Seismic Force Reduction Factor Spectra Of Shear Type MDOF Systems And P-? Effect Analysis

Due to the complexity of nonlinear dynamic analysis,the seismic force reduction factor(SFRF)is commonly used to reduce elastic seismic force to get the strength demand.Based on elastic-plastic time-history earthquake analysis of MDOF system,total 102 earthquake records belonging to site soil type C are used to calculate the structural response of the shear-beam model and frame model with the strong-column/weak-beam demand.Two characteristic periods are adopted to maintain the peak features.The effect of stiffness ratio,strength ratio and failure modes are investigated.Seismic influence of P-? effect based on the vertical load is also studied with static and dynamic inelastic analysis.Based on the analysis and comparison of different ductility approaches,and a new aseismic design method of MDOF system high-rise structure is proposed.Main contents of the dissertation are summarized as follows:(1)Seismic force reduction factor spectra of shear-type Multi-Degree-of-Freedom(MDOF)structures are investigated.The modified Clough model,capable of considering the strength-degradation/hardening and stiffness-degradation,is adopted.Based on a large number of results,it is found that the peak value of SFRF spectra may also exist for MDOF,induced by large high-mode contribution to elastic base shear,besides the mentioned two peak values.The influnce of the stiffness ratio and the strength ratio is both considered.It is found that the SFRFs with larger strength ratio are larger.For frames satisfying strong column/weak beam requirement,an approximate treatment in the MDOF shear-beam model is to enlarge the post-limit stiffness.SFRF spectra for MDOF systems with larger post-limit stiffness are remarkably larger than those without post-limit stiffness,but the influence of post-limit stiffness is limited.A modification factor for MDOF systems is proposed.Simple solutions of SFRF and modification factor are presented.(2)The frame model s introduced to investigate the effect of stiffness ratio,strength ratio,post-limit stiffness,number of degree of freedom.Plastic hinges are allowed only at the beam ends and at the column bases to meet the strong-column/weak-beam demand.Results indicate that the SFRFs are greater with larger yield strength of the top story.Spectra with practical period range and code-specified period-dependent top-to-bottom stiffness ratio are constructed.The MDOF modification factor is introduced for the quantitative analysis of the influence of MDOF systems.It is most dependent on the story number,less affected by the ductility factor.Equations are proposed for the MDOF modification factor.(3)An amplification factor for static inelastic P-? effect is derived and the simple formulas are proposed.The influence ofP-? effect on the SFRFs for SDOF system is studied based on the frame model.Both the amplification factors and SFRFs are presented separately with two kinds of period abscissas.It is found that the SFRFs with P-? effect are obviously smaller than those without P-? effect,but post-yield stiffness cannot fully counteract the adverse impact of P-? effect.Formulas for seismic P-? amplification factors are proposed and compared with results of others.Collapse capacity spectra(CCS)are reviewed,their application in codes is discussed.Available CCSs are compared with SFRFs with finite ductility computed for two ensembles of seismic records.Comparison reveals that the SFRFs are affected by seismic records,and available CCSs do not always provide upper limits for the SFRFs when the P-? coefficients are greater than 0.1 for frame models.(4)Seismic influence of the number of degree of freedom,stiffness ratio,strength ratio,ductility and failure modes for MDOF system with P-? effect is studied.The amplification factor is also introduced as a parameter.Results indicate that for shear-beam model,with the increase of number of degree of freedom,the SFRFs decrease and the amplification factors have a little change.It illustrates that higher order modes are less sensitive to P-? effect.For the frame model,the amplification factors decrease because the strong column/weak beam design method greatly improves the SFRFs without P-? effect.Another reason could be the weak story,which is produced in the frame model with larger P-? effect.(5)The seismic force reduction factor spectra of MDOF system with different ductility approaches is investigated based on the analysis of the ductility distribution and development.Taking the 10-story structure as an example,the influence of different ductility on the SFRFs spectra of the high-rise structure is studied.Results indicate that the ductility development of structure is based on the bottom story,and the upper stories are restricted by the bottom story.To make the most of the seismic performance of MDOF system,the spectra with average ductility of upper stories are introduced,which are close to SDOF system.A new aseismic design method of MDOF system is proposed.The influence of different ductility approaches on the SFRFs spectra of MDOF system with P-? effect is investigated.