A response‐spectrum‐based envelope for Mohr's circle

Mohr's circle is commonly used to determine the combinations of normal and shear stresses that act in any direction at a location of interest within a structure. During an earthquake, the radius and center of Mohr's circle naturally fluctuate with time. In such cases, an envelope that bounds the time‐varying realizations of Mohr's circle at a given location is desirable to facilitate the identification of critical combinations of normal and shear stresses at that location. In this paper, a response‐spectrum‐based procedure for predicting the envelope that bounds Mohr's circle in a linear‐elastic structure subjected to seismic loads is developed. The accuracy of the proposed envelope is evaluated by comparing it to the results of time‐history analyses performed on a concrete gravity dam 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 largest observed difference between the simulated and predicted envelopes is less than 10%. Copyright © 2003 John Wiley & Sons, Ltd.