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1.
This paper reviews the various forms of reference model adopted for studies that evaluate inelastic seismic torsional effects and assess their implications for building design. Both qualitative and quantitative comparisons are presented. The importance of selecting an appropriate reference model is in accordance with the above aims is emphasised. It is found that variations in the reference models adopted in analyses of inelastic seismic torsional effects may lead to significant differences in the results obtained and, hence, to the conclusions drawn from such studies. It is demonstrated that accidental torsional effects, as incorporated in code design provisions, result in significant changes to the distribution of element strengths and the inelastic response behaviour of symmetric and generalised torsionally balanced reference models. Such changes should be considered when employing such models to evaluate the ineslatic response of torsionally unbalanced building systems.  相似文献   

2.
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.  相似文献   

3.
This paper develops an optimized procedure for the design of torsionally unbalanced structures subjected to earthquake loading, considering both the serviceability and the ultimate limit states. An optimal design eccentricity expression, in the form of design charts, and an optimal overstrength factor equation, are proposed. Results show that the recommended design procedure can result in nearly equal performance of both the rigid edge and the flexible edge elements. For a wide combination of primary system parameters, the responses of both edge elements are consistently lower than, or in the neighbourhood of, the response of the corresponding torsionally balanced reference model. The proposed procedure retains simplicity and can be easily implemented (with certain limitations) in design practice. It also has the added advantages of requiring the structure to be analysed only once for each limit state in each principal direction (as opposed to twice, in existing code torsional provisions), and results in a significantly lower overstrength factor, compared with the overstrength factors corresponding to the torsional provisions of seismic codes in the United States and Canada. The proposed procedure is also applicable to torsionally unbalanced structures with and without transverse resisting elements. © 1997 John Wiley & Sons, Ltd.  相似文献   

4.
A large number of parameters affect the inelastic response of an eccentric system. The centre of resistance no longer remains constant due to continuous loading and unloading of various elements of the system in and out of the inelastic region. The objective of this study is to develop the concept of strength eccentricity for asymmetrical structures excited well into the inelastic region in the event of a severe earthquake. A single mass monosymmetric three-element system is selected. The torsional flexibility parameter is varied so as to obtain nine eccentric configurations covering the entire spectrum of such systems. These models were subjected to S00E component of the El Centro earthquake of 1940 which is considered to be a very severe earthquake. The concept of effective strength eccentricity is introduced which is defined as strength eccentricity at the point of intersection of ductility ratio curves of REE and FEE. It is proposed to provide additional strength in the elements of a torsionally unbalanced system independent of the design eccentricity. Empirical equations are proposed to account for design eccentricity and additional strength as well as distribution of the design strength. The proposed formulation is compared with the torsional provisions of UBC 1991, NBCC 1990 and NZC 1992. It is concluded that additional ductility demand on the REE and FEE designed based on the proposed formulation is almost nil as compared to that given by the three codes. The NZC and UBC require maximum ductility on the REE. The increase in overall strength of the system is least for the proposed formulation as compared to that given by the three codes. NBCC consistently requires the maximum total strength ratio.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.  相似文献   

8.
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.  相似文献   

9.
This paper addresses some key issues which have been the subject of dispute in recent years in studying the seismic torsional response of asymmetric structures. These issues include the interpretation of the code accidental torsional provision, and the influence of the force reduction factor and of the uncoupled lateral period, on the torsional response of asymmetric structures. The responses of single-storey torsionally unbalanced structural models, designed in accordance with the torsional provisions of seismic building codes in Europe, the United States and Canada, and subjected to seismic ground motions corresponding to both the serviceability and ultimate limit states, are studied analytically. On the basis of a better understanding of the above issues as achieved in this study, the performance of code-designed torsionally unbalanced structures for both limit states is assessed. © 1997 John Wiley & Sons, Ltd.  相似文献   

10.
Using a three element single mass model, this paper presents the ductility demands on the elements of torsionally unbalanced systems when subjected to strong earthquake shaking. Torsionally unbalanced systems based on nine structural configurations are considered, ranging from torsionally stiff systems with the centre of rigidity (CR) centrally located to torsionally flexible systems with CR eccentrically located. The strength of the elements is designed based on the Canadian and New Zealand codes, and the Uniform Building Code (UBC) of the United States. It is shown that all three codes can limit the ductility demands on the elements to that of a similar but torsionally balanced system when the system is torsionally stiff. However, substantial additional ductility demands on the element at the stiff edge of the system exist for torsionally flexible systems when the New Zealand code or UBC is used. The large ductility demand is caused by the low strength of the stiff-edge element permitted by these codes.  相似文献   

11.
Seismic ground motions induce torsional responses in buildings that can be difficult to predict. To compensate for this, most modern building codes require the consideration of accidental torsion when computing design earthquake forces. This study evaluates the influence of ASCE/SEI 7 accidental torsion seismic design requirements on the performance of 230 archetypical buildings that are designed with and without accidental torsion design provisions, taking building collapse capacity as the performance metric. The test case archetypes include a broad range of heights, gravity load levels, and plan configurations. Results show that the ASCE/SEI 7 accidental torsion provisions lead to significant changes in collapse capacity for buildings that are very torsionally flexible or asymmetric. However, only inconsequential changes in collapse capacity are observed in the buildings that are both torsionally stiff and regular in plan. Therefore, the study concludes that accidental torsion provisions are not necessary for seismic design of buildings without excessive torsional flexibility or asymmetry. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

12.
In this paper a probabilistic approach has been adopted to study both the effects of uncertainty in earthquake frequency content and the correlation between earthquake frequency content and ground motion intensity on the response of a single-storey torsionally coupled elastic structure. The earthquake ground motion has been assumed to be a Gaussian, zero mean, stationary random process which is fully characterized by a power spectrum. The ground acceleration power spectrum is idealized as a probabilistic normalized power spectrum computed from actual earthquake records. The advantage of such an idealization is that it enables the effect of the natural frequency as a controlling structural parameter in torsional coupling to be assessed. Comparisons of the dynamic amplifications of eccentricity with those obtained from modern codes of practice and conventional response spectrum analyses have been made. The results of this study have shown that the variation in the frequency content has a significant effect on the response of low frequency structures, while the correlation between the frequency content and the intensity of seismic ground motion is insignificant for the wide range of structures considered. The structure natural frequency has been shown to be an important controlling parameter in the torsionally coupled response of structures subject to seismic loading. The frequency dependence of the dynamic amplification of eccentricity was found not to be reflected in the response spectrum analysis and the torsional provisions of modern building codes.  相似文献   

13.
The inelastic earthquake response of eccentric, multistorey, frame‐type, reinforced concrete buildings is investigated using three‐ and five‐storey models, subjected to a set of 10, two‐component, semi‐artificial motions, generated to match the design spectrum. Buildings designed according to the EC8 as well as the UBC‐97 code were included in the investigation. It is found that contrary to what the simplified one‐storey, typical, shear‐beam models predict, the so‐called ‘flexible’ side frames exhibit higher ductility demands than the ‘stiff’ side frames. The substantial differences in such demands between the two sides suggest a need for reassessment of the pertinent code provisions. This investigation constitutes one of the first attempts to study the problem of inelastic torsion by means of realistic, multistorey inelastic building models. Additional studies with similar or even more refined idealizations will certainly be required to arrive at definite results and recommendations for possible code revisions. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

14.
Presented in this paper is a detailed parametric study of the coupled lateral and torsional response of single-storey building models subjected to earthquake base loadings. The aim is to assess the influence of torsional coupling on the elastic responses of buildings subjected to transient ground motion records, and to make comparisons with current code provisions which make allowance for coupling effects by means of empirical design procedures. The study of building responses to selected earthquake excitations shows that the qualitative effects of the controlling parameters on the maximum translational and torsional responses of the coupled system are similar to those observed in analyses using idealized response spectra to represent the input ground motion. It is also demonstrated that for particular ranges of the key parameters defining the structural system, typical of the properties of many actual buildings, torsional coupling induces significant amplification of earthquake forces. This amplification is shown to be inadequately accounted for in the current design provisions of major building codes. Recommendations for improving existing design practice for asymmetric structures are outlined.  相似文献   

15.
An Erratum has been published for this article in Earthquake Engng. Struct. Dyn. 2004; 33:1429. Based on structural dynamics theory, the modal pushover analysis (MPA) procedure retains the conceptual simplicity of current procedures with invariant force distribution, now common in structural engineering practice. The MPA procedure for estimating seismic demands is extended to unsymmetric‐plan buildings. In the MPA procedure, the seismic demand due to individual terms in the modal expansion of the effective earthquake forces is determined by non‐linear static analysis using the inertia force distribution for each mode, which for unsymmetric buildings includes two lateral forces and torque at each floor level. These ‘modal’ demands due to the first few terms of the modal expansion are then combined by the CQC rule to obtain an estimate of the total seismic demand for inelastic systems. When applied to elastic systems, the MPA procedure is equivalent to standard response spectrum analysis (RSA). The MPA estimates of seismic demand for torsionally‐stiff and torsionally‐flexible unsymmetric systems are shown to be similarly accurate as they are for the symmetric building; however, the results deteriorate for a torsionally‐similarly‐stiff unsymmetric‐plan system and the ground motion considered because (a) elastic modes are strongly coupled, and (b) roof displacement is underestimated by the CQC modal combination rule (which would also limit accuracy of RSA for linearly elastic systems). Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

16.
The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

17.
To deal with earthquake-induced torsion in buildings due to some uncertain factors, difficult to account for directly in design, modern codes have introduced the so-called accidental design eccentricity (ADE). This provision has been based primarily on elastic investigations with special classes of multi-story buildings or with simplified, one-story inelastic models. In the present paper, the effectiveness of this provision is investigated using inelastic models, both of the typical one-story, 3-DOF type, and the more sophisticated MDOF, frame idealizations of the plastic hinge type. One, three and five story, realistic, frame buildings with different natural eccentricities were designed for different ADEs, including those specified by the EC8 and IBC codes. The evaluation is made using mean peak ductility factors of the edge frames as measures of their inelastic response, obtained from dynamic analyses for ten pairs of semi-artificial earthquake motions. The simplified models indicate that the accidental design eccentricity is very effective in reducing ductility demands, especially for very stiff systems. However, this is not confirmed by the more accurate and detailed plastic hinge building models, which show that designs accounting for accidental eccentricity do not exhibit any substantial reduction or better distribution of ductility demands, compared to designs in which accidental eccentricity has been entirely ignored. These findings suggest that the ADE provisions in codes, especially the more complicated ones as in the IBC, should be re-examined, by weighting their importance against the additional computational work they impose on designers. In the cases examined herein this importance can be characterized as marginal. Obviously additional studies are required, to include more building types and earthquake motions, in order to arrive at firm conclusions and recommendations for code modifications.  相似文献   

18.
Static torsional provisions in most seismic codes require that the lateral force at each floor level be applied at some distance from the reference centre at that floor. However, codes do not specify how to determine the locations of these centres. As a result, several different definitions of the reference centres are being used to implement the code analysis. This investigation examined how the results using various reference centres differ and which of these centres would lead to results that are in agreement with those of dynamic analysis. For this purpose three different buildings ranging form torsionally stiff to torsionally flexible were analysed. It was shown that for the class of buildings studied in this investigation that although the locations of the reference centres were quite different, the results were very similar and nearly independent of the reference centre. Comparison of results calculated from static code equivalent lateral force procedures and results from dynamic response spectrum analyses showed that the static code procedures led to design forces very close (flexible wall) or slightly conservative (stiff wall) when compared to the dynamic analysis for the torsionally stiff building. However, the static code procedures significantly underestimated the design forces of the stiff walls and significantly overestimated the design forces of the flexible walls for the torsionally flexible buildings. © 1998 John Wiley & Sons, Ltd.  相似文献   

19.
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.  相似文献   

20.
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.  相似文献   

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