Inelastic Torsional Response Research Articles

Evaluation of seismic torsional response of ductile RC buildings with soft first story

This study investigates the inelastic torsional response of plan asymmetric ductile RC buildings with a soft first story. The buildings of Rectangular, L, T, and U plan shapes are considered for the study. Force-based fiber beam-column elements are modeled for the inelastic response prediction of the buildings. Masonry infill walls are uniformly distributed in the plan and considered for the evaluation of torsional response. The pushover methods, Extended N2 and Extended Capacity Spectrum Method – FEMA 440 are adopted to estimate the inelastic torsional response. Bi-directional nonlinear time history analysis is carried out on the buildings considering near-field and far-field ground motions. Story drift ratio and curvature demand-capacity (D/C) ratio of columns are reported at the stiff, flexible side of buildings. The torsional response of infill wall buildings is compared with that of bare frame buildings. It was observed that the torsionally irregular ductile buildings with soft first story exhibit higher seismic demand on the flexible side corner columns. Infill wall interaction amplifies the torsional response at the bottom story, causing an increase in displacements higher at the flexible side and moderate near the stiff side. This study concludes that the flexible side corner column in plan asymmetric building with a soft first story can be conservatively designed for 1.5 times the design forces obtained from the analysis. This conservative design ensures stable energy dissipation in the corner column under load reversals, without significant strength reduction under higher excitation levels. The designer shall properly distribute lateral load resisting elements in a plan to prevent premature failure of the columns located internally and close to the initial center of rigidity. The designer can avoid the collapse of columns located internally in the buildings with stiff peripheral frames by designing for forces 1.5 times higher than obtained.

The effect of accidental eccentricities on the inelastic torsional response of buildings

This paper investigates the influence of spatial varations of accidental mass eccentricities on the torsional response of inelastic multistorey reinforced concrete buildings. It complements recent studies on the elastic response of structural buildings and extends the investigation into the inelastic range, with the aim of providing guidelines for minimising the torsional response of structural buildings. Four spatial mass eccentricity configurations of common nine story buildings, along with their reversed mass eccentricities subjected to the Erzincan-1992 and Kobe-1995 ground motions were investigated, and the results are discussed in the context of the structural response of the no eccentricity models. It is demonstrated that when the initial linear response is practically translational, it is maintained into the inelastic phase of deformation as long as the strength assignment of the lateral resisting bents is based on a planar static analysis where the applied lateral loads simulate the first mode of vibration of the uncoupled structure.

Mass eccentricity effects on the torsional response of inelastic buildings

This paper investigates the role of accidental mass eccentricities on the inelastic torsional behaviour of multi-storey asymmetric buildings with a mixed type lateral load resisting system subjected to the Erzincan-1992 and Kobe-1995 ground motions. The numerical modelling results show that the effects of spatial variations of mass eccentricities are lower and smoother in the inelastic rather than the elastic state of deformation, but both the elastic and inelastic torsional response is pointing to the same optimum location of the key element for which the torsional response of the structure is minimized.

Case study of seismic performance assessment of irregular RC buildings: hospital structure of Avezzano (L’Aquila, Italy)

Most published studies on inelastic earthquake response of non-symmetric buildings are based on simplified inelastic, highly idealized models, while general conclusions regarding the inelastic torsional response of multistory building are still lacking. This paper aims to provide a useful contribution in the study of the torsional response of real irregular buildings. To this aim, the manuscript reports the comprehensive study on the seismic vulnerability of an irregular RC building: the hospital building of Avezzano (L’Aquila Italy). For this multi-story building, which is irregular in both plan and elevation, the application of nonlinear static evaluation procedures is by no means straightforward. The study proposes a nonlinear static procedure based on pushover analysis under the multimodal distribution of lateral loads and a capacity spectrum method. This pushover procedure accounts for mass distribution, higher modes contribution and mode-shapes correlation. Furthermore, due to its non-iterative feature, it avoids problems of non-convergence and multiple solutions of the conventional capacity spectrum method. Applied to a real case study, the procedure is used to investigate, in a 3D plan irregular building, the sensitivity of torsional inelastic response to lateral force distribution, higher modes contribution, accidental eccentricity and controlled point for monitoring the target displacement.

Seismic reliability analysis of buildings with torsional eccentricities

SummaryA study is presented of the influence of stiffness and strength eccentricities on the inelastic torsional response of buildings under the action of two simultaneous orthogonal horizontal ground motion components. Asymmetric buildings were obtained from their respective symmetric systems and were characterized by their stiffness and strength torsional eccentricities in both orthogonal directions. Based on the results of inelastic response of both building types (symmetric and asymmetric), the seismic reliability functions are determined for each system, and their forms of variation with different global system parameters are evaluated. Illustrative examples are presented about the use of this information for the formulation of seismic design criteria for in‐plan asymmetric multistory systems, in order to attain the same reliability levels implicit for symmetric systems designed in accordance with current seismic design codes. Copyright © 2014 John Wiley & Sons, Ltd.

Inelastic torsional seismic response of nominally symmetric reinforced concrete frame structures: Shaking table tests

This paper discusses the torsional response of a scaled reinforced concrete frame structure subjected to several uniaxial shaking table tests. The tested structure is nominally symmetric in the direction of shaking and exhibits torsion attributable to non-uniform yielding of structural components and uncertainties in the building process. Asymmetric behavior is analyzed in terms of displacement, strain in reinforcing bars, energy dissipated at plastic hinges, and damage at section and frame levels. The results show that for low levels of seismic hazard, for which the structure is expected to perform basically within the elastic range, the accidental eccentricity is not a concern for the health of the structure, but it significantly increases the lateral displacement demand in the frames (about 30%) and this might cause significant damage to non-structural components. For high levels of seismic hazard the effects of accidental torsion become less important. These results underline the need to consider accidental eccentricity in evaluating the performance of a structure for very frequent or frequent earthquakes, and suggest that consideration of torsion may be neglected for performance levels associated with rare or very rare earthquakes.

Evaluation of the Torsional Response of Multistory Buildings Using Equivalent Static Eccentricity

The equivalent static eccentricities of seismic forces are usually defined by building codes with simple expressions of the static eccentricity. The inelastic torsional response of multistory buildings using nonlinear static analysis (NL-SA) with the equivalent static eccentricities is less easily predictable because the response is influenced by the extent of plastic deformations, and the eccentricity varies story by story at each step. To overcome this weakness, it is necessary to change the location of static eccentricity in each step of the NL-SA method. In this paper, a simplified procedure for the correct calculation using the NL-SA method with varying static eccentricity based on the modal response of a single-story scheme is presented. In order to estimate torsional effects on the seismic response, the associated plastic mechanism is developed in a three dimensional model of building, using an updated version of the DRAIN-3DX program. The torsional response of three different structural systems wi...

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.

The Role of Inelastic Torsion in the Determination of Residual Deformations

Recent developments in performance-based seismic design and assessment approaches have emphasized the importance of properly assessing and limiting the residual (permanent) deformations typically sustained by a structure after a seismic event, even when designed according to current code provisions. The performance-based design framework for residual deformations, previously developed by the authors for 2-D regular structures, is further extended to the behavior of 3-D irregular (asymmetric in-plan) buildings. The seismic response of a set of single-story systems, comprising of seismic resisting frames, and modeled to represent alternative materials (concrete or steel), is investigated under uni-directional earthquake loading excitations. Different layouts in plan, leading to either torsionally unrestrained or restrained systems, are considered. The influence of varying torsional restraint is investigated to define how residual diaphragm rotations and center-of-mass displacements are affected by changing levels of stiffness and strength, or mass eccentricity. From these findings additions to the previously proposed estimation procedure are made, with a specific example used to validate the suggested changes. Finally, a general example is developed based on currently available methods of evaluating maximum torsion response. It is suggested that such approaches are likely to be insufficient as they do not explicitly define how seismic-resisting elements are influenced by inelastic torsional response.

On the inelastic torsional response of single-storey structures under bi-axial excitation

An attempt has been made to explore the general trends in the seismic response of plan-asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi-directional excitation were studied. Idealized single-storey models with bi-axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass-eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.

Inelastic earthquake response of single‐story asymmetric buildings: an assessment of simplified shear‐beam models

AbstractThe inelastic seismic torsional response of simple structures is examined by means of shear‐beam type models as well as with plastic hinge idealization of one‐story buildings. Using mean values of ductility factors, obtained for groups of ten earthquake motions, as the basic index of post‐elastic response, the following topics are examined with the shear‐beam type model: mass eccentric versus stiffness eccentric systems, effects of different types of motions and effects of double eccentricities. Subsequently, comparisons are made with results obtained using a more realistic, plastic hinge type model of single‐story reinforced concrete frame buildings designed according to a modern Code. The consequences of designing for different levels of accidental eccentricity are also examined for the aforementioned frame buildings. Copyright © 2003 John Wiley & Sons, Ltd.

변형에 기초한 비대칭 벽식 주초의 내진설계

기존의 비틀림 설계법은 구조 벽체의 강성은 강도에 무관하게 결정된다는 기본 가정하에 강성을 설계 변수로 비대칭 벽식 구조의 비틀림 효과를 최소화 하기 위한 각 부재의 강도를 결정한다. 이와는 달리 최근의 연구에 의하면 구조 벽체의 강성과 강도는 상호 연관성을 갖는 것으로 알려졌다. 이 경우 벽체의 실제 강성은 비틀림설계를 모두 마친 후에야 결정되므로 강성에 기초하여 비틀림 설계를 수행한다는 것은 모순이다. 이와 같은 문제점을 해결하기 위해 본 논문은 강성이 아닌 변형에 기초한 비대칭 벽식 구조의 비틀림 설계법을 제안한다. 기존의 비틀림 설계법은 탄성 비틀림 응답과 반응수정계수를 이용하여 비탄성 응답에 대한 설계 하중을 간접적으로 계산하지만 변형에 기초한 비틀림 설계법은 변위와 비틀림 회전각을 설계 변수로 비탄성 응답에 대한 설계 하중을 직접적으로 계산한다. 기존의 비틀림 설계법이 비틀림 효과를 최소화하는 것을 목적으로 하는 데 비하여, 변형에 기초한 비틀림 설계법은 내진역량설계법의 기본 개념에 의거하여 설계자가 의도한 비틀림 미케니즘을 발휘하는 데 그 목적을 둔다. 변위와 회전각은 비대칭 구조의 성능수준을 직접적으로 나타내는 성능 지표이므로 본 설계법은 성능기초 내진설계에 효과적으로 사용될 수 있다. Current torsional provisions focus n restricting torsional effect of asymmetric wall structures by proportioning strength of wall based on the traditional assumption that stiffness and strength are independent. Recent studies have pointed out that stiffness of structural wall is dependent on the strength. This implies that actual stiffness of walls can be determined only after torsional design is finished and current torsional provisions may result in significant errors. To overcome this shortcoming, this paper proposes deformation based torsional design for asymmetric wall structures. Contrary to the current torsional provisions, deformation-based torsional design uses displacement and rotation angle as design parameters and calculates base shear for inelastic torsional response directly. Main purpose of deformation based torsional design is not to restrict torsional response but to ensure intended torsional mechanism according to the capacity design concept. Because displacement and rotation angle can be used as performance criteria indicating performance level of asymmetric structures, this method can be applied to the performance based seismic design effectively.

Inelastic coupled response of eccentric buildings with respect to different earthquake intensity

Using five-story shear models, the inelastic torsional coupled response of eccentric buildings to different earthquake intensity was studied. Results show that the torsional couple degree is closely related to the strengh distribution of the resisting elements. Generally, the building designed by spectral modal analysis method has a tendency to move translationally as the earthquake intensity increases. The building designed by proportion rigidity method will rotate heavily to moderate earthquake, but when it is intensively excited into the inelastic phase, the coupling would decrease slightly, but could not be neglected.

Discussion of the paper ?Effect of orthogonal inplane structural elements on inelastic torsional response? by J. L. Humar and P. Kumar

Earthquake Engineering & Structural DynamicsVolume 29, Issue 8 p. 1249-1251 Discussion Discussion of the paper ‘Effect of orthogonal inplane structural elements on inelastic torsional response’ by J. L. Humar and P. Kumar† Avigdor Rutenberg, Corresponding Author Avigdor Rutenberg Faculty of Civil Engineering, Technion – Israel Institute of Technology, Haifa 32000, IsraelFaculty of Civil Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, IsraelSearch for more papers by this author Avigdor Rutenberg, Corresponding Author Avigdor Rutenberg Faculty of Civil Engineering, Technion – Israel Institute of Technology, Haifa 32000, IsraelFaculty of Civil Engineering, Technion – Israel Institute of Technology, Technion City, Haifa 32000, IsraelSearch for more papers by this author First published: 27 June 2000 https://doi.org/10.1002/1096-9845(200008)29:8<1249::AID-EQE945>3.0.CO;2-4 † Reference [1]. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. Volume29, Issue8August 2000Pages 1249-1251 RelatedInformation

Authors' Reply to discussion of the paper ?Effect of orthogonal inplane structural elements on inelastic torsional response?

Authors' Reply to discussion of the paper ?Effect of orthogonal inplane structural elements on inelastic torsional response?

Effect of orthogonal inplane structural elements on inelastic torsional response

The elastic torsional stiffness of a structure has important influence on the seismic response of an asymmetric structure, both in the elastic and inelastic range. For elastic structures it is immaterial whether the stiffness is provided solely by structural elements in planes parallel to the direction of earthquake or by a combination of such elements in parallel and orthogonal planes. The issue of how the relative contribution of structural elements in orthogonal planes affects the torsional response of inelastic structures has been the subject of continuing study. Several researchers have noted that structural elements in orthogonal planes reduce the ductility demands in both the flexible and stiff edge elements parallel to the earthquake. Some have noted that the beneficial effect of structural elements in orthogonal planes is more pronounced when such elements remain elastic. These issues are further examined in this paper through analytical studies on the torsional response of single-storey building models. It is shown that, contrary to the findings of some previous studies, the torsional response of inelastic structures is affected primarily by the total torsional stiffness in the elastic range, and not so much by whether such stiffness is contributed solely by structural elements in parallel planes or by such elements in both parallel and orthogonal planes. Copyright © 1999 John Wiley & Sons, Ltd.

Effect of orthogonal inplane structural elements on inelastic torsional response

The elastic torsional stiffness of a structure has important influence on the seismic response of an asymmetric structure, both in the elastic and inelastic range. For elastic structures it is immaterial whether the stiffness is provided solely by structural elements in planes parallel to the direction of earthquake or by a combination of such elements in parallel and orthogonal planes. The issue of how the relative contribution of structural elements in orthogonal planes affects the torsional response of inelastic structures has been the subject of continuing study. Several researchers have noted that structural elements in orthogonal planes reduce the ductility demands in both the flexible and stiff edge elements parallel to the earthquake. Some have noted that the beneficial effect of structural elements in orthogonal planes is more pronounced when such elements remain elastic. These issues are further examined in this paper through analytical studies on the torsional response of single-storey building models. It is shown that, contrary to the findings of some previous studies, the torsional response of inelastic structures is affected primarily by the total torsional stiffness in the elastic range, and not so much by whether such stiffness is contributed solely by structural elements in parallel planes or by such elements in both parallel and orthogonal planes. Copyright © 1999 John Wiley & Sons, Ltd.

Torsional motion of buildings during earthquakes. II. Inelastic response

In a previous study on the elastic torsional response of building models subjected to earthquake motion, it was shown that the current provisions of the National Building Code of Canada for design against torsion induced by earthquakes are quite conservative for the flexible edge of the building, but may be inadequate for the stiff edge. Based on the results of studies on the elastic response, a new set of design provisions was suggested. The present study deals with the inelastic torsional response of single- and multi-storey buildings designed according to the suggested provisions. Effects of both the natural and the accidental torsion are considered. It is shown that, given the complexity of inelastic response, particularly that of multistorey buildings, the suggested provisions can reasonably be used for the torsion design of single-storey buildings, as well as of multistorey buildings that are asymmetric in plan, but otherwise fairly regular.Key words: earthquake response, natural torsion, accidental torsion, inelastic torsional response, design for torsion.

Stochastic linearization of inelastic seismic torsional response: formulation and case studies

The stochastic equivalent linearization method (SELM) is adopted for the analysis of hysteretic torsionally coupled oscillators under bi-axial random earthquake loading. A new formulation of the method is presented which is based on polynomial expansions of various nonlinear terms and the implementation of the properties of Gaussian variables. The resulting expressions incorporate the interaction of the hysteretic components of the two translational modes as well as the torsional coupling and form the basis for the evaluation of the expected ductility ratio and the mean rate of hysteretic energy dissipation. The accuracy of the introduced approximations is confirmed through selected tests against numerical integrations and Monte Carlo simulations. Furthermore, the ability of the methodology to model the behaviour of one-storey torsionally coupled structures is assessed through comparisons with results reported in the literature which are based on a somewhat more realistic approach to structural modelling.

Seismic torsional response and design procedures for a class of setback frame buildings

AbstractThis paper presents results of an analytical study of the inelastic earthquake torsional response of a class of setback frame buildings. In the first part of the study, the modal response spectrum analysis procedure is utilized to determine the yielding strengths of structural members in an idealized but representative setback frame building model. Results are then presented for the inelastic dynamic response of this setback building model subjected to an ensemble of six earthquake ground motions. The results indicate that the modal response spectrum analysis procedure is inadequate for preventing excessive response leading to concentration of damage in vulnerable structural members, such as those in the tower near the notch and those in the base (the part of the structure below the tower) near the perimeter at the opposite side of the tower. The second part of the study develops a modified equivalent static force procedure for strength design of such setback frame buildings. Response analyses show that the proposed procedure results in improved and satisfactory inelastic performance of the selected class of setback frame buildings, having a wide range of realistic configurations.