Optimum design in structural engineering fields implies that the minimum cost or weight of structure is attained based on some specified constraints subjected to the structure. In this study an optimization procedure is used to obtain the optimum design for semi-rigid frames. In order to study the effect of connection flexibility on the optimum design of steel structures, several connection stiffnesses are used to cover a wide range of flexibility (high to low connection stiffness). The connections are modeled by the four parameters Richard model to represent their real behavior. The analysis procedure is simplified by using the secant stiffness method. An iterative procedure is used in a computer program to simulate the connection behavior and then to predict the frame response under service loading and develop the optimum design for the whole frame. Results of two analyzed semi-rigid frames with different connection flexibilities are obtained and compared with the optimum design of the same frames with rigid connections. The final optimum design of all considered frames (rigid and flexible) shows that it is important to consider the connection flexibility in the design in order to deal with the actual case of structural behavior.

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