Inelastic Range Of Behaviour Research Articles

Torsional irregularity indices for the seismic demand assessment of RC moment resisting frame buildings

Design standards across the world use different parameters to quantify degree of torsional irregularity of buildings. Popular among such descriptors are the normalized static eccentricity ratio, torsional radius to mass radius of gyration ratio, maximum to minimum (or average) elastic floor displacement ratio, etc. However prior research, particularly on idealized single storey systems have indicated that these parameters do not correlate well with the seismic demands at all stages of structural behaviour (i.e. elastic and inelastic). The present study aims to identify a robust torsional irregularity index that captures the susceptibility of a structure to torsional effects at all ground motion intensity levels. To this end, the correlation between the maximum interstorey drift demands and popular torsional irregularity descriptors is first examined under different intensities of ground shaking using an approach that integrates multiple stripe analysis and statistical regression analysis. The numerical study is based on the nonlinear seismic assessment of thirteen three-storey gravity designed RC moment frame buildings subjected to bidirectional seismic excitation. The results indicate that none of the scalar indices considered correlate well with the drift demands at all intensities of ground shaking. A vector comprising of the normalized static eccentricity ratio and the torsional radius to mass radius of gyration ratio is found to perform well at low shaking intensity levels, where the structure responds in an elastic manner. However, at high intensity levels where the structure undergoes significant excursions into the inelastic range of behaviour, the strength eccentricity is observed to be a better descriptor of torsional irregularity. A three-element vector comprising of the above indices is found to capture the maximum interstorey drifts accurately at all ground motion intensity levels. A seismic demand model for maximum interstorey drift, sensitive to the above torsional irregularity descriptors, is also defined.

An accurate strength amplification factor for the design of SDOF systems with P–Δ effects

SUMMARYThe response of structures subjected to seismic actions is always influenced by P–Δ effects. The importance of this effect is generally modest for structures experiencing an elastic response but often relevant for structures responding well within the inelastic range of behaviour. Seismic codes indicate that P–Δ effects may be counterbalanced through an increase in the structural strength required by a first order analysis. This increase is calculated by means of a strength amplification factor. The expressions suggested in codes for this factor are simplistic and often criticized by researchers.In this paper, the effectiveness of some of the provisions reported in the literature or suggested in seismic codes is evaluated on single degree of freedom systems with different periods of vibration. As suggested by past studies, attention is focused on the influence of the interstorey drift sensitivity coefficient, significant duration of the ground motion, class of the site soil, displacement ductility and equivalent viscous damping ratio of the system. Finally, an accurate expression of the strength amplification factor is proposed. Copyright © 2013 John Wiley & Sons, Ltd.

Predicting torsion‐induced lateral displacements for pushover analysis: Influence of torsional system characteristics

AbstractThe increasing popularity of simplified nonlinear methods in seismic design has recently led to many proposals for procedures aimed at extending pushover analysis to plan asymmetric structures. In terms of practical applications, one particularly promising approach is based on combining pushover analysis of a 3D structural model with the results of linear (modal) dynamic analysis. The effectiveness of such procedure, however, is contingent on one fundamental requirement: the elastic prediction of the envelope of lateral displacements must be conservative with respect to the actual inelastic one.This paper aims at verifying the above assumption through an extensive parametric analysis conducted with simplified single‐storey models. The main structural parameters influencing torsional response in the elastic and inelastic range of behaviour are varied, while devoting special attention to the system stiffness eccentricity and radius. The analysis clarifies the main features of inelastic torsional response of different types of building structures; in this manner, it is found that the above‐mentioned method is generally suitable for structures characterized by moderate to large torsional stiffness, whereas it cannot be recommended for extremely torsionally stiff structures, as their inelastic torsional response almost always exceeds the elastic one. Copyright © 2010 John Wiley & Sons, Ltd.

Evaluation of the AISI S213 seismic design procedures through testing of strap braced cold-formed steel walls

The North American standard for the design of lateral systems constructed of cold-formed steel (CFS) (AISI S213), which is published by the American Iron and Steel Institute (AISI), was updated in 2007. Included in this update were changes to the provisions related to strap braced walls. The 2007 version of AISI S213 includes requirements for the brace material and the use of capacity design principles; as well, the engineer is directed towards using welded connections to avoid possible net section fracture of the braces. Screw-connected braces may be used if shown to perform in a ductile fashion. The research described herein was undertaken to evaluate typical weld and screw-connected single-storey strap braced wall configurations with respect to their ability to resist lateral in-plane loads in the inelastic range of behaviour; that is, the results were used to verify the new strap braced wall seismic design provisions in AISI S213. A total of 44 tension-only X-braced walls ranging in size from 610×2440 mm 2 to 2440×2440 mm 2 (aspect ratios from 4:1 to 1:1), designed and detailed following a capacity-based approach, were tested under lateral loading using monotonic and reversed cyclic protocols. The strap braces were expected to undergo gross cross-section yielding along their length, while the other elements in the seismic force resisting system (SFRS) were selected to be able to carry the probable brace capacity. A summary of the test program is provided, including design approach, failure modes and ductility measures. The scope of the research also included the determination of “test-based” seismic force modification factors based on the measured ductility and overstrength of the test walls for comparison with the R-values recommended in AISI S213.

Inelastic performance of screw-connected cold-formed steel strap-braced walls

Cold-formed steel, screw-connected strap-braced walls (15 specimens, 2.44 m × 2.44 m each), designed following a capacity-based approach, were tested to evaluate their performance in the inelastic range of behaviour. Gross cross-section yielding of the tension braces was the specified failure mode in the design procedure. Extended tracks and additional shear anchors were installed, such that inelastic deformations would be limited to tension yielding of the braces. Walls without extended tracks were able to reach their yield level; however, damage to other frame elements occurred, thus reducing the ductility level that was attained. Cyclically loaded walls (0.5 Hz) with track extensions showed that wall performance is also dependent on the strain rate experienced by the braces. An Fu / Fy ratio greater than 1.2 is necessary to limit the possibility of brace fracture under seismic loading. Preliminary force modification factors, Rd = 2.0 and Ro = 1.3, are recommended for walls designed and detailed to achieve ductile performance.

Effects of supplemental viscous damping on inelastic seismic response of asymmetric systems

AbstractThis paper investigates the effects of supplemental viscous damping on the seismic response of one‐storey, asymmetric‐plan systems responding in the inelastic range of behaviour. It was found that addition of the supplemental damping reduces not only deformation demand but also ductility and hysteretic energy dissipation demands on lateral load resisting elements during earthquake loading. However, the level of reduction strongly depends on the plan‐wise distribution of supplemental damping. Nearly optimal reduction in demands on the outermost flexible‐side element, an element generally considered to be the most critical element, was realized when damping was distributed unevenly in the system plan such that the damping eccentricity was equal in magnitude but opposite in algebraic sign to the structural eccentricity of the system. These results are similar to those noted previously for linear elastic systems, indicating that supplemental damping is also effective for systems expected to respond in the inelastic range. Copyright © 2001 John Wiley & Sons, Ltd.

Inelastic response and design criteria of plan‐wise asymmetric systems

AbstractThe study of the torsional response of buildings in the inelastic range of behaviour is of great interest since the ability of structures to resist strong earthquakes mainly relies on their ductility and capacity for energy dissipation. Furthermore, an examination of the performance of structures during past earthquakes demonstrates that plan‐asymmetric buildings suffered greater damage due to torsional response. The paper deals with this subject by analysing a model which idealizes a one‐storey building with resisting elements oriented along two perpendicular directions. In addition to the parameters of the elastic behaviour, the inelastic system response depends on full yield capacity and plan‐wise strength distribution. The influence of the criterion adopted for the design of resisting elements on local ductility demand and damage has been evaluated by parametric analysis. In particular, a comparison has been carried out between systems with equal design levels for all elements and systems with design levels dependent on the element location. For a given elastic behaviour and total capacity, the strength distributions in plan have been defined which minimize ductility demand and structural damage. Finally, based on these findings, responses from models designed according to several seismic codes have been compared.

Experimental study of single angle columns

The paper presents the results of an experimental investigation of the buckling response of single angle columns. Equal- and unequal-legged angles were used with a range of maximum principal slenderness ratios that aimed at determining elastic and inelastic failure characteristics, including flexural and flexural-torsional effects and the influence of the width-to-thickness ratios of the legs. Verifying previous theoretical calculations and being generally in good agreement with the results of other studies, where such were available, the findings emphasize the importance of the flexural-torsional buckling mode, especially in the inelastic range of behavior. Tentative design recommendations are made, but it is also noted that further research is needed to amplify the data. In particular, the influence of the width-to-thickness ratio of the angle legs needs to be examined systematically.

Analysis of continuous steel plates subjected to uniform transverse loads

The economic design of steel caissons for drilling and production platforms in the Arctic Ocean, formed from steel plates and supported by a rectangular grid of stiffeners, beams, and girders, requires that the full strength of the plates be mobilized to withstand extreme ice forces. A comprehensive method of analysis is needed to describe the behaviour of continuous steel plates into the inelastic range when they are acted upon by transverse loads. From this analysis, design procedures could then be developed.An extensive literature search has not revealed that satisfactory solutions exist for the load–deflection response of transversely loaded flat plates beyond the elastic limit when both flexural and membrane action are taken into account. Experimental data available in the inelastic range of behaviour are also limited.By considering various limiting simplified behavioural modes for the load–deflection response of uniformly loaded flat plates of zero aspect ratio, possible load–deflection domains are established. The limiting responses investigated are: elastic–inelastic flexural action, elastic membrane action, inelastic membrane action with increased stiffness resulting from increased Poisson's ratio in the inelastic range, elastic flexural membrane action, and action of a fully yielded cross section in flexure that gradually gives away to a fully yielded cross section in tension. Within the domain so established, a load–deflection behaviour is proposed that is in reasonable agreement with the results of the limited test data available. The results of a finite element analysis using the ADINA computer program are also in reasonable agreement with the proposed analysis. Design applications are discussed. Key words: deflection, elastic, elastoplastic, flexural resistance, membrane force, membrane resistance, plates, steel, strains, stresses, transverse load.

Inelastic Earthquake Response of Steel Structures

Results from experiments in which small three story steel frame structures were subjected to simulated earthquake motions by means of a shaking table are described. The structures, weighing 132 lb (60 kg), and consisting of 1/2 in. × 1/4 in. (13 mm × 6 mm) rectangular columns and rigid beams, were designed to reproduce the overall seismic behavior of shear‐type buildings. The motions caused large inelastic deformations in the first‐story columns. The results of the experiments were used to evaluate the accuracy of a computer program by comparing computed time histories and hysteresis loops with those obtained experimentally. It is concluded that the computer program, DRAIN‐2D, can reproduce the general features in the response of these three story structures to earthquake motions even if there are large excursions into the inelastic range of behavior. However, in order to reproduce the response precisely, the simple bilinear moment‐rotation relationship used to specify nonlinear behavior would have to be modified to account for cyclic strain hardening.

Torsional Coupling and Earthquake Response of Simple Elastic and Inelastic Systems

The effects are analyzed of torsional coupling on the earthquake response of simple one-story structures in elastic and inelastic ranges of behavior. The structures considered are symmetrical about one principal axis of resistance, resulting in coupling only between lateral displacement along the perpendicular axis and the torsional displacement. Torsional coupling arising only from eccentricity between centers of mass and elastic resistance is considered. Systems with several resisting elements are idealized by a single element model. Response of such a model to a selected earthquake ground motion are presented for a range of the basic structural parameters. The response quantities presented include maximum lateral and torsional deformations of the system as well as maximum deformations of individual columns. The response in the inelastic range of behavior is effected by torsional coupling to generally a lesser degree than elastic response.