Minimum cost design of a welded stiffened steel sectorial plate

The most economic form of stiffening is required for a steel sectorial plate. Stiffeners made from halved rolled I-sections are welded to the base plate with double fillet welds. The plate is subjected to a uniformly distributed normal load. Three stiffening types are designed as follows: (a) non-equidistant tangential stiffening with constant base plate thickness, (b) equidistant tangential stiffening with base plate thickness varying stepwise, and (c) equidistant tangential stiffening with constant base plate thickness combined with radial stiffeners.
Each form of stiffening is designed so that the maximum stress due to bending from the factored normal load in the base plate parts should not exceed the yield stress. The positions of the non-equidistant tangential stiffeners are calculated by a special mathematical algorithm. The costs of materials, assembly, welding and painting are calculated for each stiffening version and the costs are compared with each other.
The cost comparison shows that - for a given numerical problem - stiffening type (b) is the cheapest and type (a) the lightest. Type (c) needs too much welding and is also the most expensive.