Frame25 – Response Spectrum Analysis of a Three-Dimensional Braced Frame!!

Problem Description

In this example a three-story, L-shaped frame structure is analyzed using a response spectrum analysis. The modal frequencies, center of mass displacement at the roof level and axial forces in several members are compared with independent results from another computer program presented in Peterson 1981.
The structure consists of four identical frames that have columns and diagonal braces only. The frame objects can carry axial loads only. This is achieved in the model by pinning the ends of each diagonal brace and pinning the bottom of each column object at each story level. The frames are connected in plan by rigid diaphragms at each story level. Beams are not required at the story levels because the rigid diaphragm prevents them from carrying any loads.
A center of mass joint is defined at each story level located 33'-4" from the origin in both the X and Y directions. All mass properties are concentrated at the center of mass joints and they are identical at each of the three levels. X and Y translational masses and a rotational mass moment of inertia about the Z axis are defined at each center of mass joint. Thus there are nine dynamic degrees of freedom and the model has nine natural modes. For consistency with Peterson 1981, only the first two modes are used in the response spectrum analysis.
Three 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 Level 3 and 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. Three 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) and ABS (absolute). The results are compared with results using CQC, SRSS, and ABS modal combinations in the independent reference.
The applied earthquake for this example, the N-S component of the 1940 El Centro earthquake, is applied in the X-direction of the model with 5% modal damping assumed for all modes.

Tested Features

•  Three-dimensional frame analysis
•  Modal analysis using eigenvectors
•  Rigid diaphragm constraint
•  Joint mass assignments
•  Response spectrum analysis