The Effect of Sway-Rotation Interaction on the Response of Multi-Storey Frames

摘要

This paper seeks to assess the effect of sway-rotation interaction in the response of multistory frames using a three storey, two bay frame subjected to vertical and horizontal loadings. Two methods of analysis were employed: one that treats rotation differently from sway as in moment distribution method and another that combines sway and rotation as in classical displacement method. In the method of moment distribution, sway corrections were applied to obtain compatibility equations for the frame. A simultaneous solution of the compatibility equations gave the factors which were used to multiply the values of the moments obtained for sway correction to obtain a set of moments consistent with force acting equal and opposite to the joint restraining forces. The canonical equations of equilibrium for classical displacement method were obtained using a set of initial value solution of a uniform beam. The coefficients of the equilibrium equation were obtained by considering the bending moment diagrams due to unit joints rotation and unit joints translation separately. For each bending moment diagram the column shears were determined and equations of statics were used to obtain the unknown reactions as the coefficients. By solving the canonical equations of equilibrium the unknown reactions were obtained and used to evaluate the final bending moments for the frame. The results obtained using the two methods were compared to determine the effect of sway-rotation interaction.