For conventional analysis and design of steel framed structures, the actual response of the beam-to-column connections is simplified to either rigid or pin-connected behaviour. Although the adoption of such idealized performance simplifies the analysis and design process, the predicted response of the idealized structure may be quite unrealistic compared to that of the actual structure. This is because most beam-to-column connections used in practical steel framed structures actually exhibit semi-rigid deformation behaviour that can contribute substantially to overall structural deformation as well as to internal force redistribution in the members of the structure. Evidently, then, the neglect of real connection behaviour may lead to unrealistic predictions of the stiffness and strength of steel structures, and to less than optimal design in steel construction. Thus, it is necessary to account for the effect of connection flexibility when designing such structures if realistic and economical designs are to be found.

Recognizing the importance of the behaviour of connections in the practice of today's steel construction, the present study has established a mathematical and numerical model of an efficient computer-based method for the optimum design of steel frameworks accounting for the behaviour of semi-rigid connections. The method accounts for both members and connections by taking members sizes and connection stiffnesses as design variables in the synthesis process. The members are sized using standard steel sections and the connections are selected from a database of conventional connections. An optimization algorithm is applied to minimize the structure (member + connection) 'cost' subject to constraints on stresses and displacements under specified design loads. A geometrical stiffness matrix for semi-rigid members is developed to enable account for both first- and second-order (P-Δ) effects in addition to nonlinear connection behaviour in the analysis and design of semi-rigid frameworks. Several steel framework examples are presented to illustrate the features of the design method.

The results of this study indicate that the proposed semi-rigid steel frame design method realistically accounts for connection behaviour and produces a more appropriate and economic design than does the traditional fully-rigid (or fully-pinned) steel frame design method currently used in professional practice.