Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 FRAME - DISPLACEMENT LOADING EXAMPLE DESCRIPTION Using a portal frame, this example verifies SAP2000 for settlement and rotation of normal supports, skewed supports (settlement only) and spring supports. Note that for spring supports, the grounded end of the spring is displaced or rotated. Six different models are created. The models are identical, except for the loading and the support condition at joint 4 as shown in the figure below. The results for various support reactions in each model are compared with independent hand calculations. Important Note: Only bending deformations are considered in the analysis. Shear and axial deformations are ignored. In SAP2000 this is achieved by setting the property modification factor for area to 100,000 and setting the property modification factor for shear area to 0. GEOMETRY AND PROPERTIES 144" 2
1
Z
3
3
Y X
1
144"
2
Material Properties E = 29,000 k/in2 Section Properties b = 12 in d = 12 in A = 144 in2 I = 1,728 in4
4 Support condition at joint 4 varies for each model
EXAMPLE 1-005 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
Model A
0.01 rad
Uz = -0.2"
Uz = -0.5"
SUPPORT CONDITION AT JOINT 4 AND LOADING
Model C
Model B 10 k
θ Model D
Model
Model E
Support Condition at Joint 4
" = -1
3
U3
0.01 rad
Joint local axes for skewed supports
1 cosθ = 0.8 sinθ = 0.6
θ Model F
Loading
A
Roller
-0.5" Z displacement at joint 4
B
Z direction translational spring, k = 10 kip/in
-0.2" Z displacement at joint 4
C
Roller
0.01 radian rotation about joint 1
D
Rotational spring about Y axis, k = 80,000 kip-in/rad
0.01 radian rotation about joint 4
E
Skewed roller
10 kip Z direction force at midpoint of frame element 2
F
Skewed roller
-1" joint local 3 direction displacement at joint 4
EXAMPLE 1-005 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
TECHNICAL FEATURES OF SAP2000 TESTED Settlement of support in frame structures Rotation of support in frame structures Settlement of support with linear (translational) spring Rotation of support with rotational spring Skewed supports Skewed support settlement RESULTS COMPARISON Independent results are hand calculated using the unit load method described on page 244 in Cook and Young 1985. Output Parameter
SAP2000
Independent
Percent Difference
Fz (jt. 1) kip
6.293
6.293
0%
My (jt. 1) kip-in
-906.250
-906.250
0%
Fz (jt. 1) kip
1.115
1.115
0%
My (jt. 1) kip-in
-160.492
-160.492
0%
Fz (jt. 1) kip
-18.125
-18.125
0%
My (jt. 1) kip-in
2,610.000
2,610.000
0%
D. Spring Support Rotation
My (jt. 1 ) kip
-473.469
-473.469
0%
Ry (jt. 4) rad.
0.00408
0.00408
0%
E. Skewed Support
Fz (jt. 1) kip
5.811
5.811
0%
F3 (jt. 4) kip
5.236
5.236
0%
Fz (jt. 1) kip
27.215
27.215
0%
My (jt. 1) kip-in
-3,918.919
-3,918.919
0%
Model A. Support Settlement B. Spring Support Settlement C. Support Rotation
F. Skewed Support Settlement
EXAMPLE 1-005 - 3
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
COMPUTER FILES: Example 1-005a, Example 1-005b, Example 1-005c, Example 1-005d, Example 1-005e, Example 1-005f CONCLUSION The SAP2000 results show an exact match with the independent results.
EXAMPLE 1-005 - 4
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
HAND CALCULATION
EXAMPLE 1-005 - 5
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 - 6
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 - 7
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 - 8
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SAP2000 0
EXAMPLE 1-005 - 9
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 - 10
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-005 - 11