Algebraic linear programming applied to optimal plastic design of steel portal frames

The paper is concerned with the minimum weight design of steel portal frames subject to the constraints of the kinematic theorem of plastic collapse. Minimum weight design is a classic linear programming problem which can be solved algebraically for classes of frames with arbitrary geometric dimensions and arbitrary load magnitudes. The solution for each class of frames is expressed in the form of a chart. This technique has been inhibited by the substantial amount of tedious algebraic manipulation necessary for each specified class of frames. In the paper, the process of algebraic linear programming is reduced to the repeated application of a number of vector formulas. A computer program is described which, using these formulas, derives the solution chart for specified classes of frames. Examples illustrate the use of the program to derive a design chart and the use of a chart to solve a specific minimum weight design problem.