A computational model of lateral displacement distribution with closed form for direct displacement based seismic design of RC frame structure

Direct displacement-based design (DDBD) is one of the most popular methods of achieving performance based structural seismic design philosophy. It begins by inputting a lateral displacement distribution representing desired structural seismic performance , and intents to design the structure achieving such desired performance under earthquake excitation by incorporating appropriate method to determining seismic moment demands of members. Because the calculated seismic moment demands of members can be used to design flexure strength of the intended plastic hinge locations and thus affect the actual inelastic deformation capacity of structure, it should be compatible with the desired lateral displacement distribution inputted into the design procedure. However, existing design procedure of DDBD do not consider such compatibility because the structure is usually expected exhibiting inelasticity, and this may lead to the actual structural displaced pattern deviating from the design expectation. In this study, a novel lateral displacement distribution model for use in DDBD of reinforcement concrete (RC) frame structure is presented to solve this problem, and on this basis an improved DDBD procedure is suggested. The presented lateral displacement distribution model is derived by firstly presetting a prescribed seismic moment distribution pattern of columns following strong column weak beam principle. Then, by decomposing the desired lateral displacements at floor levels into elastic and plastic parts within the framework of DDBD theory, a closed form solution of lateral displacement computational expression is obtained. Because by this way the derivation process of the proposed structural lateral displacement distribution model can consider its compatibility with the calculation of seismic moment of members naturally, the design results with theoretically closed form can be produced. Furthermore, to overcome the disadvantage of highly computational complexity of proposed lateral displacement distribution model, a simplified strategy of this expression is also presented for convenience of engineering application . The verification finally demonstrates the effectiveness of the proposed method.