post-tensioned girder (fahed [email protected]) good mahfuz

7/29/2019 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



fpy: 0.9 x 250000 = 225000 Psi

0.70 fpu: 0.70 x 250000 = 185000 Psi




fpy: 0.9 x 250000 = 225000 Psi0.70 fpu: 0.70 x 250000 = 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

post-tensioned girder (fahed [email protected]) good mahfuz

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