PSLoss072 Demo

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COMPANY NAME Project: Engineer: YP Project #

Date: 7/9/13 0615

PSLoss Subject: Checker: Page:

Copyright 2007 Date:

Rev. 04/04/2007

PRESTRESS LOSSES IN POST-TENSIONING TENDON

Ultimate strength of strand fpu = 270 ksi Units: US

Modulus of elasticity of strand Es = 29000 ksi

Cross-sectional area of strand 0.217 in

Number of strands in tendon 12

Cross-sectional area of tendon 2.604 in

Tendon length 220 ft

Curvature Friction Coefficient m = 0.25

Wobble Friction Coefficient K = 0.0002 1/ft

Anchor set DS = 0.375 in

Additional prestress losses DfLT = 20 ksi (long-term and elastic shortening)

Left Pull Right Pull

Stressing ratio FJack/fpu = 0.8 0.8

Stressing order 1 2

Summary of Results

Average stress after seating 187.14 ksi

Final average stress 167.14 ksi

Final average force in tendon 435.23 Kip

Left Pull Right Pull

Jacking stress FJack = 216 216 ksi

Jacking force PJack = 562.464 562.464 Kip

Anchor set influence zone Lc = 42.70 42.70 ft

Prestress losses at anchor DF = 34.58 34.58 ksi

Stress at anchor fanchor = 181.42 181.42 ksi

Stress at end of inluence zone 198.71 198.71 ksiElongation before anchor set 16.60 1.19 in

Elongation after anchor set 16.22 0.81 in

Stress ratio at anchorage 0.672

Max. stress ratio along tendon 0.736

216.0 216.0

161.4 161.4

181.4

152.5152.5

181.4181.4

198.7

181.5

198.7

181.4

161.4

178.7

161.5

178.7

161.4

150

160

170

180

190

200

210

220

0 50 100 150 200 250

Prestress,

ksi

Jacking from left end Jacking from right end After seating

Final After seating on left After seating on right

file: \\vboxsrv\conversion_tmp\scratch_5\156678979.xls.ms_office Sheet: Losses Page 1 of 8
http://www.yakpol.net/http://www.yakpol.net/


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Date: 7/9/13 0615



Rev. 04/04/2007

PRESTRESS LOSSES IN POST-TENSIONING TENDON

Angular Change per Segment

Distance

from left

end

Segment

Length

Vertical

Profile

Horizontal

Profile

Total

accumula

tive

Distance

from left

end

Stress

after

anchor

set

Stress

after

additional

losses

ft ft rad rad rad ft ksi ksi

0 0 0.00 181.4 161.4

22 22 0.08317 0.00000 0.0832 22.00 186.8 166.8

40 18 0.17096 0.00000 0.2541 40.00 196.3 176.3

50 10 0.17096 0.00000 0.4251 42.70 198.7 178.7

60 10 0.09141 0.00000 0.5165 50.00 192.3 172.3

110 50 0.09141 0.00000 0.6079 60.00 187.6 167.6

160 50 0.09141 0.00000 0.6993 110.00 181.5 161.5

170 10 0.09141 0.00000 0.7907 110.00 181.5 161.5180 10 0.17096 0.00000 0.9617 160.00 187.6 167.6

198 18 0.17096 0.00000 1.1326 170.00 192.3 172.3

220 22 0.08317 0.00000 1.2158 177.30 198.7 178.7

180.00 196.3 176.3

198.00 186.8 166.8

220.00 181.4 161.4

file: \\vboxsrv\conversion_tmp\scratch_5\156678979.xls.ms_office Sheet: Losses Page 2 of 8


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Date: 7/9/13 0615



TENDON PROFILE

All dimensions are ft Web slope H/V = 0 Angle correction factor = 1.000

Vertical Profile Horizontal Profile

Segment type DX X1 X2 H1 H2 XSegmen

t typeRadius

Sag falling 22 0 22 2 1.083 0

Sag rising 18 22 40 1.083 220 Tangent

Crown rising 10 40 50 2.63679 3.5

Crown falling 10 50 60 3.5

Sag falling 50 60 110 3.04167 0.75

Sag rising 50 110 160 0.75

Crown rising 10 160 170 3.04167 3.5

Crown falling 10 170 180 3.5

Sag falling 18 180 198 2.63679 1.083

Sag rising 22 198 220 1.083 2

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 50 100 150 200 250

Elevation,

H

Distance from left end, X

file: \\vboxsrv\conversion_tmp\scratch_5\156678979.xls.ms_office Sheet: Profile Page 3 of 8


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Date: 7/9/13 0615



EQUIVALENT POST-TENSIONING LOADS

Steel Area of tendons, Aps = 2.604 in

Construction stage:Left end Right End

Elevation of section C.G. : 2.25 2.25 ft

End forces at anchoragesPX - horizontal force (positive left to right)

PY - vertical force (positive is up)

M - moment (negative when clockwise)

PX PY M LA

Kip Kip Kip* ft ft

Left end 470.8 -39.2 117.7 0

Right end -470.8 -39.2 -117.7 220

Equivalent Prestress LoadVertical Linear Load

(positive Up) Dist. from left end

Horizontal

Uniform

WA WB LA LB WX

Kip/ft Kip/ft ft ft Kip/ft

1.790 1.843 0.00 22.00 -0.636

4.665 4.904 22.00 40.00 -1.380

-8.826 -8.933 40.00 42.70 -2.291

-8.933 -8.645 42.70 50.00 2.291

-4.590 -4.477 50.00 60.00 1.229

0.895 0.867 60.00 110.00 0.316

0.867 0.867 110.00 110.00 0.000

0.867 0.895 110.00 160.00 -0.316

-4.477 -4.590 160.00 170.00 -1.229

-8.645 -8.933 170.00 177.30 -2.291

-8.933 -8.826 177.30 180.00 2.291

4.904 4.665 180.00 198.00 1.380

1.843 1.790 198.00 220.00 0.636

After anchor set

-6

-4

-2

0

2

4

6

8

10

0 50 100 150 200 250

Equivalent PS loads

file: \\vboxsrv\conversion_tmp\scratch_5\156678979.xls.ms_office Sheet: EquivalentLoads Page 4 of 8


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PSLoss

Copyright 2006

THEORY PRESTRESSING LOSSES DUE TO FRICTION AND ANCHOR SET

FJack2

Ltendon

Stress before

Stress after

anchor 1 set

DF1DF2

Stress before

Stressing

end

1

A2A1

Fi . 2 Stressin from two ends

Stress after

Stressing

end

2

b

b

Lc

Ltendon

Stress before anchor set fx = FJacke-(ma+Kx)

DF A

DA

Fi . 1 Stressin from one end

FJack

Stressing

end

Dead

endStress after

anchor set

Note: stress after anchorset is symmerical to stress

before anchor set within Lc.

file: \\vboxsrv\conversion_tmp\scratch_5\156678979.xls.ms_office Sheet: Theory Page 5 of 8


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PSLoss

Copyright 2006

Stressing from one end (refer to Fig. 1 above)

fx= FJ acke-(ma+Kx) Stress along the tendon at distance 'x' from the stressing end.

FJ ack Jacking stress at anchor

a Accumulative angle change from stressing end to 'x'm Curvature Friction Coefficient

K Wobble Friction Coefficient

DL = A/Es Strand elongation during stressing operations.

Es Strand modulus of elasticity

A

DS = DA/Es Anchor set

DA

Lc Length of stress conversion zone.DF Prestress losses at anchor

Stressing from two ends (refer to Fig. 2 above)

DL2 = A2/Es Elongations during second pull

A2

Angle change within a parabolic segment of tendony = aX+bX+c Parabolic equation of tendon

a1 = atan[(2aX1+b)/sin(b)] Start angle adjusted for web slope

a2 = atan[(2aX2+b)/sin(b)] End angle adjusted for web slope

Da = abs(a2-a1) Angle change within a parabolic segment

a, b, c Parabolic coefficients

X1, X2 Start and End stations of parabolic segmentb = atan(v/h) Web slope angle to horizon

Combining tendon angular changes in vertical and horizontal planes

Da Total angular change within a segment

Dav, Dah Angular change in ortogonal planescos(Da)=cos(Dav)*cos(Dah)

Equivalent beam loads due to post-tensioning

http://www.gtstrudl.gatech.edu/

Area below the graph of 'stress before anchor set' and above the line of zero

stress (yellow colored area on Fig. 1)

Compute stresses at second pull before and after anchor set independently

from first pull. The resulting stress is the maximum of stresses due to first

and second pulls (red line on Fig. 2)

Area below graph 'stress before anchor 2 set' and above graph 'stress after

anchor 1 set' (orange shaded area on Fig. 2).

The explanatory paper on this subject was presented at 2002 GT STRUDL

user group conference. It's available on GATECH website at

Area below graph 'stress before anchor set' and above graph 'stress after

anchor set' (shaded area on Fig. 1)

v

h

bv/sin(b)

http://www.yakpol.net/http://www.gtstrudl.gatech.edu/http://www.gtstrudl.gatech.edu/http://www.yakpol.net/


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PSLoss

Copyright 2006

o ow ec n ca apers en scro own o na ys s o os -

Tensioned Continuous Span Bridges" by Abhijit Naik & Jay A. Quioque,

California Department of Transportation. Download 7MB powerpoint

presentation.



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PSLoss

Copyright 2006

INSTRUCTIONS FOR USING PSLoss SPREADSHEET

Spreadsheet functionality:

Computes friction and anchor set losses in prestressing tendon

Computes tendon elongations

Developes tendon vertical and horizontal profiles

Calculates equivalent beam loads due to post-tensioning

Capabilities:

Pulling from one or both ends

Multiple angle changes in three-dimensional tendon profile

SI and US measurement systems

US and international codes

Instruction for data input

All input cells in the spreadsheet are formatted as a blue text on yellow background 4.35

The custom toolbar menu provides the following functions:

Calculate ! Performs iterative calculations necessary to compute prestress losses

Tendon Profile Activates 'Tendon Profile' worksheet

PT Losses Activates 'Losses' worksheet

Equivalent Loads Activates 'Equivalent Post-Tensioning Loads' worksheet

Theory/Help Activates current worksheet

Design Units Toggles US and SI units

Disclaimer Displays PSLoss disclaimer

PSLoss Step by Step

1. Open 'Tendon Profile' worksheet (use menu Tendon Profile - Edit or click on 'Profile' tab below).

3. On the worksheet 'Losses' enter required stressing data and click command 'Calculate !'

4. Print file.

2. Establish tendon vertical profile built out of parabolic or tangent segments. Provides location of

tangent and radial segments of horizontal profile.


Documents

PSLoss072 Demo