Limit load analysis of plane frames using the force method

A fully automatic way to find the collapse load of planar frames is presented. The approach is based on the force method analysis, which provides computational advantages in linear programming applications. An algorithm is presented which uses the graph representation of the frame and forms cycles by finding the shortest path between the end nodes of its members. The algorithm provides a relatively easy computer implementation, because of the simple way that a generated cycle is checked for independence. This is done by fictitiously increasing the lengths of the members of an admissible cycle. A statical basis is then found from the cycle basis for any plane frame. Equilibrium with applied loads is satisfied through the use of cantilevers that follow the quicker way to the ground of each load. Two examples of application are given.