problem 4 001
TRANSCRIPT
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 1
EXAMPLE 4-001 ASOLID SOIL SUPPORTING UNIFORMLY LOADED CIRCULAR FOOTING
PROBLEM DESCRIPTION In this example, the asolid element is used to study distribution of vertical displacement and vertical stress in the soil beneath a uniformly loaded circular footing. The results from the axisymmetric SAP2000 model are compared with hand-calculated results.
Only a small portion of the semi-infinite soil medium is modeled. The radius of the footing is 10 feet. A one radian segment of a circular column of soil that is 250 feet deep and has a 100-foot radius is modeled. The soil is assumed to have a modulus of elasticity of 2,000 ksf and a Poissons ratio of 0.25. The footing exerts a uniform 5 ksf load on the soil.
10' 10' 90'
250'
5 ksf soil surface loading from footing Soil surface
CLCLSym
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 2
GEOMETRY, PROPERTIES AND LOADING
Z
X
10' 90'
5 ksf
250'
Ux restraint along this edge, typical
Uz restraint along base, typical
Soil PropertiesE = 2,000 k/ft2 = 0.25
Elements 5 feet wide by 5 feet deep
Elements 5 feet wide by 1 foot deep
Elements 1 foot wide by 1 foot deep
Elements 1 foot wide by 5 feet deep
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 3
TECHNICAL FEATURES OF SAP2000 TESTED Analysis using asolid elements Asolid surface pressure load Incompatible bending modes for asolid objects
RESULTS COMPARISON The independent results are calculated using data published in Poulos and Davis 1974. Results are presented separately for the models with and without the incompatible bending modes option.
With Incompatible Modes
Output Parameter Vertical Location SAP2000 Independent
Percent Difference*
z = 0 ft -0.0467 -0.0469 0%
z = -5 ft -0.0374 -0.0376 -1%
z = -10 ft -0.0284 -0.0286 -1%
z = -40 ft -0.0094 -0.0095 -1%
Uz ft
At x = 0 ft
z = -80 ft -0.0047 -0.0048 -2%
z = 0 ft -4.993 -5.000 0%
z = -5 ft -4.298 -4.553 -6%
z = -10 ft -3.285 -3.232 -2%
z = -40 ft -0.433 -0.435 0%
Vertical stress ksf
At x = 0 ft
z = -80 ft -0.122 -0.115 +6%
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 4
Without Incompatible Modes
Output Parameter Vertical Location SAP2000 Independent
Percent Difference*
z = 0 ft -0.0464 -0.0469 -1%
z = -5 ft -0.0371 -0.0376 -1%
z = -10 ft -0.0282 -0.0286 -1%
z = -40 ft -0.0094 -0.0095 -1%
Uz ft
At x = 0 ft
z = -80 ft -0.0047 -0.0048 -2%
z = 0 ft -5.260 -5.000 +5%
z = -5 ft -4.265 -4.553 -6%
z = -10 ft -3.127 -3.232 -3%
z = -40 ft -0.436 -0.435 0%
Vertical stress ksf
At x = 0 ft
z = -80 ft -0.122 -0.115 +6%
COMPUTER FILES: Example 4-001-incomp, Example 4-001-comp
CONCLUSIONS The SAP2000 results show an acceptable comparison with the independent results both with and without the incompatible bending modes option.
The results for this example problem are not controlled by bending behavior. Thus the incompatible bending modes option has little effect on the results.
In general, when bending is a significant contributor to the results of an example problem, models that do not use the incompatible bending modes option require a much more refined mesh to obtain results comparable to similar models that use the incompatible bending modes option.
In general, the incompatible bending modes option should always be used for asolid element models.
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 5
HAND CALCULATION
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Software Verification PROGRAM NAME: SAP2000 REVISION NO.: 2
EXAMPLE 4-001 - 6
EXAMPLE 4-001Asolid Soil Supporting Uniformly Loaded Circular FootingProblem DescriptionGeometry, Properties and LoadingTechnical Features of SAP2000 TestedResults ComparisonComputer Files: Example 4-001-incomp, Example 4-001-compConclusionsHand Calculation