Frame24 – Response Spectrum a of a Three-Dimensional Moment Frame
- Gokhan Alkan (Unlicensed)
Problem Description
In this example a two-story, two-bay in each direction, three-dimensional, fixed base frame structure is analyzed using a response spectrum analysis. The modal frequencies and X direction displacement at the story level centers of mass are compared with independent results from another computer program presented in Peterson 1981.
The structure is doubly symmetric in plan, except that the center of mass at each story level is eccentric and is given by the coordinates X = 38 feet and Y = 27 feet, as shown in the figure. Additional joints labeled 28 and 29 are added at the center of mass location at each story level. All of the story mass is applied at these joints.
The masses are applied in the X and Y directions only. No rotational mass inertia is used for consistency with Peterson 1981. Thus the problem has four natural modes. All four modes are used in the response spectrum analysis.
Two rigid diaphragm constraints are defined, one for each of the story levels. All of the joints at Level 2 are constrained together, including the joint at the center of mass. Similarly, all of the joints at the Roof level are constrained together. For each of the story levels, the X and Y displacements and the Z rotations for all joints are dependent on each other.
An eigenvector solution is used to obtain the modal frequencies. Four different response spectrum analyses are performed, with each using a different type of modal combination. The combination types used are CQC (complete quadratic combination), SRSS (square root sum of the squares), ABS (absolute) and NRC 10 Percent. The results are compared with results using CQC, SRSS, ABS and NRC 10 Percent modal combinations in the independent reference.
The applied response spectrum is a constant 0.4g for all modes. This spectrum is applied in the X direction of the structure only. Modal damping is assumed to be 4% for all modes.
Important Note: Only bending and axial deformations are considered in this example. Shear deformations are ignored by setting the shear area to zero for each frame object in the structure.
Tested Features
- Three-dimensional frame analysis
- Modal analysis using eigenvectors
- Rigid diaphragm constraint
- Joint mass assignments
- Response spectrum analysis