Seismic demand in columns of steel frames
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Axial force demand for column design of a seismic load resisting systems is obtained by considering load transferred from all the energy dissipating elements assuming that they have simultaneously reached their ultimate capacity. Time history analyses from the past studies have, however, indicated that simultaneous yielding of all the stories is possibly overly conservative in tall structures and may result in large uneconomical sections. Yet, no studies have proposed a method to quantify the number of simultaneously yielding stories in buildings, other than by empirical observation of results from multiple non-linear inelastic time history analyses. The research presented here was conducted in an attempt to provide one such quantification method. Using wave propagation theory, the objective was to develop a better understanding of the relationship between the input excitation and the response of the structure towards finding a systematic and efficient way of estimating the number of simultaneously yielding stories N SYS for shear-type tall steel frames. Investigation on response of a generic tall shear-type building subjected to pulse excitation of different shapes and duration revealed that story yield patterns depend on the pulse duration and amplitude of the base velocity excitation, as velocity can be directly correlated to the inter-story drift, which leads to story yielding. Mathematical expressions were derived to predict the beginning and end of the story yielding due to the incident wave in a shear-type building subjected to full-sine velocity pulse excitation. Using these two expressions, number of simultaneously yielding at any time as the incident wave propagates up the building could be conveniently obtained. The procedure of estimating N SYS value could be used for earthquake excitation by identifying the main pulse of the earthquake responsible for causing maximum number of stories to yield simultaneously and idealizing it with a full-sine velocity pulse. Simultaneous story yielding due to the constructive overlapping of the incident and the reflected waves was also considered. Application of this procedure considering eighteen different earthquakes ground motion histories showed that the estimation procedure yielded good results for earthquakes with a single (Category A) or more than one distinct pulses (Category B), while it overestimated the N SYS values for earthquakes that involved numerous high frequency pulses, often designated as non-pulse type earthquakes (Category C). Finally, the estimation procedure was applied to shear-type BRB frames subjected to the aforementioned earthquake records and the N SYS values obtained was used to estimate axial force demand in the columns. Estimation of axial force demand by considering the full capacity of the N SYS stories above the story whose axial force demand is being estimation in combination to the square root of sum of squares (SRSS) of the axial force transferred by the rest of the stories above, considering their full yield capacity, was proposed. The procedure of estimating the N SYS value and axial force demand was found to have good match with the actual values for Category A and B earthquakes while it did not work as well for the Category C earthquakes.