Effects of P-Delta and Concrete Cracking on Modal Analysis for the Seismic Response of High Rise Reinforced Concrete Buildings

This paper aims to study the effect of concrete cracking and the second-order geometric effect of P-Delta on the modal analysis for the seismic response of high rise reinforced concrete buildings. High rise reinforced concrete building models with different heights up to 50 stories are employed. To achieve this goal, the finite element code ETABS is used to analyze the structural dynamic behavior of the reinforced concrete building models when P-Delta and concrete cracking is accounted for. Different aspects of modes of vibration from modal analysis are examined including time-properties, participating factors and participation mass ratios. The study shows that time periods of vibration elongated when concrete cracking and second order effects of P-Delta are accounted for in the analyses. Generally, results show that modal analysis are significantly affected by concrete cracking and to a lesser extent by P-Delta analyses. P-Delta effects on periods and frequencies of modes of vibration are related to building height, unlike concrete cracking effect, and for buildings with less than 20 story height P-Delta effect can be neglected. Furthermore, results of the study indicate that buildings with cracked concrete sections require additional number of modes than buildings with uncracked section properties to achieve modal participation mass ratio not less than 90 %, and thus sufficient number of vibration modes are included in the analyses, whereas P-Delta analysis has negligible effect on the minimum number of modes required. The paper recommends that the P-Delta and concrete cracking effects be evaluated for tall-building systems as part of an overall assessment of their free vibration response.