problem 1 009
TRANSCRIPT
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Software Verification
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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Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 7
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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Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 7
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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Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 4
H AND C ALCULATION
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Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 5
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 6
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 7
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 8
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 9
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 10
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 11
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 12
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PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 13
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Software Verification
PROGRAM NAME: SAP2000
REVISION NO.: 7
EXAMPLE 1-009 - 14