Optimum least-cost design of a truss roof system

An algorithm is presented encompassing the application of optimization methods to the least-cost elastic design of roof systems composed of rigid steel trusses, web joists and steel roof deck. The method is capable of designing rigid trusses that can be fabricated from various grades of steel and several types of standard sections. The selection of open web joist is presently limited to standard H-series, and decking material is standard 22 gage. The design is based upon AISC allowable values where combined stresses resulting from axial forces and secondary bending moments are considered. The effective column lengths are computed using the characteristic buckling equation for a member whose ends are elastically restrained against rotation. The procedure developed considers changes in the mechanical properties of the members, geometric variations in the truss configuration and changes in topology. Selected sets of members may be chosen to be identical, and chord members may be defined as continuous over several panels. Also investigated is the problem of finding the design containing the optimum number of trusses. A number of examples are presented which demonstrate the flexibility and generality of the design approach developed.