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

This 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.     

Analytical predictions of the seismic response of friction damped timber shear walls

A new concept for the earthquake resistant design of timber shear wall structures is proposed. By providing friction devices in the corners of the framing system of the shear wall, its earthquake resistance and damage control potential can be enhanced considerably. During severe earthquake excitations, the friction devices slip and a large portion of the seismic energy input is dissipated by friction rather than by inelastic deformation of the sheathing-to-framing connectors. A simple numerical model is developed and results of inelastic time-history dynamic analyses show the superior performance of the friction damped timber shear walls compared to conventional shear wall systems. The proposed friction devices act both as safety valves by limiting the inertia forces transmitted to the structure, and as structural dampers by dissipating a significant portion of the seismic energy input. The devices can be used in any configuration of the framing system to accommodate architectural or construction requirements. The damping system may also be conveniently incorporated in existing timber shear wall buildings to upgrade significantly their earthquake resistance.     

Improved earthquake resistant design of eccentric steel buildings

Recently, a design modification has been proposed for eccentric, torsionally stiff, braced steel buildings, designed according to the current Eurocodes 3 and 8, that improves noticeably their inelastic response under the action of design level earthquakes. The improvement consists in a more uniform distribution of ductility demands throughout the building. In the present paper, a similar, though differently derived, modification is applied to torsionally flexible eccentric buildings and their response is again evaluated under pairs of design earthquake motions. A substantial improvement of their inelastic response is also observed, similar to what had been obtained for torsionally stiff buildings. The new approach is also tested with torsionally stiff buildings and leads to similarly satisfactory results. Thus it may be recommended for general application.     

The seismic behaviour of cross-braced steel frames

Analytical studies on the inelastic behaviour of concentrically braced steel frames for low-rise buildings are described in this paper. The bracing members which provide energy dissipation were used to provide information on the ductility levels that are likely to occur under differing levels of earthquake excitation. An indication of the relative performance of cross bracing is provided in terms of suitable SM values for use in the seismic provisions of New Zealand loadings code NZS 4203.     

Damaging properties of ground motions and prediction of maximum response of structures based on momentary energy response

Dynamic damaging potential of ground motions must be evaluated by the response behaviour of structures, and it is necessary to indicate what properties of ground motions are most appropriate for evaluation. For that purpose, the behaviour of energy input process and hysteretic energy dissipation are investigated in this study. It is found that the momentary input energy that is an index for the intensity of input energy is related to the characteristics of earthquakes such as cyclic or impulsive, and to the response displacement of structures immediately. On the basis of these results, a procedure is proposed to predict inelastic response displacement of structures by corresponding earthquake input energy to structural dissipated damping and hysteretic energy. In this procedure the earthquake response of structures is recognized as an input and dissipation process of energy, and therefore structural properties and damaging properties of ground motions can be taken into account more generally. Lastly, the studies of the pseudodynamic loading test of reinforced concrete structure specimens subjected to ground motions with different time duration are shown. The purpose of this test is to estimate the damaging properties of ground motions and the accuracy of the proposed prediction procedure. Copyright © 2002 John Wiley & Sons, Ltd.     

An equivalent SDOF system model for estimating the response of R/C building structures with proportional hysteretic dampers subjected to earthquake motions

For the purpose of estimating the earthquake response, particularly the story drift demand, of reinforced concrete (R/C) buildings with proportional hysteretic dampers, an equivalent single‐degree‐of‐freedom (SDOF) system model is proposed. Especially in the inelastic range, the hysteretic behavior of an R/C main frame strongly differs from that of hysteretic dampers due to strength and stiffness degradation in R/C members. Thus, the proposed model, unlike commonly used single‐spring SDOF system models, differentiates the restoring force characteristics of R/C main frame and hysteretic dampers to explicitly take into account the hysteretic behavior of dampers. To confirm the validity of the proposed model, earthquake responses of a series of frame models and their corresponding equivalent SDOF system models were compared. 5‐ and 10‐story frame models were studied as representative of low‐ and mid‐rise building structures, and different mechanical properties of dampers—yield strength and yield deformation—were included to observe their influence on the effectiveness of the proposed model. The results of the analyses demonstrated a good correspondence between estimated story drift demands using the proposed SDOF system model and those of frame models. Moreover, the proposed model: (i) led to better estimates than those given by a single‐spring SDOF system model, (ii) was capable of estimating the input energy demand and (iii) was capable of estimating the total hysteretic energy and the participation of dampers into the total hysteretic energy dissipation, in most cases. Results, therefore, suggest that the proposed model can be useful in structural design practice. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation and suggestions for improvement of seismic design procedures for R/C walls in dual systems

This paper aims to shed some further light on the seismic behaviour and design of reinforced concrete (R/C) walls which form part of dual (frame + wall) structures. The significance of post‐elastic dynamic effects is recognized by most seismic codes in the definition of the design action effects on walls, i.e. bending moments and shear forces. However, the resulting envelopes are not always fully satisfactory, particularly in the case of medium‐to‐high‐rise buildings. The relevant provisions of modern seismic codes are first summarized and their limitations discussed. Then an extensive parametric study is presented which involves typical multi‐storey dual systems that include walls with unequal lengths, designed according to the provisions of Eurocode 8 for two different ductility classes (M and H) and two effective peak ground acceleration levels (0.16 and 0.24g). The walls of these structures are also designed according to other methods, such as those used in New Zealand and Greece. The resulting different designs are then assessed by subjecting the structures to a suite of records from strong ground motions, carrying out inelastic time history analysis, and comparing the results with the design action effects. It is found that for (at least) the design earthquake intensity, the first two modes of vibration suffice for describing the seismic response of the walls. The bending moment envelope, as well as the base shear of each wall, is found to be strongly dependent on the second mode effect. As far as the code‐prescribed design action effects are concerned, only the NZ Code was found to be consistently conservative, whereas this was not always the case with EC8. A new method is then proposed which focuses on quantifying in a simple way the second mode effects in the inelastic response of the walls. This procedure seems to work better than the others evaluated herein. Copyright © 2010 John Wiley & Sons, Ltd.     

Effect of depth of soil stratum on performance of buildings for site-specific earthquakes

Towards formulating guidelines for performance evaluation of buildings to site-specific earthquakes, studies are reported in literature on the effect of various critical parameters. No study is, however, reported on the effect of depth of soil stratum. In this paper, a methodology is proposed and applied for performance evaluation of buildings for site-specific earthquakes including depth of soil stratum as a parameter. The methodology integrates independent procedures meant for performance evaluation of buildings and site-specific seismic analysis. Application of the proposed methodology enables to determine performance point of a building in terms of inelastic displacement and base shear. Numerical application of the methodology is demonstrated using the particulars of Delhi region. Two typical RC buildings (B1 and B2) with significantly different inelastic behaviour, assumed to be located on soil depths ranging from 10 to 200 m are chosen for the application study. Capacity spectra of the buildings are generated from nonlinear static analysis. Studies indicate that for building B1, with elasto-plastic behaviour, the depth of soil stratum strongly influences demand on inelastic displacement compared to that on inelastic base shear. For building B2, with continuously varying inelastic behaviour, the depth of soil stratum is observed to have significant influence on both the inelastic base shear as well as inelastic displacement. Responses of the buildings are compared with that obtained based on design spectrum of Indian seismic code. For both the cases, inelastic displacements as well as inelastic base shears are underestimated by Indian seismic code for certain depths of soil stratum. Proposed methodology enables the calculation of realistic values of inelastic base shear and corresponding displacement of a building for site-specific earthquakes by considering the actual characteristics of soil stratum.     

Implications of design philosophies for seismic response of steel moment frames

During a severe earthquake, steel moment resisting frames are expected to experience significant inelastic deformation in their members and joints. This behaviour is dependent upon several design parameters such as member sizes, frame's overstrength, member deformation capacities and the detailing of components. In this study, the influence of such aspects on the inelastic response of frames is investigated. Inelastic static and dynamic analyses were performed on four frames of different designs for a typical six-storey building. The frames were designed and detailed in accordance with current North American code requirements. The computed response of each frame was compared with the behaviour expected by the codes. Recommendations for a design procedure are suggested for improving the structural performance of low-rise steel frames subjected to strong earthquake excitation.     

Earthquake response analysis of the olive view hospital psychiatric day clinic

The collapse of the Olive View Hospital Psychiatric Day Clinic is studied using three biaxial force-deflection models to represent the columns of the building. These models are: shear collapse, elastic and inelastic. The biaxial models for shear and inelastic behaviour are new developments and are useful for non-linear structural dynamic studies. In the present study, the shear collapse model is intended to represent the actual prototype behaviour. The inelastic model, which is based on a hardening rule of plasticity, is used to study the performance of a hypothetical structure with the same storey shear capacity as the prototype but which exhibits ductile behaviour. The prototype structure had a base storey shear capacity of 25 per cent, and actually failed by shearing of all of the first floor columns. In the present study, the shear collapse model predicted this behaviour even with the El Centro accelerogram as input. This result may have far-reaching significance because many low-rise reinforced concrete buildings which were designed according to recent codes have similar storey shear capacity coefficients and column properties. According to this study, such buildings may collapse even in a moderate earthquake. In the inelastic representation, the structure was found to have a base storey shear capacity of 80 per cent when moment hinging was assumed to occur at the top and bottom of the columns. Even with this high strength capacity, the permanent offset computed from the inelastic model corresponded to a ductility factor of 5 when the Pacoima Dam accelerogram was used as input. On the basis of damage to other structures observed on the site, it seems likely that ground motion of about the Pacoima Dam intensity occurred at Olive View. From this it is concluded that a low-rise ductile frame concrete building, even with this high shear force capacity, may not prove satisfactory for hospital use when subjected to strong ground motion.     

Biaxial effects in modelling earthquake response of R/C structures

Recent studies reveal that R/C structural members subjected to biaxial flexure due to two-dimensional earthquake excitation can deform much more than would be predicted by conventional one-dimensional response analysis. The biaxial flexure may therefore have a significant effect on the dynamic collapse process of structures subjected to intense ground motions. The present paper is intended to develop a new formulation of the two-dimensional restoring force model of R/C columns acted upon by biaxial bending moments, and to discuss the dynamic response properties of R/C structures. The model considered is a two-dimensional extension of various non-linear models for one-dimensional response analysis, including the degrading trilinear stiffness model which is one of the simpler idealizations of the restoring force characteristics of flexural-failure-type R/C structures. The modelling validity is then examined by comparison with experimental data on the biaxial bending behaviour of R/C columns. Calculations are made to study the role of different system properties on the influence of inelastic biaxial bending on the dynamic structural response. It is shown that the inelastic biaxial effect is generally significant and, in some cases, critical in the case of R/C structures with stiffness-degrading properties, while the effect is not so important for the non-degrading inelastic cases.     

改进的基础隔震结构地震作用简化计算方法

在《建筑抗震设计规范》(GB50011-2001)关于隔震结构的简化计算方法中,水平向减震系数的表达式和定义有些不符,假定的隔震结构地震作用分布规律也与实际情况略有出入。本文基于水平向减震系数的定义和实际隔震结构的地震作用分布规律提出了一种改进的隔震结构水平向减震系数、隔震结构总地震作用、隔震结构上部地震作用分布的计算方法,并提出了总水平地震作用减震系数的新概念。本文提出的改进方法具有表达准确、物理意义明确的特点。将本文提出的改进算法计算结果与时程分析计算结果比较,结果显示,改进方法的计算结果与时程分析结果接近,且分布规律一致。     

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

The 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.     

Inelastic response and design criteria of plan-wise asymmetric systems

The 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.     

Seismic performance evaluation of steel arch bridges against major earthquakes. Part 1: dynamic analysis approach

In this study the inelastic behavior of steel arch bridges subjected to strong ground motions from major earthquakes is investigated by dynamic analyses of a typical steel arch bridge using a three‐dimensional (3D) analytical model, since checking seismic performance against severe earthquakes is not usually performed when designing such kinds of bridge. The bridge considered is an upper‐deck steel arch bridge having a reinforced concrete (RC) deck, steel I‐section girders and steel arch ribs. The input ground motions are accelerograms which are modified ground motions based on the records from the 1995 Hyogoken‐Nanbu earthquake. Both the longitudinal and transverse dynamic characteristics of the bridge are studied by investigation of time‐history responses of the main parameters. It is found that seismic responses are small when subjected to the longitudinal excitation, but significantly large under the transverse ground motion due to plasticization formed in some segments such as arch rib ends and side pier bases where axial force levels are very high. Finally, a seismic performance evaluation method based on the response strain index is proposed for such steel bridge structures. Copyright © 2004 John Wiley & Sons, Ltd.     

A preliminary study on seismic design criteria of offshore platforms in Bohai Sea of China

This paper analyzes the seismicity in Bohai Sea,introducing a shape factor K to characterize the seismic risk distribution in sub-regions of the sea. Based on the seismic design ground motions for 46 platforms located in the Bohai Sea,a statistical analysis was performed for different peak ground acceleration (PGA) ratios at two different probability levels. In accordance with the two-stage design method,a scheme of two seismic design levels is proposed,and two seismic design objectives are established respectively for the strength level earthquake and the ductility level earthquake. By analogy with and comparison to the Chinese seismic design code for buildings,it is proposed that the probability level for the strength level earthquake and ductility level earthquake have a return period of 200 and 1000 - 2500 years,respectively. The validity of these proposed values is discussed. Finally,the PGAs corresponding to these two probability levels are calculated for different sub-regions of the Bohai Sea.     

Accidental design eccentricity: Is it important for the inelastic response of buildings to strong earthquakes?

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.     

Kinematic soil-structure interaction effects on maximum inelastic displacement demands of SDOF systems

This paper presents a statistical study of the kinematic soil-foundation-structure interaction effects on the maximum inelastic deformation demands of structures. Discussed here is the inelastic displacement ratio defined as the maximum inelastic displacement demands of structures subjected to foundation input motions divide by those of structures subjected to free-field ground motions. The displacement ratio is computed for a wide period range of elasto-plastic single-degree-of-freedom (SDOF) systems with various levels of lateral strength ratios and with different sizes of foundations. Seventy-two earthquake ground motions recorded on firm soil with average shear wave velocities between 180 m/s and 360 m/s are adopted. The effects of period of vibration, level of lateral yielding strength and dimension of foundations are investigated. The results show that kinematic interaction will reduce the maximum inelastic displacement demands of structures, especially for systems with short periods of vibration, and the larger the foundation size the smaller the maximum inelastic displacement becomes. In addition, the inelastic displacement ratio is nearly not affected by the strength ratio of structures for systems with periods of vibration greater than about 0.3 s and with strength ratios smaller than about 3.0. Expressions obtained from nonlinear regression analyses are also proposed for estimating the effects of kinematic soil-foundation-structure interaction from the maximum deformation demand of the inelastic system subjected to free-field ground motions.     

Probabilistic site-dependent non-linear spectra

This paper presents a probabilistic approach to the estimation of lateral strengths required to provide an adequate control of inelastic deformations in structures during severe earthquake ground motions. In contrast to a deterministic approach, the approach presented herein accounts explicitly for the variability of the response of non-linear systems due to the inherent uncertainties in the intensity and characteristics of the input excitation by considering the probability distribution of maximum inelastic strength demands. This study is based on the computation of non-linear strength demands of single-degree-of-freedom (SDOF) systems experiencing different levels of inelastic deformation when subjected to 124 recorded earthquake ground motions. Using empirical cumulative distribution functions site-dependent probabilistic non-linear spectra were computed for six probabilities of exceedance of different levels of inelastic deformation. It is concluded that the lateral strength required to control displacement ductility demands is significantly affected by the maximum tolerable inelastic deformation, the system's period of vibration, the local site conditions and the level of risk in exceeding the maximum tolerable deformations.