SEQUENTIAL STIFFNESS DESIGN FOR SEISMIC DRIFT RANGES OF A SHEAR BUILDING–PILE–SOIL SYSTEM

A shear building supported by a prescribed pile–soil system is subjected to bedrock earthquake input. A new design procedure is presented for generating a sequence of stiffness designs satisfying the constraints on interstorey drifts. The mean peak interstorey drifts of the shear building subjected to a set of spectrum-compatible ground motions at the bedrock are evaluated by a modal combination rule. Tuning of the fundamental natural period of a shear building with a fixed base with that of a shear beam ground results in a non-monotonic sequence of stiffness designs with respect to a ground stiffness parameter and previous approaches cannot be applied to such a problem. This difficulty in finding such a non-monotonic sequence is overcome by utilizing the ground stiffness parameter and the superstructure stiffness parameter alternately in multiple design phases and by developing a new multi-phase perturbation technique. Fundamental characteristics of this sequence of stiffness designs and the effect of ground stiffnesses on the design of the shear building are disclosed. It is further shown that the stiffness contour method is also useful for the design procedure such that a scattering effect in the estimates of ground stiffnesses is taken into account. The usefulness of the proposed procedure of sequential stiffness design and contour line method is demonstrated through several sequential design examples.     

Seismic response analysis of an irregular base isolated building

This paper assesses the reliability of code-compliant linear and nonlinear dynamic analyses for irregular buildings with base isolation system (BIS). Comprehensive analyses are carried out for a case study comprising a large reinforced concrete multi-storey framed hospital with 327 high-damping rubber bearings. Spectral and time history (linear and nonlinear) analyses were performed on the three-dimensional (3D) finite element model (FEM) of the structure; simplified analyses were also conducted on single-degree-of-freedom (SDOF) systems. It is found that, at damageability limit state, the values of maximum interstorey drifts (d/h) computed with spectral analyses on the three-dimensional FEM range between 1/6 and 1/10 of the code limit (d/h = 0.33%); thus more stringent code limits should be required for buildings with BISs. The maximum floor acceleration is reduced by about 70% with respect to the ground acceleration (free field site); the acceleration profile is uniform along the height of the multi-storey frame. Threshold values of floor accelerations to assess the seismic performance of equipments in buildings with BIS are lacking. At ultimate limit state (ULS), spectral analyses provide values of actions and deformations that are less conservative than those derived through time history analyses. To perform reliable dynamic analyses of base isolated buildings it is crucial to select natural earthquake ground motions compliant with the fundamental period of vibration of the structural system. Nevertheless, it is not straightforward to select adequate natural strong motions in the catalogues available world-wide; buildings incorporating BISs possess periods of vibration which are generally higher than 2.0 s. As a result, distant and high-magnitude earthquakes are effective for base isolated buildings; nevertheless, such earthquakes are scarce in the seismic databases. The outcomes of the present study also demonstrate that simplified linear analyses tend to provide estimates of the response quantities, displacements of base isolators and base shear of the superstructure, which can be reliably employed at preliminary design stage. Spectral analysis results of the 3D model tend to match those of the SDOF systems, even for irregular superstructure, provided that modal mass participating ratios are greater than 85–90%. The results of spectral analyses on both SDOF and three-dimensional FEM envelope the outcomes of linear time histories.     

Optimal design of supplemental viscous dampers for linear framed structures

A methodology for the optimal design of supplemental viscous dampers for framed structures is presented. It addresses the problem of minimizing the added damping subject to a constraint on the maximal interstorey angular drift for an ensemble of realistic ground motion records while assuming linear behaviour of the damped structure. The solution is achieved by actually solving an equivalent optimization problem of minimizing the added damping subject to a constraint on a maximal weighted integral on the squared angular drift. The computational effort is appreciably reduced by first using one ‘active’ ground motion record. If the resulting optimal design fails to satisfy the constraints for other ground motions from the original ensemble, additional ground motions (loading conditions) are added one by one to the ‘active’ set until the optimum is reached. An efficient selecting process which is presented herein will usually require one or two records to attain an optimum design. Examples of optimal designs of supplemental dampers are presented for a 2‐storey shear frame and a 10‐storey industrial frame. The 2‐storey shear frame is required to withstand one given ground motion whereas the 10‐storey frame is required to withstand an ensemble of twenty ground motions. The resulting viscously damped structures have envelope values of interstorey drifts equal or less than the target drifts. Copyright © 2005 John Wiley & Sons, Ltd.     

直接基于位移可靠度的抗震设计方法中目标位移代表值的确定

针对20多个现役结构，以基于力的抗震设计方法所求基底剪力与直接基于位移的抗震设计方法所求基底剪力相等为原则，回归给出了直接基于位移的抗震设计中基底剪力的调整系数。在此基础上，通过进一步分析，提出了直接基于位移可靠度的抗震设计中层间目标位移代表值的确定方法。最后，总结给出了直接基于位移可靠度的抗震设计步骤。     

Non-monotonic optimal damper placement via steepest direction search

An efficient and systematic procedure is proposed for finding the optimal damper positioning to minimize the dynamic compliance of a 3-D shear building model. The dynamic compliance is expressed in terms of the transfer function amplitudes of the local interstorey drifts evaluated at the undamped fundamental natural frequency. The dynamic compliance is minimized subject to a constraint on the sum of the damping coefficients of added dampers. Optimality criteria are derived and the optimal damper positioning is determined via an original steepest direction search algorithm. This algorithm enables one to find an optimal damper positioning sequentially for gradually increasing damper capacity levels. A non-monotonic design path with respect to the total damper capacity level often appears in the application of this algorithm. A new augmented algorithm via parameter switching is devised to find this non-monotonic design path. Copyright © 1999 John Wiley & Sons, Ltd.     

A design study of an energy-dissipating cladding system

A design study has been conducted to explore the use of structural cladding panels with energy-dissipating cladding-to-frame connections for seismic-resistant design. The study identifies several issues involved in the modelling and analysis of frames with energy-dissipating cladding-to-frame connections, establishes concepts for design, and provides a preliminary assessment of the force and deformation demands that are likely to be placed on panels and connections. Non-linear dynamic analyses indicate that the clad frames perform well, based on observations about maximum interstorey drifts, maximum plastic hinge rotations in the frames, and maximum ductility demands on the cladding-to-frame connections.     

The role of damping in seismic isolation

In the current code requirements for the design of base isolation systems for buildings located at near-fault sites, the design engineer is faced with very large design displacements for the isolators. To reduce these displacements, supplementary dampers are often prescribed. These dampers reduce displacements, but at the expense of significant increases in interstorey drifts and floor accelerations in the superstructure. An elementary analysis based on a simple model of an isolated structure is used to demonstrate this dilemma. The model is linear and is based on modal analysis, but includes the modal coupling terms caused by high levels of damping in the isolation system. The equations are solved by a method that avoids complex modal analysis. Estimates of the important response quantities are obtained by the response spectrum method. It is shown that as the damping in the isolation system increases, the contribution of the modal coupling terms due to isolator damping in response to the superstructure becomes the dominant term. The isolator displacement and structural base shear may be reduced, but the floor accelerations and interstorey drift are increased. The results show that the use of supplemental dampers in seismic isolation is a misplaced effort and alternative strategies to solve the problem are suggested. Copyright © 1999 John Wiley & Sons, Ltd.     

Seismic drift demands in multi‐storey cross‐laminated timber buildings

This paper investigates the seismic response of multi‐storey cross‐laminated timber (CLT) buildings and its relationship with salient ground‐motion and building characteristics. Attention is given to the effects of earthquake frequency content on the inelastic deformation demands of platform CLT walled structures. The response of a set of 60 CLT buildings of varying number of storeys and panel fragmentation levels representative of a wide range of structural configurations subjected to 1656 real earthquake records is examined. It is shown that, besides salient structural parameters like panel aspect ratio, design behaviour factor, and density of joints, the frequency content of the earthquake action as characterized by its mean period has a paramount importance on the level of nonlinear deformations attained by CLT structures. Moreover, the evolution of drifts as a function of building to ground‐motion periods ratio is different for low‐ and high‐rise buildings. Accordingly, nonlinear regression models are developed for estimating the global and interstorey drifts demands on multi‐storey CLT buildings. Finally, the significance of the results is highlighted with reference to European seismic design procedures and recent assessment proposals.     

Shaking‐table tests on reinforced concrete frames with different isolation systems

The effectiveness of seismic isolation in protecting structural and non‐structural elements from damage has been assessed in an extensive programme of shaking‐table tests, carried out on four identical 1/3.3‐scale, two‐dimensional, reinforced concrete (R/C) frames. Four different isolation systems were considered, namely: (i) rubber‐based, (ii) steel‐based, (iii) shape memory alloy (SMA)‐based and (iv) hybrid, i.e. based on both SMA and steel components, isolation systems. This paper presents a comprehensive overview of the main results of the experimental tests on base‐isolated models, whose structural response is described through: (i) maximum base displacements; (ii) maximum interstorey drifts; (iii) maximum storey accelerations and (iv) maximum storey shear forces. The evolution of the fundamental frequency of vibration of the R/C frame during the tests is also described. The beneficial effects of using base isolation resulted in no or slight damage, under strong earthquakes, to both structural and non‐structural members, as well as to the internal content of the building. The comparison with the experimental results obtained in shaking‐table tests on similar fixed‐base models emphasizes these positive aspects. Finally, advantages and drawbacks related to the use of each isolation system are discussed in the paper. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic response of torsionally coupled base isolated structures

An analytical study of the seismic response of typical base isolated structures mounted on rubber bearings is presented. Isolated buildings are liable to have closely spaced lower modes of vibration with small eccentricity between centres of mass and rigidity. The isolated structure is modelled as a rigid deck with lumped masses supported on axially inextensible elastomeric rubber bearings. This simplified system has three degrees of freedom (dof), two translations and one rotation in the horizontal plane. The Green's functions for the displacement response of the 3 dof system are derived for both undamped and damped cases with small and large eccentricities. The small eccentricity case is taken from a specific isolated building, while the large eccentricity case arises from the 5 per cent accidental eccentricity which is required by various seismic codes. An interaction equation for normalized displacements is established for an idealized flat velocity spectrum or hyperbolic acceleration spectrum. An isolated building on rubber bearings would have its fundamental period fall into this range of a design spectrum. Numerical results for the specific building subjected to the El Centro earthquake of 1940 are presented. Both the time history and the response spectrum modal superposition analysis were performed. In the response spectrum analysis, the Complete Quadratic Combination (CQC) showed superiority over the Square Root of the Sum of Squares (SRSS) in estimating maximum responses. It is concluded that the effect of torsional coupling on the transient response of base isolated structures is insignificant, due to the combined effect of the time lag between the maximum translational and torsional responses and the influence of damping in the isolation system which for elastomeric bearings can be as high as 8 to 10 per cent.     

Dynamic characteristics of shear buildings on laminated rubber bearings

Analytical solutions are derived for the dynamic characteristics of base-isolated shear buildings supported on laminated rubber bearings. The solution process takes into account the combined effects of the superstructure flexibility and the base raft inertia on the dynamic characteristics. A series of parametric studies is carried out and the effects of varying the stiffness and mass of the base-isolation system on the frequencies and mode shapes are identified. Approximate solutions for the fundamental base-isolated frequency and mode shape are obtained, which are suitable for use in the preliminary design of non-rigid base-isolated buildings.     

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.     

一种直接基于位移的结构抗震设计方法

利用我国现行抗震规范,直接根据结构的底层层间目标位移反向求取结构的底层层间屈服剪力;给出了该屈服剪力与结构基底剪力之比的数学表达式,初步分析了影响该比值的主要因素及其影响规律。在此基础上,提出了一种新的直接基于位移的结构抗震设计方法。最后,通过算例分析初步考察了该方法的可行性。     

Effects of structural walls on the elastic–plastic earthquake responses of frame–wall buildings

Effects of structural walls on the elastic–plastic earthquake response of short- to medium-height reinforced concrete buildings were investigated. The analytical model consists of independent lumped mass systems representing walls and frames connected at each floor. The wall structure undergoes flexural as well as shear deformation and fails in shear at relatively small story drifts, the frames deforming only in shear. As a measure of structural damage, the ductility factor responses of frame structures were calculated for different combinations of base shear coefficients for the frames and walls. In buildings with relatively weak frames, the installation of structural walls did not improve the large plastic response of the frames up to the point where the walls were unfailed in shear and the ductility factors of the frame structure were suddenly reduced to a very small number. For relatively strong frames, however, the response displacements decreased gradually as the number of walls increased, whether or not the walls failed. Empirical formulas for the required base shear coefficients of the walls and frames which gave a target ductility factor response also were derived for two particular groups of accelerograms. These equations should be of practical use in designing frame-wall type buildings and in retrofitting damaged buildings. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical efficiency assessment of energy dissipators for seismic protection of buildings

This paper presents a two-dimensional numerical study on the nonlinear seismic response of buildings equipped with two types of energy dissipators: Constant Friction Slip Braces (CFSB) and Adding Damping and Stiffness (ADAS). Three types of reinforced concrete buildings with 3, 7 and 15 storeys, representatives of the short-medium- and long-period ranges, are considered. Dissipators are placed in steel diagonal braces in all the floors. The sliding threshold (or yielding) forces for each mechanism are selected using two different criteria: (i) they are taken as 50, 75 and 100 per cent of those generated by the equivalent static lateral forces recommended by the UBC-91 for a ductile moment resisting frame and (ii) they are constant in the whole building (this constant value is chosen equal to the maximum forces obtained with the previous criterion). The input consists of ten recorded earthquakes (normalized with respect to their Housner intensity) corresponding to medium and stiff local soil conditions. Average values on the ten registers are given for the maximum horizontal displacement, the base shear, the energy dissipated and the interstorey drift. The possibility of failure in some devices has been numerically simulated to assess the robustness of the system. The obtained results show that both devices are useful to reduce the response compared to the bare frame and that CFSB is more efficient than ADAS; for 7- and 15-storey frames the lateral displacement with CFSB is even smaller than the one for the braced frame (rigid connections instead of dissipators). The conclusions are expected to provide simple design guidelines. © 1998 John Wiley & Sons, Ltd.     

Seismic response control of smart sliding isolated buildings using variable stiffness systems: an experimental and numerical study

Effectiveness of a new semiactive independently variable stiffness (SAIVS) device in reducing seismic response of sliding base isolated buildings is evaluated analytically and experimentally. Through analytical and experimental study of force—displacement behaviour of the SAIVS device, it is shown that the device can vary stiffness continuously and smoothly between minimum and maximum stiffness. Passive sliding base isolation systems reduce interstorey drifts and superstructure accelerations, but with increased base displacements, which is undesirable, under large velocity near fault pulse type earthquakes. It is a common practice to incorporate non‐linear passive dampers into the isolation system to reduce bearing displacements. Incorporation of passive dampers, however, may result in increased superstructure accelerations and drifts; while, properly designed passive dampers can be beneficial. A viable alternative is to use semiactive variable stiffness systems, which can vary the period of the sliding base isolated buildings in real time, to simultaneously reduce bearing displacements and superstructure responses further than the passive systems, which deserves investigation. This study investigates the performance of a 1:5 scaled smart sliding base isolated building model equipped with the SAIVS device analytically and experimentally, under near fault earthquakes, by developing a new moving average non‐linear tangential stiffness control algorithm for control of the SAIVS device. The SAIVS device reduces bearing displacements further than the passive cases, while maintaining isolation level forces and superstructure responses at the same level as the passive minimum stiffness case, indicating the significant potential of the SAIVS system. Copyright © 2005 John Wiley & Sons, Ltd.     

The extended consecutive modal pushover procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings under influence of two horizontal components of ground motions

This paper aims to extend the consecutive modal pushover (CMP) procedure for estimating the seismic demands of two-way unsymmetric-plan tall buildings subjected to bi-directional seismic ground motions taking the effects of higher modes and torsion into account. Multi-stage and single-stage pushover analyses are carried out in both X and Y directions. Inelastic seismic responses obtained by multi-stage and single-stage pushover analyses for X and Y directions are combined using the SRSS combination scheme. The final seismic responses are determined by enveloping the combined results of multi-stage and single-stage pushover analyses. To evaluate the accuracy of the proposed procedure, it is applied to two-way unsymmetric-plan tall buildings which include torsionally stiff and torsionally flexible systems. The results derived from the CMP procedure are compared with those from nonlinear response history analysis (NL-RHA), as a benchmark solution. Moreover, the advantages of the proposed procedure are demonstrated by comparing the results derived from the CMP to those from pushover analysis with uniform and fundamental effective mode distributions. The proposed procedure is able to accurately predict amplification or de-amplification of the seismic displacements at the flexible and stiff edges of the two-way unsymmetric-plan tall buildings by considering the effects of higher modes and torsion. The extended CMP procedure can accurately estimate the peak inelastic responses, such as displacements and storey drifts. The CMP procedure features a higher potential in estimating plastic hinge rotations at both flexible and stiff sides of unsymmetric-plan tall buildings under bi-directional seismic excitation when compared to the uniform and fundamental effective mode force distributions.     

Displacement–acceleration control via stiffness–damping collaboration

An approach is presented to stiffness–damping simultaneous optimization for displacement–acceleration simultaneous control. To make a shear building model stiffer, the sum of mean-square interstorey drifts to stationary random excitations is minimized or the mean-square top-floor absolute acceleration is maximized subject to the constraints on total storey stiffness capacity and total damper capacity. Optimality conditions are derived and a two-step optimization method using the optimality conditions is devised. In the first step, the optimal design is found for a specified set of total storey stiffness capacity and total damper capacity. In the second step, a series of optimal designs is found with respect to a varied set of total storey stiffness capacity and total damper capacity. While increase of total stiffness capacity and increase of total damper capacity are both effective in reduction of deformation, only increase of total damper capacity is effective in reduction of acceleration. Acceleration control is carried out in the second step via increase of total damper capacity. It is shown through numerical examples that the proposed method is efficient and reliable. Copyright © 1999 John Wiley & Sons, Ltd.     

Shear building representations of seismically isolated buildings

Seismic isolation, with its capability of reducing floor accelerations and interstory drifts simultaneously, is recognized as an earthquake resistant design method that protects contents of a building along with the building itself. In research studies, superstructures of seismically isolated buildings are commonly modeled as idealized shear buildings. Shear building representation corresponds to an idealized structure where the beams are infinitely stiff in flexure and axially inextensible; columns are axially inextensible; and rigid floors are supported on these columns. Although it is more convenient to model and analyze a shear building, such an idealization may influence the seismic responses of seismically isolated buildings. This study presents a comparison of the seismic performances of seismically isolated buildings with superstructures modeled as shear buildings to those with full three dimensional superstructures. Both linear and nonlinear base isolation systems with different isolation periods and superstructures with different number of stories are considered.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.