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Determination of the Equivalent Linear Systems of Nonlinear MDOF Steel Moment Resisting Frames

Shirzadi, Tiam | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47213 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineernig
  6. Advisor(s): Rahimzadeh Rofooei, Fayyaz
  7. Abstract:
  8. The purposeof this study isto findthe propertiesof an equivalent linear Multiple Degrees of Freedom (MDOF) system, or so-called substitute structure, that its response is an approximation ofthe target actualnonlinearMDOF structure’s response (Shodja, 2013). In that regard,thestiffness anddampingmatricesofthe substitutestructure are considered as functions ofthe stiffnessand dampingmatrices ofthe actualnonlinear structure. Inthisway,the substitute structurescan be constructedthroughtrial and errorfor structures with different fundamentalperiods, damping ratios and number of floors.Inthat regard, a number of multi-story steel moment resisting frames are considered. The ductilities of these structural models were calculated using the nonlinear static analyses provisions provided by ASCE 41-13(Chopra A. Goel R., 2001, Miranda E., 1991)).Then, using theFEMA 440criteria,the effective periodof those models weredeterminedbased on theirductilities. Using a trial and error approach, thestiffness ofthe considered structural models are adjusted such thatthe firstmodeperiod(T0) ofthe linearsubstitute structures be equal to theeffective period that wasobtained using the FEMA 440 provisions. Finally, the damping ratios werecomputed by equalizing themaximumroofdisplacementresponse ofthe linearandnon-linearstructural models.Linearand non-lineartime historyanalyseswere performed using the SAC structural models toverify the applicability of the suggested substitute structure in capturing the seismic demands of the real nonlinear steel MRF structural systems (FEMA 368, 2000).Five models with different number of story and length of bays were designed according to AISC2010.Then by using the pushover method and finding the equivalent SDOF behavior and ductility factor, the effective period of structures were found according the FEMA440 relations.Inthisway, for reducing the stiffness of structures, the modulo of elasticity was reduced throughtrial and error so that the period of equivalent structures be equal to effective period. Finally, for finding the effective damping ratio of structures, the maximum displacement of roof was considered equal in two equivalent linear and real nonlinear structures according to the time history analyze
  9. Keywords:
  10. Nonlinear Behavior ; Linear Behavior ; Substitute Structure ; Equivalent Damping ; Steel Moment Resistant Frame ; Multi-Degree of Freedom Structures ; Equivalent Stiffness Matrix

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