Post Tensioned Design1

SEPAKAT SETIA SETIA PERUNDING SDN BHD (14142-M) CONSULTING ENGINNERS PROJECT DETAIL JOB NUMBER

: : :

PROJECT TITLE 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH 37478

Designed Checked

: :

KKL LTC

File name

:

W:\SCB Spreadsheet\Post-Tensio Spreadsheet\Post-Tensioned-Design.xls ned-Design.xls

Date Date

: :

16-Jan-2011 16-Jan-2011

S37T1 - EDGE BEAM (T1) DESIGN DATA : (I) (I)

Numb Number er Of Stag Stage e For For Stre Stress ssin ing g

(II) (II)

Conc Concre rete te Prop Proper erti ties es for for Pre Preca cast st Beam Beam:: (a) 1s 1st Stage : (b) 2n 2nd Stage : (c) 28 days

(III (III))

(i)

Concrete Cube Strength

(ii) (ii)

Modu Modulu lus s of Ela Elast stic icit ity y

(i)


(ii) (ii)


(i)


(ii) (ii)


2

Stages

f ci1 =

30

N/mm2

Ec1 =

28

kN/mm 2

f ci2 =

50

N/mm2

Ec2 =

34

kN/mm 2

f cu =

50

N/mm2

Ecu =

34

kN/mm 2

Pres Prestr tres essi sing ng Str Stran ands ds Pro Prope pert rtie ies s: (a) Strand Diameter Diameter

φs =

12.9

mm

(b) Cross Section Section Area

As =

100

mm2

(c) Mudulus Mudulus of Elasticity Elasticity

Es =

195

kN/mm 2

PUTS =

µ = K= draw-in =

186 0.2 0 10

kN /rad rad/m mm

(a) Relaxation of Strand Cable (At 1000 hours) (b) Creep of Concrete Concrete per unit Length

= εc =

2.5 0

% of Jacking Force per N/mm2

(c) Shrinkage per unit Length

εs =

2.00E-004

k=

0.43

(d) U.T.S per Strand Strand (e) Co-efficient Co-efficient of Friction Friction (f) Wobble Factor (g) Average Anchorage Draw in

(IV) (IV)

=

Pres Prestr tres essi sing ng Los Losse ses s Data Data::

(d) Creep reduction Coefficient

SEPAKAT SETIA PERUNDING (14142-M)

JOB NO :

POST-TENSIONED BEAM DESIGN - Calculation of Post-Tensioning Cable Profile

PROJECT TITLE 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH W:\SCB Spreadsheet\Post-Tensioned-Design.xls

Project : Detail : Filename :

(1) (a)

Designed : Checked :

KKL LTC

Date : Date :

37478

16-Jan-2011 16-Jan-2011

CALCULATION OF POST-TENSIONED CABLES PROFILE Input Data Leff =

39.00 m

Beam Length

Lbeam =

39.60 m

Cable Length

Lcable =

39.60 m

Effective Span

Nos. of Cables

4 nos

=

(b) (b)

Cabl Cable e Pro Profi file le Form Formul ula a

(i) (i)

Form Formul ulae ae used used for compu computin ting g cab cable le prof profil ile e: Y0 = Ym + (Ye - Ym) * (X0/Half beam length)2

(ii) (ii)

Formul Formulae ae used used for computi computing ng cabl cable e angle angle at ancho anchorag rage e: Angle = arctan(2 * Drape / Half beam length) Drape = Ye - Ym where,

Y0 = Height of centre-line of cable from from soffit at distance X0 from midspan. Ye = Height of centre-line of cable from soffit at beam end. Ym = Height of centre-line of cable from soffit at midspan.

(2)

CABLE INFO Height of centre-line of cable from soffit of beam

Drape

Mark

(mm)

Ye - Ym

Ye Cable Cable Cable Cable

(3) (3)

Cable angle

Cable

A B C D

1875.00 1525.00 1175.00 825.00

Ym 460.00 340.00 220.00 100.00

at anghorage

Total Nos of Strands per Cable

(mm)

(degree)

(nos)

1415.00 1185.00 955.00 725.00

8.134 6.826 5.510 4.188

19 19 19 19 76

CALCUL CALCULAT ATIO ION N OF OF CABL CABLE E PRO PROFI FILE LE Height of centre-line of cable Distance from

from soffit of beam (mm) Cable angle

Support

Midspan

X (m)

X0 (m)

19.500 18.500 17.500 16.500 15.500 14.500 13.500 12.500 11.500 10.500 9.500 8.500 7.500 6.500 5.500 4.500 3.500 2.500 1.500 0.500 -0.300 -0.300

6.826

5.510

4.188

A 19

B 19

C 19

D 19

460 464 474 492 518 550 590 637 691 752 821 897 980 1070 1167 1272 1384 1503 1629 1763 1875 1875

340 343 352 367 388 416 449 488 533 585 642 706 775 851 932 1020 1114 1214 1319 1431 1525 1525

220 222 230 242 259 281 308 339 376 417 464 515 571 632 697 768 844 924 1009 1099 1175 1175

100 102 107 117 130 146 167 191 218 250 285 324 366 413 462 516 573 634 699 768 825 825

at anchorage Cable Mark Nos. Of Strands

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 Section 10 Section 11 Section 12 Section 13 Section 14 Section 15 Section 16 Section 17 Section 18 Section 19 Section 20 Section 21 Section 22

8.134

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 19.800 19.800

SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M) Consulting Engineers Summary of Computer Analysis Output for Post-tensioned Beam Design

Job No. :

37478

SEPAKAT SETIA PERUNDING (14142-M)

JOB NO :

POST-TENSIONED BEAM DESIGN - Calculation of Post-Tensioning Cable Profile


Project : Detail : Filename :

(1) (a)


KKL LTC

Date : Date :

37478

16-Jan-2011 16-Jan-2011

CALCULATION OF POST-TENSIONED CABLES PROFILE Input Data Leff =

39.00 m

Beam Length

Lbeam =

39.60 m

Cable Length

Lcable =

39.60 m

Effective Span

Nos. of Cables

4 nos

=

(b) (b)

Cabl Cable e Pro Profi file le Form Formul ula a

(i) (i)

Form Formul ulae ae used used for compu computin ting g cab cable le prof profil ile e: Y0 = Ym + (Ye - Ym) * (X0/Half beam length)2

(ii) (ii)

Formul Formulae ae used used for computi computing ng cabl cable e angle angle at ancho anchorag rage e: Angle = arctan(2 * Drape / Half beam length) Drape = Ye - Ym where,

Y0 = Height of centre-line of cable from from soffit at distance X0 from midspan. Ye = Height of centre-line of cable from soffit at beam end. Ym = Height of centre-line of cable from soffit at midspan.

(2)

CABLE INFO Height of centre-line of cable from soffit of beam

Drape

Mark

(mm)

Ye - Ym

Ye Cable Cable Cable Cable

(3) (3)

Cable angle

Cable

A B C D

1875.00 1525.00 1175.00 825.00

Ym 460.00 340.00 220.00 100.00

at anghorage

Total Nos of Strands per Cable

(mm)

(degree)

(nos)

1415.00 1185.00 955.00 725.00

8.134 6.826 5.510 4.188

19 19 19 19 76

CALCUL CALCULAT ATIO ION N OF OF CABL CABLE E PRO PROFI FILE LE Height of centre-line of cable Distance from

from soffit of beam (mm) Cable angle

Support

Midspan

X (m)

X0 (m)

19.500 18.500 17.500 16.500 15.500 14.500 13.500 12.500 11.500 10.500 9.500 8.500 7.500 6.500 5.500 4.500 3.500 2.500 1.500 0.500 -0.300 -0.300

6.826

5.510

4.188

A 19

B 19

C 19

D 19

460 464 474 492 518 550 590 637 691 752 821 897 980 1070 1167 1272 1384 1503 1629 1763 1875 1875

340 343 352 367 388 416 449 488 533 585 642 706 775 851 932 1020 1114 1214 1319 1431 1525 1525

220 222 230 242 259 281 308 339 376 417 464 515 571 632 697 768 844 924 1009 1099 1175 1175

100 102 107 117 130 146 167 191 218 250 285 324 366 413 462 516 573 634 699 768 825 825

at anchorage Cable Mark Nos. Of Strands

Section 1 Section 2 Section 3 Section 4 Section 5 Section 6 Section 7 Section 8 Section 9 Section 10 Section 11 Section 12 Section 13 Section 14 Section 15 Section 16 Section 17 Section 18 Section 19 Section 20 Section 21 Section 22

8.134

0.000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.000 11.000 12.000 13.000 14.000 15.000 16.000 17.000 18.000 19.000 19.800 19.800

SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M) Consulting Engineers Summary of Computer Analysis Output for Post-tensioned Beam Design

Job No. :

37478

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

Job No. :

Summary of Computer Analysis Output for Post-tensioned Beam Design

37478

Summary of Computer Analysis Output for Post-tensioned Beam Design Project Detail Filename

(i) (ii) (iii)

: : :

PROJECT TITLE 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH W:\SCB Spreadsheet\ Spreadsheet\Post-Tension Post-Tensioned-Design.xl ed-Design.xls s

Beam Type Beam Position Effective Effective Span Span /Length /Length Betwee Between n Centrelin Centreline e of Bearings Bearings

Leff

(iv) (iv) Sect Sectio ion n Modu Modulu lus s :

@ Bottom Fibre of Precast Beam

(v) (v)

Sect Sectio ion n Modu Modulu lus s :

@ Bottom Fibre of Composite Beam

(vi) (vi)

Precas Precastt Beam Beam Self Selfwei weigh ghtt

(vii) (vii) Deck Deck Slab Self Selfwei weigh ghtt NOTE :


KKL LTC

Date : Date :

16-Jan-2011 16-Jan-2011

= S37T1 (SAG) = ELE 89 TO 96 = 39.000 m

Zb =

4.526E+08 mm3

Zb,p =

5.369E+08 mm3

wpre =

20.868 kN/m

wslab =

8.900 kN/m

UDLMoment = w/2(Lx) (Leff -Lx) UDL Shear =w (Leff /2-Lx)

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

NOMINAL MAXIMUM MOMENT (KNm)

NOMINAL - MOMENT Distance from Support

Nominal Moment Du Due to Dead Load Precast Insitu Sl Slab Total

Section

Lx (m)

Beam

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00 1735.79 2975 2975.6 .65 5 3719 3719.5 .56 6 3967 3967.5 .53 3 3719 3719.5 .56 6 2975 2975.6 .65 5 1735.79 0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

0.00 740.30 1269 1269.0 .08 8 1586 1586.3 .36 6 1692 1692.1 .11 1 1586 1586.3 .36 6 1269 1269.0 .08 8 740.30 0.00

0.00 2476.09 4244.73 5305.91 5659.64 5305.91 4244.73 2476.09 0.00

Nominal Moment Due to Superimposed Dead Load Diaphragm

Parapet, Kerb

Beam

& Services

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-811.40 -275.30 106.20 356.10 492.20 523.20 449.20 261.20 -62.73

Premix

-393.80 -137.90 61.42 202.30 283.20 303.60 263.30 163.20 5.03

DS.CR,DSETT

2812.00 2460.62 2109.25 1757.87 1406.50 1055.12 703.75 352.37 0.00

NOMINAL LIVE LOADING MOMENT (kNm)

HA1003 Total

1606.80 2047.42 2276.87 2316.27 2181.90 1881.92 1416.25 776.77 -57.71

-

HAHB4503

-

COMPUTER ANALYSIS OUTPUT U nf nf ac ac to tor ed ed

U nf nfa ct cto re re d

Un fa fac to tor ed ed

U nf nf ac act or ore d

511.50 433.60 1614.00 2486.00 3050.00 2903.00 2456.00 1403.00 -188.30

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

694.60 601.60 3170.00 4387.00 4885.00 4749.00 4290.00 2204.00 -329.50

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

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

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

NOMINAL - SHEAR Distance from Support

Nominal Shear Force Due to Dead Load Precast Insitu Sl Slab Total

Section

Lx (m)

Beam

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

406.93 305.19 203.46 101.73 0.00 -101.73 -203.46 -305 305.19 .19 -406 406.93 .93

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

KKHONG (DEC 1998)

173.55 130.16 86.78 43.39 0.00 -43.39 -86.78 -13 -130.16 0.16 -17 -173.55 3.55

580.48 435.36 290.24 145.12 0.00 -145.12 -290.24 -435.36 -580.48

Nominal Shear Force Due to Superimposed Dead Load Diaphragm

Parapet, Kerb

Beam

& Services

70.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -70.00

135.00 101.20 72.21 47.00 23.70 0.41 -24.79 -53.93 -88.08

Premix

62.24 49.83 37.03 23.92 10.66 -2.60 -15.70 -28.49 -40.86

DS.CR,DSETT

123.65 117.78 111.90 106.03 -100.15 -94.28 -88.40 -82.53 -76.65

NOMINAL LIVE LOADING LOADING SHEAR (kN)

HA1003 Total

390.89 268.81 221.14 176.95 -65.79 -96.46 -128.89 -164.95 -275.59

-

HAHB4503

-

COMPUTER ANALYSIS OUTPUT U nf nf ac ac to tor ed ed

U nf nfa ct cto re re d

Un fa fac to tor ed ed

U nf nf ac act or ore d

-22.75 15.81 149.50 123.70 -36.25 -98.29 -231.30 -319.40 -239.50

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-33.26 165.80 203.80 109.20 -82.27 -102.50 -459.90 -542.50 -468.80

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Page 3


Job No. :


37478

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

S.L.S - MOMENT Distance from Support

SERVICEABILITY LIMIT LIMIT STATE MOMENT MOMENT (KNm) Due to Dead Load Insitu Sl Slab Total

Due to Superimposed Dead Load

Precast

Diaphragm

Parapet, Kerb

Beam

Beam

& Services

Premix

DS.CR,DSETT

Total

HA1003

Due to Live Loading HAHB4503

-

SLS 1

SLS 1

SLS

SLS 1

SLS 1

SLS 1

SLS1

SLS

SLS 1

SLS 1

SLS 2

SLS 2

Section

Lx (m)

1.000

1.000

-

1.000

1.000

1.200

1.000

-

1.20

1.20

1.00

1.00

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00 1735.79 2975 2975.6 .65 5 3719 3719.5 .56 6 3967 3967.5 .53 3 3719 3719.5 .56 6 2975 2975.6 .65 5 1735.79 0.00

0.00 740.30 .30 1269 1269.0 .08 8 1586 1586.3 .36 6 1692 1692.1 .11 1 1586 1586.3 .36 6 1269 1269.0 .08 8 740.30 .30 0.00

0.00 2476.09 4244.73 5305.91 5659.64 5305.91 4244.73 2476.09 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-811.40 -275.30 106.20 356.10 492.20 523.20 449.20 261.20 -62.73

-472.56 -165.48 73.70 242.76 339.84 364.32 315.96 195.84 6.03

2812.00 2460.62 2109.25 1757.87 1406.50 1055.12 703.75 352.37 0.00

1528.04 2019.84 2289.15 2356.73 2238.54 1942.64 1468.91 809.41 -56.70

613.80 520.32 1936.80 2983.20 3660.00 3483.60 2947.20 1683.60 -225.96

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

694.60 601.60 3170.00 4387.00 4885.00 4749.00 4290.00 2204.00 -329.50

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

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

S.L.S - STRESS (f b) Distance from Support

SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2) Due to Dead Load Insitu Sl Slab Total


Precast

Diaphragm

Parapet, Kerb

Beam

Beam

& Services

Premix

DS.CR,DSETT

Total

HA1003

Due to Live Loading HAHB4503

-

SLS 1

SLS 1

SLS

SLS 1

SLS 1

SLS 1

SLS1

SLS

SLS 1

SLS 1

SLS 2

SLS 2

Section

Lx (m)

1.000

1.000

-

1.000

1.000

1.200

1.000

-

1.200

1.200

1.000

1.000

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00 3.83 6.57 8.22 8.77 8.22 6.57 3.83 0.00

0.00 1.64 2.80 3.50 3.74 3.50 2.80 1.64 0.00

0.00 5.47 9.38 11.72 12.50 11.72 9.38 5.47 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-1.51 -0.51 0.20 0.66 0.92 0.97 0.84 0.49 -0.12

-0.88 -0.31 0.14 0.45 0.63 0.68 0.59 0.36 0.01

5.24 4.58 3.93 3.27 2.62 1.97 1.31 0.66 0.00

2.85 3.76 4.26 4.39 4.17 3.62 2.74 1.51 -0.11

1.14 0.97 3.61 5.56 6.82 6.49 5.49 3.14 -0.42

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1.29 1.12 5.90 8.17 9.10 8.84 7.99 4.10 -0.61

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

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

S.L.S - f b(SDL+LL)

SERVICEABILITY LIMIT STATE BOTTOM STRESS (N/mm2) SDL + Live Loading

Distance from Support Section

Lx (m)

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

KKHONG (DEC 1998)

SDL + HA1003

SDL + -

SDL + HAHB4503

SDL + -

3.99 4.73 7.87 9.95 10.99 10.11 8.22 4.64 -0.53

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

4.14 4.88 10.17 12.56 13.27 12.46 10.73 5.61 -0.72

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Page 4


Job No. :


37478

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

ULTIMATE LIMIT STATE MOMENT (KNm)

U.L.S-DESIGN Moment

Distance from Support

Due to Dead Load Precast Insitu Slab Total Beam

ULS 1

ULS 1

Section

Lx (m)

1.265

1.265

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00 2195.78 3764.19 4705.24 5018.92 4705.24 3764.19 2195.78 0.00

0.00 936.48 1605.39 2006.74 2140.52 2006.74 1605.39 936.48 0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2


ULS

0.00 3132.26 5369.58 6711.98 7159.45 6711.98 5369.58 3132.26 0.00

Diaphragm

Parapet, Kerb

Beam

& Services

Premix

ULS LIVE LOADING MOMENT (kNm)

DS.CR,DSETT

Total

HA1003

-

HAHB4503

-

ULS

ULS 1

ULS 1

ULS 1

ULS 1

1.65

1.65

1.43

1.43

843.98 715.44 2663.10 4101.90 5032.50 4789.95 4052.40 2314.95 -310.70

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

993.28 860.29 4533.10 6273.41 6985.55 6791.07 6134.70 3151.72 -471.19

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ULS 1

ULS 1

ULS 1

ULS1

1.320

1.320

1.925

1.320

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-1071.05 -363.40 140.18 470.05 649.70 690.62 592.94 344.78 -82.80

-758.07 -265.46 118.23 389.43 545.16 584.43 506.85 314.16 9.67

3711.84 3248.02 2784.21 2320.39 1856.58 1392.76 928.95 465.13 0.00

1882.73 2619.16 3042.63 3179.87 3051.44 2667.81 2028.75 1124.07 -73.13

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

ULTIMATE LIMIT STATE CO-EXISTING SHEAR FORCE (KN)

U.L.S-DESIGN Shear


Due to Dead Load Insitu Slab Total

Diaphragm

Parapet, Kerb

Beam

Beam

& Services

ULS 1

ULS 1

Section

Lx (m)

1.265

1.265

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

514.76 386.07 257.38 128.69 0.00 -128.69 -257.38 -386.07 -514.76

219.54 164.66 109.77 54.89 0.00 -54.89 -109.77 -164.66 -219.54

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2


Precast

ULS

734.30 550.73 367.15 183.58 0.00 -183.58 -367.15 -550.73 -734.30

Premix

ULS LIVE LOADING SHEAR (kN)

DS.CR,DSETT

Total

HA1003

-

HAHB4503

-

ULS

ULS 1

ULS 1

ULS 1

ULS 1

1.65

1.65

1.43

1.43

-37.54 26.09 246.68 204.11 -59.81 -162.18 -381.65 -527.01 -395.18

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-47.56 237.09 291.43 156.16 -117.65 -146.58 -657.66 -775.78 -670.38

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

ULS 1

ULS 1

ULS 1

ULS1

1.320

1.320

1.925

1.320

92.40 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -92.40

178.20 133.58 95.32 62.04 31.28 0.55 -32.72 -71.19 -116.27

119.81 95.92 71.28 46.05 20.52 -5.00 -30.22 -54.84 -78.66

163.22 155.46 147.71 139.95 -132.20 -124.44 -116.69 -108.93 -101.18

553.63 384.97 314.31 248.04 -80.39 -128.90 -179.63 -234.96 -388.50

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

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

U.L.S-DESIGN

DL + SDL + LIVE LOAD


HA1003

-

HAHB4503

-

Moment

Shear

Moment

Shear

Moment

Shear

Moment

Shear

Section

Lx (m)

(kNm)

(kN)

(kNm)

(kN)

(kNm)

(kN)

(kNm)

(kN)

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

2726.70

1250.39

0.00

0.00

2876.01

1240.37

0.00

0.00

6466.86

961.78

0.00

0.00

6611.71

1172.79

0.00

0.00

11075.31

928.13

0.00

0.00

12945.31

972.89

0.00

0.00

13993.75

635.72

0.00

0.00

16165.26

587.77

0.00

0.00

15243.39

-140.21

0.00

0.00

17196.44

-198.04

0.00

0.00

14169.74

-474.65

0.00

0.00

16170.86

-459.05

0.00

0.00

11450.73

-928.43

0.00

0.00

13533.03

-1204.44

0.00

0.00

6571.28

-1312.70

0.00

0.00

7408.05

-1561.47

0.00

0.00

-383.83

-1517.98

0.00

0.00

-544.32

-1793.19

0.00

0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

KKHONG (DEC 1998)

Page 5


37478

Job No. :


MAXIMUM SHEAR FORCE WITH CO-EXISTING MOMENT FOR SHEAR REINFORCEMENT DESIGN (4a) SUMMARY OF THE NOMINAL CO-EXSITING MOMENT WITH MAXIMUM SHEAR FOR DEAD LOAD, SUPERIMPOSED DEAD LOAD AND LIVE LOADING

NOMINAL CO-EXISITING MOMENT (kNm)

NOMINAL - MOMENT Distance from Support

Nominal Moment Due to Dead Load Precast Insitu Slab Total

Section

Lx (m)

Beam

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

0.00 740.30 1269.08 1586.36 1692.11 1586.36 1269.08 740.30 0.00

Nominal Moment Due to Superimposed Dead Load

0.00 2476.09 4244.73 5305.91 5659.64 5305.91 4244.73 2476.09 0.00

Diaphragm

Parapet, Kerb

Beam

& Services

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-811.40 -275.30 106.20 356.10 492.20 523.20 449.20 261.20 -62.73

Premix

-393.80 -137.90 61.42 202.30 283.20 303.60 263.30 163.20 5.03

CR,DS,DSETTL

2812.00 2460.62 2109.25 1757.87 1406.50 1055.12 703.75 352.37 0.00

NOMINAL LIVE LOADING MOMENT (kNm)

-

-

Total

1606.80 2047.42 2276.87 2316.27 2181.90 1881.92 1416.25 776.77 -57.71

HAHB4513 HAHB4514

COMPUTER ANALYSIS OUTPUT Un fa ct ore d

Un fa ct or ed

Un fa ct ore d

U nf act or ed

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

-2510.00 -893.30 1828.00 1771.00 3481.00 1088.00 -515.50 -185.30 -210.90

654.40 508.10 2076.00 1658.00 4532.00 3706.00 4182.00 2100.00 163.00

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

NOMINAL MAXIMUM SHEAR FORCE (kN)

NOMINAL - SHEAR Distance from Support

Nominal Shear Force Due to Dead Load Precast Insitu Slab Total

Section

Lx (m)

Beam

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

406.93 305.19 203.46 101.73 0.00 -101.73 -203.46 -305.19 -406.93

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

173.55 130.16 86.78 43.39 0.00 -43.39 -86.78 -130.16 -173.55

Nominal Shear Force Due to Superimposed Dead Load

580.48 435.36 290.24 145.12 0.00 -145.12 -290.24 -435.36 -580.48

Diaphragm

Parapet, Kerb

Beam

& Services

70.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -70.00

135.00 101.20 72.21 47.00 23.70 0.41 -24.79 -53.93 -88.08

Premix

62.24 49.83 37.03 23.92 10.66 -2.60 -15.70 -28.49 -40.86

CR,DS,DSETTL

123.65 117.78 111.90 106.03 -100.15 -94.28 -88.40 -82.53 -76.65

NOMINAL LIVE LOADING SHEAR (kN)

-

-

Total

390.89 268.81 221.14 176.95 -65.79 -96.46 -128.89 -164.95 -275.59

HAHB4513 HAHB4514

COMPUTER ANALYSIS OUTPUT Un fa ct ore d

Un fa ct or ed

Un fa ct ore d

U nf act or ed

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

629.60 598.50 411.20 375.50 162.20 125.20 74.09 76.36 -506.40

-32.06 -27.81 -91.74 -88.68 -269.70 -296.30 -492.30 -506.40 76.36

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

DEAD LOAD & SUPERIMPOSED DEAD LOAD ULS FACTORS Precast

Insitu Slab

-

Beam

Diaphragm

Parapet, Kerb

Beam

& Services

Premix

CR,DS,DSETTL

LIVE LOADING ULS FACTORS -

-

-

HAHB4513 HAHB4514

Load Combinations

ULS 1

ULS 1

-

ULS 1

ULS 1

ULS 1

ULS1

-

-

-

ULS 1

ULS 1

γ f3*γ fL

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 DL + SDL + LIVE LOAD


-

-

HAHB4513

HAHB4514

Moment

Shear

Moment

Shear

Moment

Shear

Moment

Shear

Section

Lx (m)

(kNm)

(kN)

(kNm)

(kN)

(kNm)

(kN)

(kNm)

(kN)

Support 1

0.00 4.88 9.75 14.63 19.50 24.38 29.25 34.13 39.00

0.00

0.00

0.00

0.00

-1706.57

2188.26

2818.52

1242.09

0.00

0.00

0.00

0.00

4474.00

1791.55

6478.01

895.93

0.00 0.00

0.00 0.00

0.00 0.00

0.00 0.00

11026.25 12424.38

1269.48 968.58

11380.89 12262.79

550.27 304.80

0.00

0.00

0.00

0.00

15188.72

151.55

16691.65

-466.06

0.00

0.00

0.00

0.00

10935.63

-133.44

14679.37

-736.18

0.00

0.00

0.00

0.00

6661.17

-440.84

13378.59

-1250.77

0.00

0.00

0.00

0.00

3991.35

-676.50

7259.33

-1509.84

0.00

0.00

0.00

0.00

-374.72

-1846.95

159.96

-1013.61

1/8 2/8 3/8 Mid Span 5/8 6/8 7/8 Support 2

KKHONG (DEC 1998)

Page 6


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS

Job No. :

37478

Calculation of Prestress Losses & Differential Shrinkage At SLS For PRECAST POST-TENSIONED PRESTRESSED BEAM Design Project : Detail : Filename :

PROJECT TITLE 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/ W:\SCB Spreadsheet\Post-Tensioned-Design.xls

Design Data :


KKL LTC

Lbeam

S40T1 BEAM

x (1) (i)

Spanning Length & Cable Length Total Beam Length

(ii)

Edge of Precast Beam to Centreline of Bearing Pad

(iii)

Effective Span /Length Between Centreline of Bearings

(iv)

Total Cable Length/Beam Length

(2) (i)

Precast Beam Concrete Properties Number of Stage of Stressing (Max. = 2)

(ii)

Concrete Cube Strength :

Lbeam = Leff = Lbeam - 2x

x = Leff = Lcable =

m m m

@ 28 Days

Ecu =

@ Stage 1 Stressing

Ec1 =

@ Stage 2 Stressing

Ec2 =

24.0 kN/mm3

f ci1 = f ci2 =

(iv )

Concrete Density

γ con =

(3) (i)

Section Properties Of Precast Beam Cross Sectional Area

Ap =

(ii)

Total Height

(iii)

Centriod of Precast Beam To Bottom Fibre

(iv)

Centriod of Precast Beam To Top Fibre

(v)

Moment of Inertia

(vi)

Section Modulus :

(vii)

Section Modulus :

(viii)

Selfweight of Precast Beam

(4)

Stressing Cable Properties

(i)

Coeffic ient of Fric tion

(ii)

Wobble Factor

(iii)

Average Anchorage Draw in

(iv )

Strand Diameter

(v)

Ultimate Tensile Strength per Strand

(vi)

Cross Sectional Area per Strand

As =

(vii)

Modulus of Elasticity of Strand

Es =

(5)

Proposed Stressing Sequence STAGE 1 :

yt =

869500 mm2 2125 mm 1162.3 mm 962.7 mm

Ipxx =

5.26080E+11 mm4

@ Top Fibre of Precast Beam

Zt =

5.4646E+08 mm3

@ Bottom Fibre of Precast Beam

Zb =

4.5262E+08 mm3

H = yb =

wpre =

K =

φs = PUTS =

=

Stress Cable "B" to

=

Stress Cable "C" to

=

Stress Cable "D" to

=

Stress Cable "A" to

=

Stress Cable "B" to

=

Stress Cable "C" to

=

Stress Cable "D" to

=

O.K.!

O.K.! O.K.!

0.2 /rad 0 /m 10 mm 12.9 mm 186.0 kN 100 mm2 195.0 kN/mm2

draw-in =

Stress Cable "A" to

O.K.!

20.868 kN/m

µ =

STAGE 2 :

(6)

m

2 Stages 50 N/mm2 30 N/mm2 50 N/mm2 34.0 kN/mm2 28.0 kN/mm2 34.0 kN/mm2

@ Stage 2 Stressing Modulus Of Elasticity of Concrete :

39.600 0.300 39.000 39.600

Number of Stage = f cu =

@ 28 Days @ Stage 1 Stressing

(iii)

Date : 16-Jan-2011 Date : 16-Jan-2011

50 50 50 50

% of PUTS

O.K.!

% of PUTS

O.K.!

% of PUTS

O.K.!

% of PUTS

O.K.!

73 73 73 73

% of PUTS

O.K.!

% of PUTS

O.K.!

% of PUTS

O.K.!

% of PUTS

O.K.!

Jacking Force , P j (kN) = n(%of PUTS)

Jacking Force Nos. Of Strands

A 19

B 19

C 19

D 19

Total 76

p j1

Stage 1

1767.0

1767.0

1767.0

1767.0

7068.0

p j2

Stage 2

2579.8

2579.8

2579.8

2579.8

10319.3

Cable Mark

KKHONG (OCT 1998)

7 of 21


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (7) (i)

In-Situ Slab/Flange Properties Embedment of The Insitu Slab

=

Job No. :

0 mm

37478


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (7) (i)

In-Situ Slab/Flange Properties Embedment of The Insitu Slab

(ii)

Thickness of The In-situ Slab

(iii)

Width of the Top in-situ Slab

(iv)

Area of in-situ flange/slab

(v)

Concrete Grade

= t = lf = Af = f c =

Job No. :

0 mm 180 mm 1950 mm 351000 mm2 30 N/mm2 28.0 kN/mm2 8.900 kN/m

(vi)

Modulus Elasticity of In-situ

Ein-situ =

(vii)

SelfWeight Of In-Situ Slab

wslab =

(8)

Composite Beam Section Properties

(a)

Total Height of The Composite

Hc =

(b)

Cross Section Area

Ac =

(c)

Centroid from Soffit

yb,c =

2305 mm 1150300 mm2 1419.28 mm

(d)

Second Moment of Area

Icxx =

7.6205E+11 mm4

(e)

Section Moduli :

@ Top of Composite section

Zt,c =

8.6037E+08 mm3

Zt,p =

1.0798E+09 mm3

(f)

Section Moduli :

@ Top of Precast Beam

(g)

Section Moduli :

@ Bottom of Top In-situ Slab

Zb,s =

1.0798E+09 mm3

@ Bottom of Precast Beam

Zb,p =

5.3693E+08 mm3

(h)

Section Moduli :

(9)

Modular Ratio

(10) (i)

Prestress Losses Calculation Data Maximum Relaxation of Strands after 1000 h durations

(ii)

Creep of Concrete per Unit Length

(iii)

Shrinkage per Unit Length

(iv) (v)

No. of weeks of Stage 2 Prestressing after Stage 1 Allowed % of Final Losses at Stage 1 Transfer, Stage 2 Transfer and Stage 2 Service :

(Einsitu/Ecu2)

m =

During Stage 1 Stressing

=

0 per N/mm2 2.00E-04 2 weeks

Occured During Stage 1 but Before Stage 2 Stressing

Friction Losses

Draw-In Wegdes

Elast. Shrt.

-

Steel Relaxation

Shrinkage

Creep

100

100

100

-

0

33

33

At Stage 1 Transfer

% of Total Final Losses During Stage 2 Stressing

Assumed Losses

% 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

100 100

100 100

100 100

-

100 100 100

67 67 100

67 67 100

At Stage 2 Transfer At Stage 2 Service

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

Post-Tensioning Cable Profile

Distance of Section from

End Conditions

(12)

2.5 %

% of Total Final Losses During Stage 1 Stressing

Assumed Losses

(11)

0.824

% = εc =

εs =

37478

Support

Midspan

Cable Mark

Lx (m)

X0 (m)

Beam Ends 0.000 4.875 9.750 14.625 19.500

19.800 19.500 14.625 9.750 4.875 0.000

Nos. Of Strands Near End Ye

24.375 29.250 34.125 39.000

4.875 9.750 14.625 19.500

Beam Ends

19.800

Ym

Ye

Height of Centre-Line of Cables From Soffit of Beam (m) -1 * 1 * -1 * 1 * A B C D 19 19 19 19 Live End Dead End Live End Dead End

Total 76 e'

1875.0 1832.4 1232.0 803.1 545.8 460.0

1525.0 1489.4 986.5 627.3 411.8 340.0

1175.0 1146.3 741.0 451.6 277.9 220.0

825.0 803.2 495.5 275.8 143.9 100.0

1350.0 1317.8 863.8 539.5 344.9 280.0

545.8 803.1 1232.0 1832.4

411.8 627.3 986.5 1489.4

277.9 451.6 741.0 1146.3

143.9 275.8 495.5 803.2

344.9 539.5 863.8 1317.8

1875.0

1525.0

1175.0

825.0

1350.0

Far End Dead End Live End Dead End Live End Note : * = Please Type " -1 " for Dead End of Cable is in the Far End and Type " 1 " for Dead End of Cable is in the Near End. 2 * artanh [4(Drape)/L beam] θsum = θsupport1 θmidspan + θsupport2 = Sum Of Cable Deviation Angle Cable Mark Nos. Of Strands

A 19

B 19

C 19

D 19

Drape = Ye - Ym

(mm)

1415.00

1185.00

955.00

725.00

θsum

(rad)

0.2839

0.2383

0.1923

0.1462

76

Sum of Cable Angular Deviations (in radian), KKHONG (OCT 1998)

8 of 21



Stage 1 Post Tensioning

Job No. :

37478



Job No. :

37478

Stage 1 Post Tensioning Prestress Losses (1)

Immediate Losses

1(a) Friction Loss (i)

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

Force Gradient

A

B

C

D

θsum

0.2839

0.2383

0.1923

0.1462

µθsum + KLcable

0.1875

0.1783

0.1691

0.1599

0.8291

0.8367

0.8444

0.8522

302.1

288.6

275.0

261.1

1126.79

% of p j1

17.1

16.3

15.6

14.8

15.94

% of PUTS

8.5

8.2

7.8

7.4

7.97

1464.9

1478.4

1492.0

1505.9

5941.21

41.5

41.8

42.2

42.6

42.03

7.628

7.288

6.944

6.595

28.454

Cable Mark

e

-(µθ + KLcable )

Total

Total Loss of Prestr. Force due to Friction Losses pfrict.Loss = (1 - e-(µθ+KLcable ))*p j1 As a percentage of p j1 As a percentage of PUTS

pfrict.Loss (kN)

Cable Force @ Dead End after Frict. Losses pd = p j1 - pfrict.Loss pd (kN) As a percentage of PUTS

% of PUTS

Loss of Pres. Force per unit length/Force Gradient dp = (pfrict.Loss/Lcable) dp (kN/m)

(ii)

Cable Force Along Beam Length After Friction Losses Cable M ark

A

B

C

D

Suppport

Midpsan

Incre/decre.

-1 *

1 *

-1 *

1 *

Lx (m)

X0 (m)

dp (kN/m)

Distance of the section from

Total

-7.628 7.288 -6.944 6.595 Near End Live End Dead End Live End Dead End Beam Ends 19.800 1767.0 1478.4 1767.0 1505.9 6518.2 SUPPORT 1 0.000 19.500 1764.7 1480.6 1764.9 1507.8 6518.0 4.875 14.625 1727.5 1516.1 1731.1 1540.0 6514.7 9.750 9.750 1690.3 1551.6 1697.2 1572.1 6511.3 14.625 4.875 1653.2 1587.2 1663.4 1604.3 6508.0 MIDSPAN 19.500 0.000 1616.0 1622.7 1629.5 1636.4 6504.6 24.375 4.875 1578.8 1658.2 1595.7 1668.6 6501.2 29.250 9.750 1541.6 1693.8 1561.8 1700.7 6497.9 34.125 14.625 1504.4 1729.3 1528.0 1732.9 6494.5 SUPPORT 2 39.000 19.500 1467.2 1764.8 1494.1 1765.0 6491.2 Beam Ends 19.800 1464.9 1767.0 1492.0 1767.0 6491.0 Far End Dead End Live End Dead End Live 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.

KKHONG (OCT 1998)

9 of 21



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

(VSL Prestressing System)

Job No. :

37478



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

Job No. :

37478


Distance affected by Draw-in Wedges from Live End A

B

C

D

Total

22.039

22.547

23.099

23.703

-

336.22

328.65

320.79

312.62

1298.28

% of p j1

19.0

18.6

18.2

17.7

18.37

% of P UTS

9.5

9.3

9.1

8.8

9.18

Cable Mark

Distance affected by Draw-in Wedges from Live End,

w = (draw-in * E s * As * n /d p)1/2

w (m)

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

pdraw-inLoss = 2 * w * d p

pdraw-inLoss (kN)

As a percentage of p j1 As a percentage of P UTS

(ii)

(iii)

Draw-in Wedges Losses Along Beam Length Distance From

pdraw-inLoss (kN)

Suppport

Cable Mark

Total, Pdraw-inLoss

Lx (m)

A

B

C

D

(kN)

(% of P j1)

(% of PUTS)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

331.64 257.27 182.90 108.53 34.16 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 40.04 111.10 182.16 253.22 324.28

316.62 248.92 181.22 113.52 45.82 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 51.48 115.77 180.07 244.37 308.66

648.27 506.19 364.12 222.05 171.49 226.87 362.23 497.58 632.94

9.17 7.16 5.15 3.14 2.43 3.21 5.12 7.04 8.96

4.59 3.58 2.58 1.57 1.21 1.60 2.56 3.52 4.48

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

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

Lx >= w

(Lcable - Lx)>=w,

pdraw-inLoss = 0

pdraw-inLoss = 0

Cable Force Along Beam Length After Friction & Wedges Draw-in Losses Distance From Suppport

Cable Mark

A

B

C

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

1433.1 1470.3 1507.4 1544.6 1581.8 1578.8 1541.6 1504.4 1467.2

1480.6 1516.1 1551.6 1587.2 1582.7 1547.1 1511.6 1476.1 1440.5

1448.3 1482.1 1516.0 1549.8 1583.7 1595.7 1561.8 1528.0 1494.1

1507.8 1540.0 1572.1 1604.3 1585.0 1552.8 1520.7 1488.5 1456.4

Allowable

Total

D

(% of PUTS)

(kN)

(% of PUTS)

Checks

5869.77 6008.49 6147.20 6285.91 6333.11 6274.38 6135.67 5996.95 5858.24

41.52 42.50 43.49 44.47 44.80 44.39 43.40 42.42 41.44

< 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK!

KKHONG (OCT 1998)

10 of 21



Job No. :

1(c) Elastic Shortening Losses (BS 5400 : Part 4 : 199 0 : CL. 6.7.2) Immediately after transfer, the change in strain in the prestressing steel δε caused by elastic shortening of the concrete

37478



Job No. :

37478

1(c) Elastic Shortening Losses (BS 5400 : Part 4 : 199 0 : CL. 6.7.2) Immediately after transfer, the change in strain in the prestressing steel δεp caused by elastic shortening of the concrete is equal to the strain in the concrete at the steel level, εcp. The loss of prestress in the ste el, δf Loss is therefore :

δf Loss

0.5(Es/Ec1)*f tendon for post-tensioned beam

=

(ref. BS5400:Part4:Cl. 6.7.2.3)

N.B. f tendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons. ES is modulus of elasticity of the p restressing tendon Ec1 is modulus of elasticity of the precast concrete at Stage1 (i)

Moment & Concrete Stress Due To Selfweight of Precast Beam Lx

f t

M

f b 2

f tendon

(kNm)

(N/mm )

(N/mm )

(mm)

(N/mm 2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

0.000 3.176 5.445 6.807 7.260 6.807 5.445 3.176 0.000

0.000 -3.835 -6.574 -8.218 -8.766 -8.218 -6.574 -3.835 0.000

1317.8 863.8 539.5 344.9 280.0 344.9 539.5 863.8 1317.8

0.000 -0.985 -3.523 -5.780 -6.654 -5.780 -3.523 -0.985 0.000

H = Total Height of Precast Beam.

f t = M/Zt

e' = Distance from centroid of tendon to soffit.

f b = -M/Zb (ii)

e'

(m)

Moment, M = w(Lx/2)(Leff -L x)

2

f tendon = f b + [(-f b+f t)x(e'/H)]

Concrete Stress Due To Prestressing Force After Friction & Wedges Draw-in Losses Lx

e = yb - e'

Pi

f t

f b 2

f tendon 2

(m)

(mm)

(kN)

(N/mm )

(N/mm )

(N/mm 2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

5869.77 6008.49 6147.20 6285.91 6333.11 6274.38 6135.67 5996.95 5858.24

8.421 3.628 0.063 -2.174 -2.942 -2.170 0.063 3.621 8.405

4.734 10.873 15.529 18.582 19.629 18.548 15.500 10.852 4.725

7.021 7.928 11.603 15.213 16.655 15.185 11.581 7.913 7.007

e' = distance from centroid of tendon to soffit of Precast Beam e = distance from centroid of tendon to neutral axis of Precast Beam Ap = Cross Section Area of Precast Beam Pi = Total Initial Prestress Forces after Friction and Wedge Draw-in Losses f t = Pi/Ap - Pie/Zt (iii)

f b = Pi/Ap + Pie/Zb


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

Stress at Tendon Level (f tendon)

Loss of Prestress = 0.5*ftendon (Es/Ec1)

Selfweight

Prestress

Total (Stage 1)

(N/mm2)

(N/mm2)

(N/mm2)

(N/mm 2)

(kN)

(% of P j1)

(% of PUTS)

0.000 -0.985 -3.523 -5.780 -6.654 -5.780 -3.523 -0.985 0.000

7.021 7.928 11.603 15.213 16.655 15.185 11.581 7.913 7.007

7.021 6.943 8.080 9.434 10.001 9.406 8.058 6.928 7.007

24.447 24.177 28.135 32.850 34.824 32.753 28.059 24.124 24.399

185.795 183.745 213.827 249.661 264.666 248.922 213.251 183.342 185.430

2.629 2.600 3.025 3.532 3.745 3.522 3.017 2.594 2.624

1.31 1.30 1.51 1.77 1.87 1.76 1.51 1.30 1.31

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

KKHONG (OCT 1998)

11 of 21



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

Job No. :

37478



Job No. :

37478

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

% of Immediate Loss from P UTS

Immediate Losses

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Friction Loss

Draw-in Loss

Elastic Loss

Total

Friction Loss

Draw-in Loss

Elastic Loss

Total

(kN)

(kN)

(kN)

(kN)

(% of PUTS)

(% of PUTS)

(% of PUTS)

(% of PUTS)

550.0 553.3 556.7 560.0 563.4 566.8 570.1 573.5 576.8

648.27 506.19 364.12 222.05 171.49 226.87 362.23 497.58 632.94

185.795 183.745 213.827 249.661 264.666 248.922 213.251 183.342 185.430

1384.0 1243.3 1134.6 1031.7 999.6 1042.5 1145.6 1254.4 1395.2

3.89 3.91 3.94 3.96 3.99 4.01 4.03 4.06 4.08

4.59 3.58 2.58 1.57 1.21 1.60 2.56 3.52 4.48

1.31 1.30 1.51 1.77 1.87 1.76 1.51 1.30 1.31

9.79 8.79 8.03 7.30 7.07 7.38 8.10 8.87 9.87

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

Jacking Force

(m)

P j1

Immediate Loss

(kN)

(% of P j1)

(kN)

(% of PUTS)

Checks

7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0

19.58 17.59 16.05 14.60 14.14 14.75 16.21 17.75 19.74

5684.0 5824.7 5933.4 6036.3 6068.4 6025.5 5922.4 5813.6 5672.8

40.21 41.21 41.97 42.70 42.93 42.62 41.90 41.13 40.13

< 70% OK!

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Total

Cable Force After

Allowable

Immediate Loss

(% of PUTS)

< 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK!

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

1(f)

Summary of Concrete Stress After Immediate Losses And Allowable Stress Checks in Concrete at Transfer Allowable Tensile Stress @ Stage 1 Transfer Allowable Compressive Stress @ Stage 1 Transfer Lx

e

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Cable Force After Immediate Loss

= =

-1.00 15.00

(BS 5400 :Part 4 :1990 : CL. 6.3.2.4b) (BS 5400 :Part 4 :1990 : Table 23)

Concrete Stresses

Moment Due to Beam Selfweight

(N/mm2) (N/mm2)

f t

f b 2

2

f tendon

Allowable

(mm)

(kN)

(kNm)

(N/mm )

(N/mm )

(N/mm2)

Checks

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

5684.0 5824.7 5933.4 6036.3 6068.4 6025.5 5922.4 5813.6 5672.8

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

8.155 6.693 5.506 4.719 4.442 4.723 5.506 6.687 8.139

4.584 6.706 8.414 9.626 10.043 9.594 8.387 6.686 4.575

6.798 6.701 7.676 8.830 9.305 8.804 7.656 6.686 6.785

OK! OK! OK! OK! OK! OK! OK! OK! OK!

KKHONG (OCT 1998)

12 of 21


Post-Ten sionin g - Calculatio n of Post-ten si oned Prestress Losses and Differential Shrinkage @ SLS

(2)

Deferred Losses Before Stage 2 Stressing

Job No. :

37478


Post-Ten sionin g - Calculatio n of Post-ten si oned Prestress Losses and Differential Shrinkage @ SLS

(2)

Job No. :

37478

Deferred Losses Before Stage 2 Stressing

2(a) Relaxation of Steel

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

The Loss of force in the tendon allowed for in the design should be the maximum relaxation after 1000 h duration, for a jacking force equal to that imposed at transfer. No reduction in the value of relaxation los s should be made for a tendon when a load equal to or greater that the relevant jacking force has applied for time proir to anchoring of tendon. (i) (ii)

At 1000 hours, Relaxation of Steel of Cable Assumed Percentage Occurred During Stage 1 Transfer

% of Jacking Force % of final

A 19

B 19

C 19

D 19

TOTAL 76

1767.0

1767.0

1767.0

1767.0

7068

prelaxLoss (kN)

0.00

0.00

0.00

0.00

0.00

% of p j1

0.00

0.00

0.00

0.00

0.00

% of PUTS

0.00

0.00

0.00

0.00

0.00

Nos. Of Strands

Jacking Force

Relaxation Loss as percentage of pj1 Relaxation Loss as percentage of P UTS

2(b) Shrinkage of Concrete Losses (i)

2.5 0.0

n (nos) p j1 (kN)

Cable Mark

Total Relaxation Loss in Force

= =

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

From BS 5400:Part 4:1990:Table 29, Shrinkage per unit length Humid exposure Normal exposure (90% r.h) (70% r.h)

System Post-tensioning : transfer at

εs

between 7 days and 14 days after concreting

(ii)

Shrinkage Strain used in the Design,

εs =

200.0E-6

(iii)

Assumed Percentage Occurred, during Stage 1 Transfer.

%=

33

Shrinkage Strain Loss as Stress,

f shrink.Loss =

(iii)

(During Stage 1 Transfer)

(iv)

= =

70 x 10-6

200 x 10-6

per unit length

% of final

εs

x

Es

200.0E-6 12.999

x N/mm2 per strand

195000

x

0.33

C 19

D 19

TOTAL 76

x (% During Stage 1 Transfer)

Shrinkage of Concrete Losses in all Cables (During Stage 1 Transfer), pshrink.Loss A 19

Cable Mark Nos. Of Strands

Total Shrinkage Loss in Force As Loss in percentage of pi1 As Loss in percentage of PUTS

B 19

pshrink.Loss (kN)

24.7

24.7

24.7

24.698

98.790

% of p j1

1.40

1.40

1.40

1.40

1.40

% of PUTS

0.70

0.70

0.70

0.70

0.70

KKHONG (OCT 1998)

13 of 21



2(c) Creep of Concrete Losses

(BS 5400:Part 4:1990: Cl. 6.7.2.5)

Job No. :

37478




Job No. :

37478

(BS 5400:Part 4:1990: Cl. 6.7.2.5)

- The loss of prestress in the tendons due to creep of the concrete should be calculated on the assumption that creep is proportional to stress in the concrete for stress of up to one-third of the cube strength at transfer. - For Post-tensioning System : (i) (ii) (iii)

If the required cube strength at transfer is greater than 40.0 N/mm2, the creep per unit length should be taken as 3.60 x 10-5 per N/mm2. For lower values of the cube strength at transfer (f ci), the creep per unit length should be taken as 3.60 x 10-5 x (40.0/f ci) per N/mm2. Where the maximum stress anywhere in the section at transfer exceeds one-third of the cube strength, the value of the creep should be increased with the factor as below: Increased factor

=

1

+

(Max stress @ Transfer - f ci/3)*0.25 (f ci/2- f ci/3)

(iv)

Calculation of Stress in the concrete adjacent to the tendon after elastic deformation losses - Creep Strain

εc =

4.80E-05

- Assumed Concrete Creep Loss During Stage 1 Transfer - Modulus of Elasticity of Strand - Increased factor - One -third (1/3) of Concrete cube Strength at Stage 1, f ci1

%= Es =

33.33 195.0 1.000 10.00

= f ci1/3 =

(m)

After

After Steel

Immediate Loss Relaxation Loss 2

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

2

(N/mm )

(N/mm )

6.798 6.701 7.676 8.830 9.305 8.804 7.656 6.686 6.785

6.798 6.701 7.676 8.830 9.305 8.804 7.656 6.686 6.785

Maximum

% of final kN/mm2 N/mm2 . Creep Loss

Stress in the concrete adjacent to tendons level, f tendon

Lx

per N/mm2

(During Stage 1 Transfer/ Before Stage 2 Stressing)

Stress (N/mm2)

(N/mm2)

(kN)

(% of P j1)

(% of PUTS)

9.305

21.209 20.904 23.947 27.546 29.028 27.464 23.883 20.858 21.167

161.187 158.871 182.001 209.347 220.614 208.728 181.510 158.522 160.871

2.28 2.25 2.57 2.96 3.12 2.95 2.57 2.24 2.28

1.14 1.12 1.29 1.48 1.56 1.48 1.28 1.12 1.14

Where, (i) Stress in the concrete adjacent to tendons at transfer after Steel Relaxation Losses = Stress at Tendon level after Immediate Losses - The Steel Relaxation Loss at Stage 1 transfer (ii) Creep Loss = Stress at tendon level * Creep Strain (εc) * Es * Increased Factor * % occured @ Stage 1 Transfer

KKHONG (OCT 1998)

14 of 21



Job No. :

37478

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



Job No. :

37478

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

% of Deferred Loss from PUTS

Deferred Losses Relaxation Loss

Shrinkage Loss

Creep Loss

Total

Relaxation Loss

Shrinkage Loss

Creep Loss

Total

(kN)

(kN)

(kN)

(kN)

(% of PUTS)

(% of PUTS)

(% of PUTS)

(% of PUTS)

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

98.79 98.79 98.79 98.79 98.79 98.79 98.79 98.79 98.79

161.187 158.871 182.001 209.347 220.614 208.728 181.510 158.522 160.871

260.0 257.7 280.8 308.1 319.4 307.5 280.3 257.3 259.7

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70 0.70

1.14 1.12 1.29 1.48 1.56 1.48 1.28 1.12 1.14

1.84 1.82 1.99 2.18 2.26 2.18 1.98 1.82 1.84

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

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

Jacking Force

(m)

P j1

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Total

Total

Cable Force After

Total Stage 1

Immediate Loss Deferred Loss

(kN)

(% of P j1)

Losses (% of P j1)

Immediate Loss

(% of P j1)

(kN)

7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0 7068.0

19.58 17.59 16.05 14.60 14.14 14.75 16.21 17.75 19.74

3.68 3.65 3.97 4.36 4.52 4.35 3.97 3.64 3.67

23.26 21.24 20.03 18.96 18.66 19.10 20.17 21.39 23.41

5684.0 5824.7 5933.4 6036.3 6068.4 6025.5 5922.4 5813.6 5672.8

Allowable

Immediate & Deferred Losses

(% of PUTS)

(kN)

(% of PUTS)

Checks

5424.0 5567.1 5652.6 5728.1 5749.0 5717.9 5642.1 5556.3 5413.1

38.37 39.38 39.99 40.52 40.67 40.45 39.91 39.31 38.29


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

2(f)

Summary of Concrete Stress After Immediate & Deferred Losses And Allowable Stress Checks in Concrete at Transfer (Not Required to Check - Can Be Ommited) Allowable Tensile Stress @ Stage 1 Transfer Allowable Compressive Stress @ Stage 1 Transfer Lx

e

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Cable Force After All Loss

-1.00 N/mm2 15.00 N/mm2

= =

(BS 5400 :Part 4 :1990 : Table 23)

Concrete Stresses

Moment Due to Beam Selfweight

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

f t

f b 2

f tendon 2

Allowable 2

(mm)

(kN)

(kNm)

(N/mm )

(N/mm )

(N/mm )

Checks

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

5424.0 5567.1 5652.6 5728.1 5749.0 5717.9 5642.1 5556.3 5413.1

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

7.782 6.538 5.504 4.826 4.590 4.829 5.503 6.531 7.766

4.374 6.239 7.705 8.715 9.053 8.685 7.679 6.220 4.366

6.487 6.361 7.146 8.084 8.465 8.059 7.126 6.346 6.474

OK! OK! OK! OK! OK! OK! OK! OK! OK!

- END OF STAGE 1 CALCULATIONS -

KKHONG (OCT 1998)

15 of 21



Stage 2 Post Tensioning

Job No. :

37478



Job No. :

37478

Stage 2 Post Tensioning Prestress Losses (3)

Immediate Losses

3(a) Friction Loss (i)

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

Force Gradient

A

B

C

D

θsum

0.2839

0.2383

0.1923

0.1462

µθsum + KLcable

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 pfrict.Loss (kN) pfrict.Loss = (1 - e-(µθ+KLcable ))*p j2

441.0

421.4

401.5

381.3

1645.11

As a percentage of p j2

% of p j2

17.1

16.3

15.6

14.8

15.94

% of PUTS

12.5

11.9

11.4

10.8

11.64

2138.8

2158.4

2178.4

2198.6

8674.17

60.5

61.1

61.6

62.2

61.36

11.136

10.641

10.138

9.628

41.543

Cable Mark

e

-(µθ + KLcable )

As a percentage of PUTS

Cable Force @ Dead End after Frict. Losses pd = p j2 - pfrict.Loss pd (kN) As a percentage of PUTS

% of PUTS

Loss of Pres. Force per unit length/Force Gradient dp = (pfrict.Loss/Lcable) dp (kN/m)

(ii)

Total

Cable Force Along Beam Length After Friction Losses Cable M ark

A

B

C

D

Suppport

Midpsan

Incre/decre.

-1 *

1 *

-1 *

1 *

Lx (m)

X0 (m)

dp (kN/m)

Distance of the Section from

-11.136 10.641 -10.138 9.628 Live End Dead End Live End Dead End 2579.8 2158.4 2579.8 2198.6 SUPPORT 1 2576.5 2161.6 2576.8 2201.4 2522.2 2213.5 2527.4 2248.4 2467.9 2265.4 2477.9 2295.3 2413.6 2317.3 2428.5 2342.2 MIDSPAN 2359.3 2369.1 2379.1 2389.2 2305.0 2421.0 2329.7 2436.1 2250.7 2472.9 2280.2 2483.1 2196.4 2524.8 2230.8 2530.0 SUPPORT 2 2142.2 2576.6 2181.4 2576.9 2138.8 2579.8 2178.4 2579.8 Far End Dead End Live End Dead End Live End End of Cable is in the Far End and " 1 " for Dead End of Cable is in the Near End.

Total

Near End

Beam Ends 0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000 Beam Ends Note :

19.800 19.500 14.625 9.750 4.875 0.000 4.875 9.750 14.625 19.500 19.800

* = " -1 " for Dead

9516.6 9516.3 9511.4 9506.5 9501.6 9496.7 9491.8 9486.9 9482.0 9477.1 9476.8

KKHONG (OCT 1998)

16 of 21



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


Job No. :

37478



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

Job No. :

37478


Distance affected by Draw-in Wedges from Live End A

B

C

D

Total

18.240

18.660

19.117

19.617

-

Cable Mark

Distance affected by Draw-in Wedges from Live End,

w = (draw-in * E s * As * n /d p)1/2

w (m)

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

pdraw-inLoss = 2 * w * d p

pdraw-inLoss (kN)

406.25

397.11

387.61

377.74

1568.72

% of p j2

15.7

15.4

15.0

14.6

15.20

% of P UTS

11.5

11.2

11.0

10.7

11.10

As a percentage of p j2 As a percentage of P UTS

(ii)

(iii)

Draw-in Wedges Losses Along Beam Length Distance From

pdraw-inLoss (kN)

Suppport

Cable Mark

Total, Pdraw-inLoss

Lx (m)

A

B

C

D

(kN)

(% of P j2)

(% of PUTS)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

399.57 290.99 182.41 73.83 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 79.48 183.23 286.98 390.73

381.53 282.69 183.84 85.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 90.34 184.22 278.09 371.96

781.10 573.68 366.25 158.83 0.00 169.83 367.45 565.07 762.69

7.57 5.56 3.55 1.54 0.00 1.65 3.56 5.48 7.39

5.53 4.06 2.59 1.12 0.00 1.20 2.60 4.00 5.40

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

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

Lx >= w

(Lcable - Lx)>= w,

pdraw-inLoss = 0

pdraw-inLoss = 0

Cable Force Along Beam Length After Friction & Wedges Draw-in Losses Distance From Suppport

Cable Mark

A

B

C

D

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

2176.9 2231.2 2285.5 2339.8 2359.3 2305.0 2250.7 2196.4 2142.2

2161.6 2213.5 2265.4 2317.3 2369.1 2341.5 2289.6 2237.8 2185.9

2195.2 2244.7 2294.1 2343.5 2379.1 2329.7 2280.2 2230.8 2181.4

2201.4 2248.4 2295.3 2342.2 2389.2 2345.8 2298.8 2251.9 2205.0

Allowable

Total

(% of PUTS)

(kN)

(% of P UTS)

Checks

8735.23 8937.76 9140.28 9342.80 9496.73 9322.00 9119.48 8916.95 8714.43

61.79 63.23 64.66 66.09 67.18 65.95 64.51 63.08 61.65


KKHONG (OCT 1998)

17 of 21



Job No. :

3(c) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2) Immediately after transfer, the change in strain in the prestressing steel δε caused by elastic shortening of the concrete

37478



Job No. :

37478

3(c) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2) Immediately after transfer, the change in strain in the prestressing steel δεp caused by elastic shortening of the concrete is equal to the strain in the concrete at the steel level, εcp. The loss of prestress in the steel, δf Loss is therefore :

δf Loss

0.5(Es/Ec2)*f tendon for post-tensioned beam

=

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

N.B. f tendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons. ES is modulus of elasticity of the prestressing tendon Ec2 is modulus of elasticity of the precast concrete at Stage 2 Service (i)

Moment & Concrete Stress Due To Selfweight of Precast Beam Lx

f t

M

f b 2

f tendon

(kNm)

(N/mm )

(N/mm )

(mm)

(N/mm 2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

0.000 3.176 5.445 6.807 7.260 6.807 5.445 3.176 0.000

0.000 -3.835 -6.574 -8.218 -8.766 -8.218 -6.574 -3.835 0.000

1317.8 863.8 539.5 344.9 280.0 344.9 539.5 863.8 1317.8

0.000 -0.985 -3.523 -5.780 -6.654 -5.780 -3.523 -0.985 0.000

H = Total Height of Precast Beam.

f t = M/Zt

e' = Distance from centroid of tendon to soffit.

f b = -M/Zb (ii)

e'

(m)

Moment, M = w(Lx/2)(Leff -L x)

2


Concrete Stress Due To Prestressing Force After Friction & Wedges Draw-in Losses Lx

e = yb - e'

Pi

f t

f b 2

f tendon 2

(m)

(mm)

(kN)

(N/mm )

(N/mm )

(N/mm 2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

8735.23 8937.76 9140.28 9342.80 9496.73 9322.00 9119.48 8916.95 8714.43

12.532 5.397 0.094 -3.231 -4.411 -3.223 0.094 5.384 12.502

7.045 16.174 23.090 27.618 29.434 27.557 23.037 16.136 7.028

10.448 11.793 17.252 22.612 24.975 22.561 17.213 11.766 10.423

e' = distance from centroid of tendon to soffit e = distance from centroid of tendon to neutral axis of Precast Ap = Cross Section Area of Precast Beam Pi = Total Initial Prestress Forces after Friction and Wedge Draw-in Losses f t = Pi/Ap - Pie/Zt (iii)

f b = Pi/Ap + Pie/Zb


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

Stress at Tendon Level (f tendon)

Loss of Prestress = 0.5*ftendon (Es/Ec2)

Net Stress at tendon

Selfweight

Prestress

Total (Stage 2)

(Stage 2 - Stage 1)

(N/mm2)

(N/mm2)

(N/mm2)

(N/mm2)

(N/mm 2)

(kN)

(% of P j2)

(% of PUTS)

0.000 -0.985 -3.523 -5.780 -6.654 -5.780 -3.523 -0.985 0.000

10.448 11.793 17.252 22.612 24.975 22.561 17.213 11.766 10.423

10.448 10.808 13.729 16.832 18.321 16.782 13.690 10.781 10.423

3.427 3.865 5.649 7.398 8.320 7.376 5.632 3.853 3.416

9.828 11.084 16.201 21.216 23.858 21.152 16.150 11.049 9.796

74.694 84.237 123.124 161.242 181.321 160.753 122.743 83.971 74.453

0.724 0.816 1.193 1.563 1.757 1.558 1.189 0.814 0.721

0.53 0.60 0.87 1.14 1.28 1.14 0.87 0.59 0.53

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

KKHONG (OCT 1998)

18 of 21



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

Job No. :

37478



Job No. :

37478

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

% of Immediate Loss from P UTS

Immediate Losses

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Friction Loss

Draw-in Loss

Elastic Loss

Total

Friction Loss

Draw-in Loss

Elastic Loss

Total

(kN)

(kN)

(kN)

(kN)

(% of PUTS)

(% of PUTS)

(% of PUTS)

(% of PUTS)

802.9 807.8 812.7 817.7 822.6 827.5 832.4 837.3 842.2

781.10 573.68 366.25 158.83 0.00 169.83 367.45 565.07 762.69

74.694 84.237 123.124 161.242 181.321 160.753 122.743 83.971 74.453

1658.7 1465.8 1302.1 1137.7 1003.9 1158.0 1322.5 1486.3 1679.3

5.68 5.71 5.75 5.78 5.82 5.85 5.89 5.92 5.96

5.53 4.06 2.59 1.12 0.00 1.20 2.60 4.00 5.40

0.53 0.60 0.87 1.14 1.28 1.14 0.87 0.59 0.53

11.73 10.37 9.21 8.05 7.10 8.19 9.36 10.51 11.88

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

Jacking Force

(m)

P j2

Immediate Loss

(kN)

(% of P j2)

(kN)

(% of PUTS)

Checks

10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3

16.07 14.20 12.62 11.03 9.73 11.22 12.82 14.40 16.27

8660.5 8853.5 9017.2 9181.6 9315.4 9161.2 8996.7 8833.0 8640.0

61.27 62.63 63.79 64.95 65.90 64.81 63.64 62.49 61.12

< 70% OK!

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Total

Cable Force After

Allowable

Immediate Loss

(% of P UTS)

< 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK! < 70% OK!


3(f)

Summary of Concrete Stress After Immediate Losses And Allowable Stress Checks in Concrete at Transfer Allowable Tensile Stress @ Stage 2 Transfer Allowable Compressive Stress @ Stage 2 Transfer Lx

e

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

= =

Cable Force After

Moment Due to

Immediate Loss

Beam Selfweight

-1.00 20.00

(N/mm2) (N/mm2)


Concrete Stresses f t

f b 2

2

f tendon

Allowable

(mm)

(kN)

(kNm)

(N/mm )

(N/mm )

(N/mm2)

Checks

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

8660.5 8853.5 9017.2 9181.6 9315.4 9161.2 8996.7 8833.0 8640.0

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

12.425 8.522 5.538 3.632 2.934 3.639 5.538 8.510 12.396

6.985 12.187 16.205 18.924 20.107 18.864 16.153 12.149 6.968

10.359 10.697 13.497 16.442 17.844 16.393 13.458 10.670 10.334

OK! OK! OK! OK! NOT OK! OK! OK! OK! OK!

KKHONG (OCT 1998)

19 of 21


Post-Tension ing - Calculation of Post-tensio ned Prestress Losses and Differen tial Shrinkage @ SLS

(4)

Deferred Losses During Stage 2 Stressing

Jo b No. :

37478


Post-Tension ing - Calculation of Post-tensio ned Prestress Losses and Differen tial Shrinkage @ SLS

(4)

Jo b No. :

37478

Deferred Losses During Stage 2 Stressing

4(a) Relaxation of Steel

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

The Loss of force in the tendon allowed for in the design should be the maximum relaxation after 1000 h duration, for a jacking force equal to that imposed at transfer. No reduction in the value of relaxation loss should be made for a tendon when a load equal to or greater that the relevant jacking force has applied for time proir to anchoring of tendon. (i)

At 1000 hours, Relaxation of Steel of Cable

B 19

C 19

D 19

TOTAL 76

2579.8

2579.8

2579.8

2579.8

10319.28

prelaxLoss (kN)

64.50

64.50

64.50

64.50

257.98

% of p j2

2.50

2.50

2.50

2.50

2.50

% of PUTS

1.83

1.83

1.83

1.83

1.83

Jacking Force

Relaxation Loss as percentage of pj2 Relaxation Loss as percentage of P UTS

4(b) Shrinkage of Concrete Losses

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

From BS 5400:Part 4:1990:Table 29, Shrinkage per unit length Humid exposure Normal exposure (90% r.h) (70% r.h)

System Post-tensioning : transfer at between 7 days and 14 days after concreting

εs

(ii)

Shrinkage Strain used in the Design,

εs =

(iii)

Shrinkage Strain Loss as Stress, (Final Loss)

f shrink.Loss =

(iv)

% of Jacking Force

A 19

Nos. Of Strands

(i)

2.5

n (nos) p j2 (kN)

Cable Mark

Total Final Relaxatio n Loss in Force

=

= =

70 x 10-6

200 x 10-6

200.0E-6

εs 200.0E-6 39.000

Es

x x N/mm2 per strand

195000

B 19

C 19

D 19

TOTAL 76

Shrinkage of Concrete Final Losses in all Cables, pshrink.Loss A 19

Cable Mark Nos. Of Strands

Total Shrinkage Loss in Force As Loss in percentage of pi2 As Loss in percentage of PUTS

pshrink.Loss (kN)

74.1

74.1

74.1

74.100

296.400

% of p j2

2.87

2.87

2.87

2.87

2.87

% of PUTS

2.10

2.10

2.10

2.10

2.10

KKHONG (OCT 1998)

20 of 21




(BS 5400:Part 4:1990: Cl. 6.7.2.5)

Job No. :

37478




Job No. :

37478

(BS 5400:Part 4:1990: Cl. 6.7.2.5)

- The loss of prestress in the tendons due to creep of the concrete should be calculated on the assumption that creep is proportional to stress in the concrete for stress of up to one-third of the cube strength at transfer. - For Post-tensioning System : (i) (ii) (iii)

If the required cube strength at transfer is greater than 40.0 N/mm 2, the creep per unit length should be taken as 3.60 x 10 -5 per N/mm2. For lower values of the cube strength at transfer (f ci), the creep per unit length should be taken as 3.60 x 10 -5 x (40.0/f ci) per N/mm 2. Where the maximum stress anywhere in the section at transfer exceeds one-third of the cube strength, the value of the creep should be increased with the factor as below: Increased factor

=

1

+

(Max stress @ Transfer - f ci/3)*0.25 (f ci/2- f ci/3)

(iv)

Calculation of Stress in the concrete adjacent to the tendon after elastic deformation losses - Creep Strain

εc =

3.60E-05

- Modulus of Elasticity of Strand - Increased factor

Es =

195 1.022

- One -third (1/3) of Concrete cube Strength at Stage 2 - Assumed Steel Relaxation Loss During Stage 2 Transfer

= f ci2/3 =

From Stage 1 Stressing Lx

After

After Steel

Immediate Loss

(N/mm2) 6.798 6.701 7.676 8.830 9.305 8.804 7.656 6.686 6.785

6.798 6.701 7.676 8.830 9.305 8.804 7.656 6.686 6.785

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

N/mm2 . % of final

From Stage 2 Stressing


(m)

kN/mm2

16.67 100.00

%=

per N/mm2

For Creep Loss Calculation


Maximum

After

After Steel

Relaxation Loss

Stress

Immediate Loss

(N/mm2)

(N/mm2)

(N/mm2)

9.305

10.359 10.697 13.497 16.442 17.844 16.393 13.458 10.670 10.334

10.100 10.430 13.159 16.031 17.398 15.983 13.122 10.403 10.076

During Stage 2

Maximum

After Steel Relaxation Loss

Relaxation Loss

Stress

ftendon(Stage2)-ftendon(Stage1)

(N/mm2)

(N/mm2)

(N/mm2)

17.398

3.301 3.729 5.483 7.201 8.093 7.180 5.466 3.717 3.291

For Creep Loss Calculation

Creep Loss During Stage 2

Lx

During Stage 2

(Final Loss)

(m)

After Steel Relaxation Loss

Remaining Creep Loss fromStage1

ftendon(Stage2)-ftendon(Stage1)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

(N/mm2)

(N/mm2)

(kN)

(% of P j2)

(% of PUTS)

(kN)

3.301 3.729 5.483 7.201 8.093 7.180 5.466 3.717 3.291

23.683 26.752 39.336 51.662 58.057 51.506 39.215 26.667 23.606

179.987 203.312 298.955 392.631 441.235 391.442 298.033 202.673 179.408

1.74 1.97 2.90 3.80 4.28 3.79 2.89 1.96 1.74

1.27 1.44 2.11 2.78 3.12 2.77 2.11 1.43 1.27

322.423 317.789 364.056 418.757 441.295 417.518 363.075 317.092 321.789

Where, (Only for 2 stages Stressing) (i) Stress in the concrete adjacent to tendons at transfer after Steel Relaxation Loss = Stress at Tendon level after Immediate Losses - the Steel Relaxation Losses at Stage 2 Transfer (ii) Total Creep Loss At Stage 2 ( due to additional prestressing in Stage 2 compared to Stage 1) = (Stress at tendon level during Stage 2 - Stress at tendon level During Stage 1) * Creep Strain ( εc) * Es * Increased Factor

KKHONG (OCT 1998)

21 of 21



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

Job No. :

37478



Job No. :

37478

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 (ii) Shrinkage (iii) Creep (S1) (iv) Creep (S2) Lx (m)

= = = =

100.00 66.67 66.67 100.00

% of final % of final % of Stage 1 final Creep Loss % of Stage 2 final Creep Loss % of Deferred Loss from P UTS

Deferred Losses During Stage 2 Transfer Relaxation Loss

Shrinkage Loss

Creep Loss

Total

Relaxation Loss

Shrinkage Loss

Creep Loss

Total

(kN)

(kN)

(kN)

(kN)

(% of PUTS)

(% of PUTS)

(% of PUTS)

(% of PUTS)

258.0 258.0 258.0 258.0 258.0 258.0 258.0 258.0 258.0

197.61 197.61 197.61 197.61 197.61 197.61 197.61 197.61 197.61

502.410 521.101 663.010 811.389 882.530 808.961 661.108 519.765 501.198

958.0 976.7 1118.6 1267.0 1338.1 1264.6 1116.7 975.4 956.8

1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83

1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40

3.55 3.69 4.69 5.74 6.24 5.72 4.68 3.68 3.55

6.78 6.91 7.91 8.96 9.47 8.95 7.90 6.90 6.77

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

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

Jacking Force

Total

Total

Total Stage 2

(m)

P j2

Immediate Loss

Deferred Loss

Transfer Losses

Immediate Loss

(kN)

(% of P j2)

(% of P j2)

(% of P j2)

(kN)

(kN)

(% of PUTS)

Checks

10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3

16.07 14.20 12.62 11.03 9.73 11.22 12.82 14.40 16.27

9.28 9.46 10.84 12.28 12.97 12.25 10.82 9.45 9.27

25.36 23.67 23.46 23.30 22.70 23.48 23.64 23.85 25.55

8660.5 8853.5 9017.2 9181.6 9315.4 9161.2 8996.7 8833.0 8640.0

7702.5 7876.8 7898.6 7914.6 7977.3 7896.7 7880.0 7857.6 7683.2

54.49 55.72 55.88 55.99 56.43 55.86 55.74 55.59 54.35

<70%, OK!

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Cable Force After

Allowable


(% of PUTS)

<70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK!

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

4(f)

Summary of Concrete Stress After Immediate & Deferred Losses And Allowable Stress Checks in Concrete During Stage 2 Transfer Allowable Tensile Stress @ Stage 2 Transfer Allowable Compressive Stress @ Stage 2 Transfer Lx

e


Concrete Stresses

Moment Due to

All Loss

Beam Selfweight

f t

f b

f tendon

Allowable

(mm)

(kN)

(kNm)

(N/mm2)

(N/mm2)

(N/mm2)

Checks

-155.5 298.5 622.8 817.4 882.3 817.4 622.8 298.5 -155.5

7702.5 7876.8 7898.6 7914.6 7977.3 7896.7 7880.0 7857.6 7683.2

0.00 1735.79 2975.65 3719.56 3967.53 3719.56 2975.65 1735.79 0.00

11.051 7.932 5.527 4.070 3.555 4.076 5.527 7.921 11.023

6.212 10.419 13.379 15.178 15.959 15.126 13.332 10.384 6.196

9.213 9.408 11.385 13.376 14.325 13.332 11.351 9.383 9.190

OK!

(m)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Cable Force After

-1.00 N/mm2 20.00 N/mm2

= =

OK! OK! OK! OK! OK! OK! OK! OK!

KKHONG (OCT 1998)

22 of 21



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

Job No. :

37478



Job No. :

37478

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 (ii) Shrinkage (iii) Creep (S1) (iv) Creep (S2) Lx (m)

= = = =

100.00 66.67 66.67 100.00

% of final % of final % of Stage 1 Creep Loss (Remaining from Stage 1 Stres % of Stage 2 final Creep Loss % of Deferred Loss from P UTS

Deferred Losses During Stage 2 Service Relaxation Loss

Shrinkage Loss

Creep Loss

Total

Relaxation Loss

Shrinkage Loss

Creep Loss

Total

(kN)

(kN)

(kN)

(kN)

(% of PUTS)

(% of PUTS)

(% of PUTS)

(% of PUTS)

258.0 258.0 258.0 258.0 258.0 258.0 258.0 258.0 258.0

197.61 197.61 197.61 197.61 197.61 197.61 197.61 197.61 197.61

502.410 521.101 663.010 811.389 882.530 808.961 661.108 519.765 501.198

958.0 976.7 1118.6 1267.0 1338.1 1264.6 1116.7 975.4 956.8

1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83 1.83

1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40

3.55 3.69 4.69 5.74 6.24 5.72 4.68 3.68 3.55

6.78 6.91 7.91 8.96 9.47 8.95 7.90 6.90 6.77

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

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

Jacking Force

Total

Total

Total Stage 2

(m)

P j2

Immediate Loss

Deferred Loss

Service Losses

Immediate Loss

(kN)

(% of P j2)

(% of P j2)

(% of P j2)

(kN)

(kN)

(% of PUTS)

Checks

10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3 10319.3

16.07 14.20 12.62 11.03 9.73 11.22 12.82 14.40 16.27

9.28 9.46 10.84 12.28 12.97 12.25 10.82 9.45 9.27

25.36 23.67 23.46 23.30 22.70 23.48 23.64 23.85 25.55

8660.5 8853.5 9017.2 9181.6 9315.4 9161.2 8996.7 8833.0 8640.0

7702.5 7876.8 7898.6 7914.6 7977.3 7896.7 7880.0 7857.6 7683.2

54.49 55.72 55.88 55.99 56.43 55.86 55.74 55.59 54.35

<70%, OK!

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

Cable Force After

Allowable


(% of PUTS)

<70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK! <70%, OK!


- END OF STAGE 2 LOSSES CALCULATIONS -

KKHONG (OCT 1998)

23 of 21



Job No. :

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

AN INVESTIGATIONOF THE BEHAVIOUR OF

37478



Job No. :

37478

DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM AND IN-SITU SLAB (IN ACCORDANCE WITH RESEARCH REPORT NO. 15 : NOVEMBER 1963 THE COMPOSITE CONCRETE BEAMS FROM C&CA ) (BS 5400:Part4:1990 Cl.7.4.3.4)

AN INVESTIGATIONOF THE BEHAVIOUR OF

Before the two concretes could be jointed together, external forces and moments would have to be applied to the beam to straighten it. Firstly the moment is to be applied: Mb = Φ2EcIpxx

Ec = Young's modulus of the precast beam concrete

where ,

Ipxx = Second moment of area of the precast beam

Φ2 = Rotation of the beam = 1/H (s bb - sbt) sbb = free total strain movement of the bottom fibres sbt = free total strain movement of the top fibres H = Total depth of precast beam A pair of tensile forces is now applied to the ends of the slab at its centroid; these forces (F) are of such magnitude that the elongation of the slabs equals the differential shrinkage, i.e. F = δEin-situA1

δ = Differential shrinkage coefficient

where,

Ein-situ= Modulus of elasticity of the in-situ concrete A1= Area of the in-situ flange/slab Assume deck slab is cast one month after precast beams, so then 50 % of the shrinkage has taken place. Hence, δ = 0.5 * Differential shrinkage coefficient The two concrete can now be jointed together and equal and opposite forces and moments applied to cancel F and M b. Since the two concrete are now acting as a composite section, the compressive cancelling forces -F will be accompained by a moment, Mc =

Fe1

e1 = Diatance between the centroid of insitu flange

where,

to centroid of composite section The net value of the cancelling moment is therefore, Mc' =

Mc - Mb

= Fe1 - Mb

The resulting stresses in the cross-section due to these external and cancelling forces can now be dertermined, these are, f 1 = ( F/A1' - F/Ac - Mc' y1/Icxx)(Einsitu/Ec) * (k)

(Top of Insitu Slab)

f 2 = ( F/A1' - F/Ac - Mc' y2/Icxx)(Einsitu/Ec) * (k)

(Bottom of Insitu Slab)

f 3 = ( -F/Ac - Mc' y2/Icxx -Mb yt/Ipxx) * (k)

(Top of Precast Beam)

f 4 = ( -F/Ac + Mc' y4/Icxx + Mb yb/Ipxx) * (k)

(Bottom of Precast Beam)

(see Figure 1)

original length at time of casting insitu flange

sf f 1

centroid of flange

t

e1

F

-F

y1 y2 yt

f 3 f 2

centroid of sbt

composite

Mc' = Fe-Mb

section

centroid of precast beam yb

Mb

y4

sbb

f 4

where, A1 = area of in situ concrete

y2 = distance from centroid of the composite beam to top fibre of precast beam

A2 = area of precast concrete section

y4 = distance from centroid of the composite beam to soffit fo precast beam

Ac = area of composite concrete section

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

A1' = transformed area of in situ concrete = (Modular ratio) * A1 yt = d is tan ce f rom c ent ro id o f t he p rec as t be am t o t op o f p rec as t b ea m

k = creep reduction coefficient Ein-situ= M odu lu s of ela st ic it y o f t he in -s it u co nc re te

yb = d is tan ce f rom c ent ro id o f t he p rec as t be am t o s of fit of pr ec as t be a

Ec = Y ou ng' s mod ulu s of th e p re ca st b ea m c on cr et e

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

FIGURE 1 - Theoretical Approach to Differential Shrinkage

KKHONG (OCT 1998)

24 of 21



Job No. :

CALCULATION OF THE DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM

37478



Job No. :

37478

CALCULATION OF THE DIFFERENTIAL SHRINKAGE BETWEEN PRECAST BEAM AND IN-SITU SLAB (1)

Design Parameter :

(a)

Modular Ratio

(b)

Area of Insitu Slab

A1 =

(c)

Transformed Area of Insitu Slab

A1' =

(d)

Area of Precast Section

A2 =

(e)

Area of Composite Section

Ac =

0.824 351000 mm2 289059 mm2 869500 mm2 1158559 mm2

(f)

Moment of Inertia of Precast

Ipxx =

5.2608E+11 mm4

(g)

Moment of Inertia of Composite

Icxx =

7.6205E+11 mm4

(h)

Total Depth of Precast Beam

H=

(I)

Thickness of Insitu Slab

(j)

Centroid of Precast to Top fibre

yt =

Centroid of Precast to Bottom fibre

yb =

(k)

(Einsitu /Ecu)

m=

2125 mm 180 mm 963 mm 1162 mm

t=

Centroid of Composite Beam to : (l)

Top of Insitu Slab

y1 =

(m)

Top of Precast Beam

y2 =

(n)

Bottom of Precast Beam

y4 =

(o)

Centroid of Top Slab

e1 =

(p) (q)

Differential Shrinkage Coefficient Creep Reduction Coefficient

δ = k=

(r)

Modulus of Elasticity of the precast

(s)

Modulus of Elasticity of the precast

885.72 mm 705.72 mm 1419.28 mm 795.72 mm 1.00E-04

@transfer Eci2 = @service

50.0 % has occured during slab Const...)"

0.43 (BS 5400 : Part 4 : 1990: Cl.7.4.3.4) 34 kN/mm2 34 kN/mm2 28 kN/mm2

Ecu =

Ein-situ =

(t)

Modulus of Elasticity of the Insitu

(2)

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

(a)

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

Selfwt. Moment

σt

Lx

@ Stage 2 Transfer

M

(N/mm2)

(m)

Pfinal (kN)

(kNm)

DL

Pfinal / A

Pfinal (e)/Zt

Total

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

7702.54 7876.83 7898.55 7914.58 7977.28 7896.69 7880.03 7857.63 7683.19

0.000 1735.794 2975.646 3719.558 3967.529 3719.558 2975.646 1735.794 0.000

0.000 3.176 5.445 6.807 7.260 6.807 5.445 3.176 0.000

8.859 9.059 9.084 9.102 9.175 9.082 9.063 9.037 8.836

2.646 2.242 -4.315 -9.021 -11.933 -12.750 -11.787 -8.956 -4.197

11.504 14.477 10.214 6.888 4.502 3.139 2.721 3.257 4.639

Prestress Force

Selfwt. Moment

σb

Lx

@ Stage 2 Transfer

M

(N/mm2)

(m)

Pfinal (kN)

(kNm)

DL

Pfinal / A

Pfinal (e)/Zb

Total

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

7702.54 7876.83 7898.55 7914.58 7977.28 7896.69 7880.03 7857.63 7683.19

0.000 1735.794 2975.646 3719.558 3967.529 3719.558 2975.646 1735.794 0.000

0.000 -3.176 -5.445 -6.807 -7.260 -6.807 -5.445 -3.176 0.000

8.859 9.059 9.084 9.102 9.175 9.082 9.063 9.037 8.836

-2.646 -2.242 4.315 9.021 11.933 12.750 11.787 8.956 4.197

6.213 3.641 7.954 11.317 13.847 15.025 15.405 14.816 13.034

KKHONG (OCT 1998)

25 of 21


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (b)

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

Job No. :

37478


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (b)

Job No. :

37478

Now calculate the (sbb - sbt), Mb, Mc, Mc' as following : Assuming % of the Creep has occured in the precast beam (short term losses) when the in-situ slab is cast = 50.00 % of

εc = creep strain increased creep factor = δEin-situA1 = F=

Then, and

1.80E-05 1.022

per N/mm2

9.83E+02

kN

3.60E-05

per N/mm2

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

Φ2 = Rotation of the beam = 1/H (sbb - sbt) Mb = Φ2Eci2Ipxx Mc = Fe1 Mc' = Mc - Mb

Lx

(sbb - sbt)

Φ2

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

-9.73E-05 -1.99E-04 -4.16E-05 8.15E-05 1.72E-04 2.19E-04 2.33E-04 2.13E-04 1.54E-04

-4.58E-08 -9.38E-08 -1.96E-08 3.83E-08 8.09E-08 1.03E-07 1.10E-07 1.00E-07 7.27E-08

Mb

Mc

Mc'

(Nmm)

(Nmm)

(Nmm)

-8.193E+08 -1.678E+09 -3.501E+08 6.857E+08 1.447E+09 1.840E+09 1.964E+09 1.790E+09 1.300E+09

7.82E+08 7.82E+08 7.82E+08 7.82E+08 7.82E+08 7.82E+08 7.82E+08 7.82E+08 7.82E+08

1.60E+09 2.46E+09 1.13E+09 9.64E+07 -6.65E+08 -1.06E+09 -1.18E+09 -1.01E+09 -5.18E+08

(c)

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

(i)

Determination of stresses at Top of Insitu Slab , f 1

Lx

F/A1'

F/Ac

Mc' y1/Icxx

(m) * (k)

(N/mm 2)

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

(ii)

f 1

3.400 3.400 3.400 3.400 3.400 3.400 3.400 3.400 3.400

0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848

1.861 2.859 1.316 0.112 -0.773 -1.230 -1.374 -1.171 -0.602

0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354

0.245 -0.109 0.438 0.864 1.177 1.339 1.390 1.318 1.117

Mc' y2/Icxx

(m) * (k)

f 2

Determination of stresses at Bottom of Insitu Slab , f 2

Lx

F/A1'

F/Ac

(N/mm 2)

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

3.400 3.400 3.400 3.400 3.400 3.400 3.400 3.400 3.400

0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848

1.483 2.278 1.048 0.089 -0.616 -0.980 -1.095 -0.933 -0.479

0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354 0.354

0.378 0.097 0.532 0.872 1.122 1.251 1.291 1.234 1.073

KKHONG (OCT 1998)

26 of 21


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (iii)

Determination of stresses at Top of Precast Beam , f 3

Job No. :

37478


Post-Tensioning - Calculation of Post-tensioned Prestress Losses and Differential Shrinkage @ SLS (iii)

Lx

F/Ac

Mc' y2/Icxx

Mb yt/Ipxx

(k)

f 3 (N/mm2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848

1.483 2.278 1.048 0.089 -0.616 -0.980 -1.095 -0.933 -0.479

-1.499 -3.070 -0.641 1.255 2.648 3.368 3.594 3.275 2.378

0.430 0.430 0.430 0.430 0.430 0.430 0.430 0.430 0.430

-0.358 -0.024 -0.540 -0.943 -1.239 -1.391 -1.440 -1.372 -1.181

Mb yb/Ipxx

(k)

f 4

Determination of stresses at Bottom of Precast Beam , f 4

Lx

F/Ac

Mc' y4/Icxx

(m)

(N/mm2)

0.000 4.875 9.750 14.625 19.500 24.375 29.250 34.125 39.000

(3)

37478

Determination of stresses at Top of Precast Beam , f 3

(m)

(iv)

Job No. :

0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848 0.848

2.982 4.581 2.108 0.179 -1.238 -1.971 -2.201 -1.877 -0.964

-1.810 -3.707 -0.773 1.515 3.197 4.066 4.339 3.954 2.872

0.430 0.430 0.430 0.430 0.430 0.430 0.430 0.430 0.430

0.139 0.011 0.209 0.364 0.477 0.536 0.554 0.529 0.455

f 1 =

Stresses @ Top of Insitu Slab

f 2 =

Stresses @ Bottom of Insitu Slab

f 3 =

Stresses @ Top of Precast Beam

f 4 =

Stresses @ Bottom of Precast Beam

Summary Of The Resulting Stresses After Losses and Differential Shrinkage

Lx

f 1

f 2

f 3

f 4

(m)

(N/mm2)

(N/mm2)

(N/mm2)

(N/mm2)

0.000 4.875 9.750

-0.245 0.109 -0.438

-0.378 -0.097 -0.532

0.358 0.024 0.540

-0.139 -0.011 -0.209

14.625 19.500

-0.864 -1.177

-0.872 -1.122

0.943 1.239

24.375 29.250 34.125 39.000

-1.339 -1.390 -1.318 -1.117

-1.251 -1.291 -1.234 -1.073

1.391 1.440 1.372 1.181

Note :

f 1 =

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

f 2 =

( F/A1' - F/Ac - Mc' y2/Icxx)(Einsitu/Ec) * (k)

-0.364 -0.477

f 3 =

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

-0.536 -0.554 -0.529 -0.455

f 4 =

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

In the above table the sign convention has been amended to give tension as -ve for consistance with other calculations. End of Calculation Of Differential Shrinkage

KKHONG (OCT 1998)

SEPAKAT SETIA PERUNDING SDN. BHD. (14142-M) Consulting Engineers Prestress Checking at Serviceability Limit State For Post-Tensioned Beam

Prestress Checking at Deflected Sections At Serviceability Limit State For

27 of 21

Job No. :

37478


Job No. :

37478

Prestress Checking at Deflected Sections At Serviceability Limit State For Precast Prestressed Post-Tensioned Beam Design : PROJECT TITLE : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH : W:\SCB Spreadsheet\Post-Tensioned-Design.xls

Project Detail File name


Date : 16-Jan-2011 Date : 16-Jan-2011

KKL LTC

DESIGN DATA Prestressing System Post-tensioned Tensile stress permitted, but no visible cracking

=

=

Precast Beam Section

Post -Tensioned

S40T1 BEAM Precast

; Class Crack =

2 0

membe mm

Beam

(1) SECTION PROPERTIES OF PRECAST BEAM : (i)

H =

TOTAL HEIGHT OF THE PRECAST SECTION

2125 mm 0.869500 m2

HEIGHT OF CENTROID ABOVE BOTTOM FIBRE

A = yb =

SECTION MUDULI : TOP FIBRE OF PRECAST

Zt =

0.54646 m3

BOTTOM FIBRE OF PRECAST SELFWEIGHT OF PRECAST BEAM

Zb =

0.45262 m3 20.868 kN/m

(ii)

AREA OF PRECAST BEAM

(iii) (iv) (v) (vi)

w =

S40T1 BEAM

1162.3 mm

39 m Eff. Span

(2) SECTION MODULI OF COMPOSITE SECTION : Zt,c =

0.86037 m3

TOP FIBRE OF PRECAST SECTION

Zt,p =

1.07982 m3

(iii)

BOTTOM FIBRE OF TOP SLAB

Zb,s =

1.07982 m3

(iv)

BOTTOM FIBRE OF PRECAST SECTION

Zb,p =

0.53693 m3

(i)

TOP FIBRE OF COMPOSITE SECTION

(ii)

winsitu =

(3) DEAD WT OF INSITU CONCRETE

(i)

@ TRANSFER

f ci2 =

50 N/mm2

@ 28 DAYS

f cu =

50 N/mm2

f c =

30 N/mm2

Insitu Concrete :

(ii)

CLASS

2

CRACK WIDTH (mm)

0.00

8.900 kN/m

(4) CONCRETE STRENGTH: Pr esstress Conc rete :

HB45 -SLS2

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

FOR PRESTRESSING CONCRETE ALLOWABLE CONCRETE STRESSES @ TRANSFER : MEMBER

TENSION

COMPRESSION

N/mm2

N/mm2

CLASS 1

-1.000

20.000

CLASS 2

-1.000

20.000

CLASS 3

-1.000

20.000

ALLOWABLE CONCRETE STRESSES @ SERVICE/WORKING: MEMBER

TENSION

CLASS 1 CLASS 2 CLASS 3

N/mm2

0.000

20.000

-2.546

20.000

2 CRACK WIDTH f cu = 40 N/mm

u

= >=50 N/mm2

0.10

-2.87

-3.36

0.15

-3.15

-3.71

0.25

-3.85

-4.41

20.000

ALLOWABLE CONCRETE STRESSES @ TRANSFER FOR PRECAST BEAM:

(a) (i) (ii)

COMPRESSION

N/mm2

TENSILE STRESS WITH SELF WT COMPRESSIVE STRESS

(BS5400:P4:90:CL. 6.3.2.4 b(1 (BS5400:P4:1990:CL.6.3.2.2 b

-1.00 N/mm2 20.00 N/mm2

(b)

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

(i)

TENSILE STRESS

(BS5400:P4:1990:CL.6.3.2.4a)

-2.55 N/mm2

(ii)

COMPRESSIVE STRESS

(BS5400:P4:1990:CL6.3.2.2a)

20.00 N/mm2

(6) ALLOWABLE CONCRETE STRESSES FOR INSITU SLAB: (i) (ii)

(BS5400:P4:1990:CL.7.4.3.3) -3.60 N/mm2 (BS5400:P4:1990:CL.7.4.3.2) 15.00 N/mm2

TENSILE STRESS COMPRESSIVE STRESS

(7) EFFECTIVE SPAN OF PRECAST BEAM (8) MODULAR RATIO

KKHONG (NOV 1998)

(Einsitu/Ecu)

Leff = m =

39.000 m 0.824

28


KKHONG (NOV 1998)

Job No. :

37478

29


Job No. :

37478

STRESS CHECKS AT MID-SPAN AND VARIES SECTIONS ALONG THE BEAM (0) AT MIDSPAN, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

HT. ABOVE

OF STRANDS SOFFIT (mm)

D

19

C

19

220.00

B

19

340.00

A

19

460.00

76.000

280.00

TOTAL :

19.50 m

100.00

N.B.

e = distance between centroid of precast beam to centroid of tendon e = 882.30 mm

INITIAL PRESTRESS LOSSES @ TRANSFER FINAL TOTAL PRESTRESS LOSSES

9.73 % 22.70 %

ULTIMATE TENSILE STRENGTH PER STRAND 73

186.00 kN

% 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 INSITU

BOTT OF INSITU

TOP OF PRECAST

BOTT OF PRECAST

TRANSFER PRESTRESS SELF WT TOTAL @ TRANSFER

-4.33 28.87 7.26 -8.77 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 DIFF. SHRINKAGE TOTAL @ WORKING

HB45 -SLS2

6.82 -1.177 7.64

5.43 -1.122 4.31

(1) AT SUPPORT 1, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

0.00 m

HT. ABOVE

19

803.20

C

19

1146.28

B

19

1489.36

A

19

1832.45

76.000

1317.82

N.B.

e = distance between centroid of precast beam to centroid of tendon e = -155.52 mm


16.07 % 25.36 %

ULTIMATE TENSILE STRENGTH PER STRAND 73 % OF U.T.S. INITIAL PRESTRESS EFFECTIVE FORCE @ TRANSFER PER STRAND EFFECTIVE FINAL FORCE PER STRAND

TRANSFER PRESTRESS SELF WT TOTAL @ TRANSFER FINAL PRESTRESS SELF WT + DEAD INSITU TEMPERATURE DIFFERENCE SUPER. DEAD + LIVE HB45 -SLS2 DIFF. SHRINKAGE TOTAL @ WORKING

KKHONG (NOV 1998)

-13.270 (MIDSPAN) -0.477 -2.53


D

TOTAL :

6.60 1.239 14.49

186.00 135.78 113.95 101.35

TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST 12.43 0.00 12.43

-1 2.13 -0.245 0.88

1.70 -0.378 1.32

11.05 0.00 2.06 0.358 13.47

kN kN kN kN

BOTT OF PRECAST 6.98 0.00 6.98 6.21 0.00 1.00 -4.140 (SUPPORT 1) -0.139 2.93

30


Job No. :

(2) 2nd SECTION, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

4.88 m

HT. ABOVE


D

19

C

19

741.03

B

19

986.52

A

19

1232.00

76.000

863.77

TOTAL :

495.55

N.B.



14.20 % 23.67 %


186.00 135.78 116.49 103.64


TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST 5.35 3.18 8.52

FINAL PRESTRESS SELF WT + DEAD INSITU SUPER. DEAD + LIVE DIFF. SHRINKAGE TOTAL @ WORKING

2.51 0.109 2.62

2.00 -0.097 1.90

4.76 4.53 2.43 0.024 11.74

HB45 -SLS2

(3) 3rd SECTION, DISTANCE FROM SUPPORT 1 Cable Mark

NOS. 19 19

451.57

B

19

627.34

A

19

803.11

76.000

539.46

14.25 -5.47 -4.880 (SECTION 1) -0.011 3.89

9.75 m

275.80

N.B.



12.62 % 23.46 %

ULTIMATE TENSILE STRENGTH PER STRAND 73 % OF U.T.S. INITIAL PRESTRESS EFFECTIVE FORCE @ TRANSFER PER STRAND EFFECTIVE FINAL FORCE PER STRAND TOP OF INSITU -


KKHONG (NOV 1998)

BOTT OF PRECAST 16.02 -3.83 12.19

HT. ABOVE

C


kN kN kN kN


D

TOTAL :

37478

HB45 -SLS2

5.23 -0.438 4.79

186.00 135.78 118.65 103.93

BOTT OF INSITU -

4.16 -0.532 3.63

TOP OF PRECAST 0.09 5.45 5.54 0.08 7.77 5.06 0.540 13.45

kN kN kN kN

BOTT OF PRECAST 22.78 -6.57 16.20 19.95 -9.38 -10.170 (SECTION 2) -0.209 0.20

31


Job No. :

(4) 4th SECTION, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

14.63 m

HT. ABOVE


D

19

C

19

277.89

B

19

411.84

A

19

545.78

76.000

344.86

TOTAL :

143.95

N.B.



11.03 % 23.30 %


186.00 135.78 120.81 104.14


TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST -3.17 6.81 3.63


6.46 -0.864 5.59

5.14 -0.872 4.27

-2.74 9.71 6.25 0.943 14.16

HB45 -SLS2

(5) AT MID-SPAN, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

kN kN kN kN

BOTT OF PRECAST 27.14 -8.22 18.92 23.40 -11.72 -12.560 (SECTION 3) -0.364 -1.25

19.50 m

HT. ABOVE


D

19

C

19

220.00

B

19

340.00

A

19

460.00

76.000

280.00

TOTAL :

37478

100.00

N.B.



9.73 % 22.70 %

ULTIMATE TENSILE STRENGTH PER STRAND 73 % OF U.T.S. INITIAL PRESTRESS EFFECTIVE FORCE @ TRANSFER PER STRAND EFFECTIVE FINAL FORCE PER STRAND TOP OF INSITU

BOTT OF INSITU

186.00 135.78 122.57 104.96 TOP OF PRECAST

kN kN kN kN

BOTT OF PRECAST


-4.33 28.87 7.26 -8.77 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

KKHONG (NOV 1998)

32


Job No. :


NOS.

24.38 m

HT. ABOVE


D

19

C

19

277.89

B

19

411.84

A

19

545.78

76.000

344.86

TOTAL :

143.95

N.B.



11.22 % 23.48 %


186.00 135.78 120.54 103.90


TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST -3.17 6.81 3.64


6.40 -1.339 5.06

5.10 -1.251 3.85

-2.73 9.71 6.20 1.391 14.57

HB45 -SLS2


NOS.


29.25 m

HT. ABOVE

19

C

19

451.57

B

19

627.34

A

19

803.11

76.000

539.46

275.80

N.B.



12.82 % 23.64 %


186.00 135.78 118.38 103.68


TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST 0.09 5.45 5.54


5.51 -1.390 4.12

4.39 -1.291 3.10

0.08 7.77 5.34 1.440 14.62

KKHONG (NOV 1998)

kN kN kN kN


D

TOTAL :

37478

HB45 -SLS2

kN kN kN kN


33


Job No. :


NOS.

34.13 m

HT. ABOVE


D

19

C

19

741.03

B

19

986.52

A

19

1232.00

76.000

863.77

TOTAL :

495.55

N.B.



14.40 % 23.85 %

ULTIMATE TENSILE STRENGTH PER STRAND 73 % OF U.T.S. INITIAL PRESTRESS EFFECTIVE FORCE @ TRANSFER PER STRAND EFFECTIVE FINAL FORCE PER STRAND TOP OF INSITU -

TRANSFER PRESTRESS SELF WT TOTAL @ TRANSFER FINAL PRESTRESS SELF WT + DEAD INSITU SUPER. DEAD + LIVE DIFF. SHRINKAGE TOTAL @ WORKING

HB45 -SLS2

186.00 135.78 116.22 103.39

BOTT OF INSITU -

2.88 -1.318 1.56

2.30 -1.234 1.06

(9) At SUPPORT 2 SECTION, DISTANCE FROM SUPPORT 1 Cable Mark

NOS.

TOP OF PRECAST 5.33 3.18 8.51 4.74 4.53 2.79 1.372 13.44

BOTT OF PRECAST 15.98 -3.83 12.15 14.22 -5.47 -5.610 (SECTION 7) -0.529 2.61

39.00 m

HT. ABOVE

19

803.20

C

19

1146.28

B

19

1489.36

A

19

1832.45

76.000

1317.82

N.B.

e = distance between centroid of precast beam to centroid of tendon e = -155.52 mm


16.27 % 25.55 %


TRANSFER PRESTRESS SELF WT TOTAL @ TRANSFER FINAL PRESTRESS SELF WT + DEAD INSITU TEMPERATURE DIFFERENCE SUPER. DEAD + LIVE HB45 -SLS2 DIFF. SHRINKAGE TOTAL @ WORKING

KKHONG (NOV 1998)

kN kN kN kN


D

TOTAL :

37478

186.00 135.78 113.68 101.09

TOP OF INSITU -

BOTT OF INSITU -

TOP OF PRECAST 12.40 0.00 12.40

-1 -0.37 -1.117 -2.49

-0.29 -1.073 -1.37

11.02 0.00 -0.36 1.181 11.85

kN kN kN kN

BOTT OF PRECAST 6.97 0.00 6.97 6.20 0.00 1.00 0.720 (SUPPORT 2) -0.455 7.46

34

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 SECTIONS FOR PRECAST POST-TENSIONED BEAM USING STRAIN COMPATIBILITY METHOD (BS5400:PART4:1990:CL.6.3.3.1)

Project : Detail : File name :


(A) Checking Section :

4"/8 SPAN

;

(19.500 M FROM SUPP.)

Designed: Checked:

KKL LTC

;

39.00

S40T1 BEAM

(B) Design Ultimate Moment :

=

16307.98 kNm

(C) Require Ultimate Moment Capacity At Mid Span

=

18754.18 kNm

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

=

Date : Date :

16-Jan-2011 16-Jan-2011

m Effective Span

S40T1 BEAM

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

f cu =

50.00 N/mm2

(ii)

Characteristic Strength of In-situ Concrete at Service

f cu =

30.00 N/mm2

(iii) Material Safety Factor for Concrete

γ m=

1.50

(iv) Assumed Concrete Maximum Compressive Strain

εu=

0.0035

4/8 SPAN

Table 1 : Ultimate Moment Capacity From Concrete Section Concrete Section

1 In-situ slab 2 In-situ slab 3 Top Flange 4 Top Flange 5 Top Flange 6 Top Flange 7 Top Flange 8 Top Flange 9 Top Flange 10 Web

Width

Section Dimension Height

Top Fibre

Measure Depth To Bot. Fibre

Section Area

Section f cu

(mm)

(mm)

(mm)

(mm)

(mm2)

(N/mm2)

(mm)

0 1950 1920 660 220 0 0 0 220 0

0.00 180.00 120.00 70.00 0.00 0.00 0.00 0.00 120.53 0.00

0 0 180 300 370 370 370 370 370 491

0 180 300 370 370 370 370 370 491 491

0 351000 230400 46200 0 0 0 0 26517 0

30 30 50 50 50 50 50 50 50 50

0 90 240 335 370 370 370 370 415 491

Centroid

Centroid

Concrete

Compressive

Moment

Strain

Force

about N.A

(mm)

ε

(kN)

(kNm)

490.5 400.5 250.5 155.5 120.5 120.5 120.5 120.5 75.3 0.0

0.00350 0.00286 0.00179 0.00111 0.00086 0.00086 0.00086 0.00086 0.00054 0.00000

0.00 4703.40 5145.60 985.32 0.00 0.00 0.00 0.00 365.70 0.00

0.0 1883.9 1289.1 153.2 0.0 0.0 0.0 0.0 27.5 0.0

Sect. fr. Top Sect. to N.A

490.53 O.K! 654117 11200 Note : (I) Parabolic centroid = 3/8 w from start of parabolic curve, where w = depth of parabolic curve on the Stress the diagram (II) Total depth of the section in parabolic curve (mm) = 197.44 for fcu = 50.0 N/mm2 (measure from Neutral Axis) (mm) = 152.93 for fcu = 30.0 N/mm2

3354

(2) Prestressing Tendons (i)

φ =

12.9 mm

(ii) Nominal Cross Section Area of Tendon

As =

100.0 mm2

(ii) Ultimate Characteristic Strength (UTS)

PUTS =

Tendon Diameter

γ m =

(v) Material Safety Factor for Concrete (vi) Percentage of Jacking Force

186 kN

% = Lossfinal =

(vii) Final Prestress Losses

(iii) Modulus of Elasticity of Tendon

Es =

195000 N/mm2

(iv) Characteristic Strength of Tendon

f pu =

1860 N/mm2

(viii) Total Effective Jacking Force per Strand (ix) Total Final Prestress Force per Strand after all losses

1.15 75 % 25 %

Peff =

139.5 kN

Pfinal =

104.63 kN

Table 2 : Ultimate Moment Capacity From Prestressing Tendons Prestress

Number

Total Cross

Depth from

Tendon Layer

of Tendon

Section Area

Tob Fiber

2

From Bot. Fibre

(nos)

(mm )

(mm)

Layer 1

18 18 17 17 0

1800 1800 1700 1700 0

2205 2085 1965 1845 0

70

7000

1 2 3 4 5

Layer 2 Layer 3 Layer 4 Layer 5

Prestressing Tendon Strain, ε Strain

Prestrain

Total Strain

Tension

Tension

Moment About

Stress

Force

N.A Axis

(N/mm )

(kN)

(kNm)

1617.39 1617.39 1617.39 1617.39 0.00

2911.30 2911.30 2749.57 2749.57 0.00

4991.34 4641.99 4054.15 3724.20 0.00

11321.74

17411.69

2

0.01223 0.01138 0.01052 0.00966 0.00000

0.00537 0.00537 0.00537 0.00537 0.00000

0.01760 0.01674 0.01589 0.01503 0.00000

Note : (i) Strain = εu/x*(Depth of Tendon from Top Fibre - N.A D epth from Top Fibre ) (iii) Moment of Tendon Above the N.A shall be negative and Below the N.A shall be positive. (3) Reinforcement Bars (i) Characteristic Strength of Steel Reinforcement (ii) Modulus of Elasticity of Steel Reinforcement

Prestrain = Pfinal /As/Es

(ii)

f y =

460 N/mm2

(iii)

Material Safety Factor for Steel Reinforcement

Es =

200000 N/mm2

(iv)

Maximum Compressive Strain

γ m =

1.15

=

0

Table 2 : Ultimate Moment Capacity From Steel Reinforcement

1 2 3 4 5 6 7 8 9 10

Steel

Steel

Depth from

Strain

Reinforcement

Reinfor.

Top Fibre

ε

Layer

Area

from. Top

(mm2)

(mm)

0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0

Layer 1 Layer 2 Layer 3 Layer 4 Layer 5 Layer 6 Layer 7 Layer 8 Layer 9 Layer 10

0 0 0 0 0 0 0 0 0 0

0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000

Stress

Force

Moment About

Compressive

Tension

Compressive

Tension

N.A. Axis

(N/mm2)

(N/mm2)

(kN)

(kN)

(kNm)

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

0.00 0.00 0.00 0.00 0.00 0.00 Note : (i) Force in the steel Reinforcement Above N.A shall be Compressive Force and Below N.A shall be Tension Force. (F) Summary of Forces and Stresses Force

Concrete Section Prestressing Tendon Reinforcement Total Difference (I) (II) (III) (IV)

KKHONG (DEC 1998)

Moment Abt.

Compressive

Tension

N.A. Axis

(kN)

(kN)

(kNm)

11200 0

11322 0

3354 17412 0

11200 11322 -121.7

20765

Remarks: PERMISSIBLE TOLERANCE FOR FORCES EQUIVALENT PLEASE INCREACE NEUTRAL AXIS DEPTH......... DESIGN ULTIMATE MOMENT ULTIMATE MOMENT CAPACITY/DESIGN ULTIMATE MOMENT HENCE, CHANGE NEUTRAL AXIS PLEASE.......AND TRY AGAIN.....!!!

= = =

10

kN

16307.98 kNm

Page 35

SEPAKAT SETIA PERUNDING SDN BHD

(14142-M)

Consulting Engineers

JOB NO. :

Shear Design for Post-Tensioned Beam

PROJECT DETAILS FILENAME

: PROJECT TITLE : 40x40x40x40x37.5M SPAN; 0 DEG SKEW; 11.000 M C/W WIDTH : W:\SCB Spreadsheet\Post-Tensioned-Design.xls


Design Of Precast Post-Tensioned Beam At Ultimate Limit State - Shear Reinforcement Design Design Data : (1) Precast Beam Section Properties

39 m Effective Span

Total Height of Precast Section

(ii)

Cross Section Area of Precast Section

H = Ap =

(iii)

Precast Section Centroid above Bottom Fibre

yb =

(iv)

Second Moment Of Area of Precast Section

Ipre =

5.2608E-01 m4

(v)

Section Modulus of Precast Section : @ Top Fibre

(vi)

@ Bottom Fibre

(vii)

@ Composite Beam Centroid

(viii) Rib/Web Breadth of Precast Section @ Beam Ends (Supports) (ix)

@ Middle of Beams

(x)

Concrete Strength @ 28 days of Precast Section

(2)

Composite Section Properties

Date : 16-Jan-2011 Date : 16-Jan-2011

S40T1 BEAM

(BS 5400 : PART 4 : 1990 ; CL. 5.3.3 , CL. 6.3.4 & CL. 7.4.2.3)

(i)

KKL LTC

37478

2125 mm 0.869500 m2

Definations, Symbols and Notes

1162.30 mm

f pt = Stress due to prestress only at tensile fibre (bottom fibre)

Zt =

5.4646E-01 m3

γ fL = 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3)

Zb =

4.5262E-01 m3

e = Eccentricity from centroid of tendon to centroid of precast beam

Zcentroid =

2.0472E+00 m3

Mcr = Cracking Moment at Section considered

bend =

660 mm

bmiddle =

220 mm

f cu2 =

Vcr-i = Ultimate Cracking Shear Capacity (Equation 29 BS5400) 0.037bdt(f cu)1/2+ (Mcr /M)(V)

but not less than 0.1bd(f cu)1/2

b = Breadth of member/breadth of rib/web,bw

50 N/mm2

dt = Eff. depth of Centroid of tendons to Extreme Compression Fibre V & M = The shear force and bending moment (both taken as +ve) at section

(i)

Total Height of Composite Section

Hc =

2305 mm

(ii)

Cross Section Area of Composite Section

Ac =

1.15 m2

(iii)

Composite Section Centroid above Bottom Fibre

(iv)

Second moment of area of the transformed Composite Section

(v)

Modular Ratio

(3)

Prestress Strand Properties

(i)

Strand Description

γ fL = 0.87 (see BS 5400 : Part 4 : 1990 : CL 4.2.3) Ipre =

(iii)

Ultimate Tensile Strength per Strand 70

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

0.824

:

Nominal Cross Section Area per Strand,

(v)

1419.28 mm 7.6205E-01 m4

m =

(ii) (iv)

yb,c = Icomposite =

considered due to ultimate load

yb,c = Distance of tensile fibre to centroid composite beam

As =

% of U.T.S. per Strand

2

100.00 mm

PUTS =

186.00 kN

Peff =

130.20 kN

Lcable/beam =

Cable Length/Beam Length

=

0.52608 m4

yb,c - yb =

Y = Zcentroid =

0.26 m

Ipre /Y =

2.0472 m3

Vco = Ultimate shear resistance of a section uncracked in flexure = 0.67bHc(f t2+f cpf t)1/2 (Equation 28 BS5400:PART4:1990)

39.60 m

dt = Eff. depth of Centroid of tendons to Extreme Compression Fibre

(4)

Link Rebars Properties

(i)

Characteristic Strength of Links Rebars

= Hc-(yb-e) f yv =

460 N/mm2 V1 = Horizontal Interface Shear Force

(ii)

Shear Reinforcement diameter provided

φv =

12 mm

(iii)

Total Leg x-Section Area per Links

Asv =

226 mm2

Sc = First moment of area, about the neutral axis of the transformed

f strand =

460 N/mm

Characteristic Strength of Longitudinal Steel Reinforcement provided

f yL =

460 N/mm2

(vi)

Longitudinal Steel Reinforcement diameter provided (max 12 mm)

φL =

(vii)

@ Support : R.C. Shear Resistance

(iv)

Characteristic Strength of Strands (max 460)

(v)

(viii) Depth Factor

2

composite section, of the insitu concrete to one side of the interface

Ae = area of fully anchoraged reinforcement per unit length crossing the

12 mm

shear plane under consideration

vc = (0.27/γ m)*(100As(pre)/benddt)1/3*(f cu)1/3

vc =

0.7776 N/mm2

§s = greater of (500/dt)1/4 or 0.7

§s =

0.8436

(5) Data To Calculate Longitudinal Shear (i)

Note :

First moment of area, about the neutral axis of the transformed Composite sect., of the concrete to one side of the interface

Sc =

(ii)

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

v1 =

0.45 N/mm2

(iii)

Constant depending on the conc. bonding across the shear plane (Table 31:BS 5400:P4)

k1 =

0.09

(iv) (v) (vi)

Length of Shear plane under consideration Embedment of The Insitu Slab Minimum thickness of the insitu top slab

Ls = = tslab =

660 mm 0 mm 180 mm

(vii)

Insitu slab Width

lf =

1950 mm

Concrete strength of insitu top slab @ 28 days

f c =

(1) Max. Spacing of the links : Spacing of the links along the beam should not exceeded 0.75dt, nor four times the web thickness for flanged beams. When V' exceeds 1.8 Vc,

0.23001 m3

the max. spacing should be reduced to 0.5 dt. The lateral spacing of the individual legs of the links provided at a cross section should not exceed 0.75dt.(V'=V-Vprtestress)

(Surface Type 2)

(2) For longitudinal shear reinforcements : a minimum area of fully anchored reinf. of 0.15% of the area of the contact should cross this surface; the spacing of this reinf. should not exceed the lesser of ; (i) 4 times of minimum thickness of the in situ concrete flange ;

30 N/mm2

(ii) 600 mm.

KKHONG (DEC 1998)

Page 36


(14142-M)

Consulting Engineers Shear Design for Post-Tensioned Beam

JOB NO. :

37478

Support 2

CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR Section Distance From Support Distance From MidSpan (1) Summary Of The Ultimate Design Shear Forces and Moment Bending (2) Prestressing Strands Information

Support 1

Section 1

Section 2

Section 3

Mid Span

Section 5

Section 6

Section 7

Lx

(m)

0.000

4.875

9.750

14.625

19.500

24.375

29.250

34.125

39.000

Xo

(m)

19.500

14.625

9.750

4.875

0.000

4.875

9.750

14.625

19.500

Max V : Vmax M Max M : V Mmax

(kN)

2141.19

1756.25

1245.94

956.81

466.06

724.42

1227.24

1474.54

1799.88

(From Grillage Analysis)

(kNm) (kN)

-1706.57 1894.07

4085.30 1137.49

10359.91 949.36

11591.45 623.95

15803.19 198.04

13846.44 462.88

12712.25 1180.91

6870.63 1526.16

374.72 1746.11


544.32

(From Grillage Analysis) (From Grillage Analysis)

(kNm)

8143.62

6223.01

12278.97

13160.82

16307.98

13336.81

12866.69

7019.35

n

= Effective No. of Strands

(Nos)

76

76

76

76

76

76

76

76

76

e Loss Pfinal

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

(mm) (%)

-155.52 25.36

298.53 23.67

622.84 23.46

817.44 23.30

882.30 22.70

817.44 23.48

622.84 23.64

298.53 23.85

-155.52 25.55

= Total % of Prestress Losses at Service = Effective prestress Force = (n*Peff (1-%Loss))

= Combined Cables Centroid from Botttom Fibre of Beam (3) Vertical Component Shear e' Ye - Ym = Drape = (1350 - 280) = 1070 mm Force From Deflected = Combined Deflection Angle = Atan((Ye - Ym)*(2X0/(Lbeam/2)2)) Tendons, Vprestress θο

Vprestress = γ m * Pfinal * Sin(θo), where γ m = 0.8 (L.A. Clark) (4) Allowable Maximum

dt

= Effective depth of Tendons = H c-(yb-e)

Ultimate Applied

v

= Max Applied Ult.Shear Stress = [Vmaxor V-Vprestress]/bdt

Shear Stress Checks

Checks = Allowable Shear Stress = 0.75f cu1/2 or 5.8 N/mm2

(BS 5400:Part 4:1990:CL.5.3.3.1)

Checks = Applied Ultimate Shear Stress Check :

(kN)

7385.994

7553.120

7573.954

7589.322

7649.451

7572.172

7556.196

7534.710

7367.441

(mm)

1317.82

863.77

539.46

344.86

280.00

344.86

539.46

863.77

1317.82

(mm)

1070

1070

1070

1070

1070

1070

1070

1070

1070

(o)

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

(mm)

987.18

1441.23

1765.54

1960.14

2025.00

1960.14

1765.54

1441.23

987.18

(N/mm2)

2.33

4.02

2.38

1.84

1.05

1.31

2.33

3.30

1.81

(N/mm2)

5.30

5.30

5.30

5.30

5.30

5.30

5.30

5.30

5.30

Compliance within allowable within allowable within allowable within allowable

within allowable

within allowable within allowable within allowable within allowable

(5) Design Of Flexure Shears : f pt

= γ fL*(Pfinal/Ap + Pfinal*e/Zb), where γ fL = 0.87

(N/mm2)

-

11.89

16.65

19.52

20.63

19.47

16.61

11.86

Cracked in Flexure

Mcr

= [0.37(f cu)1/2 + f pt] * Icomposite/yb,c

(kNm)

-

7789.63

10342.35

11884.64

12479.74

11860.96

10321.40

7774.07

-

- For Class 1 and Class 2 member

d

= (H-y b+e)

(mm)

-

1261

1586

1780

1845

1780

1586

1261

-

(BS 5400:Part 4:1990:CL 6..3.4.3)

Vcr(min)

= min. required by code 0.1bdt(f cu)1/2

(kN)

-

224

275

305

315

305

275

224

-

Vcr1

= 0.037bdt(f cu)1/2+ (Mcr /M)(Vmax)

(kN)

-

3432

1345

1094

485

733

1098

1751

-

Vcr2

= 0.037bdt(f cu)1/2+ (Mcr /Mmax)(V)

(kN)

-

1507

901

676

268

524

1049

1773

-

f cp

= γ fL*(Pfinal/Ap - Pfinal*e/Zcentroid) taken as positive

(N/mm2)

7.878

6.599

5.574

4.957

4.786

4.946

5.560

6.583

7.859

UnCracked in Flexure

f t

= 0.24(f cu)1/2 taken as positive

(N/mm2)

1.70

1.70

1.70

1.70

1.70

1.70

1.70

1.70

1.70

(BS 5400 : Part 4:1990 : CL 6.3.4.2)

Vco

= 0.67bHc(f t2+f cpf t)1/2

(kN)

4109

1275

1193

1142

1127

1141

1192

1274

4105 -

(5a) Assume Sections

(5b) Assume Sections

(5c) Calculations of (V - V c)

-

(Vmax - Max(Vcr1,Vcr(min)) - Vprestress)

(kN)

-

-2156

-422

-299

-19

-170

-192

-757

and determination of

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

(kN)

-

-850

-274

-214

-117

-223

-189

-727

-

(V - Vc) Max

(Vmax - Vco -Vprestress)

(kN)

-2593

1

-270

-346

-661

-578

-286

-279

-2929

(V - Vco -Vprestress)

(kN)

-2840

-618

-566

-679

-929

-839

-333

-227

-2982

(V - Vc - Vprestress) Max

(kN)

-2593

1

-270

-214

-19

-170

-189

-227

-2929

(V - Vc - Vprestress) Max (Double Check)

(kN)

-2593

1

-270

-214

-19

-170

-189

-227

-2929

(5d) Flexure Shear Reinforcement Design

Asv/Sv(Min)

= V+0.4bdt-(Vc+Vprestress)/(0.87f yvdt) or 0.4b/(0.87f yv)

(mm)

3.4145

0.2208

0.2199

0.2199

0.2199

0.2199

0.2199

0.2199

2.5546

Sv(min)

Calculated

(mm)

66

1024

1029

1029

1029

1029

1029

1029

89

nos (mm2) nos (mm2)

0 0 17 1923

0 0 15 1696

0 0 11 1244

0 0 9 1018

0 0 6 679

0 0 7 792

0 0 11 1244

0 0 12 1357

0 0 14 1583

= AsLong(pre) + AsLong(Bar)

(mm2)

1923

1696

1244

1018

679

792

1244

1357

1583

= V /(2*0.87*f yL)

(mm2)

1894

1593

1154

994

582

704

1132

1307

1469

(BS 5400:Part 4:1990:CL 6.3.4.4)

(5e) Minimum Area of EXCESS AsLong(pre) : (i) Bonded Prestressing Strands EXCESS in resist bending Total Effective area of the above Prestressing Tendons Long. Bars/Strand Checks ( Note : The AsLong shall be the area AsLong(Bar): of strands/rebars which are NOT

(ii) No. of Longitudinal reinforcement EXCESS in resist bending Total Effective area of the above Longitudinal Bars

Used in the bending/ others designs.AsLongTotal (In Tension Zone Only)

AsLong(Min)

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

Checks = Minimum AsLong Checks

KKHONG (DEC 1998)

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

Page 37


(14142-M)


JOB NO. :

37478

Support 2

CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR Section Distance From Support Distance From MidSpan (1) Summary Of The Ultimate Design Shear Forces and Moment Bending (2) Prestressing Strands Information

Support 1

Section 1

Section 2

Section 3

Mid Span

Section 5

Section 6

Section 7

Lx

(m)

0.000

4.875

9.750

14.625

19.500

24.375

29.250

34.125

39.000

Xo

(m)

19.500

14.625

9.750

4.875

0.000

4.875

9.750

14.625

19.500

Max V : Vmax

(kN)

2141.19

1756.25

1245.94

956.81

466.06

724.42

1227.24

1474.54

1799.88


(kNm) (kN)

-1706.57 1894.07

4085.30 1137.49

10359.91 949.36

11591.45 623.95

15803.19 198.04

13846.44 462.88

12712.25 1180.91

6870.63 1526.16

374.72 1746.11


(kNm)

8143.62

6223.01

12278.97

13160.82

16307.98

13336.81

12866.69

7019.35

544.32


M Max M : V Mmax


n

= Effective No. of Strands

(Nos)

76

76

76

76

76

76

76

76

76

e Loss Pfinal

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

(mm) (%)

-155.52 25.36

298.53 23.67

622.84 23.46

817.44 23.30

882.30 22.70

817.44 23.48

622.84 23.64

298.53 23.85

-155.52 25.55

= Total % of Prestress Losses at Service = Effective prestress Force = (n*Peff (1-%Loss))

= Combined Cables Centroid from Botttom Fibre of Beam (3) Vertical Component Shear e' Ye - Ym = Drape = (1350 - 280) = 1070 mm Force From Deflected = Combined Deflection Angle = Atan((Ye - Ym)*(2X0/(Lbeam/2)2)) Tendons, Vprestress θο

Vprestress = γ m * Pfinal * Sin(θo), where γ m = 0.8 (L.A. Clark) (4) Allowable Maximum

dt

= Effective depth of Tendons = H c-(yb-e)

Ultimate Applied

v

= Max Applied Ult.Shear Stress = [Vmaxor V-Vprestress]/bdt

Shear Stress Checks

Checks = Allowable Shear Stress = 0.75f cu1/2 or 5.8 N/mm2

(BS 5400:Part 4:1990:CL.5.3.3.1)

Checks = Applied Ultimate Shear Stress Check :

(kN)

7385.994

7553.120

7573.954

7589.322

7649.451

7572.172

7556.196

7534.710

7367.441

(mm)

1317.82

863.77

539.46

344.86

280.00

344.86

539.46

863.77

1317.82

(mm)

1070

1070

1070

1070

1070

1070

1070

1070

1070

(o)

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

(mm)

987.18

1441.23

1765.54

1960.14

2025.00

1960.14

1765.54

1441.23

987.18

(N/mm2)

2.33

4.02

2.38

1.84

1.05

1.31

2.33

3.30

1.81

(N/mm2)

5.30

5.30

5.30

5.30

5.30

5.30

5.30

5.30

5.30

Compliance within allowable within allowable within allowable within allowable

within allowable

within allowable within allowable within allowable within allowable

(5) Design Of Flexure Shears : f pt

= γ fL*(Pfinal/Ap + Pfinal*e/Zb), where γ fL = 0.87

(N/mm2)

-

11.89

16.65

19.52

20.63

19.47

16.61

11.86

Cracked in Flexure

Mcr

= [0.37(f cu)1/2 + f pt] * Icomposite/yb,c

(kNm)

-

7789.63

10342.35

11884.64

12479.74

11860.96

10321.40

7774.07

-

- For Class 1 and Class 2 member

d

= (H-y b+e)

(mm)

-

1261

1586

1780

1845

1780

1586

1261

-

(BS 5400:Part 4:1990:CL 6..3.4.3)

Vcr(min)

= min. required by code 0.1bdt(f cu)1/2

(kN)

-

224

275

305

315

305

275

224

-

Vcr1

= 0.037bdt(f cu)1/2+ (Mcr /M)(Vmax)

(kN)

-

3432

1345

1094

485

733

1098

1751

-

Vcr2

= 0.037bdt(f cu)1/2+ (Mcr /Mmax)(V)

(kN)

-

1507

901

676

268

524

1049

1773

-

f cp

= γ fL*(Pfinal/Ap - Pfinal*e/Zcentroid) taken as positive

(N/mm2)

7.878

6.599

5.574

4.957

4.786

4.946

5.560

6.583

7.859

UnCracked in Flexure

f t

= 0.24(f cu)1/2 taken as positive

(N/mm2)

1.70

1.70

1.70

1.70

1.70

1.70

1.70

1.70

1.70

(BS 5400 : Part 4:1990 : CL 6.3.4.2)

Vco

= 0.67bHc(f t2+f cpf t)1/2

(kN)

4109

1275

1193

1142

1127

1141

1192

1274

4105 -

(5a) Assume Sections

(5b) Assume Sections

(5c) Calculations of (V - V c)

-

(Vmax - Max(Vcr1,Vcr(min)) - Vprestress)

(kN)

-

-2156

-422

-299

-19

-170

-192

-757

and determination of

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

(kN)

-

-850

-274

-214

-117

-223

-189

-727

-

(V - Vc) Max

(Vmax - Vco -Vprestress)

(kN)

-2593

1

-270

-346

-661

-578

-286

-279

-2929

(V - Vco -Vprestress)

(kN)

-2840

-618

-566

-679

-929

-839

-333

-227

-2982

(V - Vc - Vprestress) Max

(kN)

-2593

1

-270

-214

-19

-170

-189

-227

-2929

(V - Vc - Vprestress) Max (Double Check)

(kN)

-2593

1

-270

-214

-19

-170

-189

-227

-2929

(5d) Flexure Shear Reinforcement Design

Asv/Sv(Min)

= V+0.4bdt-(Vc+Vprestress)/(0.87f yvdt) or 0.4b/(0.87f yv)

(mm)

3.4145

0.2208

0.2199

0.2199

0.2199

0.2199

0.2199

0.2199

2.5546

Sv(min)

Calculated

(mm)

66

1024

1029

1029

1029

1029

1029

1029

89

AsLong(pre) :

(i) Bonded Prestressing Strands EXCESS in resist bending

nos (mm2) nos (mm2)

0 0 17 1923

0 0 15 1696

0 0 11 1244

0 0 9 1018

0 0 6 679

0 0 7 792

0 0 11 1244

0 0 12 1357

0 0 14 1583

= AsLong(pre) + AsLong(Bar)

(mm2)

1923

1696

1244

1018

679

792

1244

1357

1583

= V /(2*0.87*f yL)

(mm2)

1894

1593

1154

994

582

704

1132

1307

1469

(BS 5400:Part 4:1990:CL 6.3.4.4)

(5e) Minimum Area of EXCESS Long. Bars/Strand Checks

Total Effective area of the above Prestressing Tendons

( Note : The AsLong shall be the area AsLong(Bar):

(ii) No. of Longitudinal reinforcement EXCESS in resist bending

of strands/rebars which are NOT

Total Effective area of the above Longitudinal Bars

Used in the bending/ others designs.AsLongTotal (In Tension Zone Only)

AsLong(Min)

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

Checks = Minimum AsLong Checks

Compliance 'As' is Complied 'As' is Complied 'As' is Complied 'As' is Complied As' is Complied'As' is Complied 'As' is Complied 'As' is Complied 'As' is Complied

KKHONG (DEC 1998)

Page 37


(14142-M)


JOB NO. :

37478

Support 2

CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR (Continue) Section Distance From Support Distance From MidSpan (6) Design Of Longitudinal Shears : V1

(6a) Longditudinal Shear

Reinforcement Design

Support 1

Section 1

Section 2

Section 3

Mid Span

Section 5

Section 6

Section 7

Lx

(m)

0.000

4.875

9.750

14.625

19.500

24.375

29.250

34.125

39.000

Xo

(m)

19.500

14.625

9.750

4.875

0.000

4.875

9.750

14.625

19.500

= Max(V,Vmax)*Sc/Icomposite

k1*f c*Ls Checks = Checking of allowable V1

(BS 5400 : Part 4:1990 : CL 7.4.2.3)

Checks = the larger of (V1 - v1Ls)/(0.7f yv) and (0.15/100)*(Ls*1000) Ae

(kN/m)

646

530

376

289

141

219

370

461

543

(kN/m)

1782

1782

1782

1782

1782

1782

1782

1782

1782

Compliance

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

The Longitudinal Shear force (V1) ar e not exceeded the allowable value specified in Code (BS 5 400:Part 4:1990:C.L. 7.4.2.3).

(mm2/m)

1085

990

990

990

990

990

990

990

990

(mm)

209

228

228

228

228

228

228

228

228

(mm)

66

228

228

228

228

228

228

228

89

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

(nos)

16.1

5.4

5.4

5.4

5.4

5.4

5.4

5.4

12.3

Average No. of Links provided per m

(nos)

17

6

6

6

6

6

6

6

13

Sv

Calculated = Asv*1000/Ae

(7) Shear Reinforcement Design

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

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

Required by The Code.

-------- END OF SHEAR DESIGN ---------

KKHONG (DEC 1998)

Page 38


(14142-M)


JOB NO. :

37478

Support 2

CALCULATE SHEAR REINFORCEMENT FOR VERTICAL FLEXURAL SHEAR & LONGITUDINAL SHEAR (Continue) Section Distance From Support Distance From MidSpan (6) Design Of Longitudinal Shears : V1

(6a) Longditudinal Shear

Support 1

Section 1

Section 2

Section 3

Mid Span

Section 5

Section 6

Section 7

Lx

(m)

0.000

4.875

9.750

14.625

19.500

24.375

29.250

34.125

39.000

Xo

(m)

19.500

14.625

9.750

4.875

0.000

4.875

9.750

14.625

19.500

= Max(V,Vmax)*Sc/Icomposite

k1*f c*Ls

Reinforcement Design

Checks = Checking of allowable V1 (BS 5400 : Part 4:1990 : CL 7.4.2.3)

Checks = the larger of (V1 - v1Ls)/(0.7f yv) and (0.15/100)*(Ls*1000) Ae

(kN/m)

646

530

376

289

141

219

370

461

543

(kN/m)

1782

1782

1782

1782

1782

1782

1782

1782

1782

Compliance

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

O.K.

The Longitudinal Shear force (V1) ar e not exceeded the allowable value specified in Code (BS 5 400:Part 4:1990:C.L. 7.4.2.3).

(mm2/m)

1085

990

990

990

990

990

990

990

990

(mm)

209

228

228

228

228

228

228

228

228

(mm)

66

228

228

228

228

228

228

228

89

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

(nos)

16.1

5.4

5.4

5.4

5.4

5.4

5.4

5.4

12.3

Average No. of Links provided per m

(nos)

17

6

6

6

6

6

6

6

13

Sv

Calculated = Asv*1000/Ae

(7) Shear Reinforcement Design

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

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

Required by The Code.

-------- END OF SHEAR DESIGN ---------

KKHONG (DEC 1998)

Page 38

Post-Tensioning Losses : (1)

Immediate Losses

(a) (b) (c) (d)

Friction Loss Along Prestressing Tendon Friction Loss In The Anchorage Losses Due to Wedges Draw-in Elastic Shortening of Concrete

(2)

Deferred Losses

(a) (b) (c)

Relaxation Loss of Prestressing Tendon Shrinkage Loss of Concrete Creep Loss in Concrete

(1)

Immediate Losses

(1)(a) Friction Loss Along Prestressing Tendon Losses due to frinction in a cable can be calculated to a relatively high degree of accuracy by Coulomb's formula: P(x) = P j * e-(µθ + Kx) where, P(x) = Post-tensioning force at a distance x from the stressing anchorage (Live end) P j = Post-tensioning force at the stressing anchorage e µ θ K

= Base of Napierian logarithms = Coefficient of friction = Sum of angular deviations (in radian) of tendon in all planes over the distance x = Wobble factor (inaccuracies in placing per unit length

(1)(b) Friction Loss In The Anchorage

Post-Tensioning Losses : (1)

Immediate Losses

(a) (b) (c) (d)

Friction Loss Along Prestressing Tendon Friction Loss In The Anchorage Losses Due to Wedges Draw-in Elastic Shortening of Concrete

(2)

Deferred Losses

(a) (b) (c)

Relaxation Loss of Prestressing Tendon Shrinkage Loss of Concrete Creep Loss in Concrete

(1)

Immediate Losses

(1)(a) Friction Loss Along Prestressing Tendon Losses due to frinction in a cable can be calculated to a relatively high degree of accuracy by Coulomb's formula: P(x) = P j * e-(µθ + Kx) where, P(x) = Post-tensioning force at a distance x from the stressing anchorage (Live end) P j = Post-tensioning force at the stressing anchorage e µ θ K

= Base of Napierian logarithms = Coefficient of friction = Sum of angular deviations (in radian) of tendon in all planes over the distance x = Wobble factor (inaccuracies in placing per unit length

(1)(b) Friction Loss In The Anchorage Not Consider in the design

(1)(c) Losses Due to Wedges Draw-in By assuming a linear loss of prestressing force due to frincion, loss of prestressing force of tendon per meter length/ Force Gradient,

δp = (1 - e-(µθ + Kx) )P j /Lcable where,

δp = Loss of prestressing force in tendon per meter length/ Force Gradient -(µθ + Kx)

(1 - e

)P j = Loss

of prestressing force in tendon

Lcable = Total Cable length and the diatance affected by the draw-in of wedges, w = (Draw-in * Es * As * n)1/2

where, Draw-in = Draw-in of Wedges in mm Es = Modulus of Elasticity og post-tensioning cable in kN/m2 As = Cable cross Section Area in mm2 n = Total number of prestressing cables w = Distance affected by the draw-in of wedges (< Lcable)

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

For w < L cable /2 Px

Loss of force due to draw-in of wedges

P j Dp P j-Dp

PL w

Live End Anchorage

Dead End Anchorage

x Length of Tendon Lcable

(ii)

For w >= L cable /2 Px

Loss of force due to draw-in of wedges

P j Dp

PL

P j-Dp Live End Anchorage

w

Dead End Anchorage

x Length of Tendon Lcable

(1)(d) Elastic Shortening Losses (BS 5400 : Part 4 : 1990 : CL. 6.7.2) Immediately after transfer, the change in strain in the prestressing steel δεp caused by elastic shortening of the concrete is equal to the strain in the concrete at the steel level, εcp. The loss of prestress in the steel,

δf Loss is therefore : δf Loss

=

0.5(Es/Ec)*f tendon

for post-tensioned beam (ref. BS5400:Part4:Cl. 6.7.2.3)

Where, f tendon is calculated for prestress and dead load stresses in the concrete adjacent to the tendons. ES is modulus of elasticity of the prestressing tendon Ec is modulus of elasticity of the precast concrete at transfer

Post Tensioned Design1

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