Comparative response assessment of minimally compliant low‐rise conventional and base‐isolated steel frames

In this study, the multi‐intensity seismic response of code‐designed conventional and base‐isolated steel frame buildings is evaluated using nonlinear response history analysis. The results of hazard and structural response analysis for three‐story braced‐frame buildings are presented in this paper. Three‐dimensional models for both buildings are created and seismic response is assessed for three scenario earthquakes. The response history analysis results indicate that the design objectives are met and the performance of the isolated building is superior to the conventional building in the design event. For the Maximum Considered Earthquake, isolation leads to reductions in story drifts and floor accelerations relative to the conventional building. However, the extremely high displacement demands of the isolation system could not be accommodated under normal circumstances, and creative approaches should be developed to control displacements in the MCE. Copyright © 2010 John Wiley & Sons, Ltd.     

Hybrid simulation of a zipper‐braced steel frame under earthquake excitation

Hybrid simulation is a testing methodology that combines laboratory and analytical simulation to evaluate seismic response of complex structural framing systems. One or more portions of the structure, which may be difficult to model numerically or have properties that have not been examined before, are tested in one or more laboratories, whereas the remainder of the structure is modeled in software using one or more computers. These separate portions are assembled such that combined dynamic response of the hybrid model to excitation is computed using a time‐stepping procedure. A hybrid simulation conducted to examine the seismic response of a type of steel concentrically braced frame, the suspended‐zipper‐braced frame, is presented. The hybrid simulation testing architecture, hybrid model, test setup, solution algorithm, and the seismic response of the suspended‐zipper‐braced frame hybrid model are discussed. Accuracy of this hybrid simulation is examined by comparing hybrid and computer‐only simulations and the errors are quantified using an energy‐based approach. This comparison indicates that the deployed hybrid simulation method can be used to accurately model the seismic response of a complex structural system such as the zipper‐braced frame. Copyright © 2008 John Wiley & Sons, Ltd.     

An experimental and numerical investigation into the seismic performance of a multi-storey concentrically braced plan irregular structure

In this investigation, the seismic torsional response of a multi-storey concentrically braced frame (CBF) plan irregular structure is evaluated numerically and experimentally through a series of hybrid tests. CBF structures have become popular in seismic design because they are one of the most efficient types of steel structures to resist earthquake loading. However, their response under plan irregular conditions has received little focus mostly in part due to their complex behaviour under seismic loading conditions. The majority of research on the seismic response of plan irregular structures is based purely on numerical investigations. This paper provides much needed experimental investigation of the seismic response of a CBF plan irregular structure with the aim of characterising the response of this class of structure. The effectiveness of the Eurocode 8 torsional effects provision as a method of designing for low levels of mass eccentricity is evaluated. Results indicate that some of the observations made by purely numerical models are valid in that; torsionally stiff structures perform well and the stiff side of the structure is subjected to a greater ductility demand compared to the flexible side of the structure. The Eurocode 8 torsional effects provision is shown to be adequate in terms of ductility and interstorey drift however the structure performs poorly in terms of floor rotation. Importantly, stiffness eccentricity occurs when the provision is applied to the structure when no mass eccentricity exists and results in a significant increase in floor rotations.     

A numerical study on response factors for steel wall–frame systems

A numerical investigation was undertaken to evaluate the response of dual structural systems that consisting of steel plate shear walls and moment‐resisting frames. The primary objective of the study was to investigate the influence of elastic base shear distribution between the wall and the frame on the global system response. A total of 10 walls and 30 wall–frame systems, ranging from 3 to 15 stories, were selected for numerical assessment. These systems represent cases in which the elastic base shear resisted by the frame has a share of 10, 25, or 50% of the total base shear resisted by the dual system. The numerical study consisted of 1600 time history analyses employing three‐dimensional finite elements. All 40 structures were separately analyzed for elastic and inelastic response by subjecting them to the selected suite of earthquake records. Interstory drifts, top story drift, base shears resisted by the wall, and the frame were collected during each analysis. Based on the analysis results, important response quantities, such as the strength reduction, the overstrength, and the displacement amplification factors, are evaluated herein. Results are presented in terms of displacement measures, such as the interstory drift ratio and the top story drift ratio. Analysis results revealed that the increase in the strength reduction factor with the amount of load share is insignificant. Furthermore, there is an inverse relationship between the ductility reduction and the overtsrength. Copyright © 2010 John Wiley & Sons, Ltd.     

Collapse risk of controlled rocking steel braced frames with different post‐tensioning and energy dissipation designs

Controlled rocking steel braced frames (CRSBFs) are low‐damage self‐centring lateral force resisting systems. Previous studies have shown that designing the energy dissipation (ED) and post‐tensioning (PT) in CRSBFs using a response modification factor of R=8 can prevent collapse of structures during earthquakes beyond the design level. However, designers have unique control over the hysteretic behaviour of the system, even after the response modification factor is selected. Additionally, recent studies have suggested that CRSBFs could also be designed using R>8 while still satisfying performance limits. This paper examines how the response modification factor and the design of the ED and PT influence the collapse performance of CRSBFs with three and six storeys where collapse occurs because of over‐rotation of the base rocking joint. In addition, the influence of using an additional rocking joint above the base to mitigate higher‐mode forces is evaluated for a 12‐storey frame. A total of 18 different designs are considered for the three buildings using different ED and PT design parameters, including different response modification factors. A suite of 44 ground motions is scaled until at least 50% of the records cause collapse, and fragility curves are generated using the truncated incremental dynamic analysis curves. The results from two different assessment methodologies show that the parameters selected have a marked influence on the collapse performance of a CRSBF. Nevertheless, even CRSBFs designed using R>8 or without supplemental ED can have acceptably low probabilities of collapse, provided that the frame members are designed to remain elastic. Copyright © 2017 John Wiley & Sons, Ltd.     

Seismic retrofitting of braced frame buildings by RC rocking walls and viscous dampers

A design procedure for seismic retrofitting of concentrically and eccentrically braced frame buildings is proposed and validated in this paper. Rocking walls are added to the existing system to ensure an almost uniform distribution of the interstorey displacement in elevation. To achieve direct and efficient control over the seismic performance, the design procedure is founded on the displacement‐based approach and makes use of overdamped elastic response spectra. The top displacement capacity of the building is evaluated based on a rigid lateral deformed configuration of the structure and on the ductility capacity of the dissipative members of the braced frames. The equivalent viscous damping ratio of the braced structure with rocking walls is calculated based on semi‐empirical relationships specifically calibrated in this paper for concentrically and eccentrically braced frames. If the equivalent viscous damping ratio of the structure is lower than the required equivalent viscous damping ratio, viscous dampers are added and arranged between the rocking walls and adjacent reaction columns. The design internal forces of the rocking walls are evaluated considering the contributions of more than one mode of vibration. The proposed design procedure is applied to a large set of archetype braced frame buildings and its effectiveness verified by nonlinear dynamic analysis.     

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.     

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.     

Inelastic earthquake response of single‐story asymmetric buildings: an assessment of simplified shear‐beam models

The inelastic seismic torsional response of simple structures is examined by means of shear‐beam type models as well as with plastic hinge idealization of one‐story buildings. Using mean values of ductility factors, obtained for groups of ten earthquake motions, as the basic index of post‐elastic response, the following topics are examined with the shear‐beam type model: mass eccentric versus stiffness eccentric systems, effects of different types of motions and effects of double eccentricities. Subsequently, comparisons are made with results obtained using a more realistic, plastic hinge type model of single‐story reinforced concrete frame buildings designed according to a modern Code. The consequences of designing for different levels of accidental eccentricity are also examined for the aforementioned frame buildings. Copyright © 2003 John Wiley & Sons, Ltd.     

Rigid‐plastic models for the seismic design and assessment of steel framed structures

This paper demonstrates the applicability of response history analysis based on rigid‐plastic models for the seismic assessment and design of steel buildings. The rigid‐plastic force–deformation relationship as applied in steel moment‐resisting frames (MRF) is re‐examined and new rigid‐plastic models are developed for concentrically‐braced frames and dual structural systems consisting of MRF coupled with braced systems. This paper demonstrates that such rigid‐plastic models are able to predict global seismic demands with reasonable accuracy. It is also shown that, the direct relationship that exists between peak displacement and the plastic capacity of rigid‐plastic oscillators can be used to define the level of seismic demand for a given performance target. Copyright© 2009 John Wiley & Sons, Ltd.     

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.     

Nonlinear seismic analysis of unsymmetric-plan structures retrofitted by hysteretic damped braces

A displacement-based design procedure using hysteretic damped braces (HYDBs) is proposed for the seismic retrofitting of unsymmetric-plan structures. An expression of the viscous damping equivalent to the hysteretic energy dissipated by the damped braced frame is proposed under bidirectional seismic loads, where corrective factors are assumed as a function of design parameters of the HYDBs. To this end, the nonlinear dynamic analysis of an equivalent two degree of freedom system is firstly carried out on seven pairs of real ground motions whose displacement response spectra match, on average, the design spectrum proposed by the Italian seismic code for a high-risk seismic zone and a medium subsoil class. Then, the extended N2 method considered by the European seismic code, which combines the nonlinear static analysis along the in-plan principal directions of the structure with elastic modal analysis, is adopted to evaluate the higher mode torsional effects. The town hall of Spilinga (Italy), a reinforced concrete (r.c.) framed building with an L-shaped plan, is supposed to be retrofitted with HYDBs. Six structural solutions are compared considering two alternative in-plan distributions of the HYDBs, to eliminate (elastic) torsional effects, and three design values of the frame ductility combined with a constant design value of the damper ductility. To check the effectiveness and reliability of the DBD procedure, the nonlinear static analysis of the test structures is carried out, by evaluating the vulnerability index of r.c. frame members and the ductility demand of HYDBs for different in-plan directions of the seismic loads.     

Steel frames with bracing mechanism and hysteretic dampers

A new earthquake resistant structural system for multi‐storey frame structures, based on a dual function of its bracing components, is developed. This consists of a hysteretic damper device and a cross‐bracing mechanism with a kinetic closed circuit, working only in tension, so that cable members can be used for this purpose. Solutions are presented regarding the connections' design of three types of structural frame system, that are concerned throughout the study: braced moment free frame, braced moment resisting frame with moment free supports, and with moment resisting supports. The dynamic behaviour of the system is investigated on the basis of an SDOF model, and based on the response spectra method an approximate design approach of the controlled structures is shown. From the time history analysis of the structural systems for the El Centro earthquake the areas of appropriate stiffness relations of the frames to the hysteretic dampers and the cable braces are deduced, so that the energy dissipation of the system may be controlled by the damper‐cable bracing mechanism. Based on the results of these studies, a predesign approach is developed for the implementation of the control system in frame structures. Copyright © 2003 John Wiley & Sons, Ltd.     

Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings

Four real buildings with three to six stories, strong irregularities in plan and little engineered earthquake resistance are subjected to inelastic response‐history analyses under 56 bidirectional EC8‐spectra‐compatible motions. The average chord rotation demand at each member end over the 56 response‐history analyses is compared to the chord rotation from elastic static analysis with inverted triangular lateral forces or modal response spectrum analysis. The storey‐average inelastic‐to‐elastic‐chord‐rotation‐ratio was found fairly constant in all stories, except when static elastic analysis is applied to buildings with large higher mode effects. Except for such buildings, static elastic analysis gives more uniform ratios of inelastic chord rotations to elastic ones within and among stories than modal response spectrum analysis, but generally lower than 1.0. With increasing EPA the building‐average inelastic‐to‐elastic‐chord‐rotation‐ratio decreases but scatter in the results increases. Static elastic analysis tends to overestimate the inelastic torsional effects at the flexible or central part of the torsionally flexible buildings and underestimate them at their stiff side. Modal response spectrum analysis tends to overestimate the inelastic torsional effects at the stiff or central part of the torsionally stiff buildings and underestimate them at the flexible side. Overall, for multistorey RC buildings that typically have fundamental periods in the velocity‐sensitive part of the spectrum, elastic modal response spectrum analysis with 5% damping gives on average unbiased and fairly accurate estimates of member inelastic chord rotations. If higher modes are not significant, elastic static analysis in general overestimates inelastic chord rotations of such buildings, even when torsional effects are present. Copyright © 2007 John Wiley & Sons, Ltd.     

A cantilever beam analogy for quantifying higher mode effects in multistorey buildings

This paper examines higher mode effects in systems where the ductile mechanism for seismic design is the base moment‐rotation response. The modal properties of flexural and shear beams with uniform mass and elasticity and with a variable amount of base rotational restraint are derived. As the base fixity is released, the first mode becomes the rigid body rotation of the beam about the base, but the higher modes change much less, particularly for the shear beam model. Most response quantities that are of interest in the seismic design of typical mid‐rise buildings are controlled by the first two lateral modes, except at locations along the height where the second mode contributes little. However, the third and higher lateral modes are more significant for high‐rise buildings. Based on the theory of uniform cantilever shear beams, expressions are developed to avoid the need for a modal analysis to estimate the overturning moment, storey shear, and floor acceleration envelopes. Considering the measured response from the shake table testing of a large‐scale eight‐storey controlled rocking steel braced frame, the proposed expressions are shown to be of similar or better accuracy to a modified modal superposition technique, which combines the higher mode response from an elastic modal analysis with the response associated with achieving the maximum base overturning moment according to an inverted triangular load distribution. Because the proposed method uses only parameters that are available at the initial design stage, avoiding the analysis of a structural model, it is likely to be especially useful for preliminary design. Copyright © 2015 John Wiley & Sons, Ltd.     

Shake table testing and numerical simulation of a self‐centering energy dissipative braced frame

The self‐centering energy dissipative (SCED) brace is a new steel bracing member that provides both damping to the structure and a re‐centering capability. The goal of this study was to confirm the behavior of SCED braces within complete structural systems and to confirm the ability to model these systems with both a state‐of‐the‐art computer model as well as a simplified model that would be useful to practicing engineers. To these ends, a three‐story SCED‐braced frame was designed and constructed for testing on a shake table. Two concurrent computer models of the entire frame were constructed: one using the opensees nonlinear dynamic modeling software, and a simplified model using the commercial structural analysis software sap2000 . The frame specimen was subjected to 12 significant earthquakes without any adjustment or modification between the tests. The SCED braces prevented residual drifts in the frame, as designed, and did not show any significant degradation due to wear. Both numerical models were able to predict the drifts, story shears, and column forces well. Peak story accelerations were overestimated in the models; this effect was found to be caused by the absence of transitions at stiffness changes in the hysteretic model of the braces. Copyright © 2013 John Wiley & Sons, Ltd.     

Influence of gusset plate connections and braces on the seismic performance of X‐braced frames

Braced frames are one of the most economical and efficient seismic resisting systems yet few full‐scale tests exist. A recent research project, funded by the National Science Foundation (NSF), seeks to fill this gap by developing high‐resolution data of improved seismic resisting braced frame systems. As part of this study, three full‐scale, two‐story concentrically braced frames in the multi‐story X‐braced configuration were tested. The experiments examined all levels of system performance, up to and including fracture of multiple braces in the frame. Although the past research suggests very limited ductility of SCBFs with HSS rectangular tubes for braces recent one‐story tests with improved gusset plate designs suggest otherwise. The frame designs used AISC SCBF standards and two of these frames designs also employed new concepts developed for gusset plate connection design. Two specimens employed HSS rectangular tubes for bracing, and the third specimen had wide flange braces. Two specimens had rectangular gusset plates and the third had tapered gusset plates. The HSS tubes achieved multiple cycles at maximum story drift ratios greater than 2% before brace fracture with the improved connection design methods. Frames with wide flange braces achieved multiple cycles at maximum story drift greater than 2.5% before brace fracture. Inelastic deformation was distributed between the two stories with the multi‐story X‐brace configuration and top story loading. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic and equivalent static procedures for capacity design of controlled rocking steel braced frames

Controlled rocking steel braced frames (CRSBFs) have been proposed as a low‐damage seismic force resisting system with reliable self‐centring capabilities. Vertical post‐tensioning tendons are designed to self‐centre the system after rocking, and energy dissipation may be provided to limit the peak displacements. The post‐tensioning and energy dissipation can be designed using simple methods that rely primarily on the first‐mode response. However, the frame member forces are highly influenced by the higher‐mode response, resulting in more complex methods to design the frame members. This paper examines previous proposals and also proposes two new capacity design methods for CRSBFs. The first is a dynamic procedure that requires a truncated response spectrum analysis on a model of the frame with modified boundary conditions to consider the rocking behaviour. The second is an equivalent static method that does not require any modifications to the elastic frame model, instead using theory‐based lateral force distributions to consider the higher modes of the rocking structure. Neither method requires empirical calibration. The dynamic procedure is used to design two sets of CRSBFs with three, six, nine, twelve and eighteen stories, one set using a response modification factor of R = 8 and the other using up to R = 20. Based on the results of 800 nonlinear time history analyses, both methods are generally more accurate than the previous capacity design methods and at least as simple to implement. Finally, the displacement results suggest that taller CRSBFs designed using could still limit interstorey drifts to approximately 2.5% at the maximum considered earthquake level in the cases considered. Copyright © 2016 John Wiley & Sons, Ltd.     

Analytical prediction of seismic behaviour for concentrically-braced steel systems

This paper presents an analytical model for the inelastic response analysis of braced steel structures. A model is first presented for the behaviour of steel struts subjected to cyclic axial load, which combines the analytical formulation of plastic hinge behaviour with empirical formulas developed on the basis of experimental data. The brace is modelled as a pin-ended member, with a plastic hinge located at the midspan. Braces, with other end conditions, are handled using the effective length concept. Step-wise regression analysis is employed, to approximate the plastic conditions for the steel UC section. Verification of the brace model is performed on the basis of quasi-static analyses of individual struts and a one-bay one-storey X-braced steel frame. The comparison of analytical and experimental data has confirmed that the proposed brace model is able to accurately simulate the cyclic inelastic behaviour of steel braces and braced systems. A series of dynamic analyses has been performed on two-storey V- and X-braced frames to study the influence of brace slenderness ratio on the inelastic response, and to look at the redistribution of forces in the post-buckling range of behaviour of CBFs. Recommendations have been made as to the estimation of maximum storey drifts for concentrically-braced steel frames in major seismic event. © 1997 John Wiley & Sons, Ltd.     

Probabilistic seismic performance evaluation of SMA-braced steel frames considering SMA brace failure

This study explores seismic performance of steel frame buildings with SMA-based self-centering bracing systems using a probabilistic approach. The self-centering bracing system described in this study relies on superelastic response of large-diameter cables. The bracing systems is designed such that the SMA cables are always stressed in tension. A four-story steel frame building characterized until collapse in previous research is selected as a case-study building. The selected steel frame building is designed with SMA bracing systems considering various design parameters for SMA braces. Numerical models of these buildings are developed by taking into account the ultimate state of structural components and SMA braces as well as the effect of gravity frames on lateral load resistance. Nonlinear static analyses are conducted to assess the seismic characteristics of each frame and to examine the effect of SMA brace failure on the seismic load carrying capacity of SMA-braced frames. Incremental dynamic analyses (IDA) are performed to compute seismic response of the designed frames at various seismic intensity levels. The results of IDA are used to develop probabilistic seismic demand models for peak inter-story and residual inter-story drifts. Seismic demand hazard curves of peak and residual inter-story drifts are generated by convolving the ground motion hazard with the probabilistic seismic demand models. Results show that steel frames designed with SMA bracing systems provide considerably lower probability of reaching at a damage state level associated with residual drifts compared to a similarly designed steel moment resisting frame, especially for seismic events with high return periods. This indicates reduced risks for the demolition and collapse due to excessive residual drifts for SMA braced steel frames.