Post-Tensioned Girder (Fahed [email protected]) Good Mahfuz
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Transcript of Post-Tensioned Girder (Fahed [email protected]) Good Mahfuz
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file:///var/www/apps/conversion/tmp/scratch_3/172397520
University of Engineering and Technology Lahore, Pakistan
Bsc. Project Analysis and Design of Prestressed Structural members
Project advisior Dr. Mohammad Afzal Javaid
Engr. Azhar Saleem
Sheet Title Analysis and Design of post-tensioned Felexural members
Sheet Authers
* Only yellow Fields are to be Entered by the user
PROPERTIES OF SECTION DESCRIBED BY LAYERS (FROM TOP TO BOTTOM)Units: in
1 IN = 25 MM
Layer No. Top Width Thickness Depth (h) 36 36 5.
1 12 12 5 0 36 16 2.
2 4 4 14 5 16 8
3 12 12 5 19 8 8 5
4 0 8 24 1
5 0 24 24
6 0
7 0
8 0
9 0
10 0
Fahed Javaid 2002-C-1009
Waheed Ahmed 2002-C-1006
Ayyaz A hmed 2002-C-1023
Ferhan Nawaz 2002-C-969
-8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0
-30
-25
-20
-15
-10
-5
0
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11 0 Elastic Section Properties
12 0 Height = 24.00 in
13 0 Area = 176.00 in^2
14 0 Ix = 11994.67 in^4
15 0 Yt = 12.000 in
16 0 Yb = 12.000 in
17 0 St = 999.56 in^3
18 0 Sb = 999.56 in^3
19 0 Iy = 1514.67 in^4
20 0
21 0
22 023 0
24 0
25 0
26 0
27 0
28 0
29 0
30 0
31 0
32 0
33 0
34 0
35 0
36 0
37 0
Material Properties
Concrete: Prestress Wire:
fc': 4000 Psi fpu: 250000 Psi
150 Pcf %Loss: 15%
wire dia: 0.5 in
wire area: 0.153 in2
Pe/Pi, R: 85.00%
c:
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Permissible Concrete Stresses:
Initial Stage:
fc': 0.7 x 4000 = 2800 Psi
Top, fti: 3 x (2800)^0.5 = 158.7 Psi
Bottom, fci: - 0.6 x 2800 = -1680.0 Psi
Service Stage:
Top, fcs: - 0.6 x 4000 = -2400.0 Psi
Bottom, fts: 3 x (4000)^0.5 = 189.7 Psi
Permissible Stress in Prestress wire:
(immediately after transfer)
fpy: 0.9 x 250000 = 225000 Psi
0.70 fpu: 0.70 x 250000 = 185000 Psi
Permissible stress: 185000 Psi
Load and Moments:
span, L: 40 ft
self, wo: 176/144 x 150/1000 = 0.18 klf
Imposed DL, wd: 0.275 klf
LL, wl: 0.275 klf
Mo: 0.18 x 40^2/8 = 36 ft-kipMd: 0.275 x 40^2/8 = 55 ft-kip
Ml: 0.275 x 40^2/8 = 55 ft-kip
Section Moduli, required at midspan:
(1-R)Mo+Md+Ml: (1-0.85)36+55+55 = 115.4 ft-kip
St: 115.4x12000/(0.85x158.7-(-2400)) = 547 in3 < 999.56 OK
Sb: 115.4x12000/(189.7-0.85(-1680)) = 857 in3 < 999.56 OK
fcci: 158.7 - 12/24 x (158.7-(-1680)) = -761
Pi: -761x176/1000 = -134 kip ': minus indicates compression
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e: (158.7-(-761))x999.56/(-134x1000)+36x12/-134 = -10.08 below NA
at end, e: (158.7-(-761))x999.56/(-134x1000) = -6.86
Provided, Pi: 169
Provided, e: 5.19
Ap: 169x1000 /185000 = 0.91
No. of strands, n: 0.91 /0.153 = 5.95
Provided, n: 14 max = 35
Provided, Ap: 2.142
No. Tendons, N: 3 7-strand tendons
Stress Check at Mid Span:
Pi : ft (-169/176 + 169x5.19x/999.56)1000 = -82.7
fb (-169/176 - 169x5.19x/999.56)1000 = -1837.7
Pe:ft 0.85 (-82.7) = -70.3
fb 0.85 (-1837.7) = -1562.0
Mo:ft -36 x 12000 /999.56 = -432.2
fb 36 x 12000 /999.56 = 432.2
Md+Ml:ft -(55 + 55) x 12000 /999.56 = -1320.6
fb (55 + 55) x 12000 /999.56 = 1320.6
Initial Stage: % Margin
ft: -82.7 + (-432.2) = -514.9 < 158.7 OK 424.45%
fb: -1837.7 + 432.2 = -1405.5 < -1680 OK 16.34%
Service Stage:
ft: -70.3 + (-432.2) + (-1320.6) = -1823.1 < -2400 OK 24.04%
fb: -1562 + 432.2 + 1320.6 = 190.8 > 189.7 NOT OK -0.58%
Tendon Profile Envelop:
A = wL/2 B = w/2
Self wt, Ao: 3.6 I. Dead + Live, Ad+l: 11
Bo 0.09 Bd+l: 0.275
Ac: 176.000 Top, fti: 158.7 R: 85.00%
Mx=Ax-Bx2
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St: 999.56 Bottom, fci: -1680 Pi: 169000
Sb: 999.56 Top, fcs: -2400 Pe: 143650
Bottom, fts: 189.7
x Moment e, based on Profile Limits
Location ft Self Wt. Dead+Live fti fci fcs fts Lower Upper
0.00 L 0.00 0 0 6.61 4.25 -11.03 -7.00 4.25 -7.00
0.05 L 2.00 82080 250800 7.10 4.74 -8.71 -4.69 4.74 -4.69
0.10 L 4.00 155520 475200 7.53 5.17 -6.63 -2.61 5.17 -2.61
0.15 L 6.00 220320 673200 7.92 5.56 -4.81 -0.78 5.56 -0.78
0.20 L 8.00 276480 844800 8.25 5.89 -3.22 0.81 5.89 0.81
0.25 L 10.00 324000 990000 8.53 6.17 -1.88 2.15 6.17 2.150.30 L 12.00 362880 1108800 8.76 6.40 -0.78 3.25 6.40 3.25
0.35 L 14.00 393120 1201200 8.94 6.58 0.08 4.10 6.58 4.10
0.40 L 16.00 414720 1267200 9.07 6.71 0.69 4.71 6.71 4.71
0.50 L 20.00 432000 1320000 9.17 6.81 1.18 5.20 6.81 5.20
0.50 L 20.00 432000 1320000 9.17 6.81 1.18 5.20 6.81 5.20
0.60 L 24.00 414720 1267200 9.07 6.71 0.69 4.71 6.71 4.71
0.70 L 28.00 362880 1108800 8.76 6.40 -0.78 3.25 6.40 3.25
0.80 L 32.00 276480 844800 8.25 5.89 -3.22 0.81 5.89 0.81
0.90 L 36.00 155520 475200 7.53 5.17 -6.63 -2.61 5.17 -2.61
1.00 L 40.00 0 0 6.61 4.25 -11.03 -7.00 4.25 -7.00
Tendon Profile:
Total Tendons, N: 3Total Area, A: 2.142
Beam span: 40
1 2 3 4 0
No. of tendons: 1 1 1 1 0
Area per tendon: 1.071 1.071 2 1.071 0
End, e: 26 25.24 15.24 5.24 0
Mid, e: 27 37.49 33.99 33.99 0
Coeff, a: 0.00 0.00 0.00 0.00 0.00
b: 0.0083 0.1021 0.1563 0.2396 0.0000
c: 26 25.24 15.24 5.24 0
For parabolic tendons, y=ax2+bx+c
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x Eccentricities (inch) Profile Limits
in e1 e2 e3 e4 e5 avg, e Lower Upper
0.00 L 0.0 26.00 25.24 15.24 5.24 0.00 42.47 4.25 -7.00 No
0.05 L 24.0 26.19 27.57 18.80 10.70 0.00 49.79 4.74 -4.69 No
0.10 L 48.0 26.36 29.65 21.99 15.59 0.00 56.33 5.17 -2.61 No
0.15 L 72.0 26.51 31.49 24.80 19.90 0.00 62.11 5.56 -0.78 No
0.20 L 96.0 26.64 33.08 27.24 23.64 0.00 67.11 5.89 0.81 No
0.25 L 120.0 26.75 34.43 29.30 26.80 0.00 71.35 6.17 2.15 No
0.30 L 144.0 26.84 35.53 30.99 29.39 0.00 74.82 6.40 3.25 No
0.35 L 168.0 26.91 36.39 32.30 31.40 0.00 77.51 6.58 4.10 No
0.40 L 192.0 26.96 37.00 33.24 32.84 0.00 79.44 6.71 4.71 No
0.45 L 216.0 26.99 37.37 33.80 33.70 0.00 80.59 6.81 5.20 No
0.50 L 240.0 27.00 37.49 33.99 33.99 0.00 80.98 6.81 5.20 No
Ultimate Flexural Strength:
L: 40 ft fpu: 250000 Pe: 169000
wo: 0.18 kip fpy: 225000 Ap: 2.142
wd: 0.275 kip fc': 4000 dp: 17.19
wl: 0.275 kip fpy/fpu: 0.9 1: 0.85
Mu: 146 ft-kip L/h: 20
Pe/Ap, fpe: 78898 < 125000 (0.5 fpu) :fps approximate equations are valid. Calculate manually.
b: 18
bw: 8hf: 6
z: 1 Unbonded Tendons
0.28
0.01558
fps: 6562.5
a: 0.23 < 6 :Rec beam analysis required.
Rec beam capacity:
18 < 146 Ordinary reinforcement required
T-beam capacity:
Apf: 31.086
e withinprofile?
p:
p:
Mn:
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Apw: -28.944
-26.14 < 146 Ordinary reinforcement requiredMn:
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University of Engineering and Technology La
Bsc. Project Comparision of Analysis and Design of Prestressed Structural memb
Project advisior Dr. Mohammad Afzal Javaid
Engr. Azhar Saleem
Sheet Title Analysis and Design of post-tensioned Line members
Sheet Authers
* Only yellow Fields are to be Entered by the user
PROPERTIES OF SECTION
Units: in
Height of Sec 39 in 5 5
Width of sec 24 in 5 39
wall Thickne 4 in 29 39
middle web t 0 in 29 55 5
5 55 35 9 9
9 35
5 5 25 35
5 35 25 9
9 9
Elastic Section Prope
Height = 39.00
Area = 440.00
Ix = 78916.67
Yt = 19.500
Yb = 19.500St = 4047.01
Sb = 4047.01
r 2 = 179.36
width = 24
Material Properties
2002-C-1009 , 2002-C-1006 , 2002-C-1023 , 2002-C-969
0 5 10 15 20 2
0
5
10
15
20
25
30
35
40
45
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Concrete: Prestress Wire:
fc': 4000 Psi fpu: 250000 Psi
150 Pcf %Loss: 15%
wire dia: 0.5 in
wire area: 0.153 in2
Pe/Pi, R: 85.00%
Permissible Concrete Stresses:
Initial Stage:
fc': 0.7 x 4000 = 2800 Psi
Top, fti: 3 x (2800)^0.5 = 158.7 Psi
Bottom, fci: - 0.6 x 2800 = -1680.0 Psi
Service Stage:
Top, fcs: - 0.6 x 4000 = -2400.0 Psi
Bottom, fts: 3 x (4000)^0.5 = 189.7 Psi
Permissible Stress in Prestress wire:
(immediately after transfer)
fpy: 0.9 x 250000 = 225000 Psi
0.70 fpu: 0.70 x 250000 = 185000 Psi
Permissible stress: 185000 Psi
Permissible Stress in Prestress wire:
(immediately after transfer)
fpy: 0.9 x 250000 = 225000 Psi0.70 fpu: 0.70 x 250000 = 185000 Psi
Permissible stress: 185000 Psi
Load and Moments:
span, L: 40 ft
self, wo: 440/144 x 150/1000 = 0.46 klf
Imposed DL, wd: 0.275 klf
LL, wl: 0.275 klf
Mo: 0.46 x 40^2/8 = 92 ft-kip
Md: 0.275 x 40^2/8 = 55 ft-kip
Ml: 0.275 x 40^2/8 = 55 ft-kip
Section Moduli, required at midspan:
(1-R)Mo+Md+Ml: (1-0.85)92+55+55 = 202 ft-kip
c:
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St: 202x12000/(0.85x158.7-(-2400)) = 957 in3
Sb: 202x12000/(189.7-0.85(-1680)) = 1499 in3
fcci: 158.7 - 19.5/39 x (158.7-(-1680)) = -761
Pi: -761x440/1000 = -335 kip ': minus indi
e: (-(-761))x4047.00854700855/(-335x1000)+92x12/-335 = -12.49 below NA
at end, e: (158.7-(-761))x4047.00854700855/(-335x1000) = -11.11
Provided, Pi: 530
Provided, e: 17
Ap: 530x1000 /185000 = 2.86
No. of strands, n: 2.86 /0.153 = 18.69
Provided, n: 14 max = 35
Provided, Ap: 2.142
No. Tendons, N: 3 7-strand tendons
Stress Check at Mid Span:
Pi : ft (-530/440 + 530x17x/4047.00854700855)1000 = 1021.8
fb (-530/440 - 530x17x/)1000 = -1318.7
Pe:ft 0.85 (1021.8) = 868.5
fb 0.85 (-1318.7) = -1120.9
Mo:ft -92 x 12000 /4047.00854700855 = -272.8
fb 92 x 12000 /4047.00854700855 = 272.8
Md+Ml:ft -(55 + 55) x 12000 /4047.00854700855 = -326.2
fb (55 + 55) x 12000 / = 326.2
Initial Stage:
ft: 1021.8 + (-272.8) = 749.0