Optimization of partially prestressed concrete girders under multiple strength and serviceability criteria

A comprehensive study on the optimization of simply supported partially prestressed concrete girders is presented. Using sequential quadratic programming a set of optimal geometrical dimensions, amounts of prestressing and non-prestressing steel, and spacing between shear reinforcements are obtained. The constraints used are based upon flexural stresses, fatigue stresses, crack width, ductility, initial camber, deflection due to both dead and live loads, ultimate moment capacity of the section with respect to cracking moment and factored loads, and the ultimate shear strength. Results point to the need for non-prestressing steel to obtain economical designs. Minor savings on the material occur when the section is allowed to crack. The ultimate moment capacity and the fatigue stress controlled the design in the cracked case. The tensile stress at service and the ultimate moment capacity were the binding constraints in the uncracked case. This study automates the design of partially prestressed concrete girders and provides needed design solutions to problems which are of importance to practicing engineers.