prestress sls check
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8/13/2019 Prestress Sls Check
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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
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Instructions
1 Input the shaded cells only
2
Page 2
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8/13/2019 Prestress Sls Check
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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8/13/2019 Prestress Sls Check
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Contract Job ref.
Part of
structureCalc.sheet No.
Drawing ref. Calculated by Checked by Date
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
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8/13/2019 Prestress Sls Check
5/18
Contract Job ref.
Part of
structureCalc.sheet No.
Drawing ref. Calculated by Checked by Date
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
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8/13/2019 Prestress Sls Check
6/18
Contract Job ref.
Part of
structureCalc.sheet No.
Drawing ref. Calculated by Checked by Date
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
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7/18
Contract Job ref. 60095653
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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Part of structure Calc.sheet No.
Drawing ref. Calculations by Checked by Date
MAuNSELL | AECOM
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)
Assume slab finished after 30 days, the shrinkage losses is:
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
189888032.xls.ms_office:LOSS 8 of 18
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8/13/2019 Prestress Sls Check
9/18
Contract Job ref. 60095653
Part of structure Calc.sheet No.
Drawing ref. Calculations by Checked by Date
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
Assume slab finished after 30 days, the shrinkage losses is:
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)
cc= KL*Km*KC*Ke*Kj= 0.75
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:
cc= KL*Km*KC*Ke*Kj= 0.15
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
189888032.xls.ms_office:LOSS 9 of 18
-
8/13/2019 Prestress Sls Check
10/18
Contract Job ref. 60095653
Part of structure Calc.sheet No.
Drawing ref. Calculations by Checked by Date
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)
-
8/13/2019 Prestress Sls Check
11/18
Contract Job ref.
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
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)
Zbottom = -0.26 (m3)
Ac= 0.80 (m2)
Eccentricity of prestrssong fouce(P) e = 0.40 (m)
Stress due to tendons at transfer:
Prestressing force in tendons P = 8246.67 (kN)
Stress due to tendons:
beam top: stop1.P= -5.22 (N/mm2)
beam bottom: sbot.P= 22.93 (N/mm2)
Stress due to tendons at serviceality stage:
Prestressing force in tendons P = 6837.82 (kN)
Stress due to tendons:
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
-
8/13/2019 Prestress Sls Check
12/18
Contract Job ref. 60095653
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
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)
Zbottom = -0.26 (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)
Stress due to tendons:
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
-
8/13/2019 Prestress Sls Check
13/18
Contract Job ref. 60095653
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
2. Stress checking at serviceability stage:
f 'c.beam= 50.00 (Mpa)
f 'c.slab= 40.00 (Mpa)
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
Section modulus above top or bottom of section:
Ztop = 0.58 (m3)
Ztop1 = 0.81
Zbottom = -0.42 (m3)
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):
stop.max= 9.82 (MPa)
stop1.max= 7.07 (MPa)
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
ALLOWABLE COMPRESSIVE STRESS
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
-
8/13/2019 Prestress Sls Check
14/18
Contract Job ref.
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
3. Stress checking at serviceability stage (Consider thermal effects):
f 'c.beam= 50.00 (Mpa)
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.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
Section modulus above top or bottom of section:
Ztop = 0.58 (m3)
Ztop1 = 0.81
Zbottom = -0.42 (m3)
Moment due to loads:
Mmax = 4498.54 (kNm)
Stress due to loads moment:
stop.max= 7.73 (MPa)
stop1.max= 5.57 (MPa)
sbot.max= -10.66 (MPa)Stress due to tendons + DL1 at serviceability stage:
stop1.P+DL1= 8.63 (MPa)sbot.P+DL1= 9.94 (MPa)
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 due to tendons + all LOADS at serviceability stage:
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
ALLOWABLE COMPRESSIVE STRESS
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
ZM
=
1top.0
max
Z
M
-
8/13/2019 Prestress Sls Check
15/18
Contract Job ref. 60095653
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
2. Stress checking at serviceability stage:
f 'c.beam= 50.00 (Mpa)
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 !
Section modulus above top or bottom of section:
Ztop = 0.58 (m3)
Ztop1 = 0.81
Zbottom = -0.42 (m3)
Moment due to loads:
Mmax = 4379.13 (kNm)
Stress due to loads moment:
stop.max= 7.53 (MPa)
stop1.max= 5.42 (MPa)
sbot.max= -10.37 (MPa)Stress due to tendons + DL1 at serviceability stage:
stop1.P+DL1= 8.63 (MPa)sbot.P+DL1= 9.94 (MPa)
Stress due to temperature effect at serviceability stage:
stop.temp= 2.27 (MPa)stop1.temp= 0.30 (MPa)sbot.temp= -1.37 (MPa)
Stress due to tendons + all LOADS at serviceability stage:
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
ALLOWABLE COMPRESSIVE STRESS
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
Z
M
-
8/13/2019 Prestress Sls Check
16/18
-
8/13/2019 Prestress Sls Check
17/18
Contract Job ref. 60095653
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
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:
cc= KL*Km*KC*Ke*Kj= 0.45
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
-
8/13/2019 Prestress Sls Check
18/18
Contract Job ref. 60095653
Part of
structureCalc.sheet No.
Drawing ref. Calculations by Checked by Date
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 dead load of beam fg1= 28.39 (mm)
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)
Dflection due to dead load of beam fg2= 11.28 (mm)
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)
Dflection due to dead load of beam fg3= 2.18 (mm)
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
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