Application of MPA to estimate probability of collapse of structures

Abstract

This paper develops a modal pushover analysis-(MPA) based approximate procedure to quantify the collapse potential of structural systems. The computationally demanding incremental dynamic analysis (IDA) of the structural system is avoided by MPA of the structure in conjunction with empirical equations for the collapse strength ratio for the first-mode single-degree-of-freedom (SDF) system; higher modes of vibration play essentially no role in estimating the ground motion intensity required to cause collapse of the structure. Presented are collapse fragility curves for 6-, 9-, and 20-story regular special momentresisting teel frames computed by the exact and approximate procedures, demonstrating that the MPA-based approximate procedure requires only a small fraction (1% in one example) of the computational effort inherent in exact IDA and still achieves highly accurate results.(IDA) [15], which requires nonlinear response history analysis (RHA) of the structure for an ensemble of ground motions, each scaled to many intensity levels, selected to cover a wide range of structural response-all the way from elastic behavior to global dynamic instability.Recognizing that IDA of practical structures is computationally extremely demanding, the developers of IDA have devised the approximate method SPO2IDA [16]. Restricted to first-mode dominated structures, this procedure defines the force-deformation curve in initial loading of the SDF system to match the static pushover (SPO) curve of the structure, and determines the peak deformation of the nonlinear SDF system by Excel-based software [17]. Because the SPO curve depends on the choice of the height-wise distribution of forces, SPO curves are determined for several force distributions and the 'worst' SPO is chosen, but the choice is not unique. This procedure also requires estimating the elastic stiffness of the SDF system from the IDA curve, a task that is complicated because several vibration modes contribute to the responses plotted in the IDA curve.Modal pushover analysis (MPA) [18], an approximate analysis procedure rooted in structural dynamics theory [19], avoids the preceding issues concerning SPO2IDA. The MPA has been utilized to estimate seismic demands instead of nonlinear RHA. Encouraged by the accuracy of MPA in estimating IDA curves [20], this paper explores the potential of MPA in investigating the collapse of buildings. Collapse here is synonymous with dynamic sideway instability in one or several stories of the structural system. COLLAPSE FRAGILITY CURVESThe ground motion intensity that causes collapse of a building can be determined by IDA. This procedure requires a series of nonlinear RHA of the structure for an ensemble of ground motions, and each record is scaled to several levels of intensity to encompass the full range of structural behavior: from elastic to yielding that continues to spread, finally leading to global dynamic instability. The results of these analyses for one ground motion lead to one IDA curve. This is a plot of the ground motion i...

Approximate MPA-based method for performing incremental dynamic analysis

“…Since modal combination is valid only for combining modal displacement demands not for modal force demands, total collapse strength (A c ) cannot be computed by modal combination of A c for each mode. However, Han et al [21] showed that collapse strength considering only the first mode is sufficiently accurate since the higher mode contribution becomes smaller as ground motion intensity increases. Moreover, Vamvatsikos and Cornell [7] reported that with accumulating damage in the structure, some of the dominant frequencies seem to be "silenced" and the structure becomes more first-mode dominated.…”

“…Han et al [6,21] reported that the MPA based IDA with the strength-limited bilinear model provided accurate prediction of seismic demands and capacities for regular steel moment resisting frames. The effect of structural and hysteretic properties on C R is to be investigated through comprehensive statistical study.…”

“…This study adopts empirical equation of R c for strength limited bilinear SDF systems proposed Han et al [21]. Using the R c equation, A c is readily computed by multiplying R c by A y obtained from modal pushover analysis [ Fig.…”

Near‐optimal piecewise linear fits of static pushover capacity curves for equivalent SDOF analysis

“…These include typical code-suggested fits, e.g., as laid out in Eurocode 8 [11], FEMA-356 [12], ASCE/SEI 41-06 [13], and the Italian Code (Circolare 617/2009, [18]). In addition several bilinear, trilinear and quadrilinear fits, including solutions available in literature [15,16,20], have been investigated. Different fitting criteria, e.g., varying initial stiffness, yield point definition, and softening slope, have been employed in an attempt to pinpoint the consistent characteristics that can define an optimal or near-optimal fit.…”

“…using a 10% rule with areaminimization for the hardening segment that terminates at the peak strength. To determine the softening segment, which extends from the peak point to the ultimate, three different approaches are considered: (a) the first, termed secant, employs the slope linking the peak point with the ultimate; (b) the second, termed Han et al, which follows the graphical approach suggested in [20], provides as softening slope the bisector between the peak-to-ultimate point slope and the slope at the end of the backbone; (c) the third, termed balanced, uses areaminimization to fit the descending segment, utilizing a negative slope and, at times, a horizontal residual strength segment. The latter is only added when it can help achieve a closer fit, typically being needed for steep-mild cases.…”