Optimum Cost Design of Partially Composite Steel Beams Using LRFD

Design of composite steel beams is a trial and error process. The procedure recommended by the Manual of Steel Construction, Load and Resistance Factor Design (LRFD)1 is to first assume a depth for the steel beam and then compute a trial beam size. For a full composite action the number of shear studs is chosen with the assumption that the plastic neutral axis (PNA) is in the concrete slab. For partially composite design the number of shear studs is chosen rather arbitrarily by the designer. The flexural capacity of the composite section is then computed based on the ultimate stress distribution over the cross section. If the capacity is less than the required, the design is revised in one of several ways: by increasing the number of shear studs, by increasing the beam depth, or by choosing a heavier section. These decisions must be based on the designers judgment without any available guidelines. Shear and deflection considerations may force additional changes in the design. The resulting design is usually not the minimum cost design and at best is a feasible design. Several iterations of this entire process may be necessary if the goal is to minimize the cost. The optimum design can directly be obtained by formulating the problem as a nonlinear optimization problem. However conventional methods for solution of these nonlinear programming problems are iterative and require large computer resources.