A strength distribution criterion for minimizing torsional response of asymmetric wall‐type systems

In order to mitigate the effect of torsion during earthquakes, most seismic codes of the world provide design guidelines for strength distribution based on the traditional perception that element stiffness and strength are independent parameters. Recent studies have pointed out that for an important class of widely used structural elements such as reinforced concrete flexural walls, stiffness is a strength‐dependent parameter. This implies that the lateral stiffness distribution in a wall‐type system cannot be defined prior to the assignment of elements' strength. Consequently, stiffness eccentricity cannot be computed readily and the current codified torsional provisions cannot be implemented in a straightforward manner. In this study, an alternate guideline for strength distribution among lateral force resisting elements is presented. To develop such a guideline, certain issues related to the dynamic behaviour of asymmetric wall‐type systems during a damaging earthquake were examined. It is shown that both stiffness and strength eccentricity are important parameters affecting the seismic response of asymmetric wall‐type systems. In particular, results indicate that torsional effects can be minimized by using a strength distribution that results in the location of the centre of strength CV and the centre of rigidity CR on the opposite sides of the centre of mass CM. Copyright © 2001 John Wiley & Sons, Ltd.     

A yield displacement distribution‐based approach for strength assignment to lateral force‐resisting elements having strength dependent stiffness

Recent studies have shown that for many lateral force‐resisting elements (LFRE) stiffness is dependent on strength, and as a result strength assignment to these elements would affect both the strength and stiffness distributions in a structure. Consequently, stiffness distribution cannot be considered known prior to strength assignment. This paper presents a yield displacement distribution‐based strength assignment strategy that does not require the knowledge of stiffness distribution prior to strength assignment. It is shown that structural systems with their center of rigidity (CR) and center of strength (CV) located on the opposite sides of the center of mass (CM) will have small torsional responses under seismic excitation. Copyright © 2003 John Wiley Sons, Ltd.     

Design of torsionally unbalanced structural systems based on code provisions II: Strength distribution

This paper presents the results of an analytical study of the strength distribution of lateral load resisting elements in torsionally unbalanced systems designed based on codified torsional provisions. It is shown that the element strength can be expressed conveniently as the element strength of a similar but torsionally balanced system multiplied by a strength factor. This strength factor depends on three system parameters, namely, the location of the element relative to the centre of rigidity, and the torsional stiffness and eccentricity of the structure. In addition, it depends on the design coefficients of the code specified design eccentricity expressions. The influence of each of these factors on the element strength distribution is discussed. A new set of values for the design coefficients is proposed. By means of examples, it is shown that the proposed torsional provision is an improvement over those suggested in the National Building Code of Canada and the New Zealand code.     

A modified static procedure for the design of torsionally unbalanced multistorey frame buildings

Seismic building codes include design provisions to account for the torsional effects arising in torsionally unbalanced (asymmetric) buildings. These provisions are based on two alternative analytical procedures for determining the design load for the individual resisting structural elements. A previous study has shown that the linear elastic modal analysis procedure may not lead to conservative designs, even for multistorey buildings with regular asymmetry, when such structures are excited well into the inelastic range of response. The equivalent static force procedure as recommended by codes may also be deficient in accounting for additional ductility demand in the critical stiff-edge elements. This paper addresses the non-conservatism of existing static torsional provisions and examines aspects of element strength distribution and its influence on inelastic torsional effects. A recommendation is made for improving the effectiveness of the code-type static force procedure for torsionally unbalanced multistorey frame buildings with regular asymmetry, leading to a design approach which estimates conservatively the peak ductility demand of edge elements on both sides of the building. The modified approach also retains the simplicity of existing code provisions and results in acceptable levels of additional lateral design strength. It has recently been adopted by the new Australian earthquake code, which is due to be implemented early in 1993.     

Inelastic seismic response of torsionally unbalanced systems designed using elastic dynamic analysis

This paper evaluates the inelastic seismic response of torsionally unbalanced structural systems with strength distributed using elastic response spectrum analysis. The structural model is a single mass torsionally unbalanced system with lateral load resisting elements spanning in two principal directions. The element strength is distributed based on elastic response spectrum analysis and three different approaches to incorporate accidental torsion are considered: (a) without incorporating accidental torsion; (b) by applying static floor torques; (c) by shifting the location of the centre of mass. The seismic input is bidirectionally applied at the base of the model. It is shown that the inelastic responses depend strongly on the torsional stiffness of the system. For a torsionally stiff system, the torsional response leads to a decrease in the stiff edge displacement; however, for a torsionally flexible system, it tends to increase the stiff edge displacement. Using response spectrum analysis without including accidental torsion may lead to excessive additional ductility demand on the stiff edge element. With accidental torsion effect incorporated, the response spectrum analysis will give a strength distribution such that there will be no excessive additional ductility demands on the lateral load resisting elements.     

Effect of transverse load-resisting elements on inelastic earthquake response of eccentric-plan buildings

The accurate evaluation of code torsional provisions for plan-eccentric structures exhibiting inelastic response relies on the adoption of appropriate systems defining both the torsionally balanced (reference) and torsionally unbalanced cases. Whilst a considerable number of analytical studies of this problem have been presented in the literature, inconsistencies have arisen in their conclusions. It is evident from a review of previous studies that one factor contributing significantly to these discrepancies arises in the definition of the structural layout. An issue of particular importance is whether the transverse load-resisting elements oriented perpendicular to the assumed (lateral) direction of earthquake loading should, for purposes of realism, be included in model definitions. Given the diverse approaches in the existing literature, clarification of this issue is required in order to advance the understanding of inelastic torsional response behaviour and to assist the interpretation and comparison of previous studies. This paper aims to provide such clarification, based on analyses of a series of models defined rigorously according to code design provisions. Such models have been subjected to both uni- and bi-directional ground motion input. It is concluded that for the flexible-edge element, accurate estimates of additional ductility demand arising from torsional effects may be obtained from uni-directional models (in which both the transverse elements and the corresponding earthquake component are neglected) only for medium-period to long-period systems. Such estimates may be over-conservative for short-period systems, which constitute a large proportion of systems for which code static torsional provisions are utilized. It is further concluded that models incorporating the transverse elements but analysed under uni-directional lateral loading may underestimate by up to 100% the torsional effects in such systems, but are reasonably accurate for medium- and long-period structures.     

Inelastic torsional response of buildings to the 1985 Mexican earthquake: a parametric study

This study aims to determine the influence of torsional coupling on the inelastic response of a series of models representing typical structural configurations in real buildings. The lake bed (SCT) east-west component of the 1985 Mexico City earthquake was employed in the analysis, and is representative of a severe ground motion known to have induced large inelastic structural deformations in a high proportion of those buildings having asymmetrical distributions of stiffness and/or strength. Material non-linearity in lateral load-resisting elements has been defined using a hysteretic Ramberg-Osgood model. Structural eccentricities have been introduced into the building models by (i) asymmetrical distributions of stiffness and/or strength, (ii) asymmetrical configuration of lateral load-resisting elements, or (iii) varying post-elastic material behaviour in the resisting elements. The dynamic inelastic response of these models has been obtained by a numerical integration of the relevant equations of motion, expressed in a non-dimensional incremental form.

In the elastic range, the results correlate well with those of previous studies. In the inelastic range, it is concluded that the peak ductility demand of the worst-affected element increases with the ground excitation level across the range of building periods considered, and that the influence of torsional coupling on the key response parameters is model dependent. Most significantly, the strength eccentricity relative to the centre of mass has been shown to influence the peak edge displacement response more than conventionally employed stiffness eccentricity.     

Inelastic seismic response of code-designed multistorey frame buildings with regular asymmetry

Based on an asymmetric multistorey frame building model, this paper investigates the influence of a building's higher vibration modes on its inelastic torsional response and evaluates the adequacy of the provisions of current seismic building codes and the modal analysis procedure in accounting for increased ductility demand in frames situated at or near the stiff edge of such buildings. It is concluded that the influence of higher vibration modes on the response of the upper-storey columns of stiff-edge frames increases significantly with the building's fundamental uncoupled lateral period and the magnitude of the stiffness eccentricity. The application of the equivalent static torsional provisions of certain building codes may lead to non-conservative estimates of the peak ductility demand, particularly for structures with large stiffness eccentricity. In these cases, the critical elements are vulnerable to excessive additional ductility demand and, hence, may be subject to significantly more severe structural damage than in corresponding symmetric buildings. It is found that regularly asymmetric buildings excited well into the inelastic range may not be conservatively designed using linear elastic modal analysis theory. Particular caution is required when applying this method to the design of stiff-edge frame elements in highly asymmetric structures.     

Analytical and experimental investigations on seismic performance of exterior beam–column subassemblages of existing RC‐framed building

Seismic performance of exterior beam–column subassemblages of reinforced concrete structure designed and detailed on the basis of the provisions of Eurocode and Indian Standards at different stages of their evolution is evaluated. Performance of the subassemblages designed and detailed according to the three different stages of codal evolution (gravity load design, ‘Nonductile’, and ‘Ductile’) is evaluated through analytical formulations and experimental investigations. In the ‘NonDuctile’ specimens, it has been observed that the shear distortion and degradation in stiffness and strength are significantly high. Performance of the ‘Ductile’ specimens based on Eurocode and Indian Standards is almost similar in terms of strength and stiffness degradation. Nevertheless, the specimen designed on the basis of Indian Standard shows higher energy dissipation at a given drift ratio. In the analytical study, shear and flexural failure of members of subassemblage and shear failure of the joint are considered as possible modes of failure of the beam–column subassemblage. For evaluating the shear strength of the joint region, a soften strut‐and‐tie model is used. Analytically obtained strengths based on the failure criteria of different components of the specimens have been first validated with experimental results and then used to determine the strength of the specimens. The investigation could indicate even the mode of failure at local level. It is utmost important to mention here that even the ductile specimens dissipate most of the energy through the development of damage in the joint region, which is neither desirable nor safe for the stability of whole structure. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of steel mechanical properties on EBF seismic behaviour

Among the resisting systems suitable for the design of ductile steel structures, Eurocode 8 proposes MRFs and EBFs. The formers are considered more efficient in terms of ductility, but they suffer a strong weakness in the lateral stiffness, with following cumbersome design procedures to avoid excessive lateral displacements maintaining a quite high ductile behaviour under seismic actions. Often, the design process leads to not optimized structural members, oversized with respect to the minimum seismic requirements due to lateral deformation limitations. EBFs combine high lateral stiffness, due to bracing elements, and high dissipative capacities, provided by the plastic hinges developed in links. Eurocode 8 proposes a design procedure for EBF structures in which iterative checks are required to design links with a defined level resistance dependent on all the other links’ strength. The present paper investigates the seismic behaviour of EBFs using Incremental Dynamic Analyses (IDA) to explore their mechanical response under increasing seismic action. IDAs are executed considering the influence of variability of steel mechanical properties on the behaviour of EBFs, using seven artificial accelerograms according to Eurocode 8. The aims of IDAs are the probabilistic assessment of the response of the system with respect to the variability of the material properties, the analysis of structural safety and the ability of the structures to internally redistribute plastic phenomena during the earthquake. Structural safety conditions will be defined according to a multi-level performance approach. The paper presents also some final suggestions for possible improvements and design simplifications.     

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

The 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.     

Additional seismic inelastic deformation caused by structural asymmetry

Using a single mass monosymmetric model, this paper examines the additional seismic inelastic deformations and displacement caused by structural asymmetry of the model. Stiffness eccentricity and resistance eccentricity are used as measures of asymmetry in the elastic and inelastic range respectively. Seven ways of specifying strength distribution among resisting elements are considered, including code provisions from Canada, Mexico, New Zealand and the United States. These specifications are related t o the model resistance eccentricity. It is shown that when torsional shears are included in the strength design of the elements, the structure in general will have small resistance eccentricity, even if it has large stiffness eccentricity in the elastic range. For structures which are designed with allowance for torsional shears, the ductility demands on the elements are similar to those when the structure is symmetrical. However, the edge displacements can be up to three times that if the system is symmetrical. This finding has significant implications in evaluating adequate separation between buildings to avoid the pounding problem during earthquakes.     

An experimental and numerical investigation into the seismic performance of a multi-storey concentrically braced plan irregular structure

In this investigation, the seismic torsional response of a multi-storey concentrically braced frame (CBF) plan irregular structure is evaluated numerically and experimentally through a series of hybrid tests. CBF structures have become popular in seismic design because they are one of the most efficient types of steel structures to resist earthquake loading. However, their response under plan irregular conditions has received little focus mostly in part due to their complex behaviour under seismic loading conditions. The majority of research on the seismic response of plan irregular structures is based purely on numerical investigations. This paper provides much needed experimental investigation of the seismic response of a CBF plan irregular structure with the aim of characterising the response of this class of structure. The effectiveness of the Eurocode 8 torsional effects provision as a method of designing for low levels of mass eccentricity is evaluated. Results indicate that some of the observations made by purely numerical models are valid in that; torsionally stiff structures perform well and the stiff side of the structure is subjected to a greater ductility demand compared to the flexible side of the structure. The Eurocode 8 torsional effects provision is shown to be adequate in terms of ductility and interstorey drift however the structure performs poorly in terms of floor rotation. Importantly, stiffness eccentricity occurs when the provision is applied to the structure when no mass eccentricity exists and results in a significant increase in floor rotations.     

Evaluation of structural walls designed according to Eurocode 8 and SIA 160

For earthquake action the new design provisions of Eurocode 8 are in the process of replacing the European national earthquake codes. The paper treats the design and behaviour of multi-storey structural walls in view of the new provisions. For structural walls the provisions of the Eurocode 8 are compared with those of a national code which it is going to replace. As the national code the current Swiss earthquake standard SIA 160 is chosen. Basic design rules of both codes are introduced and compared by means of examples comprising buildings which are regular in plan and elevation and which use structural walls for lateral resistance. The height of the buildings is varied from a from four to eight storeys. In the example, both the SIA and the Eurocode design provisions are based on the static equivalent force method, and a triangular distribution of the lateral force. However, most other design provisions differ between the two codes. The structures designed are modelled numerically and subjected to non-linear time-history analysis. At first, both the SIA and Eurocode designed structures are subjected to ground motions compatible to the design spectra in the respective codes. Then all structures are subjected to a recorded ground motion. The results are discussed in view of assumptions made at the design phase. Conclusions and recommendations are provided. © 1998 John Wiley & Sons, Ltd.     

Torsional response of nonductile structures with soft‐first‐storey

In this paper, torsional response of nonductile structures with soft‐first‐storey subjected to bidirectional ground motions is studied using a simplified two‐storey model with two‐way eccentricities. The stiffness ratio of second storey to first storey is varied to create different levels of soft‐first‐storey effect, while the stiffness eccentricity is varied to create torsional effects. Different overstrength ratios are used in the simplified models to study the response of structure with different structural capacity. Hysteretic model with strength deterioration and stiffness degradation properties is used to capture the deterioration of element stiffness and strength. Ductility capacity of 2.0 is used as the models are for nonductile structures. In general, displacement amplification of irregular model with respect to regular model increases as stiffness ratio increases, while no consistent trend of changes in displacement amplification is found with increase in stiffness eccentricity. It is found that the displacement amplification due to only soft‐first‐storey effect can be conservatively taken as 1.5. Coupling of torsional and soft‐first‐storey effects is more significant in affecting the displacement amplification of elements at flexible side. The trend of changes in displacement amplification of elastic system is similar to that of inelastic system. The displacement amplification of elements at the flexible side is larger than that at the stiff side. The elements at the flexible side in the direction of shorter uncoupled lateral period have larger displacement response than those in the orthogonal direction. Ductility demand–capacity curves subsequently constructed can be used to approximately assess the seismic performance of existing structures and as guidelines for designing structures in Singapore to withstand the maximum credible earthquake considering the coupling of torsional and soft‐first‐storey effects. Copyright © 2014 John Wiley & Sons, Ltd.     

Influence of structural parameters on dynamic characteristics and wind-induced buffeting responses of a super-long-span cable-stayed bridge

A 3D finite element (FE) model for the Sutong cable-stayed bridge (SCB) is established based on ANSYS. The dynamic characteristics of the bridge are analyzed using a subspace iteration method. Based on recorded wind data, the measured spectra expression is presented using the nonlinear least-squares regression method. Turbulent winds at the bridge site are simulated based on the spectral representation method and the FFT technique. The influence of some key structural parameters and measures on the dynamic characteristics of the bridge are investigated. These parameters include dead load intensity, as well as vertical, lateral and torsional stiffness of the steel box girder. In addition, the influence of elastic stiffness of the connection device employed between the towers and the girder on the vibration mode of the steel box girder is investigated. The analysis shows that all of the vertical, lateral and torsional buffeting displacement responses reduce gradually as the dead load intensity increases. The dynamic characteristics and the structural buffeting displacement response of the SCB are only slightly affected by the vertical and torsional stiffness of the steel box girder, and the lateral and torsional buffeting displacement responses reduce gradually as the lateral stiffness increases. These results provide a reference for dynamic analysis and design of super-long-span cable-stayed bridges.     

Accidental torsion in buildings due to stiffness uncertainty

Discrepancies between the computed and actual values of the structural element stiffness imply that a building with nominally symmetric plan is actually asymmetric to some unknown degree and will undergo torsional vibration when subjected to purely translational ground motion. Such accidental torsion leads to increase in structural element deformations which is shown to be essentially insensitive to the uncoupled lateral vibration period of the system but is affected strongly by the ratio of uncoupled lateral and torsional vibration periods. The structural deformations increase, in the mean, by at most 10 and 5 per cent for R/C and steel buildings, respectively, and by much smaller amounts for a wide range of system parameters. The increase in structural deformations due to stiffness uncertainty is shown to be much smaller than implied by the accidental torsional provisions in the Uniform Building Code and most other building codes.     

On the design and seismic response of RC frame buildings designed with Eurocode 8

Performance-Based Seismic Design is now widely recognized as the pre-eminent seismic design and assessment methodology for building structures. In recognition of this, seismic codes may require that buildings achieve multiple performance objectives such as withstanding moderate, yet frequently occurring earthquakes with minimal structural and non-structural damage, while withstanding severe, but rare earthquakes without collapse and loss of life. These objectives are presumed to be satisfied by some codes if the force-based design procedures are followed. This paper investigates the efficacy of the Eurocode 8 force-based design provisions with respect to RC frame building design and expected seismic performance. Four, eight, and 16-storey moment frame buildings were designed and analyzed using the code modal response spectrum analysis provisions. Non-linear time-history analyses were subsequently performed to determine the simulated seismic response of the structures and to validate the Eurocode 8 force-based designs. The results indicate the design of flexural members in medium-to-long period structures is not significantly influenced by the choice of effective member stiffness; however, calculated interstorey drift demands are significantly affected. This finding was primarily attributed to the code’s enforcement of a minimum spectral ordinate on the design spectrum. Furthermore, design storey forces and interstorey drift demand estimates (and therefore damage), obtained by application of the code force-based design procedure varied substantially from those found through non-linear time-history analysis. Overall, the results suggest that though the Eurocode 8 may yield life-safe designs, the seismic performance of frame buildings of the same type and ductility class can be highly non-uniform.     

Inelastic seismic response of one-way plan-asymmetric systems under bi-directional ground motions

The static design requirements of some seismic codes, such as the Eurocode 8 and—in most cases—the Uniform Building Code, to allow for the effects of earthquake excitation acting in a direction other than the principal axes of the structure do not apply to one-way asymmetric systems. Therefore, with some exceptions, no specific provisions are considered for such systems to cover effects of structural asymmetry on the behaviour of elements located along the symmetric system direction. Aimed towards fulfilling this need, in this paper, a wide parametric study of the inelastic response of one-way asymmetric systems designed according to Uniform Building Code is carried out, considering two-component earthquake excitations. The analyses show that the maximum ductility demands on elements aligned along the asymmetric system direction are very close to, and even lower than, those obtained for symmetric reference systems. Conversely, the symmetric direction elements undergo significantly larger inelasticity than if they were located in symmetric reference systems. Subsequently, the overstrength needed by the symmetric direction elements to prevent such additional ductility demands for several stiffness and plan configurations is quantified. It is concluded that one-way asymmetry should be considered by seismic codes as an intrinsic system property, thus implying that specific provisions should be included for designing elements located along the symmetric system direction, in addition to those currently subscribed to design the asymmetric direction elements. © 1998 John Wiley & Sons, Ltd.     

Cyclic testing of a single bay reinforced concrete frames with various types of masonry infill

In this paper, a contribution of various types of masonry infill to the behaviour of reinforced concrete frames under lateral loads is presented. As a part of the bigger project, ten one‐bay, one‐storey reinforced concrete frames were designed according to the EC8, built in a scale 1:2.5, infilled with masonry and tested under constant vertical and cyclic lateral load. The masonry wall had various strength properties, namely, high strength hollow clay brick blocks, medium strength hollow clay brick blocks and low strength lightweight autoclaved aerated concrete blocks. There were no additional shear connectors between the masonry and frame. The results showed that the composite ‘framed wall’ structure had much higher stiffness, damping and initial strength than the bare frame structure. Masonry infill filled in the load capacity gap from very low (0.05%) to drifts when the frame took over (0.75%). The structures behaved as linear monolithic elements to drifts of 0.1%, reached the maximum lateral capacities at drift of 0.3%, maintained it to drifts of 0.75% and after that their behaviour depended on the frame. Masonry infill had severe damage at drift levels of about 0.75% but contributed to the overall system resistance to drifts of about 1%. At that drift level, the frame had only minor damage and was tested to drifts of about 2% without any loss of capacity. Improvement of the ‘infill provisions’ in the codes could be sought by taking into account the contribution of a common masonry that reduces expected damages by lowering the drift levels. Copyright © 2012 John Wiley & Sons, Ltd.