Doctoral Dissertations


"A procedure of analysis is presented for determining the dynamic instability and response of framed structures subjected to pulsating axial loads, time-dependent lateral forces, or foundation movements. Included in the analytical work are the instability criterion of a structural system, the finite element technique of structural matrix formulation, and the computer solution methods.

The dynamic instability is defined by a region in relation to transverse natural frequency, longitudinal forcing frequency and the magnitude of axial dynamic force. The axial pulsating load is expressed in terms of static buckling load for ensuring that the applied load is not greater than the buckling capacity of a structural system. Consequently, the natural frequency and static instability analyses are also included. For static instability analysis, both the concentrated and uniformly distributed axial loads are investigated.

The displacement method is used in this research for structural matrix formulation for which the elementary matrices of mass, stiffness, and stability are developed using the Lagrangian equation and the system matrices are formulated using the equilibrium and compatibility conditions of the constituent members of a system.

Two numerical integration techniques of the fourth order Runge-Kutta method and the linear acceleration method are employed for the elastic and elasto-plastic response of continuous beams, shear buildings, and frameworks. The general considerations are the bending deformation, p-Δ effect, and the effect of girder shears on columns. For the elasto-plastic analysis, the effect of axial load on plastic moment is also included.

A number of selected examples are presented and the results are illustrated on a series of charts, tables, and figures from which the significant effect of pulsating load on the amplitude of transverse vibration is observed.

The work may be considered significant in the sense that the response behavior of parametric vibrations has been throughly [sic] studied and the computer programs developed can be used for various types of frameworks"--Abstract, pages ii-iii.


Cheng, Franklin Y.

Committee Member(s)

Andrews, William A., 1922-2009
Best, John, 1925-2015
Senne, Joseph H.
Parry, Myron G.


Civil, Architectural and Environmental Engineering

Degree Name

Ph. D. in Civil Engineering


National Science Foundation (U.S.)
University of Missouri-Rolla. Department of Civil Engineering


Financial support from the National Science Foundation Grant No. GI 34966


University of Missouri--Rolla

Publication Date



xiii, 145 pages

Note about bibliography

Includes bibliographical references (pages 102-105).


© 1973 Wu-Hsiung Tseng, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Structural stability
Structural dynamics
Buildings -- Earthquake effects

Thesis Number

T 2986

Print OCLC #


Electronic OCLC #