Response spectrum techniques for three-component earthquake design

An evaluation is made of response spectrum techniques as applied to seismic analysis and design of steel template offshore platforms. Such structures are designed as braced space frames for several loading conditions, including the simultaneous action of three earthquake components. Base shears as well as gross forces and combined stresses in members of three different platforms are computed for 30 real, three-component earthquakes and response spectrum predictions, obtained by several modal-spatial combination methods, are compared to time history solutions. Results are presented in the form of error statistics. The three approximations examined are: (a) combination of modes for one component input, (b) combination of the three partial responses to obtain estimates of total response and (c) combination of gross forces to derive maximum design stresses at a section. Attention is focused on corner piles because these are among the most heavily penalized members by three-component excitations. It is shown that commonly used spatial combination rules may underestimate gross forces in design controlling corner members by 15–30 per cent on the average. This is attributed to correlations between motion components that create additive effects along certain directions. Typical estimates of combined stresses, however, are found to be slightly conservative.     

Free vibration of asymmetric shear wall-frame buildings

The Galerkin method of weighted residuals is used to determine the frequencies and associated mode shapes of asymmetric shear wall-frame structures. The governing equations are formulated using the continuum approach by idealizing the structure as a shear-flexure beam. Varying properties along the height of the building are considered. The effect of translational, rocking and torsional flexibilities of the foundation on the natural frequencies is also investigated. The method presented herein utilizes polynomial and transcendental displacement functions, and is found to be simple, versatile and efficient.     

Seismic code analysis of multi-storey asymmetric buildings

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.     

Robust control techniques for buildings under earthquake excitation

Robust control techniques are applied to civil engineering structures subjected to earthquake excitation. Full-state feedback and observer-based control laws are used to reduce the response of the building due to earthquake ground motion. Effects of actuator dynamics and a method to incorporate these dynamics into the overall design are also presented. The effectiveness of the control method is demonstrated by simulation results.     

Response spectrum analysis for floor acceleration

The peak floor acceleration (PFA) is a critical parameter influencing the performance of non‐structural elements in buildings. This paper develops a response spectrum analysis method based on the complete quadratic combination (CQC) rule to estimate the PFA. The method accounts for the rigid contribution of truncated higher modes and the cross‐correlations between all pairs of modes. The approximation is introduced in the time domain and then formulated in the frequency domain by CQC. Application of the method to a continuous cantilever beam idealizing a building with shear walls is presented and compared with alternative formulations. The proposed method is able to provide a consistent estimation of the PFA along the entire structure, not only where the PFA is principally influenced by the first few flexible modes but also where the PFA is mainly related to the rigid response of the structure, for example, near its base. Copyright © 2015 John Wiley & Sons, Ltd.     

Comparison of nonlinear static methods for the assessment of asymmetric buildings

Traditional nonlinear static methods, e.g. the original version of the N2 method implemented in Eurocode 8, are not always effective in the assessment of asymmetric structures because of the errors committed in the evaluation of the torsional response. To overcome this shortcoming, two methods have recently been suggested by Kreslin and Fajfar (Bull Earthquake Eng 10(2):695–715, 2012) and Bosco et al. (Earthq Eng Struct Dyn 41:1751–1773, 2012). In particular, the method proposed by Kreslin and Fajfar adjusts the results of the nonlinear static analysis by means of those of a standard modal response spectrum analysis. In the method proposed by Bosco et al., the researchers suggested the use of two nonlinear static analyses characterized by lateral forces applied to different points of the deck. In this paper, the two improved nonlinear static methods and the original N2 method are applied to predict the maximum dynamic response of single- and multi-storey systems subjected to artificial and recorded accelerograms. The results highlight that the improved nonlinear static methods provide estimates which are more accurate than those of the original N2 method. Further, the comparison of the results identifies the range of the structural properties within which the original N2 method is still reliable and the range within which one of the two improved methods should be preferred.     

A generalized continuum method for dynamic analysis of asymmetric tall buildings

The paper presents a continuum method for dynamic analysis of asymmetric tall buildings with uniform cross-section in which the horizontal stiffness is provided by shear walls and columns of arbitrary shape and layout, coupled by horizontal beams. The equations of motions are formulated in variational terms, including axial strain energy. Numerical solutions, obtained by using finite time differences and infinite polynomials, are presented for the response of a twenty-storey building with six shear walls to an impact load and earthquake accelerations. It is shown that omission of the axial deformations results in a substantially distorted pattern of behaviour, some of its effects being:

• 1 Overestimation of the bending stiffness of the coupled shear walls, with corresponding changes in their stiffness ratios.
• 2 Underestimation of the periods of the principal modes, with a corresponding change in the dynamic response.
• 3 Distortion of the magnitude, form, time of onset and coupling of the maximum displacements.
• 4 Pronounced change in the shear force and moment diagrams for the shear walls, the beams and the building as a whole.

     

Approximate analysis methods for asymmetric plan base‐isolated buildings

An approximate method for linear analysis of asymmetric‐plan, multistorey buildings is specialized for a single‐storey, base‐isolated structure. To find the mode shapes of the torsionally coupled system, the Rayleigh–Ritz procedure is applied using the torsionally uncoupled modes as Ritz vectors. This approach reduces to analysis of two single‐storey systems, each with vibration properties and eccentricities (labelled ‘effective eccentricities’) similar to corresponding properties of the isolation system or the fixed‐base structure. With certain assumptions, the vibration properties of the coupled system can be expressed explicitly in terms of these single‐storey system properties. Three different methods are developed: the first is a direct application of the Rayleigh–Ritz procedure; the second and third use simplifications for the effective eccentricities, assuming a relatively stiff superstructure. The accuracy of these proposed methods and the rigid structure method in determining responses are assessed for a range of system parameters including eccentricity and structure flexibility. For a subset of systems with equal isolation and structural eccentricities, two of the methods are exact and the third is sufficiently accurate; all three are preferred to the rigid structure method. For systems with zero isolation eccentricity, however, all approximate methods considered are inconsistent and should be applied with caution, only to systems with small structural eccentricities or stiff structures. Copyright © 2001 John Wiley & Sons, Ltd.     

Seismic behaviour of asymmetric buildings with supplemental damping

This paper investigates the response of asymmetric‐plan buildings with supplemental viscous damping to harmonic ground motion using modal analysis techniques. It is shown that most modal parameters, except dynamic amplification factors (DAFs), are affected very little by the plan‐wise distribution of supplemental damping in the practical range of system parameters. Plan‐wise distribution of supplemental damping significantly influences the DAFs, which, in turn, influence the modal deformations. These trends are directly related to the apparent modal damping ratios; the first modal damping ratio increases while the second decreases as CSD moves from right to left of the system plan, and their values increase with larger plan‐wise spread of the supplemental damping. The largest reduction in the flexible edge deformation occurs when damping in the first mode is maximized by distributing the supplemental damping such that the damping eccentricity takes on the largest value with algebraic sign opposite to the structural eccentricity. Copyright © 2000 John Wiley & Sons, Ltd.     

Response spectrum method for multi-support seismic excitations

A new response spectrum method is developed for seismic analysis of linear multi-degree-of-freedom, multiply supported structures subjected to spatially varying ground motions. Variations of the ground motion due to wave passage, loss of coherency with distance and variation of local soil conditions are included. The method is based on fundamental principles of random vibration theory and properly accounts for the effects of correlation between the support motions as well as between the modes of vibration of the structure.     

Alternative method to locate centre of rigidity in asymmetric buildings

Response of asymmetric buildup under earthquake excitation often involves lateral vibration coupled with torsional vibration. Floor slab is, in general, assumed as rigid along the in‐plane direction. Building code provisions to account for the torsional effect in static force procedure are based on centre of rigidity or shear centre of the building. A convenient procedure is developed here to locate the centre of rigidity or shear centre, which can be implemented, using any standard building analysis software. The procedure is applicable for orthogonal as well as non‐orthogonal building systems and accounts for all possible definitions of static eccentricity to compute the design response. An irregular building is analysed to illustrate the proposed methodology. Significant variation in member force resultants is observed due to different definitions of static eccentricity. Finally, a mathematical proof is presented to substantiate the applicability of the proposed procedure to a non‐orthogonal building. Copyright © 2006 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.     

Effect of epicentral direction on seismic response of asymmetric buildings

The paper deals with the influence of the epicentral direction on the displacement and stress response of multistorey asymmetric buildings to earthquake horizontal ground motion. A method is given for computing for each plane frame of the complex structure a particular direction of the bidirectional stationary random input for which the horizontal floor displacement of the given frame is maximized. It is shown that this direction can be considered conservative for the corresponding non-stationary process.     

Response of seismically isolated buildings considering poundings

Numerical simulations and parametric studies have been used to investigate the influence of potential poundings of seismically isolated buildings with adjacent structures on the effectiveness of seismic isolation. Poundings are assumed to occur at the isolation level between the seismically isolated building and the surrounding moat wall. After assessing some common force‐based impact models, a variation of the linear viscoelastic impact model is proposed to avoid tensile impact forces during detachment, while enabling the consideration of permanent plastic deformations at the vicinity of the impact. A large number of numerical simulations of seismically isolated buildings with different characteristics have been conducted under six earthquake excitations in order to investigate the influence of various design parameters and conditions on the peak floor accelerations and interstorey deflections during poundings. The numerical simulations demonstrate that poundings may substantially increase floor accelerations, especially t the base floor where impacts occur. Higher modes of vibration are excided during poundings, increasing the interstorey deflections, instead of retaining an almost rigid‐body motion of the superstructure, which is aimed with seismic isolation. Impact stiffness seems to affect significantly the acceleration response at the isolation level, while the displacement response is more insensitive to the variation of the impact stiffness. Finally, the results indicate that providing excessive flexibility at the isolation system to minimize the floor accelerations may lead to a building vulnerable to poundings, if the available seismic gap is limited. Copyright © 2007 John Wiley & Sons, Ltd.     

Response of base-isolated buildings to wind loading

The response of base-isolated buildings to gusting wind is analysed theoretically based on experimental data obtained in a boundary layer wind tunnel. A comparison is made with the response evaluated using existing codes. A special procedure, similar to that of current codes, for computing the alongwind and torsional responses of base-isolated buildings is presented.     

An analytical method for the evaluation of the in-plan irregularity of non-regularly asymmetric buildings

This paper describes a new method for the evaluation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ of uncoupled torsional to lateral frequencies in real multi-storey buildings. The above-mentioned parameters greatly affect the lateral-to-torsional coupling of the response of asymmetric systems and thus are of paramount importance in the assessment of the in-plan irregularity of buildings. The proposed method, which is a generalization of that suggested by Calderoni et al. (Earthq Spectra 18(2):219–231, 2002), allows the calculation of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ from the structural response to arbitrary distributions of forces and torsional couples. The effectiveness of the method is validated on some regularly and non-regularly asymmetric buildings characterised by different in-plan irregularity. The analyses demonstrate that the results of the method are rigorous in the case of regularly asymmetric systems and only slightly depend upon the heightwise distribution of the forces in the case of non-regularly asymmetric systems. Finally, the values of the static eccentricity $e_{s}$ and the ratio $\Omega _{\uptheta } $ resulting from the proposed method are compared to those obtained by means of the procedure suggested by Makarios and Anastassiadis in (Struct Des Tall Spec Build 7(1):33–55, 1998a; Struct Des Tall Spec Build 7(1):57–71, 1998b) .     

平面不规则结构非弹性扭转地震反应研究进展

不规则建筑结构在侧向地震荷载作用下由于质量中心和刚度中心的不重合导致平扭耦联反应的发生,使得结构构件的变形需求分布在结构平面内并不一致,从而产生附加的强度和变形需求。尽管不规则建筑结构在地震作用下的扭转问题一直受到研究学者的关注和研究,并取得了很多显著的成果,但仍然存在着一些争议,有待于继续深入研究。本文从结构的分析模型、影响参数及地震动输入等方面回顾总结了平面不规则建筑结构在地震作用下非弹性扭转的研究进展,结合当前的研究工作指出今后研究的发展方向。     

Evaluation of a multimode pushover procedure for asymmetric in plan buildings under biaxial seismic excitation

In this paper a recently developed multimode pushover procedure for the approximate estimation of structural performance of asymmetric in plan buildings under biaxial seismic excitation is evaluated. Its main idea is that the seismic response of an asymmetric multi-degree-of-freedom system with \(N\) degrees of freedom under biaxial excitation can be related to the responses of \(N\) ‘modal’ equivalent single-degree-of-freedom (E-SDOF) systems under uniaxial excitation. The steps of the proposed methodology are quite similar to those of the well-known modal pushover analysis. However, the establishment of the (E-SDOF) systems is based on a new concept, in order to take into account multidirectional seismic effects. The proposed methodology does not require independent analysis in the two orthogonal directions and therefore the application of simplified superposition rules for the combination of seismic component effects is avoided. After a brief outline of the theoretical background and the application process, an extensive evaluation study is presented, which shows that, in general, the proposed methodology provides a reasonable estimation for the vast majority of the calculated response parameters.     

Response of buildings to near-field pulse-like ground motions

Ground motions affected by directivity focusing at near-field stations contain distinct pulses in acceleration, velocity, and displacement histories. For the same Peak Ground Acceleration (PGA) and duration of shaking, ground motions with directivity pulses can generate much higher base shears, inter-storey drifts, and roof displacements in high-rise buildings as compared to the 1940 El Centro ground motion which does not contain these pulses. Also, the ductility demand can be much higher and the effectiveness of supplemental damping lower for pulse-like ground motions. This paper presents a simple interpretation of the response characteristics of three recorded and one synthetic near-field ground motions. It is seen that for pulse-like ground motions—similar to any other ground motion—the Peak values of Ground Acceleration, Velocity, and Displacement (PGA, PGV and PGD) are the key response parameters. Near-field ground motions with directivity effects tend to have high PGV/PGA ratio, which dramatically influences their response characteristics. Copyright © 1999 John Wiley & Sons, Ltd.     

Experimental verification of torsional response control of asymmetric buildings using MR dampers

This paper proposes a semiactive control system to reduce the coupled lateral and torsional motions in asymmetric buildings subjected to horizontal seismic excitations. Magnetorheological (MR) dampers are applied as semiactive control devices and the control input determination is based on a clipped‐optimal control algorithm which uses absolute acceleration feedback. The performance of this method is studied experimentally using a 2‐story building model with an asymmetric stiffness distribution. An automated system identification methodology is implemented to develop a control‐oriented model which has the natural frequencies observed in the experimental system. The parameters for the MR damper model are identified using experimental data to develop an integrated model of the structure and MR dampers. To demonstrate the performance of this control system on the experimental structure, a shake table is used to reproduce an El Centro 1940 N–S earthquake as well as a random white noise excitation. The responses for the proposed control system are compared to those of passive control cases in which a constant voltage is applied to the MR damper. Copyright © 2003 John Wiley & Sons, Ltd.