Minimum Cost Structures by Dynamic Programming

In the design of structures it is necessary to consider an array of possible choices in sizing elements such as beams and columns in finding an acceptable and economical design. It is only with the recent access to digital computers that designers can be relieved of some of the tedious calculations associated with structural design decisions. In further extending computer aided design, digital computers have also been used to directly determine optimum or least cost designs. Applications in steel structures have included bridge girders, wide flange beams, grillages and ship structures. One important design area that has received little attention is the optimizing of the total fabrication and material costs for a structural system composed of many elements such as multistory frames, transmission towers, and grillages. Fabrication costs can be reduced if many members or elements are constructed of a similar cross-section. This causes a penalty in extra material, since a minimum weight design often has members of many different cross-sections. This paper describes the use of a simple procedure known as Dynamic Programming to find the optimum selection of member sizes, which minimizes the overall cost including material and fabrication costs. Dynamic Programming has previously seen application in structural design and construction decisions. It is used in the GAD program developed at Case Western Reserve for the Ohio Department of Highways to design highway bridge girders, including selecting steel cross-section and material strength. It has also been used for optimum plate selection for ship structural design. In construction management Dynamic Programming has been used in conjunction with C.P.M. and PERT techniques. Before describing the Dynamic Programming method, the present design problem will be described in more detail with an example.