problem 1 009

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PROGRAM NAME:  SAP2000

REVISION NO.:  7

EXAMPLE 1-009 - 1 

EXAMPLE 1-009

FRAME – PRESTRESS APPLIED TO FRAME OBJECTS 

EXAMPLE DESCRIPTION 

The SAP2000 prestress applied to frame objects is verified in this example using

a simply supported concrete beam with a parabolic prestressing tendon profile

and different eccentricities at each end. The bending moment and deflection atthe beam center are compared with independent hand-calculated results.

SAP2000 has two options for modeling the effect of the prestress. One optionmodels the prestress as loads applied to the structure. The other models the

 prestress tendon as internal tendon elements. Both options are verified in this

example.

In SAP2000 the beam is modeled using a single frame element that is internallymeshed into two elements so that there is a node at the beam midpoint where the

displacement values are to be calculated.

Three separate models are used in this analysis. Model A has the prestress

modeled as loads. Models B and C treat the prestress as elements. Model B has a

maximum prestress tendon discretization length of 60 inches and Model C

reduces the maximum prestress tendon discretization length to 12 inches.

The effect of both wobble and curvature friction losses are included in theexample as well as elastic shortening of the concrete beam. The tendon is

stressed from the left end only.

Important Note:  Shear deformations are included in this example.

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EXAMPLE 1-009 - 2 

GEOMETRY AND LOADING 

Section A-A

CLCL

          1          0          "           3

          "

          1          0          "

30' = 360"

          3          0          "

18"Prestressing tendonT=220 k

Material Properties

E = 3600 k/in2

ν = 0.2

G= 1500 k/in2

Section Properties

b = 18 in

d = 30 in

 A = 540 in2

I = 40,500 in4

 Av = 450 in2 (shear area)

Prestressing Tendon Notes

1.

2.

3.

4.

5.

6.

7.

T is the component of the tension force in the prestressing tendon before losses.

The tendon is tensioned from the left end only.

The cable drapes at the left end, center and right end of the beam are illustrated in the figure.

The cable profile is parabolic.

The friction loss coefficient for curvature is 0.15.

The friction loss coefficient for wobble is 0.0001 / in.

Consider losses due to friction and beam elastic shortening.

Beam neutral axis

Prestress Properties

 A

 A

 A = 1.5 in2

E = 29000 k/in2

ν = 0.3

TECHNICAL FEATURES OF SAP2000 TESTED 

  Prestress tendon with parabolic tendon profile and different eccentricities at

the two ends  Prestress tendon modeled using loads  Prestress tendon modeled as elements

  Prestress losses

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EXAMPLE 1-009 - 3 

RESULTS COMPARISON 

Independent results are hand calculated using basic principles and using the unitload method described on page 244 in Cook and Young 1985.

Important Note:  A simplifying assumption is made in the hand calculations that

the distributed load the prestress imposes on the beam is uniform. Thus the

SAP2000 and hand-calculated results are not expected to match exactly.

ModelOutput

Parameter SAP2000 IndependentPercent

Difference

  A- By Loads 0.17028 +2.8%

B- Elems (60") 0.16041 -3.2%

C- Elems (12")

Uz

(center)

in0.16484

0.16564

-0.5%

A- By Loads -2061.5 +2.9%

B- Elems (60") -2013.9 +0.5%

C- Elems (12")

My 

(center)kip-in

-2001.7

-2004.3

-0.1%

COMPUTER FILES:  Example 1-009a, Example 1-009b, Example 1-009c 

CONCLUSION 

The SAP2000 results and the independent results show an acceptable match.

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EXAMPLE 1-009 - 4 

H AND C ALCULATION 

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EXAMPLE 1-009 - 5 

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EXAMPLE 1-009 - 6 

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EXAMPLE 1-009 - 7 

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EXAMPLE 1-009 - 11 

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EXAMPLE 1-009 - 12 

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EXAMPLE 1-009 - 13 

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EXAMPLE 1-009 - 14