Envelopes for Seismic Response Vectors. II: Application

In a companion paper, a response-spectrum-based procedure for predicting the envelope that bounds the simultaneous action of two or more seismic responses was developed. In the present paper, we evaluate the accuracy of the procedure and investigate its influence on the design of structural elements subjected to seismic loads. The accuracy of the proposed envelope is examined by means of comparison with time-history analyses using simulated and recorded ground motions. It is found that the proposed envelope has a level of accuracy that is commensurate with its response spectrum bases. The significance of the proposed envelope is demonstrated by designing the columns of an example reinforced concrete structure by the proposed and conventional methods. In particular, the required reinforcement ratio for each column is determined by superimposing the response envelope that bounds the axial force and biaxial bending moments acting in the column onto a prescribed moment-axial capacity surface. Savings as high as 50% in the required reinforcement ratio are gained by use of the proposed method.