Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Civil Engineering


The main objective of this investigation is to determine the optimum design variables which will minimize the weight of a structure, the number of variables was chosen to obtain a high degree of flexibility in design and to reduce linearization errors in the constraint equations. The linear equations used in the simplex method of analysis were approximated by applying Taylor's first order of expansion theorem to the nonlinear constraint equations and the objective function. This technique of approximation is known as the cutting plane method. After each optimization of the approximate linear equations by the simplex method, new coefficients for the linear constraint equations were calculated. In this study a two-bay, one-story rigid frame structure subjected to a uniformly distributed load was considered. The design variables imposed for optimization were the cross-sectional dimensions of the beams, columns, and haunches. As efficiency in construction was highly emphasized, flange width and thickness, as well as web thickness were held at a constant value for the complete frame. The depth or the webs or the columns, beams, haunches, as well as the length of each haunch were allowed to vary for each member to adjust for different loading conditions. The American Institute of Steel Construction code and working stress method of analysis have been used throughout this investigation. Although A-36 type of steel with 36 ksi for yield strength was adopted in this study, the program can be modified to any other desired type of steel. The computer program is written in Full Operating System Fortran for the use of the IBM 360 computer. The number of variables has been limited to 22 because of the core space restrictions of the computer but can be expanded when such space becomes available.

Library of Congress Subject Headings

Strains and stresses

Structural frames

Steel, Structural

South Dakota State University Theses



Number of Pages



South Dakota State University