Earthquake Spectra

The modal pushover analysis (MPA) procedure is extended for analysis of reinforced concrete special moment resisting frame (RC-SMRF) buildings, after demonstrating that the theory, assumptions, and approximations underlying this procedure are valid for such systems. The principal extension of the procedure is in the hysteretic model for modal SDF systems, chosen as the peak-oriented model to represent the global monotonic and cyclic behavior of such buildings, characterized by deterioration of stiffness and strength under cyclic deformation. The median seismic demands for 4-, 8-, 12-, and 20-story RC-SMRF buildings—designed to comply with current codes—due to an ensemble of 78 ground motions scaled to four intensity levels were computed by MPA and nonlinear RHA, and compared. It is demonstrated that, even for the most intense ground motions that deform the buildings far into the inelastic range, the MPA procedure demonstrates an adequate degree of accuracy that should make it useful for practical application in estimating seismic demands for RC-SMRF buildings. In contrast the FEMA-356 force distributions are inadequate in estimating seismic demands for the 8-, 12-, and 20-story buildings at all excitation intensities, from the weakest that causes response essentially within the linearly elastic range, to the strongest that drives the buildings far into the inelastic range.

This study evaluates the susceptibility of masonry arches to earthquake loading through experimental testing and progresses toward a specific criterion by which arches can be quickly assessed. Five different earthquake time histories, as well as harmonic base excitations of increasing amplitude, were applied to model arches, and the magnitude of the base motion resulting in collapse was determined repeatedly. Results are compared with failure predictions of an analytical model which describes the rocking motion of masonry arches under base excitation. The primary impulse of the base excitation is found to be of critical importance in causing collapse of the masonry arch. Accordingly, a suite of failure curves are presented which can be used to determine the rocking stability of masonry arches under a primary base acceleration impulse which has been extracted from an expected earthquake motion.

Fundamental dynamic periods of Quaternary deposits beneath the peninsula of Charleston, South Carolina, are characterized spatially using an updated isopach map of Quaternary thickness, characteristic small-strain shear wave velocity information, a 1:24,000 geologic map, and a simple approximating equation. The updated isopach map is developed from subsurface information from 266 investigation sites. Estimates of fundamental periods for the Quaternary sediments primarily range between 0.3 and 0.7 s. These periods are lower end estimates of actual ground periods, based on a comparison with modeled response-spectra ratios. Estimates of fundamental periods range from 0.1 to 0.4 s for over 95% of the buildings present in 1886. Thus, the overlap between the range of building periods and the range in periods corresponding to high spectral ratios is not great. This finding agrees with the observation of Marciano and Elton that damage was independent (or only slightly dependent) of building height.

A simulation-based framework for assessing seismic risk of spatially distributed buildings is developed by taking the spatial correlation of seismic excitations into account. For each of seismic events compiled in a synthetic earthquake catalog, inelastic seismic demand on buildings that are approximated by bilinear single-degree-of-freedom systems is compared with uncertain structural capacity to evaluate seismic damage severity. The proposed framework is employed to investigate the sensitivity of the estimated seismic risk of sets of buildings to the degree of spatially correlated and simultaneously occurring seismic excitations. In particular, four correlation levels—no correlation, full correlation, and partial correlation with/without intra-event components—are considered. The assignment of the partial correlation is based on a recently developed spatial correlation model, and the sets of hypothetical buildings mimic existing building stocks in downtown Vancouver. The analysis results highlight that underestimation or overestimation of correlation of seismic demand could lead to very different probabilistic characteristics of aggregate seismic loss although its mean is unaltered. The sensitivity analysis results suggest that uncertainty in structural capacities as well as average local soil conditions is of relative importance.

Suites of earthquake ground motions play an important role in the seismic design and analysis process. A semi-automated procedure is described that selects and scales ground motions to fit a target acceleration response spectrum, while at the same time the procedure controls the variability within the ground motion suite. The basic methodology selects motions based on matching the target spectral shape, and then fits the amplitude and standard deviation of the target by adjusting the individual scale factors for the motions. The selection of motions from a larger catalog of motions is performed through either a rigorous method that tries each possible suite of motions or an iterative approach that considers a smaller set of potential suites in an effort to find suites that provide an acceptable fit to the target spectrum. Guidelines are provided regarding the application of the developed procedures, and example applications are described.

Models for estimating the effects of fire following earthquake (FFE) are reviewed, including comparisons of available ignition and spread/suppression models. While researchers have been modeling FFEs for more than 50 years, there has been a notable burst of research since 2000. In particular, borrowing from other fire modeling fields and taking advantage of improved computational power and data, there is a new trend towards physics-based rather than strictly empirical spread models; and towards employing different simulation techniques, such as cellular automata, rather than assuming fires spread in an elliptical shape. Past achievements include identification of the factors affecting FFE, documentation of historical events, and years of FFE model use by practitioners. Opportunities for future advances include continued development of physics-based spread models; better treatment of slope, water and transportation system functionality, and suppression by fire departments; and more validation and sensitivity analyses.

The nees@UCLA mobile field laboratory was utilized to collect forced and ambient vibration data from a four-story reinforced concrete (RC) building damaged in the 1994 Northridge earthquake. Both low amplitude broadband and moderate amplitude harmonic excitation were applied using a linear shaker and two eccentric mass shakers, respectively. Floor accelerations, interstory displacements, and column and slab curvature distributions were monitored during the tests using accelerometers, linear variable differential transformers (LVDTs) and concrete strain gauges. The use of dense instrumentation enabled verification of common modeling assumptions related to rigid diaphragms and soil-structure-interaction. The first six or seven natural frequencies, mode shapes, and damping ratios were identified. Significant decreases in frequency corresponded to increases in shaking amplitude, most notably in the N-S direction of the building, most likely due to preexisting diagonal joint cracks that formed during the Northridge earthquake.

Logic trees have become a standard feature of probabilistic seismic hazard analyses (PSHA) for determining design ground motions. A logic tree's purpose is to capture and quantify the epistemic uncertainty associated with the inputs to PSHA and thus enable estimation of the resulting uncertainty in the hazard. There are many potential pitfalls in setting up a logic tree for PSHA, mainly related to the fact that in practice, it is questionable that the requirements that the logic-tree branches be both mutually exclusive and collectively exhaustive can actually be met. Careful consideration is also required for making use of the output; in particular, in view of how PSHA is employed in current engineering design practice, it may be more rational to determine the mean ground motion at the selected design return period rather than to find the ground motion at the mean value of this return period.

There are currently no applicable hysteresis rules or nonlinear elements available in structural analysis software that can be used to exactly model triple Friction Pendulum bearings for response-history analysis. Series models composed of existing nonlinear elements are proposed since they can be immediately implemented in currently available analysis software. However, the behavior of the triple Friction Pendulum bearing is not exactly that of a series arrangement of single concave Friction Pendulum bearings—though it is similar. This paper describes how to modify the input parameters of the series model in order to precisely retrace the true force-displacement behavior exhibited by this device. Recommendations are made for modeling in SAP2000 and are illustrated through analysis of a simple seismically isolated structure. The results are confirmed by (a) verifying the force-displacement behavior through comparison with experimental data and (b) verifying the analysis through comparison to the results obtained by direct numerical integration of the equations of motion.