A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra

This paper proposes a novel computationally economical stochastic dynamics framework to estimate the peak inelastic response of yielding structures modelled as nonlinear multi degreeof-freedom (DOF) systems subject to a given linear response spectrum defined for different damping ratios. This is accomplished without undertaking nonlinear response history analyses (RHA) or, to this effect, constructing an ensemble of spectrally matched seismic accelerograms. The proposed approach relies on statistical linearization and enforces pertinent statistical conditions to decompose the inelastic d-DOF system into d linear single DOF oscillators with effective linear properties (ELPs): natural frequency and damping ratio. Each such oscillator is subject to a different stationary random process compatible with the excitation response spectrum with damping ratio equal to the oscillator effective critical damping ratio. This equality is achieved through a small number of iterations to a pre-specified tolerance, while peak inelastic response estimates for all DOFs of interest are obtained by utilization of the excitation response spectrum in conjunction with the ELPs. The applicability of the proposed framework is numerically illustrated using a 3-storey Bouc-Wen hysteretic frame structure exposed to the Eurocode 8 elastic response spectrum. Nonlinear RHA involving a large ensemble of non-stationary Eurocode 8 spectrum compatible accelerograms is conducted to assess the accuracy of the proposed approach in a Monte Carlo-based context. It is found that the novel feature of iterative matching between the excitation response spectrum damping ratio and the ELP damping ratio reduces drastically the error of the estimates (i.e., by an order of magnitude) obtained by non-iterative application of the framework

A Seismic Performance Classification Framework to Provide Increased Seismic Resilience

Several performance measures are being used in modern seismic engineering applications, suggesting that seismic performance could be classified a number of ways. This paper reviews a range of performance measures currently being adopted and then proposes a new seismic performance classification framework based on expected annual losses (EAL). The motivation for an EAL-based performance framework stems from the observation that, in addition to limiting lives lost during earthquakes, changes are needed to improve the resilience of our societies, and it is proposed that increased resilience in developed countries could be achieved by limiting monetary losses. In order to set suitable preliminary values of EAL for performance classification, values of EAL reported in the literature are reviewed. Uncertainties in current EAL estimates are discussed and then an EAL-based seismic performance classification framework is proposed. The proposal is made that the EAL should be computed on a storey-by-storey basis in recognition that EAL for different storeys of a building could vary significantly and also recognizing that a single building may have multiple owners

A critical examination of near-field accelerograms from the sea of Marmara region earthquakes

In 1999, Turkey was struck by two major earthquakes that occurred 86 days apart on the North Anatolian Fault system. Both earthquakes had right-lateral strike-slip mechanisms with moment magnitudes greater than 7. The number of strong-motion records obtained from the Kocaeli earthquake (17 August 1999, M-w 7.4) was 34. The second event, designated as the Bolu-Duzce earthquake (12 November 1999, M-w 7.2), triggered 20 instruments. Among the records that we have from these earthquakes, seven are from near-source ground-motion data. These records were obtained from the cities of Gebze (GBZ), Yarimca (YPT), Izmit (IZT) (capital city of the province of Kocaeli), Adapazari (SKR) (capital of the province of Sakarya), Duzce (DZC) (shaken strongly in both the events), and Bolu (BOL). In many of these urban centers, extensive structural damage was observed. Although these near-field data have greatly expanded the strike-slip near-source ground-motion database worldwide for M-w > 7 earthquakes, they represent a blurred image of the actual severity of the ground motions in the epicentral area because of the sparseness of the national strong-motion network and the unrepresentative geologic conditions at the recording sites. We examine the records to determine whether they provide clues about the extensive damage on the housing stock in the epicentral region. The goal is tackled with earthquake structural engineering criteria in mind, using the drift spectrum as the primary yardstick. There appears to be conflicting evidence that the fault-normal (FN) direction should represent a greater damage-causing potential when this potential is based on ground-story drift spectra. The component with larger ground velocity does correlate better with the component with larger drift demand, but this does not always coincide with the FN direction. The period of the peak velocity pulse matches the structural period where the drift demand is the largest. Further refinements of code requirements that consider this effect are in order

An exact finite element for a beam on a two-parameter elastic foundation: a revisit

An analytical solution for the shape functions of a beam segment supported on a generalized two-parameter elastic foundation is derived. The solution is general, and is not restricted to a particular range of magnitudes of the foundation parameters. The exact shape functions can be utilized to derive exact analytic expressions for the coefficients of the element stiffness matrix, work equivalent nodal forces for arbitrary transverse loads and coefficients of the consistent mass and geometrical stiffness matrices. As illustration, each distinct coefficient of the element stiffness matrix is compared with its conventional counterpart for a beam segment supported by no foundation at all for the entire range of foundation parameters

Procedure for determining seismic vulnerability of building structures

A rationalization for ranking reinforced concrete frame buildings with masonry infill walls with regard to seismic vulnerability is presented The method essentially requires only the dimensions of the structure as input, and is expressed in terms of where its attributes are located in a two-dimensional plot of masonry wall and column percentages. It is shown that increasing drift at the ground story (which is a reasonable expression of increasing vulnerability) is attained by decreasing either attribute It is shown that a more robust estimate of the contribution of the filler wall to frame stiffness should be based on the compression-tension strength of its mortar rather than the elastic modulus, either of the masonry or of the mortar