COMPUTERS & STRUCTURES INC. R Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 0 EXAMPLE 1-009 - 1 EXAMPLE 1-009 FRAME - PRESTRESS EXAMPLE DESCRIPTION The SAP2000 beam prestress calculations are verified in this example using a simply supported concrete beam with a parabolic prestressing tendon profile and different eccentricities at each end. The beam is subjected to self weight load and prestressing load. The bending moment and deflection at the beam center are compared with independent hand calculated results. In SAP2000 the beam is modeled using two frame elements so that there is a node 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 C L C L 7" 3" 10" 30' = 360" 30" 18" Prestressing tendon T H T H =216 k Material Properties E = 4320 k/in 2 ν = 0.2 G = 1800 k/in 2 Unit weight = 0.16 k/ft 3 Section Properties b = 18 in d = 30 in A = 540 in 2 I = 40,500 in 4 A v = 450 in 2 (shear area) Prestressing Tendon Notes 1. 2. 3. T H 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 Loading Load Case 1: Prestressing alone Load Case 2: Prestressing plus self weight A A
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C OMP UTE R S &S TRU CTU R ES
IN C.
R Software VerificationPROGRAM NAME: SAP2000REVISION NO.: 0
EXAMPLE 1-009 - 1
EXAMPLE 1-009FRAME - PRESTRESS
EXAMPLE DESCRIPTION
The 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
ν = 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
C OMP UTE R S &S TRU CTU R ES
IN C.
R Software VerificationPROGRAM NAME: SAP2000REVISION NO.: 0
EXAMPLE 1-009 - 2
TECHNICAL FEATURES OF SAP2000 TESTED
Beam prestress with parabolic tendon profile and different eccentricities at thetwo ends
The effect of beam prestress on the static analysis results
RESULTS COMPARISON
Independent 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
CONCLUSION
The SAP2000 results and the independent results match exactly.
C OMP UTE R S &S TRU CTU R ES
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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 - 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
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