Optimum design of statically indeterminate beams under multiple loads

The paper presents minimum-weight designs of statically indeterminate beams under multiple loads. Under each load system consisting of external loads and self-weight the normal and shear stresses in the beams are restricted from above. The variation of the stiffness along the span of the beams is restricted to splines of order zero, one or two, thus reducing the optimization problem to a linear or non-linear programming problem depending on the cross-sectional shape. The latter is reduced to a sequence of linear programming problems which are solved by the highly-efficient active set method. Several examples are given to illustrate the potential of this method. A computer code in standard FORTRAN 77 is also provided.