Optimal Plastic Design of Pitched Roof Frames for Multiple Loadings

The paper describes the use of algebraic linear programming for 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. In a recent paper, the process of algebraic linear programming was reduced to the repeated application of a number of vector formulas and a computer program was developed for the derivation of the solution charts for specific classes of frames. In this paper the method is extended to the problem of frames subjected to multiple load cases. It is shown that simple problems whose solution can normally be displayed in the form of two-dimensional charts now require three-dimensional charts or a number of two-dimensional charts.