci) per N/mm 2.

(Max stress @ Transfer - f ci/3)*0.25

(fci/2- fci/3)

ec = per N/mm2

Es = kN/mm2

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

Stress in the concrete adjacent to tendons level, f tendon

Lx

(N/mm2) (N/mm2) (N/mm2) (N/mm2) (% of Pj1) (% of PUTS)

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





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

Deferred Losses

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

0.000 0.0 98.79 161.187 260.0 0.00 0.70 1.14 1.844.875 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 2.1819.500 0.0 98.79 220.614 319.4 0.00 0.70 1.56 2.2624.375 0.0 98.79 208.728 307.5 0.00 0.70 1.48 2.1829.250 0.0 98.79 181.510 280.3 0.00 0.70 1.28 1.9834.125 0.0 98.79 158.522 257.3 0.00 0.70 1.12 1.8239.000 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

Jacking Force Total Total Total Stage 1 Cable Force After Allowable

(m) Immediate Loss Deferred Loss Losses Immediate Loss Immediate & Deferred Losses

(kN) (kN) (kN) 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!

(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




(m) All Loss Beam Selfweight 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 -

Lx % of Deferred Loss from PUTS


Lx

Pj1 (% of PUTS)

(% of Pj1) (% of Pj1) (% of Pj1) (% of PUTS)

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

at Transfer (Not Required to Check - Can Be Ommited)

N/mm2

N/mm2

Lx

ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)





Stage 2 Post Tensioning

Prestress Losses


3(a)

(i) Force Gradient


0.2839 0.2383 0.1923 0.1462

0.1875 0.1783 0.1691 0.1599

0.8291 0.8367 0.8444 0.8522

Total Loss of Prestr. Force due to Friction Losses

441.0 421.4 401.5 381.3 1645.11

17.1 16.3 15.6 14.8 15.94

12.5 11.9 11.4 10.8 11.64

Cable Force @ Dead End after Frict. Losses

2138.8 2158.4 2178.4 2198.6 8674.17

60.5 61.1 61.6 62.2 61.36

Loss of Pres. Force per unit length/Force Gradient

11.136 10.641 10.138 9.628 41.543

(ii) Cable Force Along Beam Length After Friction Losses

Distance of the Section from Cable Mark A B C DSuppport Midpsan Incre/decre. -1 * 1 * -1 * 1 * Total

-11.136 10.641 -10.138 9.628Near End Live End Dead End Live End Dead End

Beam Ends 19.800 2579.8 2158.4 2579.8 2198.6 9516.60.000 19.500 SUPPORT 1 2576.5 2161.6 2576.8 2201.4 9516.34.875 14.625 2522.2 2213.5 2527.4 2248.4 9511.49.750 9.750 2467.9 2265.4 2477.9 2295.3 9506.5

14.625 4.875 2413.6 2317.3 2428.5 2342.2 9501.619.500 0.000 MIDSPAN 2359.3 2369.1 2379.1 2389.2 9496.724.375 4.875 2305.0 2421.0 2329.7 2436.1 9491.829.250 9.750 2250.7 2472.9 2280.2 2483.1 9486.934.125 14.625 2196.4 2524.8 2230.8 2530.0 9482.039.000 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 9476.8Far End Dead End Live End Dead End Live End

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

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

qsum

mqsum + KLcable

e-(mq + KLcable)

pfrict.Loss = (1 - e-(mq+KLcable))*pj2 pfrict.Loss (kN)



pd = pj2 - pfrict.Loss pd (kN)


dp = (pfrict.Loss/Lcable) dp (kN/m)

Lx (m) X0 (m) dp (kN/m)





3(b)

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


Distance affected by Draw-in Wedges from Live End,

w (m) 18.240 18.660 19.117 19.617 -

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

406.25 397.11 387.61 377.74 1568.72

15.7 15.4 15.0 14.6 15.20

11.5 11.2 11.0 10.7 11.10

(ii) Draw-in Wedges Losses Along Beam Length

Distance From

Suppport Cable Mark

A B C D (kN)

0.000 399.57 0.00 381.53 0.00 781.10 7.57 5.534.875 290.99 0.00 282.69 0.00 573.68 5.56 4.069.750 182.41 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 1.1219.500 0.00 0.00 0.00 0.00 0.00 0.00 0.0024.375 0.00 79.48 0.00 90.34 169.83 1.65 1.2029.250 0.00 183.23 0.00 184.22 367.45 3.56 2.6034.125 0.00 286.98 0.00 278.09 565.07 5.48 4.0039.000 0.00 390.73 0.00 371.96 762.69 7.39 5.40

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

0 0

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

Distance From Cable MarkTotal

Allowable

Suppport A B C D

(kN) 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 2342.2 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!

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

w = (draw-in * Es * As * n /dp)1/2

w < Lcable

pdraw-inLoss = 2 * w * dp pdraw-inLoss (kN)



pdraw-inLoss (kN)Total, Pdraw-inLoss

Lx (m) (% of Pj2) (% of PUTS)

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

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

(% of PUTS)

Lx (m) (% of PUTS)





3(c)

= (ref. BS 5400:Part 4:Cl. 6.7.2.3)

N.B.

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

M e'

(m) (kNm) (mm)

0.000 0.00 0.000 0.000 1317.8 0.0004.875 1735.79 3.176 -3.835 863.8 -0.9859.750 2975.65 5.445 -6.574 539.5 -3.523

14.625 3719.56 6.807 -8.218 344.9 -5.78019.500 3967.53 7.260 -8.766 280.0 -6.65424.375 3719.56 6.807 -8.218 344.9 -5.78029.250 2975.65 5.445 -6.574 539.5 -3.52334.125 1735.79 3.176 -3.835 863.8 -0.98539.000 0.00 0.000 0.000 1317.8 0.000

Moment, M = H = Total Height of Precast Beam.

e' = Distance from centroid of tendon to soffit.

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

(m) (mm) (kN)

0.000 -155.5 8735.23 12.532 7.045 10.4484.875 298.5 8937.76 5.397 16.174 11.7939.750 622.8 9140.28 0.094 23.090 17.252

14.625 817.4 9342.80 -3.231 27.618 22.61219.500 882.3 9496.73 -4.411 29.434 24.97524.375 817.4 9322.00 -3.223 27.557 22.56129.250 622.8 9119.48 0.094 23.037 17.21334.125 298.5 8916.95 5.384 16.136 11.76639.000 -155.5 8714.43 12.502 7.028 10.423

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

Cross Section Area of Precast Beam

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

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

Net Stress at tendon

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

(kN)

0.000 0.000 10.448 10.448 3.427 9.828 74.694 0.724 0.534.875 -0.985 11.793 10.808 3.865 11.084 84.237 0.816 0.609.750 -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 1.1419.500 -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 1.1429.250 -3.523 17.213 13.690 5.632 16.150 122.743 1.189 0.8734.125 -0.985 11.766 10.781 3.853 11.049 83.971 0.814 0.5939.000 0.000 10.423 10.423 3.416 9.796 74.453 0.721 0.53


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 for post-tensioned beam



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

Lx ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)

w(Lx/2)(Leff -L x)

ft = M/Zt

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

Lx e = yb - e' Pi ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)

Ap =

Pi =

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

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

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





3(d)

Immediate Losses

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

0.000 802.9 781.10 74.694 1658.7 5.68 5.53 0.53 11.734.875 807.8 573.68 84.237 1465.8 5.71 4.06 0.60 10.379.750 812.7 366.25 123.124 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 8.0519.500 822.6 0.00 181.321 1003.9 5.82 0.00 1.28 7.1024.375 827.5 169.83 160.753 1158.0 5.85 1.20 1.14 8.1929.250 832.4 367.45 122.743 1322.5 5.89 2.60 0.87 9.3634.125 837.3 565.07 83.971 1486.3 5.92 4.00 0.59 10.5139.000 842.2 762.69 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

Jacking Force Total Cable Force After Allowable

(m) Immediate Loss Immediate Loss

(kN) (kN) 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!

(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




(m) Immediate Loss Beam Selfweight Allowable


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!

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

Lx % of Immediate Loss from PUTS


Lx

Pj2 (% of PUTS)

(% of Pj2) (% of PUTS)


(N/mm2)

(N/mm2)

Lx

ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)





(4) Deferred Losses During Stage 2 Stressing

4(a)


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 forcehas 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 2579.8 2579.8 2579.8 2579.8 10319.28

Total Final Relaxation Loss in Force 64.50 64.50 64.50 64.50 257.98

Relaxation Loss as percentage of pj2 2.50 2.50 2.50 2.50 2.50

1.83 1.83 1.83 1.83 1.83

4(b)

(i) From BS 5400:Part 4:1990:Table 29, Shrinkage per unit lengthSystem Humid exposure Normal exposure

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


after concreting

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

(iii) Shrinkage Strain Loss as Stress, x

(Final Loss) = 200.0E-6 x 195000= 39.000

(iv)

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

Total Shrinkage Loss in Force 74.1 74.1 74.1 74.100 296.400

2.87 2.87 2.87 2.87 2.87

2.10 2.10 2.10 2.10 2.10


pj2 (kN)

prelaxLoss (kN)

% of pj2

Relaxation Loss as percentage of PUTS % of PUTS



es 70 x 10-6 200 x 10-6

es =


N/mm2 per strand

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

pshrink.Loss (kN)

As Loss in percentage of pi2 % of pj2

As Loss in percentage of PUTS % of PUTS





4(c)

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


(i)

(ii)

(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:



- Creep Strain 3.60E-05

- Modulus of Elasticity of Strand 195

- Increased factor = 1.022

- One -third (1/3) of Concrete cube Strength at Stage 2 16.67

- Assumed Steel Relaxation Loss During Stage 2 Transfer % = 100.00 % of final

From Stage 1 Stressing From Stage 2 Stressing For Creep Loss Calculation

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)

0.000 6.798 6.798 10.359 10.100 3.3014.875 6.701 6.701 10.697 10.430 3.7299.750 7.676 7.676 13.497 13.159 5.483

14.625 8.830 8.830 16.442 16.031 7.20119.500 9.305 9.305 9.305 17.844 17.398 17.398 8.09324.375 8.804 8.804 16.393 15.983 7.18029.250 7.656 7.656 13.458 13.122 5.46634.125 6.686 6.686 10.670 10.403 3.71739.000 6.785 6.785 10.334 10.076 3.291

For Creep Loss Calculation Creep Loss During Stage 2 Remaining

During Stage 2 (Final Loss) Creep Loss

(m) After Steel Relaxation Loss fromStage1

ftendon(Stage2)-ftendon(Stage1)

(kN) (kN)

0.000 3.301 23.683 179.987 1.74 1.27 322.4234.875 3.729 26.752 203.312 1.97 1.44 317.7899.750 5.483 39.336 298.955 2.90 2.11 364.056

14.625 7.201 51.662 392.631 3.80 2.78 418.75719.500 8.093 58.057 441.235 4.28 3.12 441.29524.375 7.180 51.506 391.442 3.79 2.77 417.51829.250 5.466 39.215 298.033 2.89 2.11 363.07534.125 3.717 26.667 202.673 1.96 1.43 317.09239.000 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)


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




(fci/2- fci/3)

ec = per N/mm2

Es = kN/mm2

fci2/3 = N/mm2 .

Lx Stress in the concrete adjacent to tendons level, f tendon Stress in the concrete adjacent to tendons level, f tendon

(N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2) (N/mm2)

Lx

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

= (Stress at tendon level during Stage 2 - Stress at tendon level During Stage 1) * Creep Strain (ec) * Es * Increased Factor





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

Deferred Losses During Stage 2 Transfer


0.000 258.0 197.61 502.410 958.0 1.83 1.40 3.55 6.784.875 258.0 197.61 521.101 976.7 1.83 1.40 3.69 6.919.750 258.0 197.61 663.010 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 8.9619.500 258.0 197.61 882.530 1338.1 1.83 1.40 6.24 9.4724.375 258.0 197.61 808.961 1264.6 1.83 1.40 5.72 8.9529.250 258.0 197.61 661.108 1116.7 1.83 1.40 4.68 7.9034.125 258.0 197.61 519.765 975.4 1.83 1.40 3.68 6.9039.000 258.0 197.61 501.198 956.8 1.83 1.40 3.55 6.77

4(e) Summary of Cable Force After Immediate & Deferred Losses and Allowable Prestressing Force Checks InCables During Stage 2 Transfer


(m) Immediate Loss Deferred Loss Transfer Losses Immediate Loss Immediate & Deferred Losses


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!

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

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




(m) All Loss Beam Selfweight Allowable


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!



Lx

Pj2 (% of PUTS)


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

N/mm2

N/mm2

Lx

ft fb ftendon

(N/mm2) (N/mm2) (N/mm2)





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

Deferred Losses During Stage 2 Service


0.000 258.0 197.61 502.410 958.0 1.83 1.40 3.55 6.784.875 258.0 197.61 521.101 976.7 1.83 1.40 3.69 6.919.750 258.0 197.61 663.010 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 8.9619.500 258.0 197.61 882.530 1338.1 1.83 1.40 6.24 9.4724.375 258.0 197.61 808.961 1264.6 1.83 1.40 5.72 8.9529.250 258.0 197.61 661.108 1116.7 1.83 1.40 4.68 7.9034.125 258.0 197.61 519.765 975.4 1.83 1.40 3.68 6.9039.000 258.0 197.61 501.198 956.8 1.83 1.40 3.55 6.77

4(h) Summary of Cable Force After Immediate & Deferred Losses and Allowable Prestressing Force Checks InCables During Stage 2 Service


(m) Immediate Loss Deferred Loss Service Losses Immediate Loss Immediate & Deferred Losses


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!

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

- END OF STAGE 2 LOSSES CALCULATIONS -



Lx

Pj2 (% of PUTS)







DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM AND IN-SITU SLAB

(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 tostraighten it. Firstly the moment is to be applied:

where , Young's modulus of the precast beam concrete

Second moment of area of the precast beam

free total strain movement of the bottom fibres

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

F = where, Differential shrinkage coefficient

Modulus of elasticity of the in-situ concrete

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,

0.5 * Differential shrinkage coefficient

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

a moment,

where, Diatance between the centroid of insitu flange

to centroid of composite sectionThe net value of the cancelling moment is therefore,

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

(Top of Insitu Slab)

(Bottom of Insitu Slab)

(Top of Precast Beam)

(Bottom of Precast Beam)

original length at time of

casting insitu flange

centroid of flange t F -F

centroid of

composite

centroid of section

precast beam

where,

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

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

area of composite concrete section moment of inertia/second moment of area of composite section

k = creep reduction coefficient

distance from centroid of the precast beam to top of precast beam Modulus of elasticity of the in-situ concrete

distance from centroid of the precast beam to soffit of precast bea Young's modulus of the precast beam concrete

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

FIGURE 1 - Theoretical Approach to Differential Shrinkage

(IN ACCORDANCE WITH RESEARCH REPORT NO. 15 : NOVEMBER 1963 - AN INVESTIGATIONOF THE BEHAVIOUR OFTHE COMPOSITE CONCRETE BEAMS FROM C&CA)

Mb = F2EcIpxx Ec =

Ipxx =

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

sbb =

sbt =

dEin-situA1 d =

Ein-situ=

A1=

d =

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

Mc = Fe1 e1 =

Mc' = Mc - Mb = Fe1 - Mb

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


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

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

sf

f1

e1 y1 f3

y2 f2

yt sbt

Mc' = Fe-Mb

yb y4 Mb

sbb f4

A1 = y2 =

A2 = y4 =

Ac = Icxx =

A1' = transformed area of in situ concrete = (Modular ratio) * A1

yt = Ein-situ=

yb = Ec =

y1 =





CALCULATION OF THE DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAMAND IN-SITU SLAB

(1) Design Parameter :

(a) Modular Ratio m = 0.824(b) Area of Insitu Slab 351000(c) Transformed Area of Insitu Slab 289059(d) Area of Precast Section 869500(e) Area of Composite Section 1158559(f) Moment of Inertia of Precast 5.2608E+11

(g) Moment of Inertia of Composite 7.6205E+11

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

(I) Thickness of Insitu Slab t = 180 mm

(j) Centroid of Precast to Top fibre 963 mm

(k) Centroid of Precast to Bottom fibre 1162 mm

Centroid of Composite Beam to :

(l) Top of Insitu Slab 885.72 mm

(m) Top of Precast Beam 705.72 mm

(n) Bottom of Precast Beam 1419.28 mm

(o) Centroid of Top Slab 795.72 mm

(p) Differential Shrinkage Coefficient 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 34(s) Modulus of Elasticity of the precast 34(t) Modulus of Elasticity of the Insitu 28

(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

@ Stage 2 Transfer M

(m) (kNm) DL Total

0.000 7702.54 0.000 0.000 8.859 2.646 11.5044.875 7876.83 1735.794 3.176 9.059 2.242 14.4779.750 7898.55 2975.646 5.445 9.084 -4.315 10.214

14.625 7914.58 3719.558 6.807 9.102 -9.021 6.88819.500 7977.28 3967.529 7.260 9.175 -11.933 4.50224.375 7896.69 3719.558 6.807 9.082 -12.750 3.13929.250 7880.03 2975.646 5.445 9.063 -11.787 2.72134.125 7857.63 1735.794 3.176 9.037 -8.956 3.25739.000 7683.19 0.000 0.000 8.836 -4.197 4.639

Prestress Force Selfwt. Moment

@ Stage 2 Transfer M

(m) (kNm) DL Total

0.000 7702.54 0.000 0.000 8.859 -2.646 6.2134.875 7876.83 1735.794 -3.176 9.059 -2.242 3.6419.750 7898.55 2975.646 -5.445 9.084 4.315 7.954

14.625 7914.58 3719.558 -6.807 9.102 9.021 11.31719.500 7977.28 3967.529 -7.260 9.175 11.933 13.84724.375 7896.69 3719.558 -6.807 9.082 12.750 15.02529.250 7880.03 2975.646 -5.445 9.063 11.787 15.40534.125 7857.63 1735.794 -3.176 9.037 8.956 14.81639.000 7683.19 0.000 0.000 8.836 4.197 13.034

(Einsitu/Ecu)

A1 = mm2

A1' = mm2

A2 = mm2

Ac = mm2

Ipxx = mm4

Icxx = mm4

yt =

yb =

y1 =

y2 =

y4 =

e1 =

d =

@transfer Eci2 = kN/mm2

@service Ecu = kN/mm2

Ein-situ= kN/mm2

st

Lx (N/mm2)

Pfinal (kN) Pfinal / A Pfinal (e)/Zt

sb

Lx (N/mm2)

Pfinal (kN) Pfinal / A Pfinal (e)/Zb





(b)

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

Then, creep strain 1.80E-05increased creep factor = 1.022

and F = 9.83E+02 kN

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

0.000 -9.73E-05 -4.58E-08 -8.193E+08 7.82E+08 1.60E+094.875 -1.99E-04 -9.38E-08 -1.678E+09 7.82E+08 2.46E+099.750 -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+0719.500 1.72E-04 8.09E-08 1.447E+09 7.82E+08 -6.65E+0824.375 2.19E-04 1.03E-07 1.840E+09 7.82E+08 -1.06E+0929.250 2.33E-04 1.10E-07 1.964E+09 7.82E+08 -1.18E+0934.125 2.13E-04 1.00E-07 1.790E+09 7.82E+08 -1.01E+0939.000 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)

(m) * (k)

(m)

0.000 3.400 0.848 1.861 0.354 0.2454.875 3.400 0.848 2.859 0.354 -0.1099.750 3.400 0.848 1.316 0.354 0.438

14.625 3.400 0.848 0.112 0.354 0.86419.500 3.400 0.848 -0.773 0.354 1.17724.375 3.400 0.848 -1.230 0.354 1.33929.250 3.400 0.848 -1.374 0.354 1.39034.125 3.400 0.848 -1.171 0.354 1.31839.000 3.400 0.848 -0.602 0.354 1.117

(ii)

(m) * (k)

(m)

0.000 3.400 0.848 1.483 0.354 0.3784.875 3.400 0.848 2.278 0.354 0.0979.750 3.400 0.848 1.048 0.354 0.532

14.625 3.400 0.848 0.089 0.354 0.87219.500 3.400 0.848 -0.616 0.354 1.12224.375 3.400 0.848 -0.980 0.354 1.25129.250 3.400 0.848 -1.095 0.354 1.29134.125 3.400 0.848 -0.933 0.354 1.23439.000 3.400 0.848 -0.479 0.354 1.073

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

per N/mm2

ec = per N/mm2

dEin-situA1 =

(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'

Determination of stresses at Top of Insitu Slab , f1

Lx F/A1' F/Ac Mc' y1/Icxx f1

(N/mm2)

Determination of stresses at Bottom of Insitu Slab , f2

Lx F/A1' F/Ac Mc' y2/Icxx f2

(N/mm2)





(iii)

(k)

(m)

0.000 0.848 1.483 -1.499 0.430 -0.3584.875 0.848 2.278 -3.070 0.430 -0.0249.750 0.848 1.048 -0.641 0.430 -0.540

14.625 0.848 0.089 1.255 0.430 -0.94319.500 0.848 -0.616 2.648 0.430 -1.23924.375 0.848 -0.980 3.368 0.430 -1.39129.250 0.848 -1.095 3.594 0.430 -1.44034.125 0.848 -0.933 3.275 0.430 -1.37239.000 0.848 -0.479 2.378 0.430 -1.181

(iv)

(k)

(m)

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

4.875 0.848 4.581 -3.707 0.430 0.011 Stresses @ Bottom of Insitu Slab

9.750 0.848 2.108 -0.773 0.430 0.209 Stresses @ Top of Precast Beam

14.625 0.848 0.179 1.515 0.430 0.364 Stresses @ Bottom of Precast Beam

19.500 0.848 -1.238 3.197 0.430 0.47724.375 0.848 -1.971 4.066 0.430 0.53629.250 0.848 -2.201 4.339 0.430 0.55434.125 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

(m)

0.000 -0.245 -0.378 0.358 -0.139

4.875 0.109 -0.097 0.024 -0.011

9.750 -0.438 -0.532 0.540 -0.209

14.625 -0.864 -0.872 0.943 -0.364

19.500 -1.177 -1.122 1.239 -0.477

24.375 -1.339 -1.251 1.391 -0.536

29.250 -1.390 -1.291 1.440 -0.55434.125 -1.318 -1.234 1.372 -0.52939.000 -1.117 -1.073 1.181 -0.455

Note : In the above table the sign convention has been amended to give tension as -vefor consistance with other calculations.

End of Calculation Of Differential Shrinkage

Determination of stresses at Top of Precast Beam , f3

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

(N/mm2)

Determination of stresses at Bottom of Precast Beam , f4

Lx F/Ac Mc' y4/Icxx Mb yb/Ipxx f4

(N/mm2)

f1 =

f2 =

f3 =

f4 =

Lx f1 f2 f3 f4

(N/mm2) (N/mm2) (N/mm2) (N/mm2)



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

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

KKHONG (NOV 1998) 28

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

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


Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 8-Apr-2023


DESIGN DATA

Prestressing System Post-tensioned = Post -Tensioned ; Class 2 memberTensile stress permitted, but no visible cracking Crack = 0 mm

Precast Beam Section = S40T1 BEAM Precast Beam

(1) SECTION PROPERTIES OF PRECAST BEAM :

S40T1 BEAM(i) TOTAL HEIGHT OF THE PRECAST SECTION H = 2125 mm

(ii) AREA OF PRECAST BEAM A = 0.869500

(iii) HEIGHT OF CENTROID ABOVE BOTTOM FIBRE 1162.3 mm

(iv) SECTION MUDULI : TOP FIBRE OF PRECAST 0.54646

39 m Eff. Span(v) BOTTOM FIBRE OF PRECAST 0.45262 (vi) SELFWEIGHT OF PRECAST BEAM w = 20.868 kN/m

(2) SECTION MODULI OF COMPOSITE SECTION :

HB45 -SLS2(i) TOP FIBRE OF COMPOSITE SECTION 0.86037

(ii) TOP FIBRE OF PRECAST SECTION 1.07982

(iii) BOTTOM FIBRE OF TOP SLAB 1.07982

CLASS 2(iv) BOTTOM FIBRE OF PRECAST SECTION 0.53693

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

CRACK WIDTH (mm) 0.00(4) CONCRETE STRENGTH:(i) Presstress Concrete : @ TRANSFER 50

@ 28 DAYS 50

(ii) Insitu Concrete : 30

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

FOR PRESTRESSING CONCRETEALLOWABLE 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:

MEMBER TENSION COMPRESSION

CLASS 1 0.000 20.000

CLASS 2 -2.546 20.000

CLASS 3 CRACK WIDTH

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

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

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

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

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

(6) ALLOWABLE CONCRETE STRESSES FOR INSITU SLAB:

(i) TENSILE STRESS (BS5400:P4:1990:CL.7.4.3.3) -3.60

(ii) COMPRESSIVE STRESS (BS5400:P4:1990:CL.7.4.3.2) 15.00

(7) EFFECTIVE SPAN OF PRECAST BEAM 39.000 m

(8) MODULAR RATIO m = 0.824

m2

yb =

Zt = m3

Zb = m3

Zt,c = m3

Zt,p = m3

Zb,s = m3

Zb,p = m3

winsitu =

fci2 = N/mm2

fcu = N/mm2

fc = N/mm2

N/mm2 N/mm2

N/mm2 N/mm2

fcu = 40 N/mm2fcu = >=50 N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

N/mm2

Leff =

(Einsitu/Ecu)




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 beamto centroid of tendon

TOTAL : 76.000 280.00 e = 882.30 mm

INITIAL PRESTRESS LOSSES @ TRANSFER 9.73 %FINAL TOTAL PRESTRESS LOSSES 22.70 %

ULTIMATE TENSILE STRENGTH PER STRAND 186.00 kN

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

EFFECTIVE FORCE @ TRANSFER PER STRAND 122.57 kN

EFFECTIVE FINAL FORCE PER STRAND 104.96 kN

TOP OF BOTT OF TOP OF BOTT OF INSITU INSITU PRECAST PRECAST

TRANSFER PRESTRESS - - -4.33 28.87 SELF WT - - 7.26 -8.77 TOTAL @ TRANSFER - - 2.93 20.11

EXCEEDED ALLOWABLE PRESTRESSING STRESSES AT TRANSFER, TRY AGAIN FINAL PRESTRESS - - -3.71 24.72 SELF WT + DEAD INSITU - - 10.36 -12.50 TEMPERATURE DIFFERENCE 2 - - -1.00

SUPER. DEAD + LIVE HB45 -SLS2 6.82 5.43 6.60 -13.270 (MIDSPAN) DIFF. SHRINKAGE -1.177 -1.122 1.239 -0.477 TOTAL @ WORKING 7.64 4.31 14.49 -2.53

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



D 19 803.20

C 19 1146.28

B 19 1489.36


TOTAL : 76.000 1317.82 e = -155.52 mm


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

EFFECTIVE FORCE @ TRANSFER PER STRAND 113.95 kNEFFECTIVE 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




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



D 19 495.55

C 19 741.03

B 19 986.52


TOTAL : 76.000 863.77 e = 298.53 mm





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


TOTAL : 76.000 539.46 e = 622.84 mm






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




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



D 19 143.95

C 19 277.89

B 19 411.84


TOTAL : 76.000 344.86 e = 817.44 mm






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



D 19 100.00

C 19 220.00

B 19 340.00


TOTAL : 76.000 280.00 e = 882.30 mm






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







D 19 143.95

C 19 277.89

B 19 411.84


TOTAL : 76.000 344.86 e = 817.44 mm






FINAL PRESTRESS - - -2.73 23.34 SELF WT + DEAD INSITU - - 9.71 -11.72 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




D 19 275.80

C 19 451.57

B 19 627.34


TOTAL : 76.000 539.46 e = 622.84 mm






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







D 19 495.55

C 19 741.03

B 19 986.52


TOTAL : 76.000 863.77 e = 298.53 mm






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



D 19 803.20

C 19 1146.28

B 19 1489.36


TOTAL : 76.000 1317.82 e = -155.52 mm





TRANSFER PRESTRESS - - 12.40 6.97 SELF WT - - 0.00 0.00 TOTAL @ TRANSFER - - 12.40 6.97

FINAL PRESTRESS - - 11.02 6.20 SELF WT + DEAD INSITU - - 0.00 0.00 TEMPERATURE DIFFERENCE -1 - - 1.00 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


SEPAKAT SETIA PERUNDING (14142-M)Consulting Engineer

Ultimate Moment Capacity Checks for Post-Tensioned Beam Job No. : 37478

ULTIMATE MOMENT CAPACITY CHECKS AT MIDSPAN & OTHER SECTIONSFOR PRECAST POST-TENSIONED BEAM USING STRAIN COMPATIBILITY METHOD(BS5400:PART4:1990:CL.6.3.3.1)

Project : PROJECT TITLE Designed: KKL Date : 8-Apr-2023

Detail : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked: LTC Date : 8-Apr-2023


(A) Checking Section : 4/8 SPAN ; (19.500 M FROM SUPP.) ; S40T1 BEAM ; 39.00 m Effective Span

(B) Design Ultimate Moment : = 16307.98 kNmS40T1 BEAM

(C) Require Ultimate Moment Capacity At Mid Span = 18754.18 kNm

(D) Depth of Neutral Axis from Top Fibre (N.A) = 490.53 mm

39.00 m Eff. Span(E) Calculation of Ultimate Moment Capacity

(1) Concrete Section

(i) Characteristic Strength of Precast Concrete at Service 50.004/8 SPAN

(ii) Characteristic Strength of In-situ Concrete at Service 30.00

(iii) Material Safety Factor for Concrete 1.50

(iv) Assumed Concrete Maximum Compressive Strain 0.0035

Table 1 : Ultimate Moment Capacity From Concrete SectionConcrete Section Dimension Measure Depth To Section Section Centroid Centroid Concrete Compressive Moment

Section Width Height Top Fibre Bot. Fibre Area Sect. fr. Top Sect. to N.A Strain Force about N.A

(mm) (mm) (mm) (mm) (mm) (mm) e (kN) (kNm)

1 In-situ slab 0 0.00 0 0 0 30 0 490.5 0.00350 0.00 0.02 In-situ slab 1950 180.00 0 180 351000 30 90 400.5 0.00286 4703.40 1883.93 Top Flange 1920 120.00 180 300 230400 50 240 250.5 0.00179 5145.60 1289.14 Top Flange 660 70.00 300 370 46200 50 335 155.5 0.00111 985.32 153.25 Top Flange 220 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.06 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.07 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.08 Top Flange 0 0.00 370 370 0 50 370 120.5 0.00086 0.00 0.09 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 3354Note : (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

(measure from Neutral Axis) (mm) = 152.93 for fcu = 30.0

(2) Prestressing Tendons

(i) Tendon Diameter 12.9 mm (v) Material Safety Factor for Concrete 1.15

(ii) Nominal Cross Section Area of Tendon 100.0 (vi) Percentage of Jacking Force % = 75 %

(ii) Ultimate Characteristic Strength (UTS) 186 kN (vii) Final Prestress Losses 25 %

(iii) Modulus of Elasticity of Tendon 195000 (viii) Total Effective Jacking Force per Strand 139.5 kN

(iv) Characteristic Strength of Tendon 1860 (ix) Total Final Prestress Force per Strand after all losses 104.625 kN

Table 2 : Ultimate Moment Capacity From Prestressing TendonsPrestress Number Total Cross Depth from 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) (mm) (kN) (kNm)

1 Layer 1 18 1800 2205 0.01223 0.00537 0.01760 1617.39 2911.30 4991.342 Layer 2 18 1800 2085 0.01138 0.00537 0.01674 1617.39 2911.30 4641.993 Layer 3 17 1700 1965 0.01052 0.00537 0.01589 1617.39 2749.57 4054.154 Layer 4 17 1700 1845 0.00966 0.00537 0.01503 1617.39 2749.57 3724.205 Layer 5 0 0 0 0.00000 0.00000 0.00000 0.00 0.00 0.00

70 7000 11321.74 17411.69Note :

(i) Strain = (ii) Prestrain =

(iii)

(3) Reinforcement Bars

(i) Characteristic Strength of Steel Reinforcement 460 (iii) Material Safety Factor for Steel Reinforcement 1.15

(ii) Modulus of Elasticity of Steel Reinforcement 200000 (iv) Maximum Compressive Strain = 0.002

Table 2 : Ultimate Moment Capacity From Steel Reinforcement Steel Steel Depth from Strain Stress Force Moment About

Reinforcement Reinfor. Top Fibre e Compressive Tension Compressive Tension N.A. Axis

Layer Area

from. Top (mm) (kN) (kN) (kNm)

1 Layer 1 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.002 Layer 2 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.003 Layer 3 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.004 Layer 4 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.005 Layer 5 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.006 Layer 6 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.007 Layer 7 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.008 Layer 8 0 0 0 0.00000 0.00 0.00 0.00 0.00 0.009 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

0.00 0.00 0.00 0.00 0.00 0.00Note : (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 - 3354Prestressing Tendon - 11322 17412Reinforcement 0 0 0

Total 11200 11322 20765Difference -121.7

Remarks:(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.....!!!

fcu = N/mm2

fcu = N/mm2

gm=

eu=

fcu

(mm2) (N/mm2)

N/mm2

N/mm2

f = gm =

As = mm2

PUTS = Lossfinal =

Es = N/mm2 Peff =

fpu = N/mm2 Pfinal =

Prestressing Tendon Strain, e

(mm2) (N/mm2)

eu/x*(Depth of Tendon from Top Fibre - N.A Depth from Top Fibre ) Pfinal /As/Es

Moment of Tendon Above the N.A shall be negative and Below the N.A shall be positive.

fy = N/mm2 gm =

Es = N/mm2

(mm2) (N/mm2) (N/mm2)


Consulting EngineersShear Design for Post-Tensioned Beam JOB NO. : 37478

SEPAKAT SETIA PERUNDING SDN BHD (14142-M)

PROJECT : PROJECT TITLE Designed : KKL Date : 8-Apr-2023

DETAILS : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH Checked : LTC Date : 8-Apr-2023

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

Design Of Precast Post-Tensioned Beam At Ultimate Limit State - Shear Reinforcement Design S40T1 BEAM(BS 5400 : PART 4 : 1990 ; CL. 5.3.3 , CL. 6.3.4 & CL. 7.4.2.3)

Design Data : 39 m Effective Span(1) Precast Beam Section Properties(i) Total Height of Precast Section H = 2125 mm

(ii) Cross Section Area of Precast Section 0.869500Definations, Symbols and Notes

(iii) Precast Section Centroid above Bottom Fibre 1162.30 mm

(iv) Second Moment Of Area of Precast Section 5.2608E-01

(v) Section Modulus of Precast Section : @ Top Fibre 5.4646E-01 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3)

(vi) @ Bottom Fibre 4.5262E-01 e = Eccentricity from centroid of tendon to centroid of precast beam

(vii) @ Composite Beam Centroid 2.0472E+00 Cracking Moment at Section considered

(viii) Rib/Web Breadth of Precast Section @ Beam Ends (Supports) 660 mm Ultimate Cracking Shear Capacity (Equation 29 BS5400)

(ix) @ Middle of Beams 220 mm

(x) Concrete Strength @ 28 days of Precast Section 50 b =

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 2305 mm considered due to ultimate load

(ii) Cross Section Area of Composite Section 1.1503 Distance of tensile fibre to centroid composite beam

(iii) Composite Section Centroid above Bottom Fibre 1419.28 mm

(iv) Second moment of area of the transformed Composite Section 7.6205E-01

(v) Modular Ratio 0.824

(3) Prestress Strand Properties 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3)

(i) Strand Description : = 0.52608

(ii) Nominal Cross Section Area per Strand, 100.00 Y = 0.25698 m

(iii) Ultimate Tensile Strength per Strand 186.00 kN 2.0472

(iv) 70 % of U.T.S. per Strand 130.20 kN Ultimate shear resistance of a section uncracked in flexure

(v) Cable Length/Beam Length 39.60 m =

Eff. depth of Centroid of tendons to Extreme Compression Fibre

(4) Link Rebars Properties =

(i) Characteristic Strength of Links Rebars 460

(ii) Shear Reinforcement diameter provided 12 mm Horizontal Interface Shear Force

(iii) Total Leg x-Section Area per Links 226 First moment of area, about the neutral axis of the transformed

(iv) Characteristic Strength of Strands (max 460) 460 composite section, of the insitu concrete to one side of the interface

(v) Characteristic Strength of Longitudinal Steel Reinforcement provided 460 area of fully anchoraged reinforcement per unit length crossing the

(vi) Longitudinal Steel Reinforcement diameter provided (max 12 mm) 12 mm shear plane under consideration

(vii) @ Support : R.C. Shear Resistance 0.7776

(viii) Depth Factor §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 0.23001

(ii) Ult. long. stress in the sect. for shear plane under considered (Table 31:BS 5400:P4) 0.45

(iii) Constant depending on the conc. bonding across the shear plane (Table 31:BS 5400:P4) 0.09 (Surface Type 2)

(iv) Length of Shear plane under consideration 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 180 mm should not exceed the lesser of ;

(vii) Insitu slab Width 1950 mm (i) 4 times of minimum thickness of the in situ concrete flange ;

Concrete strength of insitu top slab @ 28 days 30 (ii) 600 mm.

Ap = m2

yb =

Ipre = m4 fpt = Stress due to prestress only at tensile fibre (bottom fibre)

Zt = m3 gfL =

Zb = m3

Zcentroid = m3 Mcr =

bend = Vcr-i =

bmiddle = 0.037bdt(fcu)1/2+ (Mcr/M)(V) but not less than 0.1bd(fcu)1/2

fcu2 = N/mm2 Breadth of member/breadth of rib/web,bw

dt =

Hc =

Ac = m2 yb,c =

yb,c =

Icomposite = m4

m = fcp = Comp. stress due to prestress at the composite centroid axis (+ve)

gfL =

Ipre = m4

As = mm2 yb,c - yb =

PUTS = Zcentroid = Ipre /Y = m3

Peff = Vco =

Lcable/beam = 0.67bHc(ft2+fcpft)1/2 (Equation 28 BS5400:PART4:1990)

dt =

Hc-(yb-e)

fyv = N/mm2

fv = V1 =

Asv = mm2 Sc =

fstrand = N/mm2

fyL = N/mm2 Ae =

fL =

vc = (0.27/gm)*(100As(pre)/benddt)1/3*(fcu)1/3 vc = N/mm2

§s = greater of (500/dt)1/4 or 0.7

Sc = m3 0.75dt, nor four times the web thickness for flanged beams. When V' exceeds 1.8 Vc,

v1 = N/mm2 the max. spacing should be reduced to 0.5 dt. The lateral spacing of the individual

k1 = legs of the links provided at a cross section should not exceed 0.75dt.(V'=V-Vprtestress)

Ls =

tslab =

lf =

fc = N/mm2




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 (m) 0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Distance From MidSpan (m) 19.500 14.625 9.750 4.875 0.000 4.875 9.750 14.625 19.500

(1) Summary Of The (kN) 2141.19 1756.25 1245.94 956.81 466.06 724.42 1227.24 1474.54 1799.88

Ultimate Design M (kNm) -1706.57 4085.30 10359.91 11591.45 15803.19 13846.44 12712.25 6870.63 374.72Shear Forces and Max M : V (kN) 1894.07 1137.49 949.36 623.95 198.04 462.88 1180.91 1526.16 1746.11

Moment Bending (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 (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

(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 = Drape = (1350 - 280) = 1070 mm (mm) 1070 1070 1070 1070 1070 1070 1070 1070 1070

6.0759 4.5644 3.0465 1.5243 0.0000 1.5243 3.0465 4.5644 6.0759

(kN) 625.418 480.857 322.023 161.509 0.000 161.144 321.268 479.685 623.847

(4) Allowable Maximum (mm) 987.18 1441.23 1765.54 1960.14 2025.00 1960.14 1765.54 1441.23 987.18

Ultimate Applied v 2.33 4.02 2.38 1.84 1.05 1.31 2.33 3.30 1.81

Shear Stress Checks Checks 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 - 11.89 16.65 19.52 20.63 19.47 16.61 11.86 -

Cracked in Flexure (kNm) - 7789.63 10342.35 11884.64 12479.74 11860.96 10321.40 7774.07 -

- For Class 1 and Class 2 member d (mm) - 1261 1586 1780 1845 1780 1586 1261 -

(BS 5400:Part 4:1990:CL 6..3.4.3) (kN) - 224 275 305 315 305 275 224 -

(kN) - 3432 1345 1094 485 733 1098 1751 -

(kN) - 1507 901 676 268 524 1049 1773 -

(5b) Assume Sections 7.878 6.599 5.574 4.957 4.786 4.946 5.560 6.583 7.859

UnCracked in Flexure 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) (kN) 4109 1275 1193 1142 1127 1141 1192 1274 4105

(5c) (kN) - -2156 -422 -299 -19 -170 -192 -757 -

and determination of (kN) - -850 -274 -214 -117 -223 -189 -727 -

(kN) -2593 1 -270 -346 -661 -578 -286 -279 -2929

(kN) -2840 -618 -566 -679 -929 -839 -333 -227 -2982

(kN) -2593 1 -270 -214 -19 -170 -189 -227 -2929

(kN) -2593 1 -270 -214 -19 -170 -189 -227 -2929

(5d) Flexure Shear (mm) 3.4145 0.2208 0.2199 0.2199 0.2199 0.2199 0.2199 0.2199 2.5546

Reinforcement Design Calculated (mm) 66 1024 1029 1029 1029 1029 1029 1029 89 (BS 5400:Part 4:1990:CL 6.3.4.4)

(5e) nos 0 0 0 0 0 0 0 0 0Long. Bars/Strand Checks Total Effective area of the above Prestressing Tendons 0 0 0 0 0 0 0 0 0

nos 17 15 11 9 6 7 11 12 14 Total Effective area of the above Longitudinal Bars 1923 1696 1244 1018 679 792 1244 1357 1583

1923 1696 1244 1018 679 792 1244 1357 1583(In Tension Zone Only) 1894 1593 1154 994 582 704 1132 1307 1469

(BS 5400:Part 4:1990:CL 6..3.4.4) 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

Lx

Xo

Max V : VmaxVmax

Mmax Mmax

= Eccentricity @ Centroid of Precast Beam = yb-e'

Pfinal = Effective prestress Force = (n*Peff(1-%Loss))

Ye - Ym =

Tendons, Vprestress qo = Combined Deflection Angle = Atan((Ye - Ym)*(2X0/(Lbeam/2)2)) (o)

Vprestress = gm * Pfinal * Sin(qo), where gm = 0.8 (L.A. Clark)

dt = Effective depth of Tendons = Hc-(yb-e)

= Max Applied Ult.Shear Stress = [Vmaxor V-Vprestress]/bdt (N/mm2)

= Allowable Shear Stress = 0.75fcu1/2 or 5.8 N/mm2 (N/mm2)

fpt = gfL*(Pfinal/Ap + Pfinal*e/Zb), where gfL = 0.87 (N/mm2)

Mcr = [0.37(fcu)1/2 + fpt] * Icomposite/yb,c

= (H-yb+e)

Vcr(min) = min. required by code 0.1bdt(fcu)1/2

Vcr1 = 0.037bdt(fcu)1/2+ (Mcr/M)(Vmax)

Vcr2 = 0.037bdt(fcu)1/2+ (Mcr/Mmax)(V)

fcp = gfL*(Pfinal/Ap - Pfinal*e/Zcentroid) taken as positive (N/mm2)

ft = 0.24(fcu)1/2 taken as positive (N/mm2)

Vco = 0.67bHc(ft2+fcpft)1/2

Calculations of (V - Vc) (Vmax - Max(Vcr1,Vcr(min)) - Vprestress)

(V - Max(Vcr2,Vcr(min) - Vprestress)

(V - Vc) Max (Vmax - Vco -Vprestress)

(V - Vco -Vprestress)

(V - Vc - Vprestress) Max

(V - Vc - Vprestress) Max (Double Check)Asv/Sv(Min) = V+0.4bdt-(Vc+Vprestress)/(0.87fyvdt) or 0.4b/(0.87fyv)

Sv(min)

Minimum Area of EXCESS AsLong(pre) : (i) Bonded Prestressing Strands EXCESS in resist bending

(mm2)( Note : The AsLong shall be the area AsLong(Bar): (ii) No. of Longitudinal reinforcement EXCESS in resist bending

of strands/rebars which are NOT (mm2)Used in the bending/ others designs.)AsLongTotal = AsLong(pre) + AsLong(Bar) (mm2)

AsLong(Min) = V /(2*0.87*fyL) (mm2)

= Minimum AsLong Checks

(From Grillage Analysis)




F95

Maximum Allowable Shear Stress as per Table 28 of BS5400




CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR (Continue)

Section Support 1 Section 1 Section 2 Section 3 Mid Span Section 5 Section 6 Section 7 Support 2

Distance From Support (m) 0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Distance From MidSpan (m) 19.500 14.625 9.750 4.875 0.000 4.875 9.750 14.625 19.500

(6) Design Of Longitudinal Shears :

(6a) Longditudinal Shear (kN/m) 646 530 376 289 141 219 370 461 543

Reinforcement Design (kN/m) 1782 1782 1782 1782 1782 1782 1782 1782 1782

Checks 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) 1085 990 990 990 990 990 990 990 990

(mm) 209 228 228 228 228 228 228 228 228

(7) Shear Reinforcement

Design (mm) 66 228 228 228 228 228 228 228 89 (BS 5400:Part 4:1990:CL 6..3.4.4) Required by The Code.

(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 ---------

Lx

Xo

V1 = Max(V,Vmax)*Sc/Icomposite

k1*fc*Ls

= Checking of allowable V1

Ae = the larger of (V1 - v1Ls)/(0.7fyv) and (0.15/100)*(Ls*1000) (mm2/m)

Sv Calculated = Asv*1000/Ae

Minimum of Sv Calculated (From Item (5d) & (6a)) &

No of Links required per m length = (1000/Sv) + 1

Post-Tensioning Losses :

(1) Immediate 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 TendonLosses due to frinction in a cable can be calculated to a relatively high degree of accuracy by Coulomb's formula:

P(x) =

where,P(x) = Post-tensioning force at a distance x from the stressing anchorage (Live end)

Post-tensioning force at the stressing anchorage

e = Base of Napierian logarithmsCoefficient of frictionSum 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,

where,

Loss of prestressing force in tendon per meter length/ Force Gradient

Loss of prestressing force in tendon

Total Cable length

and the diatance affected by the draw-in of wedges,

w =

where,Draw-in = Draw-in of Wedges in mm

n = Total number of prestressing cables

w =

Pj * e-(mq + Kx)

Pj =

m =q =

dp = (1 - e-(mq + Kx) )Pj /Lcable

dp =(1 - e-(mq + Kx) )Pj =

Lcable =

(Draw-in * Es * As * n)1/2

Es = Modulus of Elasticity og post-tensioning cable in kN/m2

As = Cable cross Section Area in mm2

Distance affected by the draw-in of wedges (< Lcable)

Forces Along Prestressing Cable After Friction and Wedges Draw-in Losses

(i)

(ii)

(1)(d)

=(ref. BS5400:Part4:Cl. 6.7.2.3)

Where,

For w < L cable /2

For w >= L cable /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/Ec)*ftendon for post-tensioned beam



Ec is modulus of elasticity of the precast concrete at transfer

Pj

Length of Tendon Lcable

w

Dp

Pj-Dp

Px

x

Dead EndAnchorage

Loss of force due to draw-in of wedges

LiveEnd Anchorage

PL

Pj

Length of Tendon Lcable

w

Dp

Pj-Dp

Px

x

Dead EndAnchorage

Loss of force due to draw-in of wedges

LiveEnd Anchorage

PL

(2) Deferred Losses

2(a)


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

Relaxation (%) x Strand Cross Section Area x Assumed % Occured

At 1000h

2(b)

(i) From BS 5400:Part 4:1990:Table 29, Shrinkage per unit length

System Humid exposure Normal exposure(90% r.h) (70% r.h)


after concreting

- Shrinkage Strain used in the Design, per unit length

- Shrinkage Strain Loss as Stress,

x x Assumed % Occured

2(c)

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


(i)(ii)(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:



- Creep Strain

- Modulus of Elasticity of Strand

(I) Total Creep Loss At Stage 1

(II) Total Creep Loss At Stage 2 ( due to additional prestressing in Stage 2 compared to Stage 1)

where,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


frelax.Loss =



es 70 x 10-6 200 x 10-6

es =



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




(fci/2- fci/3)

ec = per N/mm2

Es = kN/mm2

= (Stress at tendon level during Stage 1) * Creep Strain (ec) * Es * Increased Factor * Assumed % Occured

= (sStage1) * ec * Es * Increased Factor * Assumed % occured

= (sStage2 - sStage1) * ec * Es * Increased Factor * Assumed % occured

Documents

Post Tensioned Design1