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EXAMPLE 1-009 - 1

EXAMPLE 1-009FRAME - PRESTRESS

EXAMPLE DESCRIPTIONThe SAP2000 beam prestress calculations are verified in this example using asimply supported concrete beam with a parabolic prestressing tendon profile anddifferent eccentricities at each end. The beam is subjected to self weight load andprestressing load. The bending moment and deflection at the beam center arecompared with independent hand calculated results.

In SAP2000 the beam is modeled using two frame elements so that there is anode at the beam midpoint where the displacement values are to be calculated.

Important Note: Shear deformations are part of this example; however,prestress losses are not included.

GEOMETRY AND LOADING

Section A-A

CLCL

7" 3"

10"

30' = 360"

30"

18"Prestressing tendon

TH TH =216 k

Material PropertiesE = 4320 k/in2

= 0.2G= 1800 k/in2

Unit weight = 0.16 k/ft3

Section Propertiesb = 18 ind = 30 inA = 540 in2

I = 40,500 in4

Av = 450 in2 (shear area)

Prestressing Tendon Notes1.

2.3.

TH is the component of the tension force in the prestressing tendon that is in the frame local 1-axis direction.The cable drapes at the left end, center and right end of the beam are illustrated in the figure.The cable profile is parabolic.

Beam neutral axis

LoadingLoad Case 1: Prestressing aloneLoad Case 2: Prestressing plus

self weight

A

A

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EXAMPLE 1-009 - 2

TECHNICAL FEATURES OF SAP2000 TESTED Beam prestress with parabolic tendon profile and different eccentricities at the

two ends The effect of beam prestress on the static analysis results

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

LoadCase

OutputParameter SAP2000 Independent

PercentDifference

My (center) kip-in -2,160.000 -2,160.000 0%1

Uz (center) in 0.15400 0.15400 0%

My (center) kip-in -1350.000 -1350.000 0%2

Uz (center) in 0.09050 0.09050 0%

COMPUTER FILE: Example 1-009

CONCLUSIONThe SAP2000 results and the independent results match exactly.

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EXAMPLE 1-009 - 3

HAND CALCULATION

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EXAMPLE 1-009 - 4

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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 - 8

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EXAMPLE 1-009 - 9

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EXAMPLE 1-009 - 10

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EXAMPLE 1-009 - 11

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EXAMPLE 1-009 - 12

EXAMPLE 1-009Frame - PrestressExample DescriptionGeometry and LoadingTechnical Features of SAP2000 TestedResults ComparisonComputer File: Example 1-009ConclusionHand Calculation