F-10 (Response Spectrum Analysis of 3D Frame) |
  
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F-10 (Response Spectrum Analysis of 3D Frame) |
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Objective
To verify the results of response spectrum analysis on a 3D frame
Problem Description
A 2-story 3D frame shown below [Ref 1] fixed at the bottom is subjected to ground motion characterized by constant 0.4g for all modes, with 5% damping.
Geometry: X direction = 2 x 35 ft; Y direction = 2 x 13 ft; Z direction = 2 x 25 ft.
Columns: E = 350,000 k/ft2. A = 4 ft2, Iz = 1.25 ft4, Iy = 1.25 ft4, J = 1.25 ft4, Ay =Az = 0 ft2
Beams: E = 500,000 k/ft2. A = 5 ft2, Iz = 2.61 ft4, Iy = 1.67 ft4, J = 1.25 ft4, Ay =Az = 0 ft2
Two additional nodes 28 (38, 13, 27) and 29 (38, 26, 27) are placed on the first and second floors as they are the center of masses for the respective floors.
Masses: 6.2112 k-sec2/ft at nodes 28 and 29 (X and Z directions).
To prevent nodes 28 and 29 from being orphaned nodes, we will add two additional beams with very small section properties (Iz = Iy = J = 1e-5 ft4, A = 1e-5 ft2) to connect node 28 with node 14 (or any other node on the first floor) and nodes 29 with node 17 (or any other node on the second floor).
Results
The following lists different results by ENERCALC 3D against the reference [Ref. 1].
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ENERCALC 3D |
Reference |
Mode 1 period (sec) |
0.2269 |
0.2271 |
Mode 2 period (sec) |
0.2152 |
0.2156 |
Mode 3 period (sec) |
0.0733 |
0.0733 |
Mode 4 period (sec) |
0.0719 |
0.0720 |
X displacement at node 29 ABSSUM modal combination (ft) |
0.02045 |
0.02050 |
X displacement at node 29 SRSS modal combination (ft) |
0.02010 |
0.02012 |
X displacement at node 29 CQC modal combination (ft) |
0.02011 |
0.02014 |
Comments
The results given by ENERCALC 3D are very close to the referenced values. This verification problem also confirms the robustness of rigid diaphragm implementation. Due to program limitation, we have to add couple of weak beams on the floors to prevent center-of-mass nodes (node 28 and 29) from being orphaned.
Reference
[1]. Example 1-024, Sap2000 Software Verification Manual, 2007, Computers and Structures, Inc., Berkeley, California.
