diseño de vigas postensadas. libre

file:///tt/file_convert/54779b6db4af9ffe248b45c3/document.xls

University of Engineering and Technology Lahore, Pakistan

Bsc. Project Analysis and Design of Prestressed Structural membersProject advisior Dr. Mohammad Afzal Javaid

Engr. Azhar SaleemSheet Title Analysis and Design of post-tensioned Felexural membersSheet Authers

* Only yellow Fields are to be Entered by the user

PROPERTIES OF SECTION DESCRIBED BY LAYERS (FROM TOP TO BOTTOM)Units: m

1 IN = 25 MM

Layer No. Top Width Thickness Depth (h) 36 36 5.21 0.6 0.6 0.1 0 36 16 2.82 0.2 0.2 14 0.1 16 8 43 12 12 5 14.1 8 8 544 0 8 24 105 0 24 24 86 07 08 09 0

10 0

Fahed Javaid 2002-C-1009Waheed Ahmed 2002-C-1006Ayyaz A hmed 2002-C-1023Ferhan Nawaz 2002-C-969

Bottom Width

-8.0 -6.0 -4.0 -2.0 0.0 2.0 4.0 6.0 8.0

-25

-20

-15

-10

-5

0

F16

Fahed Javaid: Choose the system of units form Cell C12. Only Yellow Cells are input Entry requirments by the programme. WARNING: DONOT CHANGE DATA IN ANY OTHER CELL FOR REIABLE RESULSTS FROM THE PROGRAMME.

C18

Fahed Javaid: Programme is under development for METRIC system of units. At the moment programme gives reliable results only for FPS system of units.


11 0 Elastic Section Properties12 0 Height = 19.10 m13 0 Area = 62.86 m^214 0 Ix = 427.76 m^415 0 Yt = 16.161 m16 0 Yb = 2.939 m17 0 St = 26.47 m^318 0 Sb = 145.55 m^319 0 Iy = 720.01 m^420 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 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 in2Pe/Pi, R: 0.85

gc:


Permissible Concrete Stresses:

Initial Stage:fc': 0.7 x 4000 = 2800 Psi

Top, fti: 3 x (2800)^0.5 = 158.7 PsiBottom, 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 ftself, wo: 62.86/144 x 150/1000 = 0.07 klf

Imposed DL, wd: 0.275 klfLL, wl: 0.275 klf

Mo: 0.07 x 40^2/8 = 14 ft-kipMd: 0.275 x 40^2/8 = 55 ft-kipMl: 0.275 x 40^2/8 = 55 ft-kip

Section Moduli, required at midspan:

(1-R)Mo+Md+Ml: (1-0.85)14+55+55 = 112.1 ft-kipSt: 112.1x12000/(0.85x158.7-(-2400)) = 531 in3 > 26.47 NOT OKSb: 112.1x12000/(189.7-0.85(-1680)) = 832 in3 > 145.55 NOT OK

fcci:610404072542/19.1 x (158.7-(-1680)) = -1397Pi: -1397x62.86/1000 = -88 kip ': minus indicates compression


e: (158.7-(-1397))x26.47/(-88x1000)+14x12/-88 = -2.38 below NAat end, e: (158.7-(-1397))x26.47/(-88x1000) = -0.47

Provided, Pi: 169Provided, e: 5.19

Ap: 169x1000 /185000 = 0.91No. of strands, n: 0.91 /0.153 = 5.95

Provided, n: 14 max = 35Provided, Ap: 2.142

No. Tendons, N: 3 7-strand tendons

Stress Check at Mid Span:

Pi : ft (-169/62.86 + 169x5.19x/26.47)1000 = 30447.5fb (-169/62.86 - 169x5.19x/145.55)1000 = -8714.7

Pe:ft 0.85 (30447.5) = 25880.4fb 0.85 (-8714.7) = -7407.5

Mo:ft -14 x 12000 /26.47 = -6346.8fb 14 x 12000 /145.55 = 1154.2

Md+Ml:ft -(55 + 55) x 12000 /26.47 = -49867.8fb (55 + 55) x 12000 /145.55 = 9069

Initial Stage: % Marginft: 30447.5 + (-6346.8) = 24100.7 > 158.7 NOT OK ###fb: -8714.7 + 1154.2 = -7560.5 > -1680 NOT OK -350.03%

Service Stage:ft: 25880.4 + (-6346.8) + (-49867.8) = -30334.2 > -2400 NOT OK -1163.93%fb: -7407.5 + 1154.2 + 9069 = 2815.7 > 189.7 NOT OK -1384.29%

Tendon Profile Envelop:

A = wL/2 B = w/2Self wt, Ao: 1.4 I. Dead + Live, Ad+l: 11

Bo 0.035 Bd+l: 0.275

Ac: 62.860 Top, fti: 158.7 R: 0.85

Mx=Ax-Bx2


St: 26.47 Bottom, fci: -1680 Pi: 169000Sb: 145.55 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 Upper0.00 L 0.00 0 0 0.44 -0.86 -0.03 -2.51 -0.86 -0.030.05 L 2.00 31920 250800 0.63 -0.67 1.95 -0.54 -0.67 1.950.10 L 4.00 60480 475200 0.80 -0.51 3.71 1.23 -0.51 3.710.15 L 6.00 85680 673200 0.95 -0.36 5.27 2.78 -0.36 5.270.20 L 8.00 107520 844800 1.08 -0.23 6.61 4.13 -0.23 6.610.25 L 10.00 126000 990000 1.19 -0.12 7.75 5.27 -0.12 7.750.30 L 12.00 141120 1108800 1.28 -0.03 8.69 6.20 -0.03 8.690.35 L 14.00 152880 1201200 1.35 0.03 9.41 6.92 0.03 9.410.40 L 16.00 161280 1267200 1.40 0.08 9.93 7.44 0.08 9.930.50 L 20.00 168000 1320000 1.44 0.12 10.34 7.86 0.12 10.340.50 L 20.00 168000 1320000 1.44 0.12 10.34 7.86 0.12 10.340.60 L 24.00 161280 1267200 1.40 0.08 9.93 7.44 0.08 9.930.70 L 28.00 141120 1108800 1.28 -0.03 8.69 6.20 -0.03 8.690.80 L 32.00 107520 844800 1.08 -0.23 6.61 4.13 -0.23 6.610.90 L 36.00 60480 475200 0.80 -0.51 3.71 1.23 -0.51 3.711.00 L 40.00 0 0 0.44 -0.86 -0.03 -2.51 -0.86 -0.03

Tendon Profile:

Total Tendons, N: 3Total Area, A: 2.142

Beam span: 40

1 2 3 4 0No. of tendons: 1 1 1 1 0

Area per tendon: 1.071 1.071 2 1.071 0End, e: 26 25.24 15.24 5.24 0Mid, e: 27 37.49 33.99 33.99 0

Coeff, a: 0.00 0.00 0.00 0.00 0.00b: 0.0083 0.1021 0.1563 0.2396 0.0000c: 26 25.24 15.24 5.24 0

For parabolic tendons, y=ax2+bx+c


x Eccentricities (inch) Profile Limitsin 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 -0.86 -0.03 No0.05 L 24.0 26.19 27.57 18.80 10.70 0.00 49.79 -0.67 1.95 No0.10 L 48.0 26.36 29.65 21.99 15.59 0.00 56.33 -0.51 3.71 No0.15 L 72.0 26.51 31.49 24.80 19.90 0.00 62.11 -0.36 5.27 No0.20 L 96.0 26.64 33.08 27.24 23.64 0.00 67.11 -0.23 6.61 No0.25 L 120.0 26.75 34.43 29.30 26.80 0.00 71.35 -0.12 7.75 No0.30 L 144.0 26.84 35.53 30.99 29.39 0.00 74.82 -0.03 8.69 No0.35 L 168.0 26.91 36.39 32.30 31.40 0.00 77.51 0.03 9.41 No0.40 L 192.0 26.96 37.00 33.24 32.84 0.00 79.44 0.08 9.93 No0.45 L 216.0 26.99 37.37 33.80 33.70 0.00 80.59 0.12 10.34 No0.50 L 240.0 27.00 37.49 33.99 33.99 0.00 80.98 0.12 10.34 No

Ultimate Flexural Strength:

L: 40 ft fpu: 250000 Pe: 169000wo: 0.07 kip fpy: 225000 Ap: 2.142wd: 0.275 kip fc': 4000 dp: 21.35wl: 0.275 kip fpy/fpu: 0.9 b1: 0.85

Mu: 124 ft-kip L/h: 25.13

Pe/Ap, fpe: 78898 < 125000 (0.5 fpu) :fps approximate equations are valid. Calculate manually.b: 18

bw: 8hf: 6z: 1 Unbonded Tendons

0.28

0.01254fps: 54062.5

a: 1.89 < 6 :Rec beam analysis required.

Rec beam capacity:177.22 > 124 :Section is adequate.

T-beam capacity:Apf: 3.773

e within profile?

gp:

rp:

fMn:


Apw: -1.631145.80 > 124 :Section is adequate.fMn:


Bsc. Project Comparision of Analysis and Design of Prestressed Structural membersProject advisior Dr. Mohammad Afzal Javaid

Engr. Azhar SaleemSheet Title Analysis and Design of post-tensioned Line membersSheet 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 Thicknes 4 in 29 39

middle web t 0 in 29 55 5

5 55 35 9 9

9 355 5 25 355 35 25 9

9 9

Elastic Section PropertiesHeight = 39.00

Area = 440.00Ix = 78916.67Yt = 19.500Yb = 19.500St = 4047.01Sb = 4047.01

r ^2 = 179.36width = 24

Material Properties

2002-C-1009 , 2002-C-1006 , 2002-C-1023 , 2002-C-969

0 5 10 15 20 25 30 35

0

5

10

15

20

25

30

35

40

45

F14

Fahed Javaid: Choose the system of units form Cell C12. Only Yellow Cells are input Entry requirments by the programme. WARNING: DONOT CHANGE DATA IN ANY OTHER CELL FOR REIABLE RESULSTS FROM THE PROGRAMME.

D18

Fahed Javaid: Programme is under development for METRIC system of units. At the moment programme gives reliable results only for FPS system of units.

Concrete: Prestress Wire:fc': 4000 Psi fpu: 250000 Psi

150 Pcf %Loss: 15%wire dia: 0.5 in

wire area: 0.153 in2Pe/Pi, R: 0.85

Permissible Concrete Stresses:

Initial Stage:fc': 0.7 x 4000 = 2800 Psi

Top, fti: 3 x (2800)^0.5 = 158.7 PsiBottom, 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



0.70 fpu: 0.70 x 250000 = 185000 Psi




0.70 fpu: 0.70 x 250000 = 185000 Psi


Load and Moments:

span, L: 40 ftself, wo: 440/144 x 150/1000 = 0.46 klf

Imposed DL, wd: 0.275 klfLL, wl: 0.275 klf

Mo: 0.46 x 40^2/8 = 92 ft-kipMd: 0.275 x 40^2/8 = 55 ft-kipMl: 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

gc:

St: 202x12000/(0.85x158.7-(-2400)) = 957 in3Sb: 202x12000/(189.7-0.85(-1680)) = 1499 in3

fcci: 158.7 - 19.5/39 x (158.7-(-1680)) = -761Pi: -761x440/1000 = -335 kip ': minus indicates compressione: (-(-761))x4047.00854700855/(-335x1000)+92x12/-335 = -12.49 below NA

at end, e: (158.7-(-761))x4047.00854700855/(-335x1000) = -11.11

Provided, Pi: 530Provided, e: 17

Ap: 530x1000 /185000 = 2.86No. of strands, n: 2.86 /0.153 = 18.69

Provided, n: 14 max = 35Provided, Ap: 2.142

No. Tendons, N: 3 7-strand tendons

Stress Check at Mid Span:

Pi : ft (-530/440 + 530x17x/4047.00854700855)1000 = 1021.8fb (-530/440 - 530x17x/)1000 = -1318.7

Pe:ft 0.85 (1021.8) = 868.5fb 0.85 (-1318.7) = -1120.9

Mo:ft -92 x 12000 /4047.00854700855 = -272.8fb 92 x 12000 /4047.00854700855 = 272.8

Md+Ml:ft -(55 + 55) x 12000 /4047.00854700855 = -326.2fb (55 + 55) x 12000 / = 326.2

Initial Stage:ft: 1021.8 + (-272.8) = 749.0 <fb: -1318.7 + 272.8 = -1045.9 <

Service Stage:ft: 868.5 + (-272.8) + (-326.2) = 269.5 <fb: -1120.9 + 272.8 + 326.2 = -521.9 <

Ultimate Flexural Strength:

L: 40 ft fpu: 250000 Pe: 530000wo: 0.46 kip fpy: 225000 Ap: 2.142wd: 0.275 kip fc': 4000 dp: 36.50wl: 0.275 kip fpy/fpu: 0.9 b1: 0.85

Mu: 202 ft-kip L/h: 12.31

Pe/Ap, fpe: 247432 > 125000 (0.5 fpu) :fps approximate equations are valid.b: 18

bw: 8hf: 6

z: 3 Unbonded Tendons with L/h > 350.28

0.00734fps: 225000

a: 7.88 > 6 :T-beam analysis required.

Rec beam capacity:1177.01 > 202 :Section is adequate.

T-beam capacity:Apf: 0.907

Apw: 1.2351191.36 > 202 :Section is adequate.

gp:

rp:

fMn:

fMn:


Comparision of Analysis and Design of Prestressed Structural members

Elastic Section Propertiesinin^2in^4ininin^3in^3in^4in

0 5 10 15 20 25 30 35

0

5

10

15

20

25

30

35

40

45

< 4047.01 OK< 4047.01 OK

kip ': minus indicates compression

% Margin185000 OK 99.60%-1680.0 OK 37.74%

-2400.0 OK 111.23%189.7 OK 375.12%

:fps approximate equations are valid.

-40000.00 -30000.00 -20000.00 -10000.00 0.00 10000.00 20000.00 30000.00 40000.00

-5

-4

-3

-2

-1

0

1

2

3

4

5

1; -5

2; 5

1

2

1

2

1

2

1

2

Stress Dia For

ini.prestress

initial prestress + self weigh

Effec stress +Self weight

Effec stress +Self weight+applied loads

Initial stress +Self weight+applied loads

-4000.00 -3000.00 -2000.00 -1000.00 0.00 1000.00 2000.00

-5

-4

-3

-2

-1

0

1

2

3

4

5

1; -5

2; 5

1

2

1

2

1

2

1

2

Stress Dia for

ini.prestress froce

effect of ini + self weigh

Effec +Self weight

Effec +Self weight+applied loads

Ini +Self weight+applied loads

University of Engineering & Technology Lahore, Pakistan

Bsc. Project Comparision of Analysis and Design of Prestressed structural membersProject advisior Dr. Mohammad Afzal Javaid

Engr. Azhar SaleemSheet Title Analysis of prestressed Line members

Sheet Authers

Permissible Concrete Stresses

Initial prestress Stage LimitFor Compression -1680 psiFor Tension 158.75 psiService Stage prestress LimitFor Compression -1800 psiFor Tension 189.74 psi

Moment of inertia I = 427.76 in^4Concrete Area Ac = 62.86 in^2Centriodal distance from top C1 = 16.16 inCentriodal distance from bottom C2 = 2.94 inRadius of gyration r^2 = I /Ac = 6.80Sectional modulus S1= (I / C1) = 26.47Sectional modulus S2= (I / C2) = 145.55initial prestress force after losses Pi = 169.00 kipEffective prestress force Pe = 143.65Span in Feet L = 40.00 ftSevice loads PL+Pd Wu = 0.55 k/fteccentricity e = 5.19 inBeam self weight wo = 0.07 k/ft

Stress due to ini.prestress frocen---1

2002-C-1009 , 2002-C-1006 , 2002-C-1023 , 2002-C-969

C23

Data of Yellow Fields is taken from Design Sheet.

ft = (-{pi/Ac}{1- ec1/r2}) 30449.61 psifb = (-{pi/Ac}{1+ ec1/r2}) -8714.84 psi

Stress due to Self weight

Mo = (WoxL2) / 8 14.0014.00 kip-ft

ft = (-Mo / S1) -6347.21 psifb = (+Mo / S2) 1154.27 psi

Combined effect of ini + self weight---2

ft = 24102.40 psifb = -7560.56 psi

Stres due to Effec.prestress froce

ft = f11*0.85 25882.17 psifb = f21*0.85 -7407.61 psi

Stres due to Effec +Self weight---3

ft = 19534.96 psifb = -6253.34 psi

Stress due to applied loads

Ms = (WuxL2) / 8 110.00110.00 kip -ft

ft = (-Mu / S1) -49870.97 psifb = (+Mu / S2) 9069.27 psi

Stres due to Effec +Self weight+applied loads---4

ft = -30336.01 psifb = 2815.93 psi

Stres due to Ini +Self weight+applied loads---5

ft = -25768.57 psifb = 1508.70 psi


Comparision of Analysis and Design of Prestressed structural members

Effectiveness ratio = R= Pe / Pi = 0.85


Bsc. Project Comparision of Analysis and Design of Prestressed structural membersProject advisior Dr. Mohammad Afzal Javaid

Engr. Azhar SaleemSheet Title Analysis of prestressed Line members

Sheet Authers

Permissible Concrete Stresses

Initial prestress Stage Limit

For Compression -1680 psi

For Tension 158.75 psi

Service Stage prestress Limit

For Compression -1800 psiFor Tension 189.74 psi

Moment of inertia I = 78916.67 in^4Concrete Area Ac = 440.00 in^2Centriodal distance from top C1 = 19.50 inCentriodal distance from bottom C2 = 19.50 inRadius of gyration r^2 = I /Ac = 179.36Sectional modulus S1= (I / C1) = 4047.01 in^3Sectional modulus S2= (I / C2) = 4047.01 in^3initial prestress force after losses Pi = 530.00 kipEffective prestress force Pe = 450.50Span in Feet L = 40.00 ftSevice loads PL+Pd Wu = 0.55 k/fteccentricity e = 17.00 inBeam self weight wo = 0.46 k/ft

2002-C-1009 , 2002-C-1006 , 2002-C-1023 , 2002-C-969

C24

Data of Yellow Fields is taken from Design Sheet.

Stress due to ini.prestress frocen---1

ft = (-{pi/Ac}{1- ec1/r2}) 1021.79 psifb = (-{pi/Ac}{1+ ec1/r2}) -3430.88 psi

Stress due to Self weight

Mo = (WoxL2) / 8 92.0092.00 kip-ft

ft = (-Mo / S1) -272.79 psifb = (+Mo / S2) 272.79 psi

Combined effect of ini + self weight---2

ft = 749.00 psifb = -3158.09 psi

Stres due to Effec.prestress froce

ft = f11*0.85 868.52 psifb = f21*0.85 -2916.25 psi

Stres due to Effec +Self weight---3

ft = 595.73 psifb = -2643.45 psi

Stress due to applied loads

Ms = (WuxL2) / 8 110.00110.00 kip -ft

ft = (-Mu / S1) -326.17 psifb = (+Mu / S2) 326.17 psi

Stres due to Effec +Self weight+applied loads---4

ft = 269.56 psifb = -2317.29 psi

Stres due to Ini +Self weight+applied loads---5

ft = 422.83 psifb = -2831.92 psi


Comparision of Analysis and Design of Prestressed structural members

Effectiveness ratio = R= Pe / Pi = 0.85

University of Engineering and Technology Lahore Pakistan

Project Comparision of Analysis and Design of Prestressed structural membersProject advisior Dr. Mohammad Afzal Javaid

Engr. Azhar SaleemSheet Title Losses in post-tensioned Line membersSheet Authers

CALCULATION OF LOSSES

Ap 1.836 in2Ac 524 in2Ic 22040 in4r2 42.06 in2

wo 546 plfEc 4000000 psiEp 27000000 psifc' 5000 psiCu 2.5

L 50 ftPj 300000 lbs

FRICTION LOSS

Wobble Coefficient, K 0.001 /ftCurvature Coefficient, µ 0.2

Steel Centroid, y 12.23 inx 50 ft :L/2 for jacking at both ends

2002-C-1009 , 2002-C-1006 , 2002-C-1023 , 2002-C-969

Central Angle, α 0.163 rad :8y/x

KL+µα 0.0826 < 0.3 :approximate friction loss equation can be used.

fpj 163399 psi

∆fr 13499 psi :(KL+µα)fpj

fp 149900 psi :effective stress

ANCHORAGE SLIP LOSS

0.1 inL 25 ft∆fanc 9000 psi

ELASTIC SHORTENING LOSS

∆f=0 if all the tendons are jacked at once.

Pi 3000 lbsMo 500 lbs-fte 25 in

fcs -83.99414np 6.75∆fel 567.0 psi

AT INITIAL STAGE, TOTAL STRESS LOSS

∆fi 23066

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

12.00

LIMITING TENDON ENVELOPE

Lower Tendon Limit Upper Tendon Limit

LENGTH (ft)

EC

CE

NT

RIC

ITY

(in

)

a a A Ab b B Bc c C Cd d D D

e e E E DO NOT CHANGE THESE SYMBOLSf f F Fg g G Gh h H Hi i I Ij j J Jk k K Kl l L Lm m M Mn n N No o O Op p P Pq q Q Qr r R Rs s S St t T Tu u U Uv v V Vw w W Wx x X Xy y Y Yz z Z Z

DO NOT CHANGE THESE SYMBOLS

16:05:40 04/09/2023

Engineer: Sheet: Section_by_layers_old File: document.xls

CROSS-SECTION PROPERTIES Described by Layers (from top to bottom)

Section Title: 41" Deck Bulb Tee with 72" deck

Units: in

0 0.000 72.00 0.000 1 5.805 72.00 5.805 2 0.000 51.00 5.805 3 3.000 12.00 8.805 4 2.000 8.00 10.805 5 27.000 8.00 37.805 6 3.000 27.00 40.805 7 6.000 27.00 46.805 8 0.000 9 0.000 Elastic Section Properties

10 0.000 Height = 46.805 in11 0.000 Area = 962.96 in^212 0.000 I = 263132 in^413 0.000 Yt = 17.127 in14 0.000 Yb = 29.678 in15 0.000 St = 15363 in^316 0.000 Sb = 8866 in^317 0.000 18 0.000 19 0.000

Section Number

Thickness of Layer

Width of Section

Dist. to Section

from Top

-40 -30 -20 -10 0 10 20 30 40

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

CROSS-SECTION

B10

Always 0.000

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