Inelastic response of RC frame buildings with seismic isolation

A comprehensive parametric study on the inelastic seismic response of seismically isolated RC frame buildings, designed for gravity loads only, is presented. Four building prototypes, with 23 m × 10 m floor plan dimensions and number of storeys ranging from 2 to 8, are considered. All the buildings present internal resistant frames in one direction only, identified as the strong direction of the building. In the orthogonal weak direction, the buildings present outer resistant frames only, with infilled masonry panels. This structural configuration is typical of many existing RC buildings, realized in Italy and other European countries in the 60s and 70s. The parametric study is based on the results of extensive nonlinear response‐time history analyses of 2‐DOF systems, using a set of seven artificial and natural seismic ground motions. In the parametric study, buildings with strength ratio (F_y/W) ranging from 0.03 to 0.15 and post‐yield stiffness ratio ranging from 0% to 6% are examined. Three different types of isolation systems are considered, that is, high damping rubber bearings, lead rubber bearings and friction pendulum bearings. The isolation systems have been designed accepting the occurrence of plastic hinges in the superstructure during the design earthquake. The nonlinear response‐time history analyses results show that structures with seismic isolation experience fewer inelastic cycles compared with fixed‐base structures. As a consequence, although limited plastic deformations can be accepted, the collapse limit state of seismically isolated structures should be based on the lateral capacity of the superstructure without significant reliance on its inherent hysteretic damping or ductility capacity. Copyright © 2012 John Wiley & Sons, Ltd.     

Inelastic torsion of multistorey buildings under earthquake excitations

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.     

一类多层偏心结构的地震反应研究

本文用空间的两向抗侧力体系振动模型对五层结构分别分析了首层偏心,中间层偏心,顶层偏心和均匀偏心等不同偏心情况下的弹性地震反应规律,研究了静力偏心距,结构的基本平动周期,平扭频率比,非激励方向的平动频率等对结构的名义基底剪力和偏心层构件的最大剪力系数的影响。     

Earthquake response of steel-framed multistorey buildings with set-backs

A study is made of the dynamic behaviour of multistorey steel rigid-frame buildings with set-back towers. The effects of set-backs upon the building frequencies and mode shapes are examined. Then the effects of set-backs on seismic response are investigated by analysing the response of a series of set-back building frame models to the El Centro ground motion. Finally, the computed responses to the El Centro earthquake are compared with some code provisions dealing with the seismic design of set-back buildings. The conclusions derived from the study include the following:

• 1. The higher modes of vibration of a set-back building can make a very substantial contribution to its total seismic response; this contribution increases with the slenderness of the tower.
• 2. Some of the important response parameters for the tower portion of a set-back building are substantially larger than for a related uniform building.
• 3. For very slender towers, the transition region between the tower and the base may be subjected to very large storey shears.

     

Yielding seismic response of code-designed single-storey asymmetric structures

A study on the seismic performance of asymmetric structures with non-linear behaviour and random properties is presented. The structural response of single-storey models, designed using different code criteria is studied using both a deterministic and a probabilistic approach. The worst structural behaviour, in terms of ductility demands, is obtained for symmetric models considering uncertain properties. It is shown that an arbitrary increase of the total lateral strength of the structures does not lead to an increment of the structural safety proportional to the total lateral strength increase, implying that an expensive structure is not always the safest. © 1998 John Wiley & Sons, Ltd.     

Estimation of inelastic deformation demands in multistorey RC frame buildings

Estimation of peak inelastic deformation demands is a key component of any displacement-based procedure for earthquake-resistant design of new structures or for seismic evaluation of existing structures. On the basis of the results of over a thousand non-linear dynamic analyses, rules are developed for the estimation of mean and upper-characteristic peak inelastic interstorey drifts and member chord rotations in multistorey RC frame buildings, either bare or infilled in all storeys but the first. For bare frame structures, mean inelastic deformation demands can be estimated from a linear, equivalent static, or preferably multimodal response spectrum analysis with 5 per cent damping and with the RC members considered with their secant stiffness at yielding. 95 per cent characteristic values can be estimated as multiples of the mean deformations. For open-first-storey buildings, the linear analysis can be equivalent static, with the infills modelled as rigid bidiagonal struts and all RC members considered with their secant stiffness to yielding. Copyright © 1999 John Wiley & Sons, Ltd.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

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.     

Seismic response of nonstructural components attached on multistorey buildings

The maintenance of integrity and functionality of nonstructural components during earthquake excitations is of paramount importance since mechanical failure of those systems can have dramatic consequences in terms of property damage and life safety of the buildings' occupants. This paper explores the dynamic response of nonstructural elements attached on multistory buildings with well‐established floor diaphragm action. Depending on the type of support conditions, seismic response of nonstructural components may be controlled either by acceleration or displacement: Nonstructural components that are subjected to uniform support excitation are controlled primarily by the absolute spectral acceleration developing at their point of attachment on the supporting building. On the contrary, seismic response of multiply supported nonstructural components depends primarily on the relative displacements between successive support points that are imposed by the supporting building during lateral sway. These findings are illustrated from the analytical formulation and its solution through time history analysis of the governing dynamic equation of motion of the primary and secondary components of a system modeled using finite elements. The model encompasses the assembly of a multistory building along with a multiply supported gas pipeline network. It is shown that the dependence of the seismic response of nonstructural components may be linked to the deformed shape of the supporting building at the state of its maximum lateral roof displacement, thereby enabling the definition of design procedures for these systems. Copyright © 2014 John Wiley & Sons, Ltd.     

Damage response of multistorey r/c buildings with different structural systems subjected to seismic motion of arbitrary orientation

In the present study the combined influence of seismic orientation and a number of parameters characterizing the structural system of Reinforced Concrete (R/C) buildings on the level of expected damages are examined. For the purposes of the above investigation eight medium‐rise buildings are designed on the basis of the current seismic codes. The structural characteristics examined are the ratio of the base shear received by the structural walls, the ratio of horizontal stiffness in two orthogonal directions and the structural eccentricity. Then, the buildings are analyzed by nonlinear time response analysis using 100 bidirectional earthquake ground motions. The two horizontal accelerograms of each ground motion are applied along horizontal orthogonal axes, forming 72 different angles with the structural axes. The structural damage is expressed in terms of the Park and Ang damage index. The results of the analyses revealed that the damage level of the buildings is strongly affected by the incident angle of the ground motion. The extent at which the orientation of the seismic records influences the damage response depends on the structural system and the distance of the record to the fault rupture. As a consequence, the common practice of applying the earthquake records along the structural axes can lead to significant underestimation of structural damage. Also, it was shown that the structural eccentricity can significantly differentiate the seismic damage level, as well as the impact of the earthquake orientation on the structural damage. Copyright © 2015 John Wiley & Sons, Ltd.     

Earthquake response analysis of multistorey buildings including foundation interaction

An efficient method, based on the Ritz concept, for dynamic analysis of response of multistorey buildings including foundation interaction to earthquake ground motion is presented. The system considered is a shear building on a rigid circular disc footing attached to the surface of a linearly elastic halfspace. In this method, the structural displacements are transformed to normal modes of vibration of the building on a rigid foundation. The analysis procedure is developed and numerical results are presented to demonstrate that excellent results can be obtained by considering only the first few modes of vibration. As the number of unknowns are reduced by transforming to generalized co-ordinates, the method presented is much more efficient than direct methods.     

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.     

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 simple eccentric structures

The maximum ductility demand and the edge displacement of a simple single mass eccentric model is evaluated when the system is subjected to ground motions represented by the El Centro 1940 and Taft 1952 earthquake records. The resisting elements are taken to be bilinear hysteretic. It is found that the ductility demand depends to a great extent on the energy content of the ground motions, particularly in the period range beyond the elastic period of the system. Unlike elastic response, the coincidence of uncoupled torsional and lateral frequencies does not lead to exceptionally high inelastic response. An increase by a factor of two in ductility demand is not uncommon for a system with large eccentricity as compared to a symmetrical system. Therefore, system eccentricity has a larger effect on ductility demand than earlier studies indicated. Using Clough's model to allow for stiffness degradation effect, results are found to be within 20 per cent of those calculated based on the bilinear hysteretic model.     

规则钢筋混凝土异形柱框架结构的抗震性能研究

本文按现行规范及技术规程设计了设防烈度为8度的一个规则的钢筋混凝土异形柱框架,并进行了单向水平地震作用下的空间三维非线性地震反应分析,考查了异形柱框架结构在设防和罕遇地震水准下的整体抗震性能,对结构能否达到抗震设防目标进行了初步评价。结果表明,8度区按规范设计的结构在设防烈度及罕遇烈度地震作用下基本能够达到预期的抗震设防目标。     

Simplified seismic sidesway collapse analysis of frame buildings

This paper presents the development and assessment of a simplified procedure for estimating the seismic sidesway collapse margin ratio of building structures. The proposed procedure is based on the development of a robust database of seismic peak displacement responses of nonlinear single‐degree‐of‐freedom systems for various seismic intensities and uses nonlinear static (pushover) analysis without the need for nonlinear time history dynamic analysis. The proposed simplified procedure is assessed by comparing its collapse capacity predictions on 72 different building structures with those obtained by nonlinear incremental dynamic analyses. The proposed simplified procedure offers a simple, yet efficient, computational/analytical tool that is capable of predicting collapse capacities with acceptable accuracy for a wide variety of frame building structures. Copyright © 2013 John Wiley & Sons, Ltd.     

Analytical solution for frequency response of equipment in laterally loaded multistorey buildings

An analytical and closed-form frequency response of equipment mounted on multistorey buildings subjected to horizontal ground motion is proposed. In this study, the dynamics of the equipment and the building is expressed as a state-flow graph model, in which the interaction effect between the equipment and the building is considered. Based on the graph model, the analytical results for the frequency response of the acceleration of the equipment and the internal force in the support are derived. One of the advantages of this method is that the closed-form solutions of the frequency response expressed by polynomial form will be easily examined by analytical and numerical computations without complex operation. Moreover, the dynamic of the primary and secondary systems and their dynamic interaction are expressed separately in the derived formula. Thus most of the items in the formula need not be computed repeatedly for different supports of the equipment in design. Copyright © 1999 John Wiley & Sons, Ltd.     

Influence of earthquake direction on the seismic response of irregular plan RC frame buildings

The nonlinear response of structures is usually evaluated by considering two accelerograms acting simultaneously along the orthogonal directions. In this study, the infl uence of the earthquake direction on the seismic response of building structures is examined. Three multi-story RC buildings, representing a very common structural typology in Italy, are used as case studies for the evaluation. They are, respectively, a rectangular plan shape, an L plan shape and a rectangular plan shape with courtyard buildings. Nonlinear static and dynamic analyses are performed by considering different seismic levels, characterized by peak ground acceleration on stiff soil equal to 0.35 g, 0.25 g and 0.15 g. Nonlinear dynamic analyses are carried out by considering twelve different earthquake directions, and rotating the direction of both the orthogonal components by 30° for each analysis(from 0° to 330°). The survey is carried out on the L plan shape structure. The results show that the angle of the seismic input motion signifi cantly infl uences the response of RC structures; the critical seismic angle, i.e., the incidence angle that produces the maximum demand, provides an increase of up to 37% in terms of both roof displacements and plastic hinge rotations.     

高层钢框架-支撑结构二阶非线性随机地震响应分析

针对常用的高层钢框架－支撑结构，考虑材料非线性和几何非线性，建立了框架部分、支撑部分的二阶动力分析模型。用等效线性方法对结构进行非线性随机地震响应分析，结合工程算例，论述不同场地土、不同层数、不同支撑情况下，二阶效应对结构地震响应统计量的影响。     

底层框架砌体房屋抗震性能分析

底层框架多层砌体房屋为上刚下柔的结构体系，因此这类房屋对抗震性能提出更高的要求，本文从结构体系的强度、刚度和延性3方面分析了增强其抗震能力的方法。