A Critical Review of European and American Provisions for the Seismic Assessment of Existing Steel Moment-Resisting Frame Buildings

The publication of Part 3 of Eurocode 8 (EC8-3), dedicated to the seismic assessment of existing buildings, took place a decade ago. However, its application in engineering practice has been limited. Moreover, no studies have been conducted regarding the application of EC8-3 to steel structures. In this paper, a critical review and practical application of EC8-3 and ASCE41-13 are carried out. Issues related to the definition of the performance requirements, compliance criteria, and the consistency of the analysis procedures proposed by both standards are identified. Conceptual differences between both documents are highlighted, and several inconsistencies in EC8-3 are discussed.     

Influence of Time Step of Ground Motions on Site Effect and Structural Response Analyses for Long-Duration Earthquakes

Long-duration ground motions may be down-sampled to speed up the computational process. However, using ground motions with large time step (Δt) would inevitably bring in numerical errors. The influence of Δt on the site effect and structural response analyses was quantitatively examined in this study. The results show that the nonlinear site response method is more sensitive to a change of Δt than the equivalent-linear method. For the structural analysis, the impact of Δt is highly dependent on the magnitude of damage parameters. Thus, using input motions with Δt as 0.005 s is recommended for structures subjected to strong shakings.     

Simplification and Assessment of Modal-Based Story Damage Index for Reinforced Concrete Frames Subjected to Seismic Excitations

Different relations have been represented for the local damage index of structures to date, while the same application is defined for them as can be an indicator of relative sustained damage by the components or stories. Since different force-resisting systems subjected to the ground motions can behave differently, some well-known story damage indices are evaluated for the reinforced concrete frames with regards to their operation during nonlinear time history analysis. Two general concepts of story damage determination are selected for this purpose. SDI is a modal-based story damage index, which is calculated by the modal frequency and mode shapes. The behavior of this local index is evaluated during the seismic excitations. The results were compared with Park-Ang and modal flexibility story damage indices. Based on analytical study on seismic responses of some RC frames subjected to a suit of earthquake records a new story damage index has been developed. It has been derived from a simple global damage equation (softening index) using a normalized ratio of inelastic story shear to its drift. A procedure is recommended to use the proposed equation without any requirement to perform nonlinear dynamic analysis, which can significantly reduce the computational efforts. Distribution of the new represented SDI along the structural height shows a good agreement with damaged state of the RC frames after seismic excitations.     

Fire and man in post-glacial woodlands of Eastern England

It has for long been suggested that English early post-glacial woodlands, particularly those dominated by hazel, were a fire-climax vegetation type. This conflicts with the evidence of fire frequency in present-day woodlands. Charcoal and pollen analyses of post-glacial lake sequences in East Anglia, England, suggest that early post-glacial woodlands were not fire-climax types. The pre-5000 BP charcoal record can be best interpreted as a record of intensity of occupation beside lake shores. After 5000 BP, charcoal deposition may reflect increasing use of fire as an agent in land clearance.     

Nonlinear Static Methods vs. Experimental Shaking Table Test Results

Three different Nonlinear Static Methods (NSM's), based on pushover analysis, are applied to a 3-story, 2-bay, RC frame. They are (i) the Capacity Spectrum Method (CSM), described in ATC-40, (ii) the Displacement Coefficient Method (DCM), presented in FEMA-273 and further developed in FEMA 356, and (iii) the N2 Method, implemented in the Eurocode 8. Pushover analyses are conducted with DRAIN-3DX by using four different lateral force distributions, according to the acceleration profile assumed along the height of the structure: uniform, triangular, modal-proportional, and multimodal fully adaptive. In the numerical model, RC members are modeled as fiber elements.

The numerical predictions of each method are compared to the experimental results of the shaking table tests carried out on two similar 1:3.3-scale structural models, with and without infilled masonry panels, respectively. The comparison is made in terms of maximum story displacements, interstory drifts, and shear forces. All the NSM's are found to predict with adequate accuracy the maximum seismic response of the structure, provided that the associated parameters are properly estimated. The lateral load pattern, instead, is found to little affect the accuracy of the results for the three-story model considered, even if collapse occurs with a soft story mechanism.     

Evaluation of Side Boundary Effects on Dynamic Numerical Modeling for Centrifugal Model Tests

Four different boundary conditions consisting of fixed nodes, motion of roller only in the z or the x direction, and equivalent motion of two side boundaries were applied with a finite element code to simulate seismic behavior of two foundation conditions consisting of dry loose and dense sands. Comparing numerical results with physical model tests indicates that data obtained from the finite element code when considering soil nonlinearity with a sand model based on the tij concept have acceptable agreements with those from dynamic centrifuge tests regardless of the boundary conditions. The results from the boundary conditions of roller in the x direction and equivalent motion of two side boundaries agree well with the experimental data in wave peaks. The two side boundary conditions also keep the ground middle undisturbed and provide the results that are similar to those obtained from the wave amplification experimental data. For numerical simulations of centrifuge model tests, the side boundary condition with roller in the x direction is recommended because of low computation time and high simulation quality.     

Optimum Design Approaches for Improving the Seismic Performance of 3D RC Buildings

In this article, a number of design approaches for 3D reinforced concrete (RC) buildings are formulated in the framework of structural optimization problems and are assessed in terms of their performance under earthquake loading. In particular, three design approaches for RC buildings are considered in this study. In the first, the initial construction cost is considered as the objective function to be minimized. The second one is formulated as a minimization problem of the torsional response, while a combined formulation is also examined as the third design approach. The third approach is considered with two distinctive formulations. According to the first approach, the torsional behavior is minimized by minimizing the eccentricity between the mass and rigidity centers, while the second one is achieved by minimizing the eccentricity between the mass and strength centers. It is shown that the optimized designs obtained according to the minimum eccentricity of the rigidity center behave better in frequent (50/50 hazard level) and occasional (10/50 hazard level) earthquakes, while the designs obtained according to the minimum eccentricity of the strength center formulation was found better in rare (2/50 hazard level) events. Designs obtained through a combined formulation seem to behave equally well in the three hazard levels examined.     

Probabilistic Calibration and Experimental Validation of the Seismic Design Criteria for One-Story Concrete Frames

This article investigates the seismic performance of one-story reinforced concrete structures for industrial buildings. To this aim, the seismic response of two structural prototypes, a cast-in-situ monolithic frame and a precast hinged frame, is compared for four different levels of translatory stiffness and seismic capacity. For these structures an incremental nonlinear dynamic analysis is performed within a Monte Carlo probabilistic simulation. The results obtained from the probabilistic analysis prove that precast structures have the same seismic capacity of the corresponding cast-in-situ structures and confirm the overall goodness of the design criteria proposed by Eurocode 8, even if a noteworthy dependency of the actual structural behavior from the prescribed response spectrum is pointed out.

The experimental verification of these theoretical results is searched for by means of pseudodynamic tests on full-scale structures. The results of these tests confirm the overall equivalence of the seismic behavior of precast and cast-in-situ structures. Moreover, two additional prototypes have been designed to investigate the seismic behavior of precast structures with roof elements placed side by side. The results of these further tests show that an effective horizontal diaphragm action can be activated even if the roof elements are not connected among them, and confirm the expected good seismic performance of these precast systems. Finally, the results of the experimental tests are compared with those obtained from nonlinear structural analyses. The good agreement between numerical and experimental results confirms the accuracy of the theoretical model and, with it, the results of the probabilistic investigation.     

Simple Models for Inelastic Seismic Analysis of Asymmetric Multistory RC Buildings

A simple stick model is presented for the inelastic seismic analysis in 3D of two-way eccentric multistory RC buildings. It has 3 DoFs per floor, point hinges at the ends of the vertical elements connecting floors, elastic story stiffness derived from the corresponding story force-interstory deformation relations of the elastic 3D structure under inverted-triangular floor loading (by torques for torsional stiffness, by horizontal forces for the lateral ones), story yield forces derived from the total resistant shear of the story vertical elements, but no coupling between lateral and torsional inelasticity. It is evaluated on the basis of comparisons of response histories of floor displacements to those from full nonlinear models in 3D of four actual buildings. Alternative locations of the story vertical element with respect to the floor mass center are examined: (a) the floor “center of twist” of the elastic 3D building under inverted-triangular floor torques; (b) the story “effective center of rigidity,” through which application of inverted triangular lateral forces does not induce twisting of floors; (c) the centroid of the secant stiffness of the story vertical members at yielding and (d) the centroid of the lateral force resistance of story vertical elements. Among alternatives (a)–(d), the floor “center of twist” provides the best agreement with floor displacement response-histories from full 3D nonlinear models. This means that the static eccentricity that matters for torsional response may be taken as that of the floor “center of twist.” The center of resistance comes up as the second-best choice.     

Seismic Analysis of Non Proportionally Damped Two-Way Asymmetric Elastic Buildings Under Bi-Directional Seismic Ground Motions

This study investigates the effectiveness of the modal analysis using three-degree-of freedom (3DOF) modal equations of motion to deal with the seismic analysis of two-way asymmetric elastic systems with supplemental damping. The 3DOF modal equations of motion possessing the non proportional damping property enable the two modal translations and one modal rotation to be non proportional in an elastic state. The simple approximation method is to use the single degree-of-freedom (SDOF) modal equations of motion, which are obtained by neglecting the off-diagonal elements of the transformed damping matrix. One, one-story and one, three-story non proportionally damped two-way asymmetric buildings under the excitation of bi-directional seismic ground motions are analyzed. The analytical results are obtained by using the proposed method, noted simple approximation method, and direct integration of the equation of motion. It is seen that the proposed method can significantly improve the accuracy of the analytical results compared with those obtained by using the simple approximation method. Moreover, the proposed method does not substantially increase the computational efforts.