Flexural Members and Beam-Column Joints
The purpose of structural analysis is to predict or explain in a rational way the response of structures to specified loads. The task of analyzing reinforced concrete frames subjected to earthquake loads is among the most difficult ones known, because the
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C. Meyer Columbia University, New York, NY, USA F.C. Filippou University of California Berkeley, Berkeley, CA, USA P. Gergelyt Cornell University, Ithaca, NY, USA
2.1 Introduction 2.1.1 General Comments on Structural Analysis The purpose of structural analysis is to predict or explain in a rational way the response of structures to specified loads. The task of analyzing reinforced concrete frames subjected to earthquake loads is among the most difficult ones known, because the loading is highly random and the load-deformation relationships for the structure and its individual components very nonlinear, with marked stiffness and strength degradation. As a result, the choice of an appropriate analysis method is not an easy one, but it has far-reaching consequences. When analyzing static linear elastic response of structures, approximate methods are quite acceptable, because inelastic moment redistribution can "correct" for the errors inherent in the underlying assumptions. Whenever reference is made to an exact analysis, the use of quotation marks is in order as a reminder that our mathematical tools and analysis methods have their limits. This applies particularly to concrete structures. As long as a structure possesses sufficient ductility, discrepancies between analysis results and actual behavior are relatively unimportant. In the case of dynamic loading, the differences between analytical and actual response can become unacceptable. The analysis results may be at times barely
C. Meyer (ed.), Modelling and Analysis of Reinforced Concrete Structures for Dynamic Loading © Springer-Verlag Wien 1998
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C. Meyer, F.C. Filippou and P. Gergely
better than guesswork, especially if a static analysis for so-called "equivalent" lateral loads is involved. Yet the use of such static analysis results for design purposes is rather standard practice and typically justified because of the unpredictable nature of the loading, which does not seem to warrant a more exact analysis. The logical way for dealing with the uncertainty of the loading is to treat it as a random process and to use random vibration analysis techniques to predict structural response in a statistical sense (see Appendix). If numerical simulation is used, such as a Monte Carlo technique, then each artificially generated earthquake ground motion history will permit the determination of the corresponding response. The differences between the results for different sample runs may then be taken as a measure of accuracy that would be acceptable for the selected analysis method. For example, if the standard deviation for maximum interstory drifts is 10%, calculations to five significant figures are obviously not warranted. When nonlinear dynamic response is involved, the picture changes again. Linear static analysis results may bear no resemblance with reality anymore. Not even the randomness of the loading can any longer be used to justify grossly simplified analyses, because these are likely to provide the designer with no or completely unreliable information
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