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EXAMPLE 2-020

SHELL -PRESTRESSAPPLIED TOAREA OBJECTS

EXAMPLE DESCRIPTION

The SAP2000 prestress applied to area objects is verified in this example using asimply supported concrete beam with a parabolic prestressing tendon profile and

different eccentricities at each end. The deflection, and the top and bottom

stresses, at the beam center are compared with independent hand- calculatedresults.

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 4x10 area object mesh. Thus, each areaobject is 7.5 inches high by 36 inches long. This yields an aspect ratio of 4.8.

Two separate models are used in this analysis. Model A has the prestressmodeled as loads. Models B treats the prestress as elements.

The effect of both wobble and curvature friction losses are included in the

example as well as elastic shortening of the concrete beam. The tendon isstressed from the left end only.

Important Note: Shear deformations are included in this example.

EXAMPLE 2-020 - 1

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GEOMETRY AND LOADING

Section A-A

CLCL

10" 3

"

10"

30' = 360"

30"

18"Prestressing tendonT=220 k

Material PropertiesE = 3600 k/in2

= 0.2

G= 1500 k/in2

Section Propertiesb = 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.

8.

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.

Set the maximum tendon discretization length to 12 in.

Beam neutral axis

Prestress Properties

A

A

A = 1.5 in2

E = 29000 k/in2 = 0.3

TECHNICAL FEATURES OF SAP2000TESTED

Prestress tendon with parabolic tendon profile and different eccentricities at

the two ends Prestress tendon modeled using loads and applied to area objects Prestress tendon modeled as elements and applied to area objects Prestress losses

RESULTS COMPARISON

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

presented separately for the thin plate option and the thick plate option.

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

the distributed load the prestress imposes on the beam is uniform. Thus theSAP2000 and hand-calculated results are not expected to match exactly.

EXAMPLE 2-020 - 2

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Thin Plate Option

ModelOutput

Parameter SAP2000 IndependentPercent

Difference

A- By Loads 0.16464 -0.6%

B- By Elements

Uz(center)

in 0.16085

0.16564

-2.9%

A- By Loads 0.3702 +0.6%

B- By Elements

Avg. S11

(top center)

kip/in2 0.3598

0.3681

-2.3%

A- By Loads -1.1285 +1.1%

B- By Elements

Avg. S11

(bot. center)kip/in

2 -1.0982-1.1163

-1.6%

Thick Plate Option

ModelOutput

Parameter SAP2000 IndependentPercent

Difference

A- By Loads 0.16464 -0.6%

B- By Elements

Uz(center)

in 0.16085

0.16564

-2.9%

A- By Loads 0.3702 +0.6%

B- By Elements

Avg. S11

(top center)

kip/in2 0.3598

0.3681-2.3%

A- By Loads -1.1285 +1.1%

B- By Elements

Avg. S11

(bot. center)

kip/in2 -1.0982

-1.1163

-1.6%

COMPUTER FILES: Example 2-020a-thick, Example 2-020a-thin,Example 2-020b-thick, Example 2-020b-thin

CONCLUSION

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

EXAMPLE 2-020 - 3

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HAND CALCULATION

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EXAMPLE 2-020 - 15