Spectra of seismic force reduction factors of MDOF systems normalized by two characteristic periods

Seismic force reduction factor(SFRF) spectra of shear-type multi-degree-of-freedom(MDOF) structures are investigated. The modified Clough model, capable of considering the strength-degradation/hardening and stiffnessdegradation, is adopted. The SFRF mean spectra using 102 earthquake records on a typical site soil type(type C) are constructed with the period abscissa being divided into three period ranges to maintain the peak features at the two sitespecific characteristic periods. 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 contributions to elastic base shear, besides the mentioned two peak values. The variations of the stiffness ratio λk and the strength ratio λF of the top to bottom story are both considered. It is found that the SFRFs for λF ≤λk are smaller than those for λF > λk. A SFRF modification factor for MDOF systems is proposed with respect to SDOF. It is found that this factor is significantly affected by the story number and ductility. With a specific λF(= λk0.75), SFRF mean spectra are constructed and simple solutions are presented for MDOF systems. For frames satisfying the strong column/weak beam requirement, an approximate treatment in the MDOF shear-beam model is to assign a post-limit stiffness 15%-35% of the initial stiffness to the hysteretic curve. SFRF spectra for MDOF systems with 0.2 and 0.3 times the post-limit stiffness are remarkably larger than those without post-limit stiffness. Thus, the findings that frames with beam hinges have smaller ductility demand are explained through the large post-limit stiffness.

Development of seismic force requirements for buildings in Taiwan

This paper describes static and dynamic procedures to calculate seismic demand specified by the current seismic design code for buildings in Taiwan, which was issued in 2005. For design levels with a return period of 475 years, the design spectral response acceleration can be developed for general sites, near-fault sites and Taipei Basin. In addition, in order to prevent building collapse during extremely large earthquakes and yielding of structural components and elements during frequent small earthquakes, the required seismic demands at the maximum considered earthquake level （MCE, 2%/50 years） and operational level are also included in the new seismic design code.For dynamic analysis procedures, both the response spectrum method and time history method are specified in the new seismic design code. Finally, procedures to generate spectrum compatible ground motions for time history analysis are illustrated in this paper.

Study on the Distribution Law of Horizontal Seismic Forces between Slab-Column and Shear Wall

In slab column-shear wall structures,both the whole structure′s seismic behavior and failure mode are greatly influenced by the distribution of horizontal seismic forces between slab-column and shear wall.In this paper,a pushover analysis of topical slab column-shear wall structure was carried out,the seismic shear force that the slab-column and shear wall should undertake was worked out,the influences of plastic internal force redistribution and structure stiffness characteristic value on horizontal seismic distribution were studied and the calculation formula was given.The analysis results showed that with the yield of the shear walls,the story shear force was undertaken by slab-columns correspondingly increased while with the decrease of characteristic value of stiffness of a structure,and the horizontal seismic force was undertaken by slab-columns correspondingly decreased.According to the code,the design of horizontal force distribution may be cause insecurity problems,so it is necessary to give the distribution law of horizontal seismic forces in slab-column shear wall structures as the supplement to the corresponding regulation of the Code.

Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

Static and dynamic inelastic P-Δ effect for seismic design

Seismic influence of P-Δ effect is the subject of this study.First,it is pointed out that the elastic static amplification factor shall be isolated in formulating the dynamic inelastic second order effect.An amplification factor for the static inelastic P-Δ effect is derived.Seismic force reduction factors(SFRF)for given ductility and stability coefficients are computed for one-story,one-span frames.The P-Δ amplification factors for seismic base shears are obtained by dividing SFRFs with and without P-Δ effect.Both P-Δ amplification factors and SFRFs are presented separately with two kinds of period abscissas.The P-Δ amplification factors are dependent on periods with the maximum occurring at about 0.75 s for site type C and approach to the static inelastic counterpart at long periods.Post-yield stiffness cannot fully counteract the adverse impact of the P-Δ effect.Formulas for seismic P-Δ amplification factors are proposed and compared to results of others.Collapse capacity spectra(CCS)are reviewed and their application in codes discussed.Available CCSs are compared with SFRFs with finite ductility computed for two ensembles of seismic records.A comparison reveals that the SFRFs are affected by seismic records,and available CCSs do not always provide upper limits for the SFRFs when stability coefficients are greater than 0.1 for frame models.

A comparison of IBC with 1997 UBC for modal response spectrum analysis in standard-occupancy buildings

This paper presents a comparison of the seismic forces generated from a Modal Response Spectrum Analysis （MRSA） by applying the provisions of two building codes, the 1997 Uniform Building Code （UBC） and the 2000-2009 International Building Code （IBC）, to the most common ordinary residential buildings of standard occupancy. Considering IBC as the state of the art benchmark code, the primary concern is the safety of buildings designed using the UBC as compared to those designed using the IBC. A sample of four buildings with different layouts and heights was used for this comparison. Each of these buildings was assumed to be located at four different geographical sample locations arbitrarily selected to represent various earthquake zones on a seismic map of the USA, and was subjected to code-compliant response spectrum analyses for all sample locations and for five different soil types at each location. Response spectrum analysis was performed using the ETABS software package. For all the cases investigated, the UBC was found to be significantly more conservative than the IBC. The UBC design response spectra have higher spectral accelerations, and as a result, the response spectrum analysis provided a much higher base shear and moment in the structural members as compared to the IBC. The conclusion is that ordinary office and residential buildings designed using UBC 1997 are considered to be overdesigned, and therefore they are quite safe even according to the IBC provisions.

Seismic safety evaluation methodology for masonry building and retrofitting using splint and bandage technique with wire mesh

The paper presents a seismic safety assessment of unreinforced masonry(URM)building using two approaches.The first approach uses the‘Pier Analysis’method,based on the concept of equivalent lateral stiffness,where in-plane and out-of-plane actions are considered independently.The second approach is developed with the program SAP2000,where the linear response is evaluated using continuum‘finite element modelling’(FEM).Both methods are compared to evaluate the safety of wall piers and the differences in the outcomes under combined gravitational and lateral seismic forces.The analysis results showed that few wall elements are unsafe in in-plane and out-of-plane tension.It is also observed that the pier analysis method is conservative compared to FEM,but can be used as a simplified and quick tool in design offices for safety assessment,with reasonable accuracy.To safeguard the URM wall piers under lateral loads,a retrofitting technique is adopted by providing vertical and horizontal belts called splints and bandages,respectively,using welded wire mesh(WWM)reinforcement.The study using the‘Pier Analysis’shows that the lateral load capacity of unsafe URM piers can be enhanced up to 3.67 times and made safe using the applied retrofitting technique.Further,the retrofitting design methodology and recommendations for application procedures to on-site URM buildings are discussed in detail.