Procedure to predict the storey where plastic drift dominates in two‐storey building under strong ground motion

A procedure is presented to predict the storey where plastic drift dominates in two‐storey buildings under strong ground motion. The procedure utilizes the yield strength and the mass of each storey as well as the peak ground acceleration. The procedure is based on two different assumptions: (1) the seismic force distribution is of inverted triangular form and (2) the rigid‐plastic model represents the system. The first and the second assumptions, respectively, lead to lower and upper estimates of the base shear coefficient under which the drift of the first storey exceeds that of the second storey. The efficiency of the procedure is verified by dynamic response analyses using elasto‐plastic model. Copyright © 2008 John Wiley & Sons, Ltd.     

Control of the earthquake and wind dynamic response of steel‐framed buildings by using additional braces and/or viscoelastic dampers

The insertion of steel braces equipped with viscoelastic dampers (VEDs) (‘dissipative braces’) is a very effective technique to improve the seismic or wind behaviour of framed buildings. The main purpose of this work is to compare the earthquake and wind dynamic response of steel‐framed buildings with VEDs and achieve optimal properties of dampers and supporting braces. To this end, a numerical investigation is carried out with reference to the steel K‐braced framed structure of a 15‐storey office building, which is designed according to the provisions of Eurocodes 1 and 3, and to four structures derived from the first one by the insertion of additional diagonal braces and/or VEDs. With regard to the VEDs, the following cases are examined: absence of dampers; insertion of dampers supported by the existing K‐braces in each of the structures with or without additional diagonal braces; insertion of dampers supported by additional diagonal braces. Dynamic analyses are carried out in the time domain using a step‐by‐step initial stress‐like iterative procedure. For this purpose, the frame members and the VEDs are idealized, respectively, by a bilinear model, which allows the simulation of the nonlinear behaviour under seismic loads, and a six‐element generalized model, which can be considered as an in‐parallel‐combination of two Maxwell models and one Kelvin model. Artificially generated accelerograms, whose response spectra match those adopted by Eurocode 8 for a medium subsoil class and for different levels of peak ground acceleration, are considered to simulate seismic loads. Along‐wind loads are considered assuming, at each storey, time histories of the wind velocity for a return period T_r=5 years, according to an equivalent spectrum technique. Copyright © 2010 John Wiley & Sons, Ltd.     

SOFIE project – 3D shaking table test on a seven‐storey full‐scale cross‐laminated timber building

Multi‐storey buildings made of cross‐laminated timber panels (X‐lam) are becoming a stronger and economically valid alternative in Europe compared with traditional masonry or concrete buildings. During the design process of these multi‐storey buildings, also their earthquake behaviour has to be addressed, especially in seismic‐prone areas such as Italy. However, limited knowledge on the seismic performance is available for this innovative massive timber product. On the basis of extensive testing series comprising monotonic and reversed cyclic tests on X‐lam panels, a pseudodynamic test on a one‐storey X‐lam specimen and 1D shaking table tests on a full‐scale three‐storey specimen, a full‐scale seven‐storey building was designed according to the European seismic standard Eurocode 8 and subjected to earthquake loading on a 3D shaking table. The building was designed with a preliminary action reduction factor of three that had been derived from the experimental results on the three‐storey building. The outcomes of this comprehensive research project called ‘SOFIE – Sistema Costruttivo Fiemme’ proved the suitability of multi‐storey X‐lam structures for earthquake‐prone regions. The buildings demonstrated self‐centring capabilities and high stiffness combined with sufficient ductility to avoid brittle failures. The tests provided useful information for the seismic design with force‐based methods as defined in Eurocode 8, that is, a preliminary experimentally based action reduction factor of three was confirmed. Valid, ductile joint assemblies were developed, and their importance for the energy dissipation in buildings with rigid X‐lam panels became evident. The seven‐storey building showed relatively high accelerations in the upper storeys, which could lead to secondary damage and which have to be addressed in future research. Copyright © 2013 John Wiley & Sons, Ltd.     

A macro‐element model for inelastic building analysis

A three‐dimensional model for approximate inelastic analysis of buildings is presented herein. The model is based on a single macro‐element per building storey. The inelastic properties of the model are characterized by the so‐called ultimate storey shear and torque (USST) surfaces. Different algorithms for the construction of these surfaces, as well as their applications in building modelling, are presented and discussed. Two alternative procedures are developed to integrate the force‐deformation constitutive relationship of the macro‐elements. The first one follows the exact trajectory of the load path of the structure on the USST, and the second uses linear programming without ever forming the USST surface. The accuracy of the model and integration procedure is evaluated by means of the earthquake response of single‐storey systems. The model and integration procedure developed is finally used to compute the inelastic response of a seven‐storey R/C building. The results of this investigation show that the model proposed, although approximate, can be effective in estimating the inelastic deformation demand of a building. It also enables the engineer to capture and interpret important features of the three‐dimensional inelastic response of a structure even before performing any inelastic dynamic analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Influence of the soil–structure interaction on the fundamental period of buildings

This paper includes an investigation of the influence of the soil–structure interaction (SSI) on the fundamental period of buildings. The behaviour of both the soil and the structure is assumed to be elastic. The soil‐foundation system is modelled using translational and rotational discrete springs. Analysis is first conducted for one‐storey buildings. It shows that the influence of the SSI on the fundamental frequency of building depends on the soil–structure relative rigidity K_ss. Analysis is then extended for multi‐storey buildings. It allows the generalization of the soil–structure relative rigidity K_s to such complex structures. Charts are proposed for taking into account the influence of the SSI in the calculation of the fundamental frequency of a wide range of buildings. Copyright © 2007 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.     

Active control of building seismic response by energy dissipation

Active energy dissipation is proved to be very effective for abating seismic effects on buildings. The implementation of this concept in seismic design of buildings is studied by response simulations of a single storey building subjected to earthquake motion. Active energy dissipaters can be installed as part of the building lateral load bracing, and they regulate the strength and stiffness of the bracing during the building's response to the seismic events. The energy is dissipated when the bracing load exceeds the axial strength provided by the dissipater, and the bracing telescopes in and out. The design parameters of active energy dissipaters are described using the simulated response of a single storey building to ground pulse and harmonic ground excitation. The feasibility of the energy dissipater is demonstrated by the development and construction of a full-scale prototype device called an Active Slip Bracing Device (ASBD). The device utilizes Coulomb friction. The active characteristics are implemented by a computer controlled clamping mechanism on the friction interface. The ASBD's control of the strength and stiffness is investigated.     

Aluminium shear-links for enhanced seismic resistance

An aluminium beam shear-link is developed for earthquake-resistant structures. The aluminium beam is designed to yield in shear mode to limit the maximum lateral force which is transmitted to primary structural members and to provide significant energy dissipation potential. Aluminium was chosen because of its low yield strength, which enables the use of thicker webs, reducing the problems of web buckling. Cyclic load tests on medium scale (1:4) models were conducted to study the hysteretic behaviour and energy dissipation potential of shear-links made of two alloys of aluminium (3003-O and 6061-O). The links were also tested at faster rates (cycling frequencies of 5, 10 and 17 Hz) to determine the effect of strain rate. The links exhibited very ductile shear yielding and excellent energy dissipation capacity. Unpinched and full hysteresis loops were observed until 10 per cent shear strain, and a relatively small influence of strain rates was observed on the link's performance. Simple design equations are developed to proportion these shear-links, using data from the cyclic load tests. In chevron-type braced systems, the shear-link is sandwiched between the tops of diagonal braces and a girder from the floor above, resulting in yielding at a lateral force less than that required to buckle the compression brace. A Shear-Link Braced Frame (SLBF) system was designed and its seismic performance was compared to that of an Ordinary Concentric Braced Frame (OCBF) with chevron braces. The SLBF system demonstrated more uniform distribution of storey drifts, reduced base shear, and a larger energy dissipation capacity per unit drift. © 1998 John Wiley & Sons, Ltd.     

Determination of column size for displacement‐based design of reinforced concrete frame buildings

This article reports a method to determine the storey‐wise column size for displacement‐based design of reinforced concrete frame buildings with a wide range of storey drift and building plan. The method uses a computer program based algorithm. The basic relation used in the algorithm is formulated by considering the various possible deformation components involved in the overall frame deformation. As a necessity to represent the deformation component due to plastic rotation of beam members, a relation between the beam plastic rotation and the target‐drift is adopted. To control the dynamic amplification of interstorey drift, a target‐drift dependant design‐drift reduction factor is used. The dynamic amplification of column moment is accounted with the help of an approximate conversion of fundamental period of the building from the effective period of the equivalent SDOF system. To avoid the formation of plastic hinge in column members, a design‐drift dependant column–beam moment capacity ratio is used. The method successfully determines the storey‐wise column size for buildings of four plans of different varieties, heights up to 12 storeys and target‐drift up to 3%. Copyright © 2013 John Wiley & Sons, Ltd.     

Aftershock collapse fragility curves for non‐ductile RC buildings: a scenario‐based assessment

Recent studies have addressed the computation of fragility curves for mainshock (MS)‐damaged buildings. However, aftershock (AS) fragilities are generally conditioned on a range of potential post‐MS damage states that are simulated via static or dynamic analyses performed on an intact building. Moreover, there are very few cases where the behavior of non‐ductile reinforced concrete buildings is analyzed. This paper presents an evaluation of AS collapse fragility conditioned on various return periods of MSs, allowing for the rapid assessment of post‐earthquake safety variations based solely on the intensity of the damaging earthquake event. A refined multi‐degree‐of‐freedom model of a seven‐storey non‐ductile building, which includes brittle failure simulations and the evaluation of a system level collapse, is adopted. Aftershock fragilities are obtained by performing an incremental dynamic analysis for a number of MS–AS ground motion sequences and a variety of MS intensities. The AS fragilities show that the probability of collapse significantly increases for higher return periods for the MS. However, this result is mainly ascribable to collapses occurred during MSs. When collapse cases that occur during a MS are not considered in the assessment of AS collapse probability, a smaller shift in the fragility curves is observed as the MS intensity increases. This result is justified considering the type of model and collapse modes introduced, which strongly depend on the brittle behavior of columns failing in shear or due to axial loads. The analysis of damage that is due to MSs when varying the return period confirms this observation. Copyright © 2017 John Wiley & Sons, Ltd.     

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.     

A comparative study of semi-active control strategies for base isolated buildings

A comparative analytical study of several control strategies for semi-active(SA) devices installed in baseisolated buildings aiming to reduce earthquake induced vibrations is presented.Three force tracking schemes comprising a linear controller plus a "clipped" algorithm and a nonlinear output feedback controller(NOFC) are considered to tackle this problem.Linear controllers include the integral controller(I),the linear quadratic regulator(LQR) and the model predictive controller(MPC).A single degree-of-freedom system subjected to input accelerograms representative of the Portuguese seismic actions are first used to validate and evaluate the feasibility of these strategies.The obtained results show that structural systems using SA devices can in general outperform those equipped with passive devices for lower fundamental frequency structural systems,namely base-isolated buildings.The effectiveness of the proposed strategies is also evaluated on a 10 storey base-isolated dual frame-wall building.The force tracking scheme with an integral controller outperforms the other three as well as the original structure and the structure equipped with passive devices.     

Lateral force distributions for the linear static analysis of base-isolated buildings

This paper presents a new approach for the evaluation of accurate lateral force distributions for the Linear Static Analysis (LSA) of Base Isolated (BI-) buildings. In essence, the proposed lateral force distributions depend on a factor measuring the degree of non- linearity of the Isolation System (IS) and on the ratio between the effective period of the BI-structure (T_is) and the fundamental period of the Fixed Based (FB-) structure (T_fb). The proposed approach is fully compatible with the Direct Displacement-Based Design (DDBD) method, recently developed by Priestley and co-workers. The proposed lateral force distributions have been derived from the results of a large number of Nonlinear Time-History Analyses (NTHA), carried out on six numerical models of multi-storey buildings, differing in storey number (3, 5 and 8, respectively) and fundamental period of vibration (from 0.25 to 0.8 s) in the fixed-base configuration. A great variety of Isolation Systems (ISs), characterised by either Elasto-Plastic with Hardening (EPH) or Flag-Shaped (FS) force-displacement behaviour, have been considered in the NTHA. The numerical parameters of the IS models have been varied in such a way as to reproduce the actual mechanical behaviour of the main currently used ISs, including: (i) Lead Rubber Bearings (LRB), (ii) High-Damping Rubber Bearings (HDRB), (iii) Friction Pendulum Bearings (FPB), (iv) combinations of flat Sliding Bearings (SB) and Low-Damping Rubber Bearings (LDRB) and (v) Combinations of flat SB and re-centring devices based on Shape Memory Alloys (SMA). Comparisons between the storey shear forces derived with the proposed method and those obtained from NTHA clearly show the great improvements in the accuracy of LSA predictions, when using the proposed lateral force distributions.     

Experimental tests on full‐scale RC unretrofitted frame and retrofitted with buckling‐restrained braces

The results of experimental tests carried out on reinforced concrete (RC) full‐scale 2‐storey 2‐bays framed buildings are presented. The unretrofitted frame was designed for gravity loads only and without seismic details; such frame was assumed as a benchmark system in this study. A similar RC frame was retrofitted with buckling‐restrained braces (BRBs). The earthquake structural performance of both prototypes was investigated experimentally using displacement‐controlled pushover static and cyclic lateral loads. Modal response properties of the prototypes were also determined before and after the occurrence of structural damage. The results of the dynamic response analyses were utilized to assess the existing design rules for the estimation of the elastic and inelastic period of vibrations. Similarly, the values of equivalent damping were compared with code‐base relationships. It was found that the existing formulations need major revisions when they are used to predict the structural response of as‐built RC framed buildings. The equivalent damping ratio ξ_eq was augmented by more than 50% when the BRBs was employed as bracing system. For the retrofitted frame, the overstrength Ω and the ductility µ are 1.6 and 4.1, respectively; the estimated R‐factor is 6.5. The use of BRBs is thus a viable means to enhance efficiently the lateral stiffness and strength, the energy absorption and dissipation capacity of the existing RC substandard frame buildings. The foundation systems and the existing members of the superstructure are generally not overstressed as the seismic demand imposed on them can be controlled by the axial stiffness and the yielding force of the BRBs. Copyright © 2011 John Wiley & Sons, Ltd.     

Case studies of damage to 19‐storey irregular steel moment‐frame buildings under near‐source ground motion

This paper describes the three‐dimensional nonlinear analysis of six 19‐storey steel moment‐frame buildings, designed per the 1997 Uniform Building Code, under strong ground motion records from near‐source earthquakes with magnitudes in the range of 6.7–7.3. Three of these buildings possess a reentrant corner irregularity, while the remaining three possess a torsional plan irregularity. The records create drift demands of the order of 0.05 and plastic rotation demands of the order of 4–5% of a radian in the buildings with reentrant corners. These values point to performance at or near ‘Collapse Prevention’. Twisting in the torsionally sensitive buildings causes the plastic rotations on the moment frame on one face of the building (4–5% of a radian) to be as high as twice of that on the opposite face (2–3% of a radian). The asymmetric yield pattern implies a lower redundancy in the lateral force‐resisting system as the failure of the heavily loaded frame could result in a total loss of resistance to torsion. Copyright © 2006 John Wiley & Sons, Ltd.     

An experimental study of a midbroken 2-bay, 6-storey reinforced concrete frame subject to earthquakes

A 2-bay, 6-storey model test reinforced concrete frame (scale l:5) subjected to sequential earthquakes of increasing magnitude is considered in this paper. The frame was designed with a weak storey, in which the columns are weakened by using thinner and weaker reinforcement bars. The aim of the work is to study the global response to a damaging strong motion earthquake event of such buildings. Special emphasis is put on examining to what extent damage in the weak storey can be identified from global response measurements during an earthquake where the structure survives, and what level of excitation is necessary in order to identify the weak storey. Furthermore, emphasis is put on examining how and where damage develops in the structure and especially how the weak storey accumulates damage. Besides the damage in each storey the structure is identified by a static load at the top storey while measuring the horizontal displacement of the stories and also visual inspection is performed. From the investigations it is found that the reason for failure in the weak storey is that the absolute value of the stiffness deteriorates to a critical value where large plastic deformations occur and the storey is not capable of transferring the shear forces from the storeys above so failure is unavoidable.     

Advances in theory of plastic mechanism control: closed form solution for MR‐Frames

In this paper new advances in the application of ‘Theory of Plastic Mechanism Control’ (TPMC) are presented. TPMC is aimed at the design of structures assuring a collapse mechanism of global type. The theory has been developed in the nineties with reference to moment‐resisting frames (MRFs) and progressively extended to all the main structural typologies commonly adopted as seismic‐resistant structural systems. In particular, the outcome of the theory is the sum of the plastic moments of the columns required, at each storey, to prevent undesired failure modes, i.e. partial mechanisms and soft‐storey mechanisms. The theory is used to provide the design conditions to be satisfied, in the form of a set of inequalities where the unknowns are constituted by the column plastic moments. This set of inequalities was originally solved by means of an algorithm requiring an iterative procedure. The advances presented in this paper are constituted by the identification of a ‘closed form solution’ and by the use of TPMC in a more systematic design approach. This result is very important, because the practical application of TPMC can now be carried out even with very simple hand calculations. The practical application of TPMC is herein presented with reference to the design of a multi‐storey frame whose pattern of yielding is validated by means of both push‐over analysis and incremental dynamic analyses. Copyright © 2014 John Wiley & Sons, Ltd.     

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。     

Multiplication factor for open ground storey buildings–a reliability based evaluation

Open Ground Storey(OGS) framed buildings where the ground storey is kept open without infill walls, mainly to facilitate parking, is increasing commonly in urban areas. However, vulnerability of this type of buildings has been exposed in past earthquakes. OGS buildings are conventionally designed by a bare frame analysis that ignores the stiffness of the infill walls present in the upper storeys, but doing so underestimates the inter-storey drift(ISD) and thereby the force demand in the ground storey columns. Therefore, a multiplication factor(MF) is introduced in various international codes to estimate the design forces(bending moments and shear forces) in the ground storey columns. This study focuses on the seismic performance of typical OGS buildings designed by means of MFs. The probabilistic seismic demand models, fragility curves, reliability and cost indices for various frame models including bare frames and fully infilled frames are developed. It is found that the MF scheme suggested by the Israel code is better than other international codes in terms of reliability and cost.     

Seismic retrofit of low‐rise steel buildings in Canada using rocking steel braced frames

This article examines the use of rocking steel braced frames for the retrofit of existing seismically deficient steel building structures. Rocking is also used to achieve superior seismic performance to reduce repair costs and disruption time after earthquakes. The study focuses on low‐rise buildings for which re‐centring is solely provided by gravity loads rather than added post‐tensioning elements. Friction energy dissipative (ED) devices are used to control drifts. The system is applied to 2‐storey and 3‐storey structures located in 2 seismically active regions of Canada. Firm ground and soft soil conditions are considered. The seismic performance of the retrofit scheme is evaluated using nonlinear dynamic analysis and ASCE 41‐13. For all structures, rocking permits to achieve immediate occupancy performance under 2% in 50 years seismic hazard if the braces and their connections at the building's top storeys are strengthened to resist amplified forces due to higher mode response. Base shears are also increased due to higher modes. Impact at column bases upon rocking induces magnified column forces and vertical response in the gravity system. Friction ED is found more effective for drift control than systems with ring springs or bars yielding in tension. Drifts are sufficiently small to achieve position retention performance for most nonstructural components. Horizontal accelerations are generally lower than predicted from ASCE 41 for regular nonrocking structures. Vertical accelerations in the gravity framing directly connected to the rocking frame are however higher than those predicted for ordinary structures. Vertical ground motions have limited effect on frame response.