Doctoral Dissertations


"A method to optimize the weight of plane frames subjected to dynamic loads is presented. Restrictions are imposed upon the maximum dynamic stresses and displacements, desirable section moduli of the constituent members, and the range of values allowed for natural frequencies. Various considerations for rigid frame design include damping, the P-Δ effect, static girder loads, static column loads and girder shears transferred to the columns. A finite difference approach is presented to evaluate the shock spectrum which is used in conjunction with modal superposition to obtain the peak upperbound dynamic displacements and stresses for multistory and multibay frames. The displacement method is used for the structural matrix formulation from which the optimization process is shown in relation to the change of the design variables in the condensed stiffness matrix.

A direct, non-linear mathematical programming method, the method of feasible directions, is used to minimize the weight of the structure, as the objective function, subject to the aforementioned linear and non-linear constraints. Using this method requires the calculation of the normals to the various response quantities of stresses, displacements, eigenvalues and eigenvectors. These are obtained by taking derivatives with respect to the design variables where the equations remain in closed form due to the utilization of information obtained from the shock spectrum and the eigensolution.

The objective function is linearized by using wide flange sections as structural elements since the section modulus of each wide flange can be expressed linearly as a function of the depth and area.

Several applications of the proposed method are presented to show the design process related to active constraints and the significant effects of various considerations on optimum design"--Abstract, pages ii-iii.


Cheng, Franklin Y.

Committee Member(s)

Andrews, William A., 1922-2009
Senne, Joseph H.
Best, John, 1925-2015
Davis, Robert L.


Civil, Architectural and Environmental Engineering

Degree Name

Ph. D. in Civil Engineering


University of Missouri--Rolla

Publication Date



xv, 172 pages

Note about bibliography

Includes bibliographical references (pages 115-117).


© 1973 Mark Eugene Botkin, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Damping (Mechanics) -- Mathematical models
Structural dynamics -- Computer programs
Vibration -- Mathematical models

Thesis Number

T 2816

Print OCLC #


Electronic OCLC #