| In the design or analysis of structures for seismic loads, the effects of forces acting simultaneously in a member must be considered. The most common example is the interaction of bending moments and axial load in a column. The usual response spectrum method provides the maximum values of individual responses, but the critical combination of these responses may not involve any of these maxima.; In this thesis, a response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is developed. It is shown that, for an assumed orientation of the principal axes along which the ground motion components are uncorrelated, this envelope is an ellipsoid. For the case when the orientation of the principal axes is unknown, a “supreme” envelope is derived, which corresponds to the most critical orientation of the axes. The coordinates of these envelopes are computed by using values available in conventional response spectrum analyses, i.e., response spectral shapes in one, two or three directions, and the modal properties of the structure. The response envelope can be superimposed on a capacity surface to determine the adequacy of a given design.; The accuracy of the elliptical envelope for linear structures is examined by means of comparison with time-history analyses using artificial and recorded ground motions. It is found that the elliptical envelope has a level of accuracy that is commensurate with its response spectrum bases. The significance of the proposed envelopes is demonstrated by designing the columns of an example reinforced concrete bridge by the proposed and conventional methods. Savings as high as 45% in the required reinforcement ratio are gained by use of the proposed method.; Linear analyses are appropriate for serviceability limit states associated with moderate-intensity ground motions. However, when a structure is subjected to high-intensity ground motions, its behavior is expected to be nonlinear and, hence, the response spectrum method cannot be used. Furthermore, the envelope bounding a vector of responses is usually not elliptical. In this study, a comprehensive investigation is carried out using time-history analyses with artificial and recorded ground motions to simulate and examine the envelopes that bound vectors of seismic responses in a nonlinear structure. New and practical insight into the behavior of nonlinear structures and the effectiveness of current seismic design methodologies is gained by examining these response envelopes in the multidimensional response space. Particularly noteworthy are (1) the adverse effects of near-fault ground motions on the nonlinear response of the structure, (2) the effectiveness of plastic hinges as fuses to limit the forces transmitted to critical elements of the structure and (3) the use of simulated response envelopes to identify the spatial distribution of plastic hinges in the structure and the expected sway mechanism under severe seismic loading. |
