On the inelastic torsional response of single‐storey structures under bi‐axial excitation

An attempt has been made to explore the general trends in the seismic response of plan‐asymmetric structures without any restrictions imposed by a particular code. Systems with structural elements in both orthogonal directions under bi‐directional excitation were studied. Idealized single‐storey models with bi‐axial eccentricity were employed. The systems were torsionally stiff and, in the majority of cases, mass‐eccentric. The main findings are: in general, inelastic torsional response is qualitatively similar to elastic torsional response. Quantitatively, the torsional effect on the flexible side, expressed as an increase of displacements due to torsion, decreases slightly with increasing plastic deformation, unless the plastic deformations are small. The response on the stiff side generally strongly depends on the effect of several modes of vibration and on the influence of the ground motion in the transverse direction. These influences depend on the structural and ground motion characteristics in both directions. Reduction of displacements due to torsion, typical for elastic torsionally stiff structures, usually decreases with increasing plastic deformations. As an additional effect of large plastic deformations, a flattening of the displacement envelopes in the horizontal plane usually occurs, indicating that torsional effects in the inelastic range are generally smaller than in the elastic range. The dispersion of the results of inelastic torsional response analysis is generally larger than that of elastic analysis. Copyright © 2005 John Wiley & Sons, Ltd.     

On the inelastic seismic response of asymmetric buildings under bi‐axial excitation

The elastic and inelastic seismic response of plan‐asymmetric regular multi‐storey steel‐frame buildings has been investigated under bi‐directional horizontal ground motions. Symmetric variants of these buildings were designed according to Eurocodes 3 and 8. Asymmetric buildings were created by assuming a mass eccentricity in each of the two principal directions. The torsional response in the elastic and inelastic range is qualitatively similar with the exception of the stiff edge in the strong direction of torsionally stiff buildings and the stiff edge in the weak direction of torsionally flexible buildings. The response is influenced by the intensity of ground motion, i.e. by the magnitude of plastic deformation. In the limiting case of very strong ground motion, the behaviour of initially torsionally stiff and initially torsionally flexible buildings may become qualitatively similar. A decrease in stiffness due to plastic deformations in one direction may substantially influence the behaviour in the orthogonal direction. The response strongly depends on the detailed characteristics of the ground motion. On average, torsional effects are reduced with increasing plastic deformations, unless the plastic deformations are small. Taking into account also the dispersion of results which is generally larger in the inelastic range than in the elastic one, it can be concluded that (a) the amplification of displacements determined by the elastic analysis can be used as a rough estimate also in the inelastic range and (b) any favourable torsional effect on the stiff side of torsionally stiff buildings, which may arise from elastic analysis, may disappear in the inelastic range. The conclusions are limited to fairly regular buildings and subject to further investigations. Copyright © 2005 John Wiley & Sons, Ltd.     

Seismic performance of laminated timber frames with fiber‐reinforced joints

A series of dynamic experiments was performed on two‐story glue‐laminated timber frames. The tests included sinusoidal sweeps in one direction, arbitrary signals simulating earthquake loads in two directions, and harmonic free vibration at the fundamental frequency. Two experimental frames were manufactured and tested: (1) a control with horizontal laminations and no reinforcement at joint areas, and (2) a new frame design with densified material in the joint area that was further reinforced by glass‐fiber composite material. Preliminary tests of scaled and full‐size beam‐to‐column connections were performed to obtain connection characteristics needed for subsequent analytical modeling. Copyright © 2004 John Wiley & Sons, Ltd.     

Performance‐based seismic assessment method for Taiwanese historic Dieh‐Dou timber structures

Lateral force, response spectrum and step‐by‐step pushover analyses are performed and compared with the post‐earthquake survey of two Dieh‐Dou buildings seriously affected in the 1999 Chi‐Chi earthquake in Taiwan. The results show that the proposed FE model with finite translational and rotational stiffness can successfully be employed to assess the vulnerability of the frames. The fundamental period of Dieh‐Dou structures is about 1.0 s higher than that calculated by the simplified approach of the codes for regular frames; a modal analysis is, therefore, essential for this typology of structure. The elastic analysis, either lateral force or response spectrum, is shown to be reliable to assess Dieh‐Dou frames when quick results are desired. However, a non‐linear step‐by‐step pushover analysis has the advantage of greater accuracy, as it allows mapping the failure trend and indicating the critical elements. The lateral drifts are compared with the actual observed damage pattern and when the damage level is related to the peak ground acceleration on a vulnerability curve plot, it is shown that the joint failure combined with the lateral drift gives an indication of the global structural behaviour of this historic construction typology. Owing to the unique construction features of the Dieh‐Dou, the joint failure represents also a critical criterion in terms of maximum retention for conservation. Based on a damage level approach, an assessment methodology is suggested that would allow optimizing a strengthening strategy, for protection of these precious structures from future earthquakes while avoiding unnecessary interventions. Copyright © 2010 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.     

Experimental–numerical investigation on the seismic behaviour of moment‐resisting timber frames with densified veneer wood‐reinforced timber joints and expanded tube fasteners

This paper investigates the seismic behaviour of moment‐resisting timber frames with beam‐column joints fastened with expanded tubes and reinforced with densified veneer wood. Laboratory experiments are carried out on single joints to investigate the cyclic behaviour and, more specifically, the impairment of strength, the ductility ratio and the equivalent viscous damping ratio. A phenomenological numerical model is proposed, where the beams and columns are schematized using linear‐elastic beam elements, and the joints with non‐linear hysteretic spring calibrated on the results of the experimental tests. The model is used to analyse some representative moment‐transmitting structures characterised by different number of bays and storeys. After an estimation of the lateral load‐carrying capacity using a pushover analysis, the numerical model is used to estimate the behaviour factor. An incremental dynamic analysis is performed using a set of accelerograms spectrum consistent with a chosen design spectrum. The analyses lead to an estimation of the behaviour factor of 3 and 6 for a portal frame and a five‐storey, three‐bay frame, respectively, which confirms the highly dissipative behaviour of this kind of moment connection. Copyright © 2017 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.     

Application of wavelet theory to identify yielding in seismic response of bi‐linear structures

The time–frequency and the time‐scale analysis methods are used in this paper to identify the dynamic characteristics of non‐linear seismic response of structural systems with single degree of freedom (SDOF) and multiple degrees of freedom (MDOF). Based on the floor acceleration response time histories of bi‐linear SDOF and MDOF structures, the current study compares the results of system identification using the short‐time Fourier transform (STFT), continuous wavelet transform (CWT) and discrete wavelet transform (DWT) methods. The aim is to identify the frequency variations and the time at on‐set of yielding and unloading of a bi‐linear structural system during seismic response. The results demonstrate that the CWT method is better than the STFT method in both time and frequency resolutions, and that the DWT method is the best at detecting the time at on‐set of yielding and unloading. Combining the results of CWT and DWT methods therefore provides accurate information of both frequency variations and yielding time in non‐linear seismic response. To alleviate the problems associated with noise‐contaminated signals, e.g. seismic response data recorded on site, the study suggests that low‐pass filtering be carried out before applying the DWT method to decompose the signals into multiple levels of details. Copyright © 2001 John Wiley & Sons, Ltd.     

Determination of the seismic performance factors for post‐tensioned rocking timber wall systems

Post‐tensioned technologies for concrete seismic resistant buildings were first developed in the 1990s during the PREcast Seismic Structural Systems program. Among different solutions, the hybrid system proved to be the most resilient solution providing a combination of re‐centering and energy dissipative contributions respectively by using post‐tensioned tendons and mild steel reinforcement. The system, while providing significant strength and energy dissipation, reduces structural element damage and limits post‐earthquake residual displacements. More recently, the technology was extended to laminated veneer lumber (LVL) structural members, and extensive experimental and numerical work was carried out and allowed the development of reliable analytical and numerical models as well as design guidelines. On the basis of the experimental and numerical outcomes, this paper presents the evaluation of the seismic performance factors for post‐tensioned rocking LVL walls using the FEMA P‐695 procedure. Several archetype buildings were designed considering different parameters such as the building and story height, the type of seismic resistant system, the magnitude of gravity loads and the seismic design category. Lumped plasticity models were developed for each index archetype to simulate the behavioral aspects and collapse mechanisms. Non‐linear quasi‐static analyses were carried out to evaluate the system over‐strength factor; moreover, non‐linear time history analyses were performed using the incremental dynamic analysis concept to assess the collapse of each building. From the results of quasi‐static and dynamic analyses the response modification factor, R, system over‐strength factor, Ω₀, and deflection amplification factor, C_d, values of, respectively, 7, 3.5 and 7.5 are recommended. Copyright © 2016 John Wiley & Sons, Ltd.     

Seismic response of three‐dimensional r/c multi‐storey frame building under uni‐ and bi‐directional input ground motion

This paper deals with seismic analysis of plan‐asymmetric r/c frame multi‐storey buildings. Non‐linear numerical analyses are carried out by using a lumped plasticity model for beams and a multi‐spring model for columns, the latter one introduced to account for axial force–biaxial bending moment interaction. A comparison between numerical analyses and experimental test results is reported in order to calibrate the numerical model, showing that the adopted model is very suitable. In order to study the effects of the earthquake orthogonal component, the seismic response of the modelled structure under uni‐directional excitation is compared to the one under bi‐directional excitation. Such comparison shows that the maximum base shear and the top displacement are not very sensitive to the presence of the orthogonal component, which, conversely, leads to large increase in the column plastic excursions. Copyright © 2007 John Wiley & Sons, Ltd.     

Evaluation of three‐dimensional modal pushover analysis for unsymmetric‐plan buildings subjected to two components of ground motion

The accuracy of the three‐dimensional modal pushover analysis (MPA) procedure in estimating seismic demands for unsymmetric‐plan buildings due to two horizontal components of ground motion, simultaneously, is evaluated. Eight low‐and medium‐rise structures were considered. Four intended to represent older buildings were designed according to the 1985 Uniform Building Code, whereas four other designs intended to represent newer buildings were based on the 2006 International Building Code. The median seismic demands for these buildings to 39 two‐component ground motions, scaled to two intensity levels, were computed by MPA and nonlinear response history analysis (RHA), and then compared. Even for these ground motions that deform the buildings significantly into the inelastic range, MPA offers sufficient degree of accuracy. It is demonstrated that PMPA, a variant of the MPA procedure, for nonlinear systems is almost as accurate as the well‐known standard response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative to nonlinear RHA, whereby seismic demands can be estimated directly from the (elastic) design spectrum. In contrast, the nonlinear static procedure specified in the ASCE/SEI 41‐06 Standard is demonstrated to grossly underestimate seismic demands for some of the unsymmetric‐plan buildings considered. Copyright © 2011 John Wiley & Sons, Ltd.     

Seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions

An approximation approach of seismic analysis of two‐way asymmetric building systems under bi‐directional seismic ground motions is proposed. The procedures of uncoupled modal response history analysis (UMRHA) are extended to two‐way asymmetric buildings simultaneously excited by two horizontal components of ground motion. Constructing the relationships of two‐way base shears versus two‐way roof translations and base torque versus roof rotation in ADRS format for a two‐way asymmetric building, each modal pushover curve bifurcates into three curves in an inelastic state. A three‐degree‐of‐freedom (3DOF) modal stick is developed to simulate the modal pushover curve with the stated bifurcating characteristic. It requires the calculation of the synthetic earthquake and angle β. It is confirmed that the 3DOF modal stick is consistent with single‐degree‐of‐freedom modal stick in an elastic state. A two‐way asymmetric three‐story building was analyzed by UMRHA procedure incorporating the proposed 3DOF modal sticks. The analytical results are compared with those obtained from nonlinear response history analysis. It is shown that the 3DOF modal sticks are more rational and effective in dealing with the assessment of two‐way asymmetric building systems under two‐directional seismic ground motions. Copyright © 2007 John Wiley & Sons, Ltd.     

A component approach for the hysteretic behaviour of connections in cross‐laminated wooden structures

In this paper, a numerical model to estimate the dissipative capacity and describe the cyclic response of cross‐laminated (X‐lam) timber buildings is presented. The connections between panels and to the foundation (metal hold‐downs and angle brackets, and screwed connectors) are modelled with nonlinear hysteretic multispring elements taking into account the strength interaction between different degrees of freedom according to a predefined domain. The timber components (solid X‐lam floors and wall panels) are modelled using elastic shell elements. By calibration on experimental cyclic tests carried out on each degree of freedom, important features of timber connection behaviour such as post‐peak strength, pinching and stiffness degradation can all be considered. In addition, the effect of friction at the interface between panels and with foundation can be taken into account. These springs have been implemented as external subroutines in a widespread software package such as Abaqus. By comparison with the experimental results of cyclic tests carried out on single X‐lam walls, coupled X‐lam walls and a single‐storey X‐lam building, the accuracy of the proposed model is demonstrated. Copyright © 2013 John Wiley & Sons, Ltd.     

A new steel framing system for seismic protection of timber platform frame buildings. Implementation with hysteretic energy dissipators

This paper describes a new seismic protection system for timber platform frame buildings, either for new construction or retrofit. The system consists in connecting the timber frame to a steel structure that includes hysteretic energy dissipators designed to absorb most of the seismic input energy thus protecting the timber frame and the other steel members; alternatively, the system might use other types of dissipative devices. The steel structure consists of four steel stacks (located at each of the four façades) and steel collectors embracing each slab; the stacks and the collectors are connected, at each floor level, through the energy dissipators. The steel structure is self‐supporting, that is, the timber frame is not affected by horizontal actions and can be designed without accounting for any seismic provision; in turn, the steel members do not participate in the main load‐carrying system. The timber‐steel interface is designed to avoid any stress concentration in the transfer of horizontal forces and to guarantee that the yielding of the dissipators occurs prior to any timber failure. The energy dissipation capacity of the suggested system is discussed, and an application example on a six‐story timber building is presented; this case corresponds to highly demanding conditions because of the relatively large building height and weight, the high local seismicity, and the soft soil condition. This research belongs to a wider project aiming to promote the structural use of timber by improving the seismic capacity of wooden buildings; this research includes experiments and advanced numerical simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

A shrub bending model to calculate the albedo of shrub‐tundra

At high latitudes, the albedo and energy budget of shrub‐tundra landscapes is determined by the relationship between the fractional snow cover and the fraction of vegetation protruding above the snowpack. The exposed vegetation fraction is affected by the bending and/or burial of shrubs in winter and their spring‐up during melt. Little is known about the meteorological conditions and snowpack and shrub properties required to cause bending, and few quantitative measurements of bending processes exist. Here, a model combining the few, mostly qualitative, observations available with a biomechanical model representing branches as cantilevers is proposed to provide a first approximation of bending mechanisms. The exposed vegetation fraction is then calculated using structural parameters of shrubs measured at two sites in Canada: the Granger Basin in the Yukon Territory and Trail Valley Creek in the Northwest Territories. The exposed vegetation fraction is in turn used to calculate albedo, which is evaluated against measurements at the two sites. The model considerably improves modelled albedo compared to a model which only buries but does not bend shrubs at TVC, where shrubs become completely buried. However, the model overestimates albedo at GB where only a few shrubs get buried. The bending model is then used to calculate a compression factor for use in a simple parameterization of the exposed vegetation fraction proposed by previous investigators. The parameterization, which is simpler and computationally less expensive than the full model, is evaluated and found to perform well. Despite the need for further developments, the model provides a first approximation of bending processes and contributes to the identification of measurements that are needed in order to improve the model and our understanding of the bending of shrubs. Copyright © 2012 John Wiley & Sons, Ltd.     

Experimental testing of a rocking timber shear wall with slip‐friction connectors

Allowing a structure to uplift and rock during an earthquake is one way in which activated forces can be capped and damage to the structure avoided or minimised. Slip‐friction connectors (also known as slotted‐bolt connectors) were originally developed for use in steel construction, but for this research have been adapted for use as hold‐downs in an experimental 2.4 m × 2.4 m rigid timber shear wall. A novel approach is used to achieve the desired sliding threshold in the connectors, and the wall uplifts when this threshold is reached. From a series of quasi‐static cyclic tests, it is shown that slip‐friction connectors can impart ductile and elasto‐plastic characteristics to what would otherwise be essentially brittle structures. Because forces on the wall were capped by the slip‐friction connectors to levels well below the design level, no damage to the wall was observed. Self‐centring potential was also found to be excellent. The slip‐friction connectors themselves are of a unique design and have proven to be robust and durable, adequately performing their duty even after almost 14 m of cumulative travel under high contact pressures. To resist base shear without unduly affecting rocking behaviour, a new type of shear‐key is proposed and implemented, and a procedure developed to quantify its influence on overall wall behaviour. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental testing and numerical modelling of a heavy timber moment‐resisting frame with ductile steel links

This paper presents the development, experimental testing, and numerical modelling of a new hybrid timber‐steel moment‐resisting connection that is designed to improve the seismic performance of mid‐rise heavy timber moment‐resisting frames (MRF). The connection detail incorporates specially designed replaceable steel links fastened to timber beams and columns using self‐tapping screws. Performance of the connection is verified through experimental testing of four 2/3 scale beam‐column connections. All 4 connection specimens met the acceptance criteria specified in the AISC 341‐10 provisions for steel moment frames and exhibit high strength, ductility, and energy dissipation capacity up to storey drifts exceeding 4%. All of the timber members and self‐tapping screw connections achieved their design objective, remaining entirely elastic throughout all tests and avoiding brittle modes of failure. To assess the global seismic performance of the newly developed connection in a mid‐rise building, a hybrid timber‐steel building using the proposed moment‐resisting connection is designed and modelled in OpenSees. To compare the seismic performance of the hybrid MRF with a conventional steel MRF, a prototype steel‐only building is also designed and modelled in OpenSees. The building models are subject to a suite of ground motions at design basis earthquake and maximum credible earthquake hazard levels using non‐linear time history analysis. Analytical results show that drifts and accelerations of the hybrid building are similar to a conventional steel building while the foundation forces are significantly reduced for the hybrid structure because of its lower seismic weight. The results of the experimental program and numerical analysis demonstrate the seismic performance of the proposed connection and the ability of the hybrid building to achieve comparable seismic performance to a conventional steel MRF.     

Experimental and numerical behaviour of dissipative devices based on carbon‐wrapped steel tubes for the retrofitting of existing precast RC structures

The 2012 Emilia earthquake (in Northern Italy) caused extensive damage to existing prefabricated reinforced concrete structures. These buildings were found being extremely vulnerable because, being designed for vertical loads only, they featured friction‐based connections between structural elements, most commonly between beams and columns. Given the large diffusion of these structures, their seismic retrofit is critical. Various techniques have been proposed in the literature, in most of which friction‐based connections are removed by inserting mechanical connectors that will make beam‐column connections hinged. These approaches lead to a significant increase of the base shear and therefore require strengthening of columns. The paper presents dissipative devices based on carbon‐wrapped steel tubes to be used as an alternative low‐damage solution for the retrofit of beam‐column connections. The first part of the paper presents results of experimental tests on the devices and discusses their dissipative behaviour. The succeeding parts of the paper present numerical analyses on simple structures reinforced with the proposed device. The results of the numerical study show how the introduction of the dissipative devices produces a significant reduction of forces transmitted to the structure, by comparing the seismic response of simple frame structures equipped with dissipative devices with the response of equivalent elastic systems.     

Three‐dimensional modal pushover analysis of buildings subjected to two components of ground motion,including its evaluation for tall buildings

The modal pushover analysis (MPA) procedure, presently restricted to one horizontal component of ground motion, is extended to three‐dimensional analysis of buildings—symmetric or unsymmetric in plan—subjected to two horizontal components of ground motion, simultaneously. Also presented is a variant of this method, called the practical modal pushover analysis (PMPA) procedure, which estimates seismic demands directly from the earthquake response (or design) spectrum. Its accuracy in estimating seismic demands for very tall buildings is evaluated, demonstrating that for nonlinear systems this procedure is almost as accurate as the response spectrum analysis procedure is for linear systems. Thus, for practical applications, the PMPA procedure offers an attractive alternative whereby seismic demands can be estimated directly from the (elastic) design spectrum, thus avoiding the complications of selecting and scaling ground motions for nonlinear response history analysis. Copyright © 2010 John Wiley & Sons, Ltd.