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SAP2000 7
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 at the beam center are compared with independent hand-calculated results. SAP2000 has two options for modeling the effect of the prestress. One option models 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 internally meshed 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 the example 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.
EXAMPLE 1-009 - 1
Software Verification SAP2000 7
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GEOMETRY AND LOADING CL
A
18"
Prestressing tendon
10"
A
Material Properties E = 3600 k/in2 ν = 0.2 G = 1500 k/in2
30"
3"
Beam neutral axis
10"
T=220 k
Section A-A
30' = 360" Section Properties b = 18 in d = 30 in A = 540 in2 I = 40,500 in4 Av = 450 in2 (shear area)
Prestress Properties A = 1.5 in2 E = 29000 k/in2 ν = 0.3
Prestressing Tendon Notes 1. T is the component of the tension force in the prestressing tendon before losses. 2. The tendon is tensioned from the left end only. 3. The cable drapes at the left end, center and right end of the beam are illustrated in the figure. 4. The cable profile is parabolic. 5. The friction loss coefficient for curvature is 0.15. 6. The friction loss coefficient for wobble is 0.0001 / in. 7. Consider losses due to friction and beam elastic shortening.
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
EXAMPLE 1-009 - 2
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SAP2000 7
RESULTS COMPARISON Independent results are hand calculated using basic principles and using the unit load 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.
Model
Output Parameter
A- By Loads B- Elems (60")
A- By Loads
C- Elems (12")
Independent
0.17028 Uz (center) in
C- Elems (12")
B- Elems (60")
SAP2000
My (center) kip-in
0.16041
Percent Difference +2.8%
0.16564
-3.2%
0.16484
-0.5%
-2061.5
+2.9%
-2013.9
-2004.3
-2001.7
+0.5% -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.
EXAMPLE 1-009 - 3
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HAND CALCULATION
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EXAMPLE 1-009 - 14