## Assessing seismic collapse safety of modern reinforced concrete moment frame buildings

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##### Abstract

A primary goal of seismic design requirements of building codes is to protect the life safety of building inhabitants during extreme earthquakes. First and foremost, this requires that the likelihood of structural collapse be at an acceptably low level. However, building codes and standards are empirical in nature, which results in the collapse safety of new buildings not being well understood. In this research, we develop the tools and methods to quantitatively assess the collapse risk of reinforced concrete (RC) special moment frame (SMF) buildings designed by the 2003 International Building Code. While RC SMF buildings are the focus on this study, the methodology and many of the tools can be used to assess any type of structural system. This rigorous analytical collapse assessment requires careful consideration of many issues from ground motions to structural modeling to quantification of uncertainty. To facilitate accurate structural modeling, we calibrate a RC element model to 255 tests of RC columns; this model is capable of capturing the important modes of deterioration that lead to global sidesway collapse. Using these calibration data, we develop a full set of empirical equations that can be used to predict the parameters (mean and uncertainty) of a lumped plasticity element model. These parameters include: initial stiffness, post-yield hardening stiffness, plastic rotation capacity, post-capping rotation capacity, and cyclic energy dissipation capacity. The equations are applicable to any rectangular RC element that fails in flexural or flexure-shear. This portion of the study reveals that the median plastic rotation capacity of modern RC elements is larger than reflected in documented such as FEMA 356 (FEMA 2000a). For a RC column with ductile detailing and low axial load, the median plastic rotation capacity is typically 0.05-0.08 radians. The uncertainty (logarithmic standard deviation) is 0.45 or 0.54, for estimation of the total or plastic rotation capacities, respectively. To ensure that we properly treat ground motions, we look closely at the proper spectral shape (s) of ground motions and investigate two methods to account for this. We verified previous findings regarding the critical importance of accounting for a in ground motion selection; neglecting this typically leads to an underestimation of the median collapse capacity by a factor of 1.5 and overestimation of the mean annual frequency of collapse by more than a factor of 20. Accounting fors typically requires selection of a site-specific and building-specific set of ground motions. To make it easier to account for s, we develop a simplified method that involves (a) evaluating collapse based on a general far-field ground motion set that is selected without regard to s, then (b) adjusting both the mean and uncertainty of the collapse capacity distribution to account for the proper s value at the site and hazard level of interest. This study also considers how structural design and modeling uncertainties affect the uncertainty in collapse capacity. This study shows that structural modeling uncertainty is a critical aspect of the collapse assessment and can increase the mean annual rate of collapse estimate by nearly a factor of 10. For a 4-story RC SMF building, we find that the best estimate for collapse capacity uncertainty, not including record-to-record variability, is 6LN(sa,col) = 0.45. We find that correlation assumptions are critical when estimating this value and the most dominant modeling uncertainty is associated with the element plastic rotation capacity. We use the above tools and methods to assess the collapse risk of 30 RC SMF buildings designed according to the ASCE7-02 design provisions. These 30 building designs are chosen systematically, in order to obtain a generalized collapse prediction that is representative of RC SMF buildings designed by current building codes in the western United States. For these modem RC SMF buildings, the collapse probability conditioned on a 2% in 50 year ground motion ranges from 0.03 to 0.20, with an average of 0.11. The mean annual frequency of collapse ranges from Q.7x10'4 to 7.0x10'4, with an average of 3.1x10'4; this corresponds to an average collapse return period of 3,200 years, with a range of 1,400 to 14,000 years. We then used the same collapse assessment tools to investigate how collapse safety is changed by the removal of the minimum design base shear requirement in the updated ASCE7-05 provisions. The results of this investigation suggest that the minimum base shear requirement (ASCE 7-02 equation 9.5.5.2.1-3) was an important component of ensuring relatively consistent collapse risk for buildings of varying height. Removing this requirement has made taller buildings significantly more vulnerable to collapse; this should be considered in future revisions of ASCE7. With these new tools and methods for collapse performance assessment, we are also able to quantitatively predict how design changes will affect the collapse performance. Specifically, we investigate changes to the design base shear strength (R-factor), strong-column weak-beam (SCWB) ratio, and drift limits. As expected, the R-factor and SCWB ratio have important influences on collapse safety. For all the buildings considered in this study, a 2x increase in design base shear strength increases the median collapse capacity by a factor of 1.2 to 2.4, decreases the mean annual frequency of collapse by a factor of 1.5 to 13, and decreases the collapse probability by 5 to 41%. Similarly, a 3x increase in the SCWB ratio increases the median collapse capacity by a factor of 1.6 to 2.1, decreases the mean annual frequency of collapse by a factor of 5 to 14, and decreases the collapse probability by 27 to 30%. In addition, we find that decreased strength also leads to decreased drift capacity, due to damage concentrating in fewer stories of the building. The benefit of increasing the SCWB ratio saturates at a ratio of about 1.5 for a four-story building; this occurs when the building collapses in a complete mechanism and additional column strength is not able to improve the mechanism any further. For a 12-story building, this saturation does not occur because the building collapses in a partial mechanism, even up to a SCWB ratio of 3.0. Lastly, this study finds that that aspects of the structural design (height, framing layout, etc.) have less impact on the final performance prediction than the aspects of the collapse assessment methodology (structural modeling uncertainties, and spectral shape). This emphasizes the importance of developing a systematic codified assessment method that can be used to demonstrate the performance of a structural system. Without a codified assessment method, a collapse performance prediction will depend almost entirely on how the analyst carried out the performance assessment.