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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