Optimum Design of Welded Steel Columns

A method for the discrete minimum weight design of welded steel columns is developed. The design problem is formulated as a discrete nonlinear programming problem. The problem is solved using an interior penalty function method combined with a variable metric discrete search technique. Starting with an initial feasible solution, the first unconstrained problem is solved by searching along the direction of the integer gradient of the modified objective function. For the next unconstrained problems the direction of search is modified by the inverse of the Hessian matrix of the objective function. This way the slow convergence of the gradient method near the optimum is avoided. An example is given to show the efficiency and rapid convergence of the method. The results obtained show that more efficient use of materials can be achieved by using welded steel sections. The method presented can also be used to find the minimum cost design of welded steel sections if the cost factors are known.