Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-004 FRAME - ROTATED LOCAL AXES EXAMPLE DESCRIPTION This example tests SAP2000 for various types of loading on a frame element with its local 2 and 3 axes not parallel to the global axes. A W12X106 cantilever beam is used with the local 2 axis rotated 30 degrees from the global Z axis as shown in the figure below. The free end displacements in the global Y and Z directions are compared with independent hand calculations. The W12X106 section properties are read from the SECTIONS8.pro section database provided with SAP2000. Important Note: Only bending deformations are considered in the analysis. In SAP2000 shear deformations are ignored by setting the property modification factor for the shear area to zero. GEOMETRY, PROPERTIES AND LOADING 30°
144" C
C
Z
Geometry
3 Section C-C
Y
Load Case 1 X
2
Y
0.01 k/in
Z
Material Properties E = 29,000 k/in2
1 kip
Load Case 2 240 k-in
Section Properties W12X106 I33 = 933 in4 I22 = 301 in4
Load Cases Load Case 1: 0.01 kip/in uniform distributed load in global Z direction Load Case 2: 1 kip concentrated load at free end in global Z direction Load Case 3: 240 k-in concentrated moment at free end about global Z axis
Load Case 3
EXAMPLE 1-004 - 1
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
TECHNICAL FEATURES OF SAP2000 TESTED Frame local axes rotated from global axes Use of AISC sections RESULTS COMPARISON The independent results are calculated using the beam deflection formulas in Table 3 item 1a and Table 3 item 2a on pages 96 and 98, respectively, in Table 3 in Roark and Young 1975. Load Case
Output Parameter
SAP2000
Independent
Percent Difference
Uy (free end) in
-0.01806
-0.01806
0%
Uz (free end) in
-0.03029
-0.03029
0%
Uy (free end) in
-0.03345
-0.03345
0%
Uz (free end) in
-0. 05610
-0. 05610
0%
Uy (free end) in
-0.08361
-0.08361
0%
Uz (free end) in
-0.14024
-0.14024
0%
1
2
3
COMPUTER FILE: Example 1-004 CONCLUSION The SAP2000 results show an exact match with the independent solution.
EXAMPLE 1-004 - 2
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
HAND CALCULATION
EXAMPLE 1-004 - 3
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-004 - 4
Software Verification PROGRAM NAME: REVISION NO.:
SAP2000 0
EXAMPLE 1-004 - 5