Dynamic behavior of perimeter lateral‐system structures with flexible diaphragms

Building structures are typically designed using the assumption that the floor systems serve as a rigid diaphragm between the vertical elements of the lateral load‐resisting system. However, long‐floor span structures with perimeter lateral load‐resisting systems possess diaphragms which behave quite flexibly. The dynamic behaviour of such structures is dissimilar to the behavior expected of typical structures. This difference can lead to unexpected force and drift patterns. If force levels are sufficiently under‐estimated, inelastic diaphragm behaviour can occur, exacerbating the effects of diaphragm flexibility. Such response may lead to a non‐ductile diaphragm failure or structural instability due to high drift demands in the gravity system. Analytical models were developed which capture the diaphragm flexibility of structures with long‐floor spans and perimeter lateral‐systems. Modal examination and time‐history analyses were performed to determine the effect of diaphragm flexibility and diaphragm inelastic behaviour on the dynamic behaviour of these structures. Copyright © 2001 John Wiley & Sons, Ltd.     

In-plane floor flexibility effects on torsionally unbalanced systems

This paper presents the results of an analytical work addressed to understand the effects of in-plane floor flexibility on torsionally unbalanced (TU) systems subjected to bidirectional firm-soil earthquake records. The study uses a structural system consisting of a linear-elastic diaphragm supported by non-linear frames oriented along two orthogonal directions. The diaphragm is modelled with plane-stress finite elements and frames with stiffness-degrading flexural elements. Results indicate that an increase of in-plane diaphragm flexibility leads to a reduction of frame displacements for systems with initial lateral period of vibration T>0·4 s. For systems with T⩽0·4 s, in-plane floor flexibility can lead to significant frame displacement increments (50 per cent higher). Results show that these variations on displacements decrease for increasing values of both the seismic-force reduction factor and the system initial lateral period. Copyright © 1999 John Wiley & Sons Ltd.     

Evaluation of diaphragm conditions in AAC floor structures with RC beams

Diaphragm action in floor structures is an important aspect that affects both local behaviors of individual members and consequently, the global response of a structure. The diaphragm action of a built structure, therefore needs to be compatible with the assumed diaphragm condition in the design phase to prevent unpredicted overloading of load bearing members in a seismic action. Autoclaved aerated concrete (AAC) is a cost-effective, lightweight and energy efficient material, and its usage as a construction material has rapidly increased in recent decades. However, there is a limited experience regarding the in-plane behavior of the floor structures made of AAC panels in terms of diaphragm action. In this paper, the in-plane response of AAC floors is experimentally investigated and the floor performance of a typical building is analytically investigated according to ASCE 7-16 (ASCE/SEI in Minimum design loads for buildings and other structures, The American Society of Civil Engineers, Reston, 2016). Full-scale experiments carried out through loading AAC floors in lateral directions to the panels, either parallel or perpendicular, provided important information about the damage progress and overall performance of such floors. A number of finite element modeling techniques that are generally used for modeling of AAC floors were examined and then validated through comparisons with test results. Finally, the diaphragm condition of a three-story building made of AAC walls and floor panels was assessed. The results indicated that the AAC floors in the examined building can be idealized as rigid diaphragms according to ASCE 7-16.     

Establishment of performance‐based seismic design factors for precast concrete floor diaphragms

This paper presents an analytical study used to establish design factors for a new seismic design methodology for precast concrete floor diaphragms. The design factors include diaphragm force amplification factors Ψ and diaphragm shear overstrength factors Ω_v. The Ψ factors are applied to the ASCE7‐05 diaphragm design forces to produce diaphragm design strengths aligned to different performance targets. These performance targets are based on diaphragm detailing choices, and include: (i) elastic diaphragm behavior or (ii) limiting inelastic deformation demand on the diaphragm reinforcement (connectors between precast units or reinforcing bars in a topping slab) to within their reliable deformation capacities. The Ω_v factors provide overstrength relative to the diaphragm bending strength for capacity protection against shear failure. The analytical study was performed by conducting nonlinear time history analyses of a simple evaluation structure, of which the dimensions and structural properties were varied. The analytical model used in the study is constructed and calibrated on the basis of extensive physical testing. The analytically obtained values of the diaphragm design factors are presented as functions of the geometric and structural properties of the building. The design factors presented here have been verified through evaluation of a set of realistic precast prototype structures. The diaphragm design methodology is currently in the codification process. Copyright © 2015 John Wiley & Sons, Ltd.     

Analytical models for low-rise buildings with flexible floor diaphragms

The observed behaviour of buildings during earthquakes indicates clearly the importance of the flexibility of floor and roof diaphragms in the response of many structures. This paper presents a new analytical method for the dynamic analysis of some one- and two-storey buildings whose floors may have significant in-plane flexibility. The method begins by treating the floors as bending beams and the walls as shear beams. The equations of motion and the boundary conditions for the floors and the walls are then formulated in one coordinate system and solved exactly to obtain the characteristic equation for the system, which can be solved numerically to obtain the natural frequencies. These, in turn, can be used to determine the mode shapes of the system and the participation factors for earthquake response. Solutions are given for one- and two-storey buildings that resist lateral loads in the transverse direction by two end walls. Perturbation techniques are also applied to simplify further the determination of the fundamental frequency of such single-storey structures. To illustrate the method, a two-storey structure, the Arvin (California) High School Administration Building, damaged in the Kern County earthquake of 1952, has been analysed in its transverse direction. It is seen that the first two modes, dominated by the floor and the roof vibrations, make the largest contributions to the total base shear in the structure.     

Optimum lateral load pattern for seismic design of elastic shear‐buildings incorporating soil–structure interaction effects

Recently, several new optimum loading patterns have been proposed by researchers for fixed‐base systems while their adequacy for soil–structure systems has not been evaluated yet. Through intensive dynamic analyses of multistory shear‐building models with soil–structure interaction subjected to a group of 21 artificial earthquakes adjusted to soft soil design spectrum, the adequacy of these optimum patterns is investigated. It is concluded that using these patterns the structures generally achieve near optimum performance in some range of periods. However, their efficiency reduces as soil flexibility increases especially when soil–structure interaction effects are significant. In the present paper, using the uniform distribution of damage over the height of structures, as the criterion, an optimization algorithm for seismic design of elastic soil–structure systems is developed. The effects of fundamental period, number of stories, earthquake excitation, soil flexibility, building aspect ratio, damping ratio and damping model on optimum distribution pattern are investigated. On the basis of 30,240 optimum load patterns derived from numerical simulations and nonlinear statistical regression analyses, a new lateral load pattern for elastic soil–structure systems is proposed. It is a function of the fundamental period of the structure, soil flexibility and structural slenderness ratio. It is shown that the seismic performance of such a structure is superior to those designed by code‐compliant or recently proposed patterns by researchers for fixed‐base structures. Using the proposed load pattern in this study, the designed structures experience up to 40% less structural weight as compared with the code‐compliant or optimum patterns developed based on fixed‐base structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Seismic control of flexible rocking structures using inerters

Allowing flexible structures to uplift and rock during earthquakes can significantly reduce the force demands and residual displacements. However, such structures are still susceptible to large deformations and accelerations that can compromise their functionality. In this paper, we examine the dynamic response of elastic rocking oscillators and suggest that their lateral drifts and accelerations can be limited effectively by using inerter devices. To this end, we offer a detailed examination of the effects of structural flexibility on the efficiency of the proposed system. The analytical expressions governing the motion of deformable structures with base uplift are revisited to incorporate the effects of the supplemental rotational inertia. The proposed model is then used to study the structural demands of flexible rocking structures under coherent pulses as well as noncoherent real pulse-like ground motions. Our results show that combining rocking with inerters can be an efficient strategy to control the deformation and acceleration demands in uplifting flexible systems.     

Out‐of‐plane seismic response of vertically spanning URM walls connected to flexible diaphragms

A simplified numerical model was used to investigate the out‐of‐plane seismic response of vertically spanning unreinforced masonry (URM) wall strips. The URM wall strips were assumed to span between two flexible diaphragms and to develop a horizontal crack above the wall mid‐height. Three degrees of freedom were used to accommodate the wall displacement at the crack height and at the diaphragm connections, and the wall dynamic stability was studied. The equations of dynamic motion were obtained using principles of rocking mechanics of rigid bodies, and the formulae were modified to include semi‐rigid wall behaviour. Parametric studies were conducted that included calculation of the wall response for different values of diaphragm stiffness, wall properties, applied overburden, wall geometry and earthquake ground motions. The results of the study suggest that stiffening the horizontal diaphragms of typical low‐rise URM buildings will amplify the out‐of‐plane acceleration demand imposed on the wall and especially on the wall–diaphragm connections. It was found that upper‐storey walls connected to two flexible diaphragms had reduced stability for applied earthquake accelerograms having dominant frequency content that was comparable with the frequency of the diaphragms. It was also found that the applied overburden reduced wall stability by reducing the allowable wall rotations. The results of this study suggest that the existing American Society of Civil Engineers recommendations for assessment of vertically spanning walls overestimate the stability of top‐storey walls in multi‐storey buildings in high‐seismic regions or for walls connected to larger period (less stiff) diaphragms. Copyright © 2015 John Wiley & Sons, Ltd.     

Methodology for practical seismic assessment of unreinforced masonry buildings with historical value

Historical constructions are part of the world heritage, and their survival is an important priority. Comprising mostly unreinforced, load‐bearing masonry, heritage buildings may date anywhere from antiquity to the 19th and early 20th century. Being exposed to the elements over the years, they are in various states of disrepair and material degradation. Based on postearthquake reconnaissance reports, these structures occasionally behave rather poorly, even in moderate seismic events, undergoing catastrophic damage and collapse, whereas retrofitting is governed by international conventions regarding noninvasiveness and reversibility of the intervention. The complexity of their structural systems (continuous structural components, lack of diaphragm action, material brittleness, and variability) challenges the established methods of condition assessment of preretrofitted and postretrofitted heritage constructions. The most advanced state of the art in materials and analysis tools is required, far more complex than with conventional buildings. Thus, an assessment procedure specifically geared to this class of structures is urgently needed, in order to assist engineers in this endeavor. The objective of this paper is the development of a performance‐based assessment framework that is palatable to practitioners and quite accurate in seismic assessment of unreinforced masonry buildings with no diaphragm action. The underlying theoretical background of the method is illustrated with reference to first principles: global demand is obtained from the design earthquake scenario for the region, using empirical estimates for the prevailing translational period of the system; deformation demands are localized using an approximation to the translational 3‐D shape of lateral response, estimated using a uniform gravitational field in the direction of action of the earthquake; acceptance criteria are specified in terms of relative drift ratios, referring to the in‐plane and the out‐of‐plane action of the masonry piers. The quantitative accuracy of the introduced procedure is evaluated through comparison with detailed time‐history dynamic analysis results, using a real life example case study. Qualitative relevance of the results is evaluated through comparison of the location and extent of anticipated damage estimated from the proposed assessment procedure, with reported records of the building damages that occurred during a significant past earthquake event.     

Response analysis of rigid structures rocking on viscoelastic foundation

In this paper the rocking response of slender/rigid structures stepping on a viscoelastic foundation is revisited. The study examines in depth the motion of the system with a non‐linear analysis that complements the linear analysis presented in the past by other investigators. The non‐linear formulation combines the fully non‐linear equations of motion together with the impulse‐momentum equations during impacts. The study shows that the response of the rocking block depends on the size, shape and slenderness of the block, the stiffness and damping of the foundation and the energy loss during impact. The effect of the stiffness and damping of the foundation system along with the influence of the coefficient of restitution during impact is presented in rocking spectra in which the peak values of the response are compared with those of the rigid block rocking on a monolithic base. Various trends of the response are identified. For instance, less slender and smaller blocks have a tendency to separate easier, whereas the smaller the angle of slenderness, the less sensitive the response to the flexibility, damping and coefficient of restitution of the foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

CRITICAL CROSS POWER SPECTRAL DENSITY FUNCTIONS AND THE HIGHEST RESPONSE OF MULTI-SUPPORTED STRUCTURES SUBJECTED TO MULTI-COMPONENT EARTHQUAKE EXCITATIONS

The highest response of multi-supported structures subjected to partially specified multi-component earthquake support motions is considered. The seismic inputs are modelled as incompletely specified vector Gaussian random processes with known autospectral density functions but unknown cross spectral densities and these unknown functions are determined such that the steady state response variance of a given linear system is maximized. The resulting cross power spectral density functions are shown to be dependent on the system properties, autospectra of excitation and the response variable chosen for maximization. It emerges that the highest system response is associated neither with fully correlated support motions, nor with independent motions, but, instead, specific forms of cross power spectral density functions are shown to exist which produce bounds on the response of a given structure. Application of the proposed results is demonstrated by examples on a ground based extended structure, namely, a 1578 m long, three span, suspension cable bridge and a secondary system, namely, an idealized piping structure of a nuclear power plant.     

Earthquake response of structures with partial uplift on winkler foundation

The effects of transient foundation uplift on the earthquake response of flexible structures are investigated. The structural idealization chosen in this study is relatively simple but it incorporates the most important features of foundation uplift. In its fixed base condition the structure itself is idealized as a single-degree-of-freedom system attached to a rigid foundation mat which is flexibly supported. The flexibility and damping of the supporting soil are represented by a Winkler foundation with spring-damper elements distributed over the entire width of the foundation. Based on the response spectra presented for several sets of system parameters, the effects of foundation-mat uplift on the maximum response of structures are identified. The influence of earthquake intensity, structural slenderness ratio, ratio of foundation mass to structural mass, foundation flexibility and p-δ effects on the response of uplifting structures is also investigated.     

不同场地条件下地连墙对地铁车站结构地震动力响应的影响

地铁车站多采用基于地下连续墙(简称：地连墙)的明挖施工方法,施工后地连墙作为永久结构与车站共同受力。在车站结构抗震分析中,考虑到地连墙可能对结构抗震的有利作用,出于安全储备考虑通常忽略地连墙的存在,但地连墙对车站结构地震响应的影响规律和机理仍有待深入研究。以某典型两层三跨地铁车站结构为对象,基于近场波动有限元方法并结合黏弹性人工边界条件,开展有无地连墙情况车站结构地震响应特性对比研究,揭示不同场地条件下地连墙对车站结构地震响应的影响规律,阐明地连墙的影响机理。研究结果表明：地连墙具有减小车站结构总体层间位移效应,有利于侧墙和底层中柱抗震,但同时放大了顶底板与侧墙连接处的弯矩和正应力;地连墙对结构顶层中柱端部及中跨中板板端的内力和正应力的影响与场地条件相关,坚硬和中硬场地条件下具有减小效应,软弱场地下略有增大作用。上述结构响应规律的原因可归结为地连墙增加了结构侧墙刚度,降低了结构整体侧向变形,但限制了侧墙的弯曲变形,导致结构顶底板与侧墙交接处的弯曲变形和内力增大。     

Optimal instrumentation of structures on flexible base for system identification

A criterion previously developed by Heredia-Zavoni and Esteva for selecting optimal sensor locations is used to analyse the optimal instrumentation of structures on soft soils. The stochastic response of a linear structural system on a flexible base is formulated for use of the criterion. The case of MDOF shear systems on flexible base, with uncertain lateral stiffness and subjected to random earthquake ground motions, is studied. The optimal location of accelerometers, the reduction of prior uncertainty on the lateral stiffness, the effects of the base flexibility, the relative influence of translation and rocking of the base, and the influence of recording noise are assessed and discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Out-of-plane shaking table tests of full-scale historic adobe corner walls retrofitted with timber elements

Historic adobe structures pose a high seismic risk mainly because of the poor out-of-plane bending response of their walls that may produce fatalities and significant economic, cultural, and heritage losses. In this paper, we propose a retrofitting technique that increases the wall strength for both in-plane and out-of-plane directions. This technique consists of vertical and horizontal timber elements symmetrically installed on each face of the wall to form a confining wood frame, supplemented with vertical tensors that pre-compress the wall. This study evaluates the performance of this retrofitting technique with a two-set experimental program on full-scale historic adobe walls. On the first set, four specimens were subjected to a static overturning test with boundary conditions representing the confinement effect at both ends by orthogonal walls. On the second set, three full-scale specimens, one unretrofitted and two retrofitted, were subjected to four ground motion records on a shaking table to assess the out-of-plane dynamic behavior of typical corner walls. The unretrofitted specimen collapsed during the second motion (peak ground acceleration [PGA] = 0.39 g), while both retrofitted walls survived all four motions (maximum PGA of 0.75 g) proving the high effectiveness of the proposed retrofitting. The addition of base anchors as a variation of the retrofitting technique significantly reduced the rocking effects and the residual drifts of the system, thus improving its overall seismic performance. Further research is needed to develop guidelines for seismic retrofit of heritage buildings including multistory full-scale tests of specimens with various types of openings and retrofitting strategies that minimize their architectural impact.     

An analytical model of a deformable cantilever structure rocking on a rigid surface: experimental validation

This paper describes an experimental program to examine the dynamic response of deformable cantilevers rocking on a rigid surface. The primary goal of the tests is to verify and validate a dynamic rocking model that describes the behavior of these structures. The benchmark response data was obtained from shaking‐table tests on deformable rocking specimens with different natural vibration frequencies and different aspect ratios excited by analytical pulses and recorded ground motions. The responses computed using the model are found to be in good agreement with the benchmark test results. Widely used impact, restitution and damping assumptions are revisited based on the experiment results and the analytical model findings. Copyright © 2015 John Wiley & Sons, Ltd.     

Test,analysis, and design of ovally-perforated vertically-flexible steel plate shear wall (OVSPW)

A new type of steel plate shear wall (SPSW) with oval-curved architectural openings and vertically flexible horizontal connection elements is proposed. The vertical flexibility of the wall accommodates the construction settlement introduced by column contraction under the dead loads of the upper stories and allows sequential installation from the lower stories. A quasi-static cyclic loading test and finite element (FE) analysis verified the stable seismic behaviors of the ovally-perforated vertically-flexible steel plate shear wall (OVSPW). The results of FE parametric analysis showed that an OVSPW with an appropriate thickness of boundary elements effectively accommodated the construction settlement that could lead to large in-plane compression for a conventional SPSW. The horizontal connection elements made of steel tubes realized the vertical stiffness of OVSPW to less than 2% of the original value without changing the lateral stiffness. New design equations of the OVSPW were derived through integral and extreme value solutions to predict the mechanical behavior of OVSPW.     

Ground motion amplification at flange level of bushings mounted on electric substation transformers

A study was conducted to quantify the ground motion amplification that takes place at the base of bushings mounted on electric substation transformers as a result of the flexibility of the transformer tank and turrets to which they are connected. This study was undertaken to assess the adequacy of the amplification factor of 2.0 specified by the Institute of Electrical and Electronic Engineers in Standard IEEE 693‐1997 for the seismic qualification of transformer bushings. The study included field tests of typical 500‐kV transformers to obtain experimentally their natural frequencies and damping ratios, the development of simple analytical models that closely matched the experimental data, and the calculation of the transformers' dynamic response under different earthquake excitations using these analytical models. Amplification factors were then computed for each of the excitations considered, defining these amplification factors as the peak shear force at the base of the bushings over the corresponding shear force obtained when the bushings are assumed mounted directly on the ground. It is found that the amplification factors for the 500‐kV bushings are within the amplification factor of 2.0 specified by Standard IEEE 693, but not those for the 230‐kV bushings, which exceed the IEEE 693 amplification factor by almost a factor of two. Copyright © 2001 John Wiley & Sons, Ltd.     

Two-dimensional scattering of in-plane body waves due to a discontinuity in bedrock

The direct boundary integral equation technique is used to study in-plane surface amplification of in-plane seismic body waves for the case of an inhomogeneity in a bedrock half-space. In the studied soil configuration, a soil layer rests on a rock half-space which includes a rock inclusion. The rock inclusion considered is a semi-infinite horizontal rock layer in which its upper boundary borders the soil layer. Materials in the soil–rock configuration are considered viscoelastic except for the section of the rock half-space below the level of the rock inclusion which is considered elastic. A parametric study is performed to determine controlling factors for surface displacement due to in-plane body waves. The study investigates varying the stiffness and the thickness of the rock inclusion for a range of frequencies and wave incidence angles. Anti-plane waves for this type of soil-rock configuration have been addressed in a previous article by Heymsfield (Earthquake Engng. Struct. Dyn. 28 : 841–855 (1999)). Copyright © 1999 John Wiley & Sons, Ltd.