Civil Engineering ETDs

Publication Date

5-10-1971

Abstract

To pate, only special cases of dynamic stability have been solved. In this dissertation, an attempt is made to obtain practical solutions to the stability problem in earthquake engineering.

A column supporting a concentrated mass at the top is treated as a single-degree-of-freedom system. The system is assumed to be linearly e·1astic with viscous damping. It is subjected to both horizontal and vertical random acceleration at the base, which are taken to be a band limited white noise simulating earthquake motions. The objective of this investigation is to find the probability of instability of the system.

Two methods of solution are presented. In the first method, the problem is treated as a crossing problem. First, the expected value of the fraction of time that the response process spends above a certain level is found by fixing the instantaneous frequency as a constant. Then the expected value of the fraction of time that the instantaneous frequency is between two given levels is found. The product of the two gives the solution by the first method. The second method is a solution of the nonhomogeneous Mathieu equation. First, the deterministic equation is solved, then the parameters are randomized numerically. Therefore, the probability statements resulting from the second method arc empirical. The results of the second method are utilized for the purpose of comparison with those of the first method.

Probabilities of instability of twenty-five columns selected from the AISC Steel Construction Manual are computed by using the first method. The probabilities of instability of five of these columns are also computed by the second method. Comparison of the two methods for these columns seems to be reasonable. Then the probabilities of instability for the twenty-five columns computed by the first method are plotted against such column parameters as Po/Pcr, Lef/ry and w. The trends in these relationships are indicated. The probabilities of failure by yielding in the absence of vertical forces are also computed for the twenty-five columns by using the first method. Then the ratios of probability of instability of each column to the probability of failure by yielding in the absence of vertical forces are computed and plotted.

The probabilities of instability for all columns studied are found to be significant. It is also found that the coupling effect can increase the probability of instability of certain columns by as much as ten thousand times. On the basis of this study, design curves can be prepared for all column sizes to enable design engineers in choosing safer columns in practice.

Document Type

Dissertation

Language

English

Degree Name

Civil Engineering

Level of Degree

Doctoral

Department Name

Civil Engineering

First Committee Member (Chair)

James Tsu-Ping Yao

Second Committee Member

Cyrus Omid Varan

Third Committee Member

Gerald William May

Fourth Committee Member

Marion Marvin Cottrell

Download

Share

COinS