Volume 15, Issue 5 (2015)                   MCEJ 2015, 15(5): 213-222 | Back to browse issues page

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Akbari J. Determination of Seismic Response of Structures based on Spectral Analysis using Elliptic Envelope. MCEJ 2015; 15 (5) :213-222
URL: http://mcej.modares.ac.ir/article-16-8475-en.html
Deputy of Faculty of Engineering
Abstract:   (4221 Views)
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 case is the interaction of bending moments and axial load in columns. 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 Paper, the response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is implemented. 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 response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares. 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 case is the interaction of bending moments and axial load in columns. 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 Paper, the response-spectrum-based procedure for predicting the envelope that bounds two or more responses in a linear structure is implemented. 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 response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares. 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 response envelope can be superimposed on the capacity curve to determine the adequacy of a given design. In the commercial softwares such as SAP and ETABS seismic designs of structures are based on rectangular spectrums that they are usually over estimated ones. Therefore, implementation of such accurate envelope instead of rectangular one is felt in design softwares.
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Article Type: Original Manuscript | Subject: ---------
Received: 2014/02/22 | Accepted: 2015/07/22 | Published: 2015/08/23

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