Prestress Sls Check

8/13/2019 Prestress Sls Check

1/18

Instructions

Title

Prestress Concrete SLS Check

NOTE

Revision

Vision Revision Date Made by

1.0 First version 11/28/2011

Spreadsheet Limitations

1

2

3

Instructions

Although I have endeavoured to check this spreadsheet, I cannot gaurantee that it

contains no errors. I recommend that you complete your own design check of the

results prior to using this for detailed design.

This spreadsheet is designed to Prestress Concrete SLS Check

Page 1


2/18

Instructions

1 Input the shaded cells only

2

Page 2


3/18

Contract Job ref. 60095653

Part of

structureCalc.sheet No.

Drawing ref. Calculated by Checked by Date

1. Properties of Concrete:

Characteristic compressive cylinder strength of concrete at 28 days(f 'c):

For beam: f 'c.beam= 50.00 (Mpa)

For slab: f 'c.slab= 40.00 (Mpa)

At transfer Strength of concrete fcpis: 0.80 f 'c (To propose)

fcp= 0.8f 'c= 40.00 (Mpa)

Elasticity modulus Ec.50= (MPa)

Elasticity modulus Ec.40= (MPa)

2. Concrete stress limitation for prestressing:

(1). Allowable compressive stress (refer to BS5400 part4 clause 6.3.2.2):

At transfer: sc.transfer= 0.5 fcp= 20.00 (Mpa)Serviceability stage:sc.serviceability.top= 0.40 f 'c.beam= 20.00 (Mpa)

sc.serviceability.bot= 0.40 f 'c.beam= 20.00 (Mpa)(2). Allowable tensile stress (refer to BS5400 part4 clause 6.3.2.4):

At transfer: st.transfer = -1.00 (Mpa)class 1: Serviceability stage:st.serviceability.top= 0.00 (Mpa)

st.serviceability.bot= 0.00 (Mpa)

class 2:Serviceability stage:s

t.serviceability.top=

-3.20 (Mpa)st.serviceability.bot= -3.20 (Mpa)3. Properties of Tendons :

For 7-wire super standard fp= 1770.00 (Mpa)

fpy= 1504.50 (Mpa) (0.85fp)

Ap= 150.00 (mm2)

Breaking load (kN) Pbreaking= 265.00 (kN)

Elasticity modulus Ep= 195000 (Mpa)

dp= 15.70 (mm)

4.Properties of Reinforcement:

Foe grade D500N deformed bars fsy= 500.00(Mpa)

Elasticity modulus Es= 200000(Mpa)

MAuNSELL | AECOM

3.1 Material properties

27400.00

24000.00

189888032.xls.ms_office:3.1STRENGHT 3 of 18


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Contract Job ref.

Part of



1. Properties of Tendons: Beam converse-section 2 Beam-slab conversion-section 2

fp= 1770.00 (Mpa) modular ratio n= 7.117

fpy= 1504.50 (Mpa) (0.85fp) Area of converse-section

Ap= 150.00 (mm2) A1= 1.788 (m

2) A2= 2.195 (m

2)

Breaking load (kN) Pbreaking= 265.00 (kN) first moment of tendons about the neutral axis of gross

Jackingforces Pjack= 0.75 Pbreaking= 198.75 (kN) cross-section Sg1= 0.008 (m3) Sg2= 0.011 (m

3)

Jackingstress sjack= 0.75 fp= 1327.50 (Mpa) distance from the barycenter of the conversion-section to2. Allowable compressive & tensile stress for concrete: barycenter of the gross cross-section dh1= 0.004 (m) dh2= 0.005 (m)

sc.transfer= 20.00 (Mpa) barycenter of the converse-section y1= 0.791 (m) y2= 0.939 (m)st.transfer = -1.00 (Mpa) moment of inertia of converse-section I1= 0.328 (m4) I2= 0.542 (m4)

3. Section properties: dslab= 0.20 (m)

Beam solid section 1 Beam-slab conversion-section 2 cross-section 2 solid section 1

Ae1= 0.964 (m2) Abeam= 1.788 (m

2) 1.766 (m

2) A0= 2.195 (m

2) 2.173 (m

2) Ae2= 1.371 (m

2)

Ie1= 0.045 (m4) Ibeam= 0.328 (m

4) 0.326 (m

4) I0= 0.542 (m

4) 0.536 (m

4) Ie2= 0.106 (m

4)

ye1= 0.384 (m) ybeam= 0.791 (m) 0.796 (m) y0= 0.939 (m) 0.944 (m) ye2= 0.520 (m)

de1= 0.750 (m) dbeam= 1.500 (m) 1.500 (m) d0= 1.700 (m) 1.700 (m) de2= 0.950 (m)

Ze1t= 0.122 (m3) Zbeam.top= 0.463 (m

3) 0.462 (m

3) Z0.top= 0.712 (m

3) 0.710 (m

3) Ze2t= 0.246 (m

3)

Ze1b= -0.116 (m3) Zbeam.bot= -0.415 (m

3) -0.409 (m

3) Z0.bot= -0.577 (m

3) -0.568 (m

3) Ze2b= -0.204 (m

3)

Z0.top1= 0.966 (m3) 0.965 (m

3) Ze2.top1= 0.460 (m

3)

Beam converse-section 3 Beam-slab conversion-section 3 Beam-slab conversion-section 3 cross-section 3

Area of converse-section Abeam= 1.106 (m2) 1.084 (m

2) A0= 1.525 (m

2) 1.502 (m

2)

A1= 1.106 (m2) A2= 1.525 (m

2) Ibeam= 0.216 (m

4) 0.215 (m

4) I0= 0.468 (m

4) 0.463 (m

4)

first moment of tendons about the neutral axis of gross ybeam= 0.680 (m) 0.685 (m) y0= 0.930 (m) 0.937 (m)

ss-section Sg1= 0.005 (m3) Sg2= 0.011 (m3) dbeam= 1.500 (m) 1.500 (m) d0= 1.700 (m) 1.700 (m)

distance from the barycenter of the conversion-section to Zbeam.top= 0.264 (m3) 0.264 (m

3) Z0.top= 0.607 (m

3) 0.606 (m

3)

barycenter of the gross cross-section dh1= 0.005 (m) dh2= 0.007 (m) Zbeam.bot= -0.318 (m3) -0.314 (m

3) Z0.bot= -0.503 (m

3) -0.494 (m

3)

barycenter of the converse-section y1= 0.680 (m) y2= 0.930 (m) Z0.top1= 0.820 (m3) 0.821 (m

3)

moment of inertia of converse-section I1= 0.216 (m4) I2= 0.468 (m

4)

Beam converse-section 4 Beam-slab conversion-section 4 Beam-slab conversion-section 4 cross-section 4

Area of converse-section Abeam= 0.796 (m2) 0.752 (m

2) A0= 1.210 (m

2) 1.166 (m

2)

A1= 0.796 (m2) A2= 1.210 (m

2) Ibeam= 0.176 (m

4) 0.176 (m

4) I0= 0.416 (m

4) 0.393 (m

4)

first moment of tendons about the neutral axis of gross ybeam= 0.670 (m) 0.693 (m) y0= 0.985 (m) 1.012 (m)

ss-section Sg1= 0.019 (m3) Sg2= 0.033 (m

3) dbeam= 1.500 (m) 1.500 (m) d0= 1.700 (m) 1.700 (m)

distance from the barycenter of the conversion-section to Zbeam.top= 0.212 (m3) 0.219 (m

3) Z0.top= 0.582 (m

3) 0.571 (m

3)

barycenter of the gross cross-section dh1= 0.023 (m) dh2= 0.027 (m) Zbeam.bot= -0.262 (m3) -0.254 (m

3) Z0.bot= -0.422 (m

3) -0.388 (m

3)

barycenter of the converse-section y1= 0.670 (m) y2= 0.985 (m) Z0.top1= 0.808 (m3) 0.821 (m

3)

moment of inertia of converse-section I1= 0.176 (m4) I2= 0.416 (m

4)

4. Section properties accounting for tendons:

No. of strand at height of yi(mm)

60.00 110.00 160.00 210.00 260.00 500.00 1400.00

60.00 50.00 50.00 50.00 50.00 240.00 900.00 (ybeam-yp) (y0-yp) Ibeam/ep.beam I0/ep.0

2 6 0 8 4 0 0 6 24.00 10880.00 453.33 0.34 0.49 0.97 1.11

3 6.25 0.25 8 4 0 0 6 24.50 10922.50 445.82 0.35 0.49 0.95 1.10

3 6.25 0.25 8 4 0 0 6 24.50 10922.50 445.82 0.23 0.48 0.92 0.97

4 7 4 8 4 0 0 6 28.50 11325.00 397.37 0.27 0.59 0.64 0.71

5 15 9 8 4 0 0 6 42.00 12410.00 295.48 0.37 0.69 0.47 0.60

6 17 10.50 8 4 0 0 6 45.50 12695.00 279.01 0.39 0.71 0.45 0.59

7 17 13 8 4 0 0 6 48.00 12970.00 270.21 0.40 0.71 0.44 0.58

8 17 13 8 4 0 0 6 48.00 12970.00 270.21 0.40 0.71 0.44 0.58

9 17 13 8 4 0 0 6 48.00 12970.00 270.21 0.40 0.71 0.44 0.58

10 17 10.50 8 4 0 0 6 45.50 12695.00 279.01 0.39 0.71 0.45 0.59

11 15 9 8 4 0 0 6 42.00 12410.00 295.48 0.37 0.69 0.47 0.60

12 7 4 8 4 0 0 6 28.50 11325.00 397.37 0.27 0.59 0.64 0.71

13 6.25 0.25 8 4 0 0 6 24.50 10922.50 445.82 0.23 0.48 0.92 0.97

13 6.25 0.25 8 4 0 0 6 24.50 10922.50 445.82 0.35 0.49 0.95 1.10

14 6 0 8 4 0 0 6 24.00 10880.00 453.33 0.34 0.49 0.97 1.11

A B C D E F G

60095653

MAuNSELL | AECOM

Z0.p

(m3)

ebeam.p

(m)

e0.p

(m)

3.2 Tendons design

Sniyi yp(mm)NODE Sni

Zbeam.p

(m3)

Beam transform-section 4gross cross-section

4

gross cross-section

2Beam transform-section 2

Beam transform-section 3gross cross-section

3


5/18

Contract Job ref.

Part of



60095653

MAuNSELL | AECOM

5. Stress of section due to tendons:

Assume effect prestress = 70.00% Pjeck

sbot.P MDL1(kNm) stop.P sbot.P stop.P sbot.P sc st

2 24 3600.00 3339.00 0.34 4.59 113.66 0.25 -0.27 -0.32 4.31 20.00 -1.00 OK !

3 25 3675.00 3408.56 0.35 4.75 361.19 0.78 -0.87 0.14 3.88 20.00 -1.00 OK !

3 25 3675.00 3408.56 0.23 5.59 361.19 1.37 -1.14 1.42 4.46 20.00 -1.00 OK !

4 29 4275.00 3965.06 0.27 9.10 597.25 2.82 -2.28 2.69 6.83 20.00 -1.00 OK !

5 42 6300.00 5843.25 0.37 15.69 1170.95 5.53 -4.47 2.53 11.22 20.00 -1.00 OK !

6 46 6825.00 6330.19 0.39 17.39 1581.79 7.47 -6.03 3.73 11.36 20.00 -1.00 OK !

7 48 7200.00 6678.00 0.40 18.57 1828.76 8.64 -6.98 4.41 11.60 20.00 -1.00 OK !

8 48 7200.00 6678.00 0.40 18.57 1911.99 9.03 -7.29 4.81 11.28 20.00 -1.00 OK !

9 48 7200.00 6678.00 0.40 18.57 1831.41 8.65 -6.99 4.43 11.59 20.00 -1.00 OK !

10 46 6825.00 6330.19 0.39 17.39 1587.22 7.50 -6.05 3.76 11.34 20.00 -1.00 OK !

11 42 6300.00 5843.25 0.37 15.69 1179.72 5.57 -4.50 2.57 11.19 20.00 -1.00 OK !

12 29 4275.00 3965.06 0.27 9.10 608.17 2.87 -2.32 2.75 6.78 20.00 -1.00 OK !

13 25 3675.00 3408.56 0.23 5.59 374.81 1.42 -1.18 1.47 4.41 20.00 -1.00 OK !

13 25 3675.00 3408.56 0.35 4.75 374.81 0.81 -0.90 0.17 3.84 20.00 -1.00 OK !

14 24 3600.00 3339.00 0.34 4.59 116.71 0.25 -0.28 -0.32 4.31 20.00 -1.00 OK !-0.569

-3.001

-3.001

-3.743

-4.227

-4.227

-0.636

0.055

-3.743

-0.127

Allowable stress

(MPa)

effect

prestress

70%PjackkN

Stress due to prestress (MPa)Stress in cross

(MPa)ebeam.p(m) CHECKINGNODE SniTendons area

Ap(mm2)

0.055

-0.127

-4.227

Stress due to DL1 at SLS (MPa)

stop.P

-0.569

-0.636

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Allowable compressive stress

stress of beam top

stress of beam bottom

Allowable tensile stress


6/18

Contract Job ref.

Part of



60095653

MAuNSELL | AECOM

Stress due to tendons at transfer:

Prestressing force in tendons P = 6678.00 (kN)

Eccentricity of prestrssong fouce(P) e = 0.40 (m)

Section modulus attop or bottom of section:

Ztop = 0.21 (m3)

Zbottom = -0.26 (m3)

Ac= 0.80 (m2)

Stress due to tendons:

beam top: stop.P= -4.23 (MPa)

beam bottom: sbot.P= 18.57 (MPa)

=Z

eP-

A

P

topc

=Z

eP-

A

P

botc


7/18


Part of structure Calc.sheet No.

Drawing ref. Calculations by Checked by Date

1. Properties of Tendons:

Ep= 195000 (Mpa)

Ec= 27400.0 (Mpa)

fp= 1770.00 (Mpa)

fpy= 1504.50 (Mpa) (0.85fp)

Ap= 150.00 (mm2

)Breaking load (kN) Pbreaking= 265.00 (kN)

Pjack= 198.75 (kN)

Jackingstress sjack= 1327.50 (Mpa)2. Loss due to prestress tendons relaxation

considered the steam curing ,the relaxation loss take as 8% of initial prestress

R= 0.080

At transfer Rtransfer= 70%Rjack= 74.34 (Mpa)

At serviceability stage Rserviceality= 30%Rjack= 31.86 (Mpa)

3. Stress losses at transfer

(1) Anc horag e seating Loss dur ing anchor ingDL1 = 0.00 (mm)

(2) Loss due to prest ress tendons relaxat ion

DsR.tranfer= Rtransfer= 74.34 (Mpa)(3) L oss of elast ic con crete

For section 8: P = 9540.00 (kN)

Pinitial= 9004.75

ebeam.p= 0.40 (m)

Abeam= 0.80 (m2)

Zbeam.p= 0.4394 (m3)

c = 12.96 (Mpa)

fcp= 40.00 (Mpa)

Ec.50.80%= 2.4E+04 (Mpa) m= 8.13

ee= 539.95 (10-6)Dse.tranfer= Epee= 105.29 (Mpa)

(3) Total loss at transfer

For other section:

NODE Sni Pjack(kN) tendon arearelaxation

lossPi

Abeam

(m2)

ebeam.p (m)Zbeam.p

(m3)

Moment

due to DL1

stress due

to DL1c (MPa) ee (10

-6)

Dse

(MPa)Pe,tran(kN)

Pe,tran/P

%

2 24 4770.00 3600.00 267.62 4502.38 1.79 0.34 0.97 113.66 -0.12 3.86 160.95 31.39 4389.39 92.02

3 25 4869.38 3675.00 273.20 4596.18 1.79 0.34 0.95 361.19 -0.38 3.71 154.76 30.18 4485.27 92.11

3 25 4869.38 3675.00 273.20 4596.18 1.11 0.23 0.92 361.19 -0.39 4.75 198.00 38.61 4454.28 91.48

4 29 5664.38 4275.00 317.80 5346.57 0.80 0.27 0.64 597.25 -0.93 7.56 314.84 61.39 5084.12 89.76

5 42 8347.50 6300.00 468.34 7879.16 0.80 0.37 0.47 1170.95 -2.50 12.15 506.29 98.73 7257.18 86.94

6 46 9043.13 6825.00 507.37 8535.75 0.80 0.39 0.45 1581.79 -3.52 12.71 529.77 103.31 7830.70 86.59

7 48 9540.00 7200.00 535.25 9004.75 0.80 0.40 0.44 1828.76 -4.16 13.15 547.84 106.83 8235.58 86.33

8 48 9540.00 7200.00 535.25 9004.75 0.80 0.40 0.44 1911.99 -4.35 12.96 539.95 105.29 8246.67 86.44

9 48 9540.00 7200.00 535.25 9004.75 0.80 0.40 0.44 1831.41 -4.17 13.14 547.59 106.78 8235.94 86.33

10 46 9043.13 6825.00 507.37 8535.75 0.80 0.39 0.45 1587.22 -3.53 12.70 529.27 103.21 7831.37 86.60

11 42 8347.50 6300.00 468.34 7879.16 0.80 0.37 0.47 1179.72 -2.52 12.13 505.52 98.58 7258.13 86.95

12 29 5664.38 4275.00 317.80 5346.57 0.80 0.27 0.64 608.17 -0.94 7.54 314.13 61.26 5084.70 89.77

13 25 4869.38 3675.00 273.20 4596.18 1.11 0.23 0.92 374.81 -0.41 4.74 197.39 38.49 4454.72 91.48

13 25 4869.38 3675.00 273.20 4596.18 1.79 0.34 0.95 374.81 -0.39 3.70 154.16 30.06 4485.70 92.12

14 24 4770.00 3600.00 267.62 4502.38 1.79 0.34 0.97 116.71 -0.12 3.86 160.82 31.36 4389.48 92.02

MAuNSELL | AECOM

3.3 Calculation of prestress losses

=

c.50.80%

c

E

=

+ Z

eP

A

P

beam.p

p.beam

beam

189888032.xls.ms_office:LOSS 7 of 1


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6. Stress losses at beam installation - 30 days

(1) Loss due to shrinkag e of concrete (Say shrinkage loss at30 days)

Cs= 3.00 Ag= 0.75 (m2)

KL= 250.00 figure 14 ue= 7.81 (m)

KC= 1.00 figure 11 th= 192.62 (mm)

Ke= 0.80 figure 15

Kj = 0.25 figure 13

Assume slab finished after 30 days, the shrinkage losses is:

Shrinkage strains at transfer cs10-6

= Cs*KL*KC*Ke*Kj= 150.00

Loss due toshrinkage Dss= 29.25 (Mpa) (at 30 days)

(2) Loss due to creep o f conc rete (Say creep loss on 30 days )

For section 8:

Sustained stressciin the concrete at the level of the centroid of the tendons calculation:

P = 8246.67 (kN)

MDL1= 1912 (kN.m)

ebeam.p= 0.40 (m)Zbeam.p= 0.44 (m

3)

Abeam= 0.80 (m2)

Ap= 7200.00 (mm2)


cc= KL*Km*KC*Ke*Kj= 0.45

KL= 2.10

Km= 1.00

Ke= 0.85

sci.beam= 13.51 (Mpa)

creep strains cc.beam= 220.03 (10-6)

Loss due to creep Dsc.beam= Epcc.beam= 42.91 (Mpa) (at 30 days)For other section:

30 days cc= 0.45

ci (MPa) ecc

(10-6

)

Dsc

(MPa)

sci.beam. ecc.beam Dsc.beam

2 4389.39 1.79 0.34 0.97 113.66 -0.12 3.87 62.96 12.28

3 4485.27 1.79 0.35 0.95 361.19 -0.38 3.76 61.24 11.94

3 4454.28 1.11 0.23 0.92 361.19 -0.39 4.77 77.61 15.13

4 5084.12 0.80 0.27 0.64 597.25 -0.93 7.61 123.94 24.17

5 7257.18 0.80 0.37 0.47 1170.95 -2.50 12.41 202.17 39.42

6 7830.70 0.80 0.39 0.45 1581.79 -3.52 13.13 213.83 41.70

7 8235.58 0.80 0.40 0.44 1828.76 -4.16 13.68 222.73 43.43

8 8246.67 0.80 0.40 0.44 1911.99 -4.35 13.51 220.03 42.91

9 8235.94 0.80 0.40 0.44 1831.41 -4.17 13.67 222.64 43.41

10 7831.37 0.80 0.39 0.45 1587.22 -3.53 13.12 213.66 41.66

11 7258.13 0.80 0.37 0.47 1179.72 -2.52 12.40 201.90 39.37

12 5084.70 0.80 0.27 0.64 608.17 -0.94 7.59 123.68 24.12

13 4454.72 1.11 0.23 0.92 374.81 -0.41 4.75 77.38 15.09

13 4485.70 1.79 0.35 0.95 374.81 -0.39 3.75 61.01 11.90

14 4389.48 1.79 0.34 0.97 116.71 -0.12 3.86 62.91 12.27

(3) Total losses at 30 days (MPa):

For other section:

DsR.tranfer Dse.transfer S Dss.transfer Dsc.transfer S Pjeck(kN) Ap(mm2) P30days(kN)

2 74.34 31.39 105.73 29.25 12.28 147.25 4770.00 3600.00 4239.89 88.89

2 74.34 30.18 104.52 29.25 11.94 145.71 4869.38 3675.00 4333.90 89.00

3 74.34 38.61 112.95 29.25 15.13 157.34 4869.38 3675.00 4291.17 88.13

4 74.34 61.39 135.73 29.25 24.17 189.15 5664.38 4275.00 4855.75 85.72

5 74.34 98.73 173.07 29.25 39.42 241.74 8347.50 6300.00 6824.53 81.76

6 74.34 103.31 177.65 29.25 41.70 248.59 9043.13 6825.00 7346.48 81.24

7 74.34 106.83 181.17 29.25 43.43 253.85 9540.00 7200.00 7712.28 80.84

8 74.34 105.29 179.63 29.25 42.91 251.79 9540.00 7200.00 7727.14 81.00

9 74.34 106.78 181.12 29.25 43.41 253.78 9540.00 7200.00 7712.75 80.85

10 74.34 103.21 177.55 29.25 41.66 248.46 9043.13 6825.00 7347.38 81.25

11 74.34 98.58 172.92 29.25 39.37 241.54 8347.50 6300.00 6825.82 81.77

12 74.34 61.26 135.60 29.25 24.12 188.96 5664.38 4275.00 4856.56 85.74

13 74.34 38.49 112.83 29.25 15.09 157.17 4869.38 3675.00 4291.77 88.14

13 74.34 30.06 104.40 29.25 11.90 145.55 4869.38 3675.00 4334.49 89.02

14 74.34 31.36 105.70 29.25 12.27 147.22 4770.00 3600.00 4240.01 88.89

NODE Pinitial(kN) ebeam.p (m)

NODE

AT TRANSFER

Moment

due to DL1

stress

due to

DL1

Abeam(m2)

Zbeam.p

(m3)

P30days/P%

30 days Effect prestress at 30 days

E

c.50

ci.beam

cc

s

=

+ Z

eP

A

P

beam.p

p.beam

beam

=EpD cs

=u

A2

e

g



9/18




MAuNSELL | AECOM

7. Stress losses at serviceability stage

(1) Los s due to pres tress tendon s relaxation

DsR.serviceability= Rserviceability= 31.86 (Mpa)(2) Los s due to sh rinkage of con crete (Say shrinkage loss at 30 years)

Cs= 3.00 Ag= 1.21 (m2)

KL= 250.00 ue= 5.65 (m)

KC= 1.00 th= 428.18 (mm)Ke= 0.52

Kj = 1.00


Shrinkage strains at transfer cs10-6

= Cs*KL*KC*Ke*Kj= 390.00

Loss due toshrinkage Dss= 76.05 (Mpa) (at 30 years)

Loss due to shrinkage from 30 days to 30 years is:

ecs10-6=ecs.30years- ecs.30days= 240.00Loss due to shrinkage Dss=Dss.30years- Dss.30days= 46.80 (Mpa)

(3) Los s du e to creep of co ncrete (Say creep loss at 30 years)


KL= 2.10

Km= 0.50

Ke= 0.71

For section 8:

Sustained stressciin the concrete at the level of the centroid of the tendons calculation:

Pe,transfe= 8246.67 (kN)

e0.p= 0.71 (m)

A0= 1.21 (m2)

Z0.p= 0.58 (m4)

sci.0= 16.95 (Mpa)

MDL2,SDL= 1181.19 (KN*m)

sG= -6.38 (Mpa)

s= 10.57 (Mpa)

creep strains ecc.0= 287.54 (10-6)Loss due to creep Dsc.0= Epecc.0= 56.07 (Mpa) (at 30 years)

Before finishing slab (30 days), the creep losses is:


Km= 1.00

Kj = 0.10

sci.0= 10.57 (Mpa)

creep strains ecc.0= 57.51 (10-6)

Loss due to creep Dsc.0= Epecc.0= 11.21 (Mpa) (at 30 days)Loss due to creep from 30 days to 30 years is:

ecc10-6=ecc.30years- ecc.30days= 230.04Loss due to creep Dsc=Dss.30years- Dss.30days= 44.86 (Mpa)

For other section:

= 0.75 30 days = 0.15

ecc

(10-6

)

Dsc

(MPa)ci (MPa)

ecc

(10-6

)Dsc (MPa) ecc (10

-6)

Dsc

(MPa)

Mdl2,sdl sci.0 ecc.0 Dsc.0 sci.0 ecc.0 Dsc.0 ecc.0 Dsc.0

2 4389.39 2.20 0.49 1.11 120.92 3.69 100.37 19.57 3.69 20.07 3.91 80.30 15.66

3 4485.27 2.20 0.49 1.10 472.63 3.25 88.43 17.24 3.25 17.69 3.45 70.74 13.79

3 4454.28 1.52 0.48 0.97 472.63 4.27 116.17 22.65 4.27 23.23 4.53 92.93 18.12

4 5084.12 1.21 0.59 0.71 604.54 6.64 180.76 35.25 6.64 36.15 7.05 144.61 28.20

5 7257.18 1.21 0.69 0.60 878.45 10.34 281.44 54.88 10.34 56.29 10.98 225.15 43.90

6 7830.70 1.21 0.71 0.59 1052.55 10.55 287.10 55.98 10.55 57.42 11.20 229.68 44.79

7 8235.58 1.21 0.71 0.58 1150.93 10.79 293.49 57.23 10.79 58.70 11.45 234.80 45.79

8 8246.67 1.21 0.71 0.58 1181.19 10.57 287.54 56.07 10.57 57.51 11.21 230.04 44.86

9 8235.94 1.21 0.71 0.58 1145.47 10.79 293.61 57.25 10.79 58.72 11.45 234.88 45.80

10 7831.37 1.21 0.71 0.59 1044.37 10.56 287.19 56.00 10.56 57.44 11.20 229.75 44.80

11 7258.13 1.21 0.69 0.60 873.40 10.34 281.21 54.84 10.34 56.24 10.97 224.97 43.87

12 5084.70 1.21 0.59 0.71 607.47 6.62 180.21 35.14 6.62 36.04 7.03 144.17 28.11

13 4454.72 1.52 0.48 0.97 491.49 4.24 115.25 22.47 4.24 23.05 4.49 92.20 17.98

13 4485.70 2.20 0.49 1.10 491.49 3.22 87.58 17.08 3.22 17.52 3.42 70.07 13.66

14 4389.48 2.20 0.49 1.11 122.94 3.68 100.24 19.55 3.68 20.05 3.91 80.19 15.64

From 30 days to 30 years

Z0.p (m3)e0.p (m)NODE A0(m

2) ci (MPa)

30 years

Pinitial (kN)

= E

c

ci.0

cc

=

+ Z

eP

A

P

0.p

0.pdays100

0

days100

= E

c

ci.0

cc

=

+ Z

eP

A

P

0.p

0.pdays100

0

days100

=EpDcs

=uA2e

g



10/18




MAuNSELL | AECOM

(4) Total loss es at s erviceabi l ity s tage (MPa):

For section 8: DsR.serviceability= 31.86 (Mpa)Dss.serviseability= 46.80 (Mpa)Dsc.serviceability= 44.86 (Mpa)

Total losses SDsserviceability 123.52 (Mpa)For other section:

DsR.serviceability Dss.serviceability Dsc.serviceability SP30days

(kN)Ap(mm

2)

Pe(kN) (30

years)Pjack(kN) %

2 31.86 46.80 15.66 94.32 4239.89 3600.00 3900.34 4770.00 81.77 1083.43 1239.00 ok!

3 31.86 46.80 13.79 92.45 4333.90 3675.00 3994.12 4869.38 82.03 1086.84 1239.00 ok!

3 31.86 46.80 18.12 96.78 4291.17 3675.00 3935.49 4869.38 80.82 1070.88 1239.00 ok!

4 31.86 46.80 28.20 106.86 4855.75 4275.00 4398.93 5664.38 77.66 1028.99 1239.00 ok!

5 31.86 46.80 43.90 122.56 6824.53 6300.00 6052.37 8347.50 72.51 960.69 1239.00 ok!

6 31.86 46.80 44.79 123.45 7346.48 6825.00 6503.95 9043.13 71.92 952.96 1239.00 ok!

7 31.86 46.80 45.79 124.45 7712.28 7200.00 6816.27 9540.00 71.45 946.70 1239.00 ok!

8 31.86 46.80 44.86 123.52 7727.14 7200.00 6837.82 9540.00 71.68 949.70 1239.00 ok!

9 31.86 46.80 45.80 124.46 7712.75 7200.00 6816.62 9540.00 71.45 946.75 1239.00 ok!

10 31.86 46.80 44.80 123.46 7347.38 6825.00 6504.76 9043.13 71.93 953.08 1239.00 ok!

11 31.86 46.80 43.87 122.53 6825.82 6300.00 6053.89 8347.50 72.52 960.93 1239.00 ok!

12 31.86 46.80 28.11 106.77 4856.56 4275.00 4400.10 5664.38 77.68 1029.26 1239.00 ok!

13 31.86 46.80 17.98 96.64 4291.77 3675.00 3936.63 4869.38 80.84 1071.19 1239.00 ok!

13 31.86 46.80 13.66 92.32 4334.49 3675.00 3995.20 4869.38 82.05 1087.13 1239.00 ok!

14 31.86 46.80 15.64 94.30 4240.01 3600.00 3900.54 4770.00 81.77 1083.48 1239.00 ok!

Summary of strain at each stage:

DeR.tranfer10-6

Dee.transfer10-6

Des.30days 10-6 Dec.30days10-6

DeR.serviceability10

-6Des.serviceability

10-6

Dec.serviceability10

-6 S eR.loss10

-6 S ee.loss

10-6 S e

s.loss

10-6 S ec.loss 10

-6

[1] [2] [3] [4] [5] [6] [7] [8]=[1]+[5] [9]=[2] [10]=[3]+[6] [11]=[4]+[7]

2 381.23 160.95 150.00 62.96 163.38 240.00 80.30 544.62 160.95 390.00 143.26

3 381.23 154.76 150.00 61.24 163.38 240.00 70.74 544.62 154.76 390.00 131.98

3 381.23 198.00 150.00 77.61 163.38 240.00 92.93 544.62 198.00 390.00 170.55

4 381.23 314.84 150.00 123.94 163.38 240.00 144.61 544.62 314.84 390.00 268.55

5 381.23 506.29 150.00 202.17 163.38 240.00 225.15 544.62 506.29 390.00 427.33

6 381.23 529.77 150.00 213.83 163.38 240.00 229.68 544.62 529.77 390.00 443.51

7 381.23 547.84 150.00 222.73 163.38 240.00 234.80 544.62 547.84 390.00 457.52

8 381.23 539.95 150.00 220.03 163.38 240.00 230.04 544.62 539.95 390.00 450.07

9 381.23 547.59 150.00 222.64 163.38 240.00 234.88 544.62 547.59 390.00 457.52

10 381.23 529.27 150.00 213.66 163.38 240.00 229.75 544.62 529.27 390.00 443.41

11 381.23 505.52 150.00 201.90 163.38 240.00 224.97 544.62 505.52 390.00 426.87

12 381.23 314.13 150.00 123.68 163.38 240.00 144.17 544.62 314.13 390.00 267.85

13 381.23 197.39 150.00 77.38 163.38 240.00 92.20 544.62 197.39 390.00 169.58

13 381.23 154.16 150.00 61.01 163.38 240.00 70.07 544.62 154.16 390.00 131.08

14 381.23 160.82 150.00 62.91 163.38 240.00 80.19 544.62 160.82 390.00 143.10

NODE

At serviseability stage (30d to 30y)At 30 daysAt transfer

NODE

Effect prestress at 30 years

check70% fp

Total strains

Total losses at serviceality stage (MPa) Pe/ Pjack

sp(MPa)


11/18

Contract Job ref.

Part of



f 'c.beam= 50.00 (Mpa)

f 'c.slab= 40.00 (Mpa)

Pjack= 198.75 (kN)

Abeam(m2) Z

beam.top

(m3)

Zbeam.bot

(m3)

ebeam.p(m) A0(m2) Z

0.top1

(m3)

Z0.bot

(m3)

e0.p(m) P (kN)stop.P

(N/m2)

sbot.P

(N/m2)

Pe(kN) stop1.P

(N/m2)

sbot.P

(N/m2)

[1] [2] [3] [5] [8] [9] [10] [12] [4]

[6]=

[4]/[1]-

[4][5]/[2]

[7]=

[4]/[1]-

[4][5]/[3]

[11]

[13]=

[11]/[8]-

[11][12]/[9]

[14]=

[11]/[8]-

[11][12]/[10]

2 1.79 0.46 -0.41 0.34 2.20 0.97 -0.58 0.49 4389.39 -0.75 6.03 3900.34 -0.19 5.07

3 1.79 0.46 -0.41 0.35 2.20 0.97 -0.58 0.49 4485.27 -0.84 6.25 3994.12 -0.22 5.24

3 1.11 0.26 -0.32 0.23 1.52 0.82 -0.50 0.48 4454.28 0.07 7.31 3935.49 0.26 6.36

4 0.80 0.21 -0.26 0.27 1.21 0.81 -0.42 0.59 5084.12 -0.16 11.67 4398.93 0.43 9.76

5 0.80 0.21 -0.26 0.37 1.21 0.81 -0.42 0.69 7257.18 -3.73 19.48 6052.37 -0.17 14.89

6 0.80 0.21 -0.26 0.39 1.21 0.81 -0.42 0.71 7830.70 -4.63 21.51 6503.95 -0.31 16.25

7 0.80 0.21 -0.26 0.40 1.21 0.81 -0.42 0.71 8235.58 -5.21 22.90 6816.27 -0.40 17.18

8 0.80 0.21 -0.26 0.40 1.21 0.81 -0.42 0.71 8246.67 -5.22 22.93 6837.82 -0.40 17.23

9 0.80 0.21 -0.26 0.40 1.21 0.81 -0.42 0.71 8235.94 -5.21 22.90 6816.62 -0.40 17.18

10 0.80 0.21 -0.26 0.39 1.21 0.81 -0.42 0.71 7831.37 -4.63 21.52 6504.76 -0.31 16.26

11 0.80 0.21 -0.26 0.37 1.21 0.81 -0.42 0.69 7258.13 -3.73 19.48 6053.89 -0.17 14.89

12 0.80 0.21 -0.26 0.27 1.21 0.81 -0.42 0.59 5084.70 -0.16 11.67 4400.10 0.43 9.76

13 1.11 0.26 -0.32 0.23 1.52 0.82 -0.50 0.48 4454.72 0.07 7.31 3936.63 0.26 6.37

13 1.79 0.46 -0.41 0.35 2.20 0.97 -0.58 0.49 4485.70 -0.84 6.25 3995.20 -0.22 5.24

14 1.79 0.46 -0.41 0.34 2.20 0.97 -0.58 0.49 4389.48 -0.75 6.03 3900.54 -0.19 5.07

Section modulus above top or bottom of section:

Ztop.1 = 0.21 (m3)


Ac= 0.80 (m2)

Eccentricity of prestrssong fouce(P) e = 0.40 (m)

Stress due to tendons at transfer:



beam top: stop1.P= -5.22 (N/mm2)

beam bottom: sbot.P= 22.93 (N/mm2)

Stress due to tendons at serviceality stage:



beam top: stop1.P= -0.40 (N/mm2)

beam bottom: sbot.P= 17.23 (N/mm2)

MAuNSELL | AECOM

NODE

AT TRANSFER AT SERVICEABILITY STAGEBEAM SECTION

3.4 Sections Stress due to Tendons

BEAM-SLAB SECTION

60095653

=Z

eP-

A

P

topc

=Z

eP-

A

P

botc

=Z

eP-

A

P

topc

=Z

eP-

A

P

topc

=Z

eP-

A

P

botc

189888032.xls.ms_office:P-STRESS 11 of 18


12/18


Part of



1. Stress checking at transfer:

fcp= 40.00 (Mpa)

sc.transfer= 20.00 (Mpa)st.transfer= -1.00 (Mpa)

stop.P

(N/mm

2

)

sbot.P

(N/mm

2

)

MOMENT

(kNm)

stop.DL1

(N/mm

2

)

sbot.DL1

(N/mm

2

)

stop

(N/mm

2

)

sbot

(N/mm

2

)

sc

(N/mm

2

)

st

(N/mm

2

)

CHECKING

[1] [2] [3] [4] [5] [6] [7]=[6]/[2] [8]=[6]/[3] [9]=[4]+[7] [10]=[5]+[8] [11] [12] [13]

2 1.788 0.463 -0.415 -0.75 6.03 113.66 0.25 -0.27 -0.50 5.76 20.00 -1.00 OK !

3 1.788 0.463 -0.415 -0.84 6.25 361.19 0.78 -0.87 -0.06 5.37 20.00 -1.00 OK !

3 1.106 0.264 -0.318 0.07 7.31 361.19 1.37 -1.14 1.44 6.17 20.00 -1.00 OK !

4 0.796 0.212 -0.262 -0.16 11.67 597.25 2.82 -2.28 2.66 9.39 20.00 -1.00 OK !

5 0.796 0.212 -0.262 -3.73 19.48 1170.95 5.53 -4.47 1.81 15.02 20.00 -1.00 OK !

6 0.796 0.212 -0.262 -4.63 21.51 1581.79 7.47 -6.03 2.84 15.48 20.00 -1.00 OK !

7 0.796 0.212 -0.262 -5.21 22.90 1828.76 8.64 -6.98 3.43 15.93 20.00 -1.00 OK !

8 0.796 0.212 -0.262 -5.22 22.93 1911.99 9.03 -7.29 3.81 15.64 20.00 -1.00 OK !

9 0.796 0.212 -0.262 -5.21 22.90 1831.41 8.65 -6.99 3.44 15.92 20.00 -1.00 OK !10 0.796 0.212 -0.262 -4.63 21.52 1587.22 7.50 -6.05 2.87 15.46 20.00 -1.00 OK !

11 0.796 0.212 -0.262 -3.73 19.48 1179.72 5.57 -4.50 1.85 14.98 20.00 -1.00 OK !

12 0.796 0.212 -0.262 -0.16 11.67 608.17 2.87 -2.32 2.71 9.35 20.00 -1.00 OK !

13 1.106 0.264 -0.318 0.07 7.31 374.81 1.42 -1.18 1.49 6.13 20.00 -1.00 OK !

13 1.788 0.463 -0.415 -0.84 6.25 374.81 0.81 -0.90 -0.03 5.34 20.00 -1.00 OK !

14 1.788 0.463 -0.415 -0.75 6.03 116.71 0.25 -0.28 -0.50 5.75 20.00 -1.00 OK !

Moment due to selfweight of super T (DL1):

MDL1 = 1911.99 (kNm)

Section peculiarity:

Ztop = 0.21 (m3)


Ac= 0.80 (m2)

Stress due to DL1:

beam top: stop.DL1= 9.03 (N/mm2)beam bottom: sbot.DL1= -7.29 (N/mm2)


beam top: stop.P= -5.22 (N/mm2)beam bottom: sbot.P= 22.93 (N/mm2)

Stress section top: stop=stop.DL1+ stop.P= 3.81 (N/mm2) OK !Stress section bpttom: sbot=sbot.DL1+ sbot.P= 15.64 (N/mm2) OK !

MAuNSELL | AECOM

SRETSS DUE TO TENDON

NODE

3.5 Stress Checking

Zbeam.bot

(m3)

Zbeam.top

(m3)

Abeam

(m2)

STRESS CHECKING AT TRANSFERSTRESS DUE TO DL1

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

STRESS OF BEAM TOP

STRESS OF BEAM BOTTOM

ALLOWABLE COMPRESSIVE STRESS

ALLOWABLE TRNSILE STRESS

=

top

1DL

Z

M

=

bot

1DL

Z

M

189888032.xls.ms_office:At transfer 12 of 18


13/18


Part of



2. Stress checking at serviceability stage:



sc.serviceability.top = 20.00 (Mpa) sc.serviceability.bot = 20.00 (Mpa)st.serviceability.top = 0.00 (Mpa) st.serviceability.bot = 0.00 (Mpa)

A

stop1.P sbot.Ptop1.DL1

2

bot.DL1

2

[1] [2] [3] [4] [5] [6] [7]=[6]/[2] [8]=[6]/[3]=[4]+[7]=[4]+[8]2 0.463 -0.415 -0.19 5.07 113.66 0.25 -0.27 0.06 4.79

3 0.463 -0.415 -0.22 5.24 361.19 0.78 -0.87 0.56 4.37

3 0.264 -0.318 0.26 6.36 361.19 1.37 -1.14 1.63 5.23

4 0.212 -0.262 0.43 9.76 597.25 2.82 -2.28 3.26 7.48

5 0.212 -0.262 -0.17 14.89 1170.95 5.53 -4.47 5.37 10.42

6 0.212 -0.262 -0.31 16.25 1581.79 7.47 -6.03 7.16 10.22

7 0.212 -0.262 -0.40 17.18 1828.76 8.64 -6.98 8.24 10.20

8 0.212 -0.262 -0.40 17.23 1911.99 9.03 -7.29 8.63 9.94

9 0.212 -0.262 -0.40 17.18 1831.41 8.65 -6.99 8.25 10.19

10 0.212 -0.262 -0.31 16.26 1587.22 7.50 -6.05 7.19 10.20

11 0.212 -0.262 -0.17 14.89 1179.72 5.57 -4.50 5.41 10.39

12 0.212 -0.262 0.43 9.76 608.17 2.87 -2.32 3.31 7.44

13 0.264 -0.318 0.26 6.37 374.81 1.42 -1.18 1.68 5.19

13 0.463 -0.415 -0.22 5.24 374.81 0.81 -0.90 0.59 4.3414 0.463 -0.415 -0.19 5.07 116.71 0.25 -0.28 0.07 4.78

A stop.max

MAX. MIN. MAX. MIN. stop stop1 sbot stop stop1 sbot MAX. MIN. MAX. MIN. stop stop1 sbot stop stop1 sbot

[1] [2] [3] [4] [5] [6] [7] [8]=[6]/[1] [9]=[6]/[2] [10]=[6]/[3] [11]=[7]/[1] [12]=[7]/[2] [13]=[7]/[3] [4] [5] [6] [7] [8]=[6]/[1] [9]=[6]/[2][10]=[6]/[

3]

[11]=[7]/[1

]

[12]=[7]/[

2]

[13]=[7]/[

3]

2 2.195 0.712 0.966 -0.577 0.000 0.000 294.52 85.31 0.41 0.30 -0.51 0.12 0.09 -0.15 0.000 0.000 475.27 50.42 0.67 0.49 -0.82 0.07 0.05 -0.09 0.67

3 2.195 0.712 0.966 -0.577 0.000 0.000 1138.22 335.77 1.60 1.18 -1.97 0.47 0.35 -0.58 0.000 0.000 1834.20 200.63 2.58 1.90 -3.18 0.28 0.21 -0.35 2.58

3 1.525 0.607 0.820 -0.503 0.000 0.000 1138.22 335.77 1.87 1.39 -2.26 0.55 0.41 -0.67 0.000 0.000 1834.20 200.63 3.02 2.24 -3.64 0.33 0.24 -0.40 3.02

4 1.210 0.582 0.808 -0.422 0.000 0.000 1534.05 509.65 2.64 1.90 -3.63 0.88 0.63 -1.21 0.000 0.000 2582.18 417.66 4.44 3.20 -6.12 0.72 0.52 -0.99 4.44

5 1.210 0.582 0.808 -0.422 0.000 0.000 2371.04 787.69 4.08 2.94 -5.62 1.35 0.98 -1.87 0.000 0.000 4141.62 742.13 7.12 5.13 -9.81 1.28 0.92 -1.76 7.12

6 1.210 0.582 0.808 -0.422 0.000 0.000 2920.62 930.67 5.02 3.62 -6.92 1.60 1.15 -2.20 0.000 0.000 5127.47 906.87 8.81 6.35 -12.15 1.56 1.12 -2.15 8.81

7 1.210 0.582 0.808 -0.422 0.000 0.000 3192.84 1026.51 5.49 3.95 -7.56 1.76 1.27 -2.43 0.000 0.000 5617.28 1014.43 9.66 6.95 -13.31 1.74 1.26 -2.40 9.66

8 1.210 0.582 0.808 -0.422 0.000 0.000 3240.17 1070.74 5.57 4.01 -7.68 1.84 1.33 -2.54 0.000 0.000 5713.63 1062.73 9.82 7.07 -13.53 1.83 1.32 -2.52 9.82

9 1.210 0.582 0.808 -0.422 0.000 0.000 3180.59 1019.39 5.47 3.94 -7.53 1.75 1.26 -2.41 0.000 0.000 5595.83 1007.38 9.62 6.93 -13.26 1.73 1.25 -2.39 9.62

10 1.210 0.582 0.808 -0.422 0.000 0.000 2902.33 919.44 4.99 3.59 -6.88 1.58 1.14 -2.18 0.000 0.000 5094.69 895.50 8.76 6.31 -12.07 1.54 1.11 -2.12 8.76

11 1.210 0.582 0.808 -0.422 0.000 0.000 2360.12 782.56 4.06 2.92 -5.59 1.35 0.97 -1.85 0.000 0.000 4121.10 735.56 7.08 5.10 -9.76 1.26 0.91 -1.74 7.08

12 1.210 0.582 0.808 -0.422 0.000 0.000 1551.63 509.93 2.67 1.92 -3.68 0.88 0.63 -1.21 0.000 0.000 2601.78 413.50 4.47 3.22 -6.16 0.71 0.51 -0.98 4.47

13 1.525 0.607 0.820 -0.503 0.000 0.017 1199.42 342.89 1.98 1.46 -2.38 0.56 0.42 -0.68 0.000 0.000 1916.31 195.09 3.16 2.34 -3.81 0.32 0.24 -0.39 3.16

13 2.195 0.712 0.966 -0.577 0.000 0.017 1199.42 342.89 1.68 1.24 -2.08 0.48 0.35 -0.59 0.000 0.000 1916.31 195.09 2.69 1.98 -3.32 0.27 0.20 -0.34 2.69

14 2.195 0.712 0.966 -0.577 0.000 0.000 305.04 86.90 0.43 0.32 -0.53 0.12 0.09 -0.15 0.000 0.000 487.64 49.37 0.68 0.50 -0.85 0.07 0.05 -0.09 0.68


Ztop = 0.58 (m3)

Ztop1 = 0.81


Moment due to loads(HB25):

Mmax = 3240.17 (kNm)

Stress due to loads moment:

stop.max= 5.57 (MPa)

stop1.max= 4.01 (MPa)

sbot.max= -7.68 (MPa)Moment due to loads(HB45):

Mmax = 5713.63 (kNm)

Stress due to loads moment(HB45):



sbot.max= -13.53 (MPa)Stress due to tendons + DL1 at serviceability stage:

stop1.P+DL1= 8.63 (MPa)sbot.P+DL1= 9.94 (MPa)

Stress due to tendons + all LOADS at serviceability stage:

Stress section top: stop= stop.max 9.82 (MPa) OK !stop1= stop1.max+ stop1.P+DL1= 15.71 (MPa) OK !

Stress section bpttom: sbot= sbot.max+ sbot.P+DL1= 2.26 (MPa) OK !

STRESS DUE TO OTHER LOADS(HB45) (MPa)

N(KN) MOMENT (kNm)

MAX.MOMENTMOMENT (kNm) STRESS DUE TO MAX.MOMENT

MIN.MONENT

MOMEN

T (kNm)

stop1.DL1

(MPa)

=MAX([8],[11])

STRESS

MAuNSELL | AECOM

3.5 Stress Checking

NODEZ0.top

(m3)

Z0.top1

(m3)

Z0.bot

(m3)

NODEZbeam.top

(m3)

Zbeam.bot

(m3)

sbot.DL1

(MPa)

SRETSS DUE TO

TENDON + DL (MPa)

STRESS DUE TO MIN.MONENT

STRESS DUE TO DL1Zbeam.top

1

(m3)

SRETSS DUE TO

TENDON (MPa)

N(KN)

STRESS DUE TO OTHER LOADS (HB25)(MPa)

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


MAX. STRESS OF SLAB TOP

MAX. STRESS OF BEAM TOP

MIN. STRESS OF BEAM TOP

MAX.STRESS OF BEAM BOTTOM

MIN STRESS OF BEAM BOTTOM

ALLOWABLE TRANSILE STRESS

=

top.0

max

Z

M

=

bot.0

max

Z

M

=

1top.0

max

ZM

=

top.0

max

Z

M

=

bot.0

max

Z

M

=

1top.0

max

Z

M


14/18

Contract Job ref.

Part of



3. Stress checking at serviceability stage (Consider thermal effects):



sc.serviceability.top= 20.00 (Mpa) sc.serviceability.bot= 20.00 (Mpa)st.serviceability.top= -3.20 (Mpa) st.serviceability.bot= -3.20 (Mpa)

A

stop1.P sbot.Ptop1.DL1

2

bot.DL1

2

[1] [2] [3] [4] [5] [6]= = =[4]+[7]=[4]+[8]

2 0.463 -0.415 -0.19 5.07 113.66 0.25 -0.27 0.06 4.79

3 0.463 -0.415 -0.22 5.24 361.19 0.78 -0.87 0.56 4.37

3 0.264 -0.318 0.26 6.36 361.19 1.37 -1.14 1.63 5.23

4 0.212 -0.262 0.43 9.76 597.25 2.82 -2.28 3.26 7.48

5 0.212 -0.262 -0.17 14.89 1170.95 5.53 -4.47 5.37 10.42

6 0.212 -0.262 -0.31 16.25 1581.79 7.47 -6.03 7.16 10.22

7 0.212 -0.262 -0.40 17.18 1828.76 8.64 -6.98 8.24 10.20

8 0.21 -0.262 -0.40 17.23 1911.99 9.03 -7.29 8.63 9.94

9 0.212 -0.262 -0.40 17.18 1831.41 8.65 -6.99 8.25 10.19

10 0.212 -0.262 -0.31 16.26 1587.22 7.50 -6.05 7.19 10.20

11 0.212 -0.262 -0.17 14.89 1179.72 5.57 -4.50 5.41 10.39

12 0.212 -0.262 0.43 9.76 608.17 2.87 -2.32 3.31 7.44

13 0.264 -0.318 0.26 6.37 374.81 1.42 -1.18 1.68 5.19

13 0.463 -0.415 -0.22 5.24 374.81 0.81 -0.90 0.59 4.34

14 0.463 -0.415 -0.19 5.07 116.71 0.25 -0.28 0.07 4.78

A stop.max stop1.max stop.min sbot.max sbot.min

MAX. MIN. MAX. MIN. stop stop1 sbot stop stop1 sbotsc

[1] [2] [3] [4] [5] [6] [7] [8]=[6]/[1] [9]=[6]/[2] [10]=[6]/[3] [11]=[7]/[1] [12]=[7]/[2] [13]=[7]/[3]

2 2.195 0.71 0.97 -0.58 0.00 0.00 398.66 64.52 0.56 0.41 -0.69 0.09 0.07 -0.11 0.56 0.47 0.13 4.68 4.10 20

3 2.195 0.71 0.97 -0.58 0.00 0.00 1540.32 251.77 2.16 1.59 -2.67 0.35 0.26 -0.44 2.16 2.15 0.82 3.93 1.70 20

3 1.525 0.61 0.82 -0.50 0.00 0.00 1540.32 251.77 2.54 1.88 -3.06 0.41 0.31 -0.50 2.54 3.51 1.94 4.73 2.17 20

4 1.210 0.58 0.81 -0.42 0.00 0.00 2130.73 419.79 3.66 2.64 -5.05 0.72 0.52 -0.99 3.66 5.89 3.78 6.49 2.43 20

5 1.210 0.58 0.81 -0.42 0.00 0.00 3316.53 622.35 5.70 4.11 -7.86 1.07 0.77 -1.47 5.70 9.47 6.14 8.95 2.57 20

6 1.210 0.58 0.81 -0.42 0.00 0.00 4071.45 678.18 7.00 5.04 -9.64 1.17 0.84 -1.61 7.00 12.20 8.00 8.61 0.58 20

7 1.210 0.58 0.81 -0.42 0.00 0.00 4438.04 722.93 7.63 5.49 -10.51 1.24 0.90 -1.71 7.63 13.74 9.14 8.49 -0.31 20

8 1.210 0.58 0.81 -0.42 0.00 0.00 4498.54 750.16 7.73 5.57 -10.66 1.29 0.93 -1.78 7.73 14.20 9.56 8.16 -0.72 20

9 1.210 0.58 0.81 -0.42 0.00 0.00 4419.43 715.06 7.60 5.47 -10.47 1.23 0.89 -1.69 7.60 13.73 9.14 8.50 -0.28 20

10 1.210 0.58 0.81 -0.42 0.00 0.00 4043.21 665.61 6.95 5.01 -9.58 1.14 0.82 -1.58 6.95 12.19 8.01 8.63 0.62 20

11 1.210 0.58 0.81 -0.42 0.00 0.00 3298.99 615.78 5.67 4.08 -7.81 1.06 0.76 -1.46 5.67 9.49 6.17 8.93 2.58 20

12 1.210 0.58 0.81 -0.42 0.00 0.00 2150.09 419.09 3.70 2.66 -5.09 0.72 0.52 -0.99 3.70 5.97 3.83 6.45 2.35 20

13 1.525 0.61 0.82 -0.50 0.00 0.00 1614.66 256.13 2.66 1.97 -3.21 0.42 0.31 -0.51 2.66 3.65 1.99 4.68 1.98 20

13 2.195 0.71 0.97 -0.58 0.00 0.00 1614.66 256.13 2.27 1.67 -2.80 0.36 0.27 -0.44 2.27 2.26 0.85 3.89 1.54 20

14 2.195 0.71 0.97 -0.58 0.00 0.00 410.60 65.36 0.58 0.42 -0.71 0.09 0.07 -0.11 0.58 0.49 0.13 4.67 4.07 20


Ztop = 0.58 (m3)

Ztop1 = 0.81


Moment due to loads:

Mmax = 4498.54 (kNm)






Stress due to thermal effects:

stop.TL.max = 0.00 (MPa) stop.TL.min = 0.00 (MPa)stop1.TL.max= 0.00 (MPa) stop1.TL.min= 0.00 (MPa)sbot.TL.max= 0.00 (MPa) sbot.TL.min= 0.00 (MPa)


Stress section top: stop= stop1.max+ stop1.TL= 7.73 (MPa) OK !stop1= stop1.max+ stop1.P+DL1+stop1.TL= 14.20 (MPa) OK !

Stress section bottom: sbot= stop1.max+ sbot1.P+DL1+sbot.TL= -0.72 (MPa) OK !

60095653

ST

SER

3.5 Stress Checking

STRESS DUE TO DL1 SRETSS DUE TOTENDON + DL (MPa)

MOMENT

(kNm)

stop1.DL1

(MPa)

sbot.DL1

(MPa)

N(KN)NODEZ0.top

(m3)

MAuNSELL | AECOM

NODEZbeam.top

(m3)

Zbeam.top1

(m3)

Zbeam.bot

(m3)

SRETSS DUE TO

TENDON (MPa)

Z0.top1

(m3)

Z0.bot

(m3)

STRESS DUE TO OTHER LOADS (MPa)

MOMENT (kNm) STRESS DUE TO MAX.MOMENT STRESS DUE TO MIN.MONENT

STRESS DUE TO LOADS + PRESTRESS (MPa)

=+MIN([10],[13])

=MAX([8],[11])

=+MAX([9],[12])

=+MIN([9],[12])

=+MAX([10],[13])

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15








=

top.0

max

Z

M

=

bot.0

max

ZM

=

1top.0

max

Z

M


15/18


Part of



2. Stress checking at serviceability stage:


f 'c.slab= 40.00 (Mpa)sc.serviceability.top= 20.00 (Mpa) sc.serviceability.bot= 20.00 (Mpa)st.serviceability.top= -3.20 (Mpa) st.serviceability.bot= -3.20 (Mpa)

A

stop1.P sbot.Pstop1.DL1

2

sbot.DL12

stop stop1 sbot stop stop1 sbot stop stop1 sbot stop stop1

[1] [2] [3] [4] [5] [6] [7]=[6]/[2] [8]=[6]/[3]=[4]+[7]=[4]+[8] {1} {2} {3} {4} {5} {6} [a1] [a2] [a3] [b1] [b2]2 0.463 -0.415 -0.19 5.07 113.66 0.25 -0.27 0.06 4.79 0.000 0.000 0.000 0.000 0.000 0.000 2.701 -0.284 0.965 -1.339 0.016

3 0.463 -0.415 -0.22 5.24 361.19 0.78 -0.87 0.56 4.37 0.000 0.000 0.000 0.000 0.000 0.000 2.701 -0.284 0.965 -1.339 0.016 3 0.264 -0.318 0.26 6.36 361.19 1.37 -1.14 1.63 5.23 0.000 0.000 0.000 0.000 0.000 0.000 2.379 -0.574 0.884 -1.152 0.206

4 0.212 -0.262 0.43 9.76 597.25 2.82 -2.28 3.26 7.48 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

5 0.212 -0.262 -0.17 14.89 1170.95 5.53 -4.47 5.37 10.42 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

6 0.212 -0.262 -0.31 16.25 1581.79 7.47 -6.03 7.16 10.22 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

7 0.212 -0.262 -0.40 17.18 1828.76 8.64 -6.98 8.24 10.20 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

8 0.21 -0.26 -0.40 17.23 1911.99 9.03 -7.29 8.63 9.94 0.00 0.00 0.00 0.00 0.00 0.00 2.265 -0.675 0.857 -1.068 0.296

9 0.212 -0.262 -0.40 17.18 1831.41 8.65 -6.99 8.25 10.19 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

10 0.212 -0.262 -0.31 16.26 1587.22 7.50 -6.05 7.19 10.20 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

11 0.212 -0.262 -0.17 14.89 1179.72 5.57 -4.50 5.41 10.39 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

12 0.212 -0.262 0.43 9.76 608.17 2.87 -2.32 3.31 7.44 0.000 0.000 0.000 0.000 0.000 0.000 2.265 -0.675 0.857 -1.068 0.296

13 0.264 -0.318 0.26 6.37 374.81 1.42 -1.18 1.68 5.19 0.000 0.000 0.000 0.000 0.000 0.000 2.379 -0.574 0.884 -1.152 0.206

13 0.463 -0.415 -0.22 5.24 374.81 0.81 -0.90 0.59 4.34 0.000 0.000 0.000 0.000 0.000 0.000 2.701 -0.284 0.965 -1.339 0.01

14 0.463 -0.415 -0.19 5.07 116.71 0.25 -0.28 0.07 4.78 0.000 0.000 0.000 0.000 0.000 0.000 2.701 -0.284 0.965 -1.339 0.016

A stop.max stop1.max stop1.min sbot.max sbot.min

MAX. MIN. MAX. MIN. stop stop1 sbot stop stop1 sbot sc(MPa) st

CHECKING

[1] [2] [3] [4] [5] [6] [7] [8]=[6]/[1] [9]=[6]/[2] [10]=[6]/[3] [11]=[7]/[1] [12]=[7]/[2] [13]=[7]/[3]

2 2.195 0.712 0.966 -0.577 0.000 0.000 392.54 70.64 0.55 0.41 -0.68 0.10 0.07 -0.12 3.25 0.48 -0.15 5.63 2.39 20.00 -3.20 OK !

3 2.195 0.712 0.966 -0.577 0.000 0.000 1515.76 276.33 2.13 1.57 -2.63 0.39 0.29 -0.48 4.83 2.14 0.56 4.85 0.02 20.00 -3.20 OK !

3 1.525 0.607 0.820 -0.503 0.000 0.000 1515.76 276.33 2.50 1.85 -3.01 0.46 0.34 -0.55 4.88 3.68 1.39 5.56 0.71 20.00 -3.20 OK !

4 1.210 0.582 0.808 -0.422 0.000 0.000 2091.59 458.93 3.60 2.59 -4.95 0.79 0.57 -1.09 5.86 6.14 3.15 7.25 1.16 20.00 -3.20 OK !

5 1.210 0.582 0.808 -0.422 0.000 0.000 3242.33 763.21 5.57 4.01 -7.68 1.31 0.94 -1.81 7.84 9.68 5.64 9.47 1.37 20.00 -3.20 OK !

6 1.210 0.582 0.808 -0.422 0.000 0.000 3972.16 917.87 6.83 4.92 -9.41 1.58 1.14 -2.17 9.09 12.38 7.62 8.90 -0.56 20.00 -3.20 OK !

7 1.210 0.582 0.808 -0.422 0.000 0.000 4323.69 1019.92 7.43 5.35 -10.24 1.75 1.26 -2.42 9.70 13.89 8.83 8.64 -1.41 20.00 -3.20 OK !

8 1.210 0.582 0.808 -0.422 0.000 0.000 4379.13 1066.12 7.53 5.42 -10.37 1.83 1.32 -2.53 9.79 14.35 9.28 8.27 -1.81 20.00 -3.20 OK !

9 1.210 0.582 0.808 -0.422 0.000 0.000 4304.97 1013.09 7.40 5.33 -10.20 1.74 1.25 -2.40 9.67 13.88 8.83 8.65 -1.38 20.00 -3.20 OK !

10 1.210 0.582 0.808 -0.422 0.000 0.000 3943.70 907.11 6.78 4.88 -9.34 1.56 1.12 -2.15 9.04 12.37 7.64 8.91 -0.51 20.00 -3.20 OK !

11 1.210 0.582 0.808 -0.422 0.000 0.000 3224.43 758.39 5.54 3.99 -7.64 1.30 0.94 -1.80 7.81 9.70 5.67 9.45 1.39 20.00 -3.20 OK !

12 1.210 0.582 0.808 -0.422 0.000 0.000 2110.51 458.68 3.63 2.61 -5.00 0.79 0.57 -1.09 5.89 6.22 3.20 7.21 1.07 20.00 -3.20 OK !

13 1.525 0.607 0.820 -0.503 0.000 0.000 1589.55 281.24 2.62 1.94 -3.16 0.46 0.34 -0.56 5.00 3.82 1.45 5.51 0.52 20.00 -3.20 OK !

13 2.195 0.712 0.966 -0.577 0.000 0.000 1589.55 281.24 2.23 1.65 -2.76 0.39 0.29 -0.49 4.93 2.25 0.60 4.81 -0.14 20.00 -3.20 OK !

14 2.195 0.712 0.966 -0.577 0.000 0.000 404.35 71.61 0.57 0.42 -0.70 0.10 0.07 -0.12 3.27 0.50 -0.14 5.62 2.37 20.00 -3.20 OK !


Ztop = 0.58 (m3)

Ztop1 = 0.81


Moment due to loads:

Mmax = 4379.13 (kNm)






Stress due to temperature effect at serviceability stage:

stop.temp= 2.27 (MPa)stop1.temp= 0.30 (MPa)sbot.temp= -1.37 (MPa)


Stress section top: stop= stop.max+top.temp 9.79 (MPa) OK !stop1= stop1.max+ stop1.P+DL1+top1.temp= 14.35 (MPa) OK !

Stress section bpttom: sbot= sbot.max+ sbot.P+DL1+ bot.temp= -1.81 (MPa) OK !

STRESS DUE TO MIN.MONENT

STRESS DUE TO OTHER LOADS (MPa) STRESS DUE TO LOADS + PRESTRESS (MPa)

=+MIN({3}+[a3],{6}+[b3])+

MIN([10],[13])

= MAX({1}+[a1],{4} +[b1])+

MAX([8],[11])

=+MAX({2}+[a2],{5}+[b

2])+MAX([9],[1

2])

=+MIN({2}+[a2],{5}+[b

2]

)+MIN([9],[12

])

=+MAX({3}+ [a3],{6}+

[b3])+MAX([10],

[13])

Negative

SRETSS DUE TO

TENDON + DL (MPa)

NODEZ0.top

(m3)

Z0.top1

(m3)

Z0.bot

(m3)

STRESS CHECKING AT

SERVICEABILITY STAGEN(KN) MOMENT (kNm) STRESS DUE TO MAX.MOMENT

STRESS SUM DUE TO THERMAL EFFETS (MPa)

MAX. MIN.MOMEN

T (kNm)

stop1.DL1

(MPa)

sbot.DL1

(MPa)

MAuNSELL | AECOM

3.5 Stress Checking

NODEZbeam.top

(m3)

Zbeam.top

1

(m3)

Zbeam.bot

(m3)

SRETSS DUE TO

TENDON (MPa)

RESIDUE TEMPERATURE STRESS (MPa

(FROM LOAD ANALYSIS)

Positive

STRESS DUE TO DL1

-5.00

0.00

5.00

10.00

15.00

20.00

25.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15








=

top.0

max

Z

M

=

bot.0

max

Z

M =1top.0

max

Z

M


16/18


17/18


Part of



MAuNSELL | AECOM

yi

ni

Section

(2,4) 6 0 8 4 0 0 6

(4,5) 7 4 8 4 0 0 6

(5,6) 15 9 8 4 0 0 6 (6,7) 17 11 8 4 0 0 6

(7,8) 17 13 8 4 0 0 6

(7,8) 17 13 8 4 0 0 6

(6,7) 17 11 8 4 0 0 6

(5,6) 15 9 8 4 0 0 6

(4,5) 7 4 8 4 0 0 6

(2,4) 6 0 8 4 0 0 6

For section (2,4)

Value of the moment in M diagram M1= P X ni ( yb - yi )=P[n1(yb-y1)+n2(yb-y2)+]= 1022.80 (KNm)

Area of the virtual M diagram A1= 1/2 Xl1X 1/2 X l1= 1.156 (m2)

For other sections:

NODE Mi (KNm) A i(m2) MiX A i

(2,4) 1022.80 1.156 1181.969

(4,5) 1497.71 5.220 7818.070

(5,6) 2966.85 9.425 27962.547

(6,7) 3347.08 13.630 45620.667

(7,8) 3605.99 17.835 64312.828

(7,8) 3605.99 18 64312.828

(6,7) 3347.08 13.630 45620.667

(5,6) 2966.85 9.425 27962.547

(4,5) 1497.71 5.220 7818.070

(2,4) 1022.80 1.156 1181.969

iX i

The short term deflection due to prestressing fp= -69.40 (mm)

qg1= pre.conX Ab= 18.43 (KN/m)

Dflection due to dead load of beam fg1= 32.41 (mm)

Deflection due to prestressing and dead load of beam at tranfer is:

ftransfer= fp+fg1= -36.98 (mm)

5. 28 days

fc28d= 50 (Mpa)

E28d= 27400.00 (Mpa)

5.1 Prestress loss due to shrinkage from 0 to 28 days.

Cs= 3.00 Ag= 0.75 (m2)

KL= 250.00 ue= 7.81 (m)

KC= 1.00 th= 192.62

Ke= 0.80

Kj = 0.25

The design shrinkage strain 1.cs28d= Cs*KL*KC*Ke*Kj= 150.00

Plossshrinkage28d= EpX 1.cs28dX ApX = 4.388 (KN)

5.2 Prestress loss due to shrinkage from 0 to 28 days.

Using the interpolation method, the creep strain coefficient can get as follow:


KL= 2.10

Km= 1.00

Ke= 0.85

For the node 5:

sci.beam= 13.51 (Mpa)

creep strains ecc.28d= 220.03 (10-6)

Loss due to creep Dsc.28d= Epecc.28d= 42.906 (Mpa) (at 28 days)Plosscreep.28d=Dsc.28dX Ap= 6.436 (KN)

For other nodes:

28 days cc=

ci (MPa) ecc

(10-6

)Dsc (MPa) Plosscreep.28d.i

sci.28d. ecc.28d Dsc.28d (KN)2 4389.39 1.79 0.34 0.97 113.66 -0.12 3.87 62.96 12.28 1.84

4 5084.12 0.80 0.27 0.64 597.25 -0.93 7.61 123.94 24.17 3.63

5 7257.18 0.80 0.37 0.47 1170.95 -2.50 12.41 202.17 39.42 5.91

6 7830.70 0.80 0.39 0.45 1581.79 -3.52 13.13 213.83 41.70 6.25

7 8235.58 0.80 0.40 0.44 1828.76 -4.16 13.68 222.73 43.43 6.51

8 8246.67 0.80 0.40 0.44 1911.99 -4.35 13.51 220.03 42.91 6.44

9 8235.94 0.80 0.40 0.44 1831.41 -4.17 13.67 222.64 43.41 6.51

10 7831.37 0.80 0.39 0.45 1587.22 -3.53 13.12 213.66 41.66 6.25

11 7258.13 0.80 0.37 0.47 1179.72 -2.52 12.40 201.90 39.37 5.91

12 5084.70 0.80 0.27 0.64 608.17 -0.94 7.59 123.68 24.12 3.62

14 4389.48 1.79 0.34 0.97 116.71 -0.12 3.86 62.91 12.27 1.84

0.45

Zbeam.p

(m3)

Moment due

to DL1

stress due

to DL1NODE

Pe,tran

(kN)Abeam(m

2)

ebeam.p

(m)

No. of strand at height of yi (m)

0.2600.060 0.110 0.160 0.210

293792.162

1.4000.500

efb

ii

IE

AM

efb

g

IE

Lq

384

5 4

1

=

+ Z

eP

A

P

beam.p

p.beam

beam

=

u

A2

e

g

E

c.50

ci.beam

cc

s

DEFLECTION Page


18/18


Part of



MAuNSELL | AECOM

5.3 Use chart multiplication method to calculate deflection

Iefb=Ib= 0.1764 (m4)

E=E28d= 27400.00 (Mpa)

For section (0,1/8)

The prestress P28d1= Pt - Plossshrinkage.28d -( Plosscreep28d.1+Plosscreep28d.2)/2= 170.40 (KN)

Value of the moment in M diagram M1= P28d1X ni ( yb - yi )=P[n1(yb-y1)+n2(yb-y2)+]= 981.77 (KNm)

Area of the virtual M diagram A1= 1/2 Xl1X 1/2 X l1= 1.156 (m2)

For other sections:

NODE P28di(KN) Mi (KNm) A i(m2) MiX A i

(2,4) 170.40 981.77 1.156 1134.56

(4,5) 168.36 1420.46 5.220 7414.79

(5,6) 167.05 2791.84 9.425 26313.08

(6,7) 166.79 3144.71 13.630 42862.45

(7,8) 166.62 3384.56 17.835 60363.56

(7,8) 166.62 3384.56 18 60363.56

(6,7) 166.79 3144.76 13.630 42863.10

(5,6) 167.05 2791.95 9.425 26314.10

(4,5) 168.37 1420.52 5.220 7415.14

(2,4) 170.40 981.79 1.156 1134.59

iX ifpi=fp= -69.40 (mm)

The short term deflection due to prestressing fp.28d= -57.14 (mm)

qg1= pre.conX Ab= 18.43 (KN/m)


Dflection due to prestressing and dead load of beam at tranfer is:

f28d= fp.28d+(fpi+fp.28d) Xcc28d/2+fg1(1+cc28d)= -44.31 (mm)

6.Short term deflection due to dead load of slab

qg2= pre.conX bf X ts = 7.32 (KN/m)

Iefb=Ib= 0.1764 mm4

E=E28d= 27400.00 (Mpa)


7.Short term deflection due to dead load of DWS

qg3= sur.1X bf X td = 3.14 (KN/m)

Iefb

=Ic= 0.3925

mm

4

E=E28d= 27400.00 (Mpa)


8.Total short term deflection at mid span based on 28 days

fs= f28d+fg2+fg3= -30.86 (mm)

276178.908

efb

ii

IE

AM

efb

g

IE

Lq

384

5 4

1

efb

g

IE

Lq

384

5 4

2

efb

g

IE

Lq

384

5 4

3

C O 18

Prestress Sls Check

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Transcript of Prestress Sls Check