Seismic performance and probabilistic collapse resistance assessment of steel moment resisting frames with fluid viscous dampers

This paper evaluates the seismic resistance of steel moment resisting frames (MRFs) with supplemental fluid viscous dampers against collapse. A simplified design procedure is used to design four different steel MRFs with fluid viscous dampers where the strength of the steel MRF and supplemental damping are varied. The combined systems are designed to achieve performance that is similar to or higher than that of conventional steel MRFs designed according to current seismic design codes. Based on the results of nonlinear time history analyses and incremental dynamic analyses, statistics of structural and non‐structural response as well as probabilities of collapse of the steel MRFs with dampers are determined and compared with those of conventional steel MRFs. The analytical frame models used in this study are reliably capable to simulate global frame collapse by considering full geometric nonlinearities as well as the cyclic strength and stiffness deterioration in the plastic hinge regions of structural steel members. The results show that, with the aid of supplemental damping, the performance of a steel MRF with reduced design base shear can be improved and become similar to that of a conventional steel MRF with full design base shear. Incremental dynamic analyses show that supplemental damping reduces the probability of collapse of a steel MRF with a given strength. However, the paper highlights that a design base shear equal to 75% of the minimum design base shear along with supplemental damping to control story drift at 2% (i.e., design drift of a conventional steel MRF) would not guarantee a higher collapse resistance than that of a conventional MRF. At 75% design base shear, a tighter design drift (e.g., 1.5% as shown in this study) is needed to guarantee a higher collapse resistance than that of a conventional MRF. 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.     

Seismic design procedure and seismic response of post‐tensioned self‐centering steel frames

Post‐tensioned (PT) self‐centering moment‐resisting frames (MRFs) have recently been developed as an alternative to welded moment frames. The first generation of these systems incorporated yielding energy dissipation mechanisms, whereas more recently, PT self‐centering friction damped (SCFR) moment‐resistant connections have been proposed and experimentally validated. Although all of these systems exhibited good stiffness, strength and ductility properties and stable dissipation of energy under cyclic loading, questions concerning their ultimate response still remained and a complete design methodology to allow engineers to conceive structures using these systems was also needed. In this paper, the mechanics of SCFR frames are first described and a comprehensive design procedure that accounts for the frame behavior and the nonlinear dynamics of self‐centering frames is then elaborated. A strategy for the response of these systems at ultimate deformation stages is then proposed and detailing requirements on the beams in order to achieve this response are outlined. The proposed procedure aims to achieve designs where the interstory drifts for SCFR frames are similar to those of special steel welded moment‐resisting frames (WMRFs). Furthermore, this procedure is adapted from current seismic design practices and can be extended to any other PT self‐centering steel frame system. A six‐story building incorporating WMRFs was designed and a similar building incorporating SCFR frames were re‐designed by the proposed seismic design procedure. Time‐history analyses showed that the maximum interstory drifts and maximum floor accelerations of the SCFR frame were similar to those of the WMRF but that almost zero residual drifts were observed for the SCFR frame. The results obtained from the analyses confirmed the validity of the proposed seismic design procedure, since the peak drift values were similar to those prescribed by the seismic design codes and the SCFR frames achieved the intended performance level under both design and maximum considerable levels of seismic loading. Copyright © 2008 John Wiley & Sons, Ltd.     

Evaluation of building period formulas for seismic design

Building period formulas in seismic design code are evaluated with over 800 apparent building periods from 191 building stations and 67 earthquake events. The evaluation is carried out with the formulas in ASCE 7‐05 for steel and RC moment‐resisting frames, shear wall buildings, braced frames, and other structural types. Qualitative comparison of measured periods and periods calculated from the code formulas shows that the formula for steel moment‐resisting frames generally predicts well the lower bound of the measured periods for all building heights. But the differences between the periods from code formula and measured periods of low‐ to‐medium rise buildings are relatively high. In addition, the periods of essential buildings designed with the importance factor are about 40% shorter than the periods of non‐essential buildings. The code formula for RC moment‐resisting frames describes well the lower bound of measured periods. The formula for braced frames accurately predicts the lower bound periods of low‐to‐medium rise buildings. The formula for shear wall buildings overestimates periods for all building heights. For buildings that are classified as other structural types, the measured building periods can be much shorter than the periods calculated with the code formula. Based on these observations, it is suggested to use C_r factor of 0.015 for shear walls and other structural types. Copyright © 2010 John Wiley & Sons, Ltd.     

An innovative methodology for seismic retrofitting of existing RC buildings by metal shear panels

In the present paper, the seismic upgrading of existing reinforced concrete (RC) structures by means of steel and pure aluminium shear panels is examined. After a preliminary experimental evaluation of the performance of the bare RC structure, a design approach based on the capacity spectrum method has been developed according to the procedure provided in the ATC 40 American guidelines. First, the geometrical configuration of the applied shear panels has been defined according to simplified analytical relationships, while appropriate steel members have been designed to allow the insertion of shear panels in the existing RC structure. Then, complex finite element models have been implemented in order to check the reliability of the proposed design procedure. Also, a numerical evaluation of the global response of the upgraded structure has been processed aiming at evaluating the interaction between the RC structure and the metal devices. Finally, the effectiveness of the applied shear panels has been proven by means of full‐scale experimental tests, which confirmed the significant improvement of the RC structure performance, in terms of strength, stiffness and deformation capacity. Copyright © 2008 John Wiley & Sons, Ltd.     

Inclusion of P–Δ effect in displacement‐based seismic design of steel moment resisting frames

A procedure for treating the P– Δ effect in the direct displacement‐based seismic design of regular steel moment resisting frames with ideal elastoplastic material behaviour is proposed. A simple formula for the yield displacement amplification factor as a function of ductility and the stability coefficient is derived on the basis of the seismic response of an inelastic single degree‐of‐freedom system taking into account the P– Δ effect. Extensive parametric seismic inelastic analyses of plane moment resisting steel frames result in a simple formula for the dynamic stability coefficient as a function of the number of stories of a frame and the column to beam stiffness ratio. Thus, the P– Δ effect can be easily taken into account in a direct displacement‐based seismic design through the stability coefficient and the yield displacement amplification factor. A simple design example serves to illustrate the application of the proposed method and demonstrate its merits. Copyright © 2007 John Wiley & Sons, Ltd.     

Tests and model calibration of high‐strength steel tubular beam‐to‐column and column‐base composite joints for moment‐resisting structures

Performance‐based engineering (PBE) methodologies allow for the design of more reliable earthquake‐resistant structures. Nonetheless, to implement PBE techniques, accurate finite element models of critical components are needed. With these objectives in mind, initially, we describe an experimental study on the seismic behaviour of both beam‐to‐column (BTC) and column‐base (CB) joints made of high‐strength steel S590 circular columns filled with concrete. These joints belonged to moment‐resisting frames (MRFs) that constituted the lateral‐force‐resisting system of an office building. BTC joints were conceived as rigid and of partial strength, whereas CB joints were designed as rigid and of full strength. Tests on a BTC joint composed of an S275 steel composite beam and high‐strength steel concrete‐filled tubes were carried out. Moreover, two seismic CB joints were tested with stiffeners welded to the base plate and anchor bolts embedded in the concrete foundation as well as where part of a column was embedded in the foundation with no stiffeners. A test programme was carried out with the aim of characterising these joints under monotonic, cyclic and random loads. Experimental results are presented by means of both force–interstory drift ratio and moment–rotation relationships. The outcomes demonstrated the adequacy of these joints to be used for MRFs of medium ductility class located in zones of moderate seismic hazard. Then, a numerical calibration of the whole joint subassemblies was successfully accomplished. Finally, non‐linear time‐history analyses performed on 2D MRFs provided useful information on the seismic behaviour of relevant MRFs. Copyright © 2015 John Wiley & Sons, Ltd.     

Towards a seismic design method for plane steel frames using equivalent modal damping ratios

A method for seismic design of plane steel moment resisting frames based on the use of equivalent modal damping ratios is developed. The method determines the design base shear of the structure through spectrum analysis using rationally obtained equivalent modal damping ratios instead of the crude strength reduction (behavior) factor. An equivalent linear structure, which retains the mass and initial stiffness of the original non-linear structure and takes into account geometrical non-linearity and inelasticity in the form of equivalent, time-invariant, modal damping ratios is established. The equivalent damping ratios for the first few significant modes are numerically computed by first iteratively forming a frequency response transfer function modulus until it satisfies certain smoothness criteria and then by solving a set of non-linear algebraic equations. Thus, design equations providing equivalent damping ratios as functions of period and allowable deformation and damage are constructed using extensive numerical data coming from plane steel moment resisting frames excited by various seismic motions. These equations can be used in conjunction with a design spectrum, appropriately constructed for high damping values, and modal synthesis tools to calculate the seismic design forces of the structure. The proposed method is illustrated by numerical examples. It is concluded that unlike the usual approach of seismic codes employing a single common value of the strength reduction factor value for all modes, the proposed approach working with deformation and damage dependent equivalent modal damping ratios leads to more accurate and deformation and damage controlled results.     

Seismic performance and new design procedure for chevron‐braced frames

The paper is concerned with the seismic design of steel‐braced frames in which the braces are configured in a chevron pattern. According to EuroCode 8 (EC8), the behaviour factor q, which allows for the trade‐off between the strength and ductility, is set at 2.5 for chevron‐braced frames, while 6.5 is assigned for most ductile steel moment‐resisting frames. Strength deterioration in post‐buckling regime varies with the brace's slenderness, but EC8 adopts a unique q value irrespective of the brace slenderness. The study focuses on reevaluation of the q value adequate for the seismic design of chevron‐braced frames. The present EC8 method for the calculation of brace strength supplies significantly different elastic stiffnesses and actual strengths for different values of brace slenderness. A new method to estimate the strength of a chevron brace pair is proposed, in which the yield strength (for the brace in tension) and the post‐buckling strength (for the brace in compression) are considered. The new method ensures an identical elastic stiffness and a similar strength regardless of the brace slenderness. The advantage of the proposed method over the conventional EC8 method is demonstrated for the capacity of the proposed method to control the maximum inter‐storey drift. The q values adequate for the chevron‐braced frames are examined in reference to the maximum inter‐storey drifts sustained by most ductile moment‐resisting frames. When the proposed method is employed for strength calculation, the q value of 3.5 is found to be reasonable. It is notable that the proposed method does not require larger cross‐sections for the braces compared to the cross‐sections required for the present EC8 method. Copyright © 2005 John Wiley & Sons, Ltd.     

Parametric study of ductile moment‐resisting steel frames: A first step towards Eurocode 8 calibration

A parametric study of 13 608 ductile moment‐resisting steel frames designed according to Eurocodes 3 and 8 is performed. A flowchart for the evaluation of the seismic‐resistant capacity of the designed frames is developed based on the N2 method. The design structural overstrength, ductility supply, plastic redistribution parameter, supply reduction factor and performance ratio of the frames are analysed. We determine that the frames have performance ratios higher than 1, mostly due to high values of design structural overstrength, showing that the seismic supply produced by the restraints of Eurocodes 3 and 8 is always higher than the seismic demand. Copyright © 2008 John Wiley & Sons, Ltd.     

Seismic reliability of steel moment resisting framed buildings retrofitted with buckling restrained braces

The present paper investigates the seismic reliability of the application of buckling restrained braces (BRBs) for seismic retrofitting of steel moment resisting framed buildings through fragility analysis. Samples of regular three‐storey and eight‐storey steel moment resisting frames were designed with lateral stiffness insufficient to comply with the code drift limitations imposed for steel moment resisting frame systems in earthquake‐prone regions. The frames were then retrofitted with concentrically chevron conventional braces and BRBs. To obtain robust estimators of the seismic reliability, a database including a wide range of natural earthquake ground motion records with markedly different characteristics was used in the fragility analysis. Nonlinear time history analyses were utilized to analyze the structures subjected to these earthquake records. The improvement of seismic reliability achieved through the use of conventional braces and BRBs was evaluated by comparing the fragility curves of the three‐storey and eight‐storey model frames before and after retrofits, considering the probabilities of four distinct damage states. Moreover, the feasibility of mitigating the seismic response of moment resisting steel structures by using conventional braces and BRBs was determined through seismic risk analysis. The results obtained indicate that both conventional braces and especially BRBs improve significantly the seismic behavior of the original building by increasing the median values of the structural fragility curves and reducing the probabilities of exceedance of each damage state. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of deterioration modelling on the seismic response of steel moment frames designed to Eurocode 8

This paper assesses the influence of cyclic and in‐cycle degradation on seismic drift demands in moment‐resisting steel frames (MRF) designed to Eurocode 8. The structural characteristics, ground motion frequency content, and level of inelasticity are the primary parameters considered. A set of single‐degree‐of‐freedom (SDOF) systems, subjected to varying levels of inelastic demands, is initially investigated followed by an extensive study on multi‐storey frames. The latter comprises a large number of incremental dynamic analyses (IDA) on 12 frames modelled with or without consideration of degradation effects. A suite of 56 far‐field ground motion records, appropriately scaled to simulate 4 levels of inelastic demand, is employed for the IDA. Characteristic results from a detailed parametric investigation show that maximum response in terms of global and inter‐storey drifts is notably affected by degradation phenomena, in addition to the earthquake frequency content and the scaled inelastic demands. Consistently, both SDOF and frame systems with fundamental periods shorter than the mean period of ground motion can experience higher lateral strength demands and seismic drifts than those of non‐degrading counterparts in the same period range. Also, degrading multi‐storey frames can exhibit distinctly different plastic mechanisms with concentration of drifts at lower levels. Importantly, degrading systems might reach a “near‐collapse” limit state at ductility demand levels comparable to or lower than the assumed design behaviour factor, a result with direct consequences on optimised design situations where over‐strength would be minimal. Finally, the implications of the findings with respect to design‐level limit states are discussed.     

Behaviour and modelling of partial‐strength beam‐to‐column composite joints for seismic applications

A refined component model is proposed to predict the inelastic monotonic response of exterior and interior beam‐to‐column joints for partial‐strength composite steel–concrete moment‐resisting frames. The joint typology is designed to exhibit ductile seismic response through plastic deformation developing simultaneously in the column web panel in shear, the bolted end‐plate connection, the column flanges in bending and the steel reinforcing bars in tension. The model can handle the large inelastic deformations consistent with high ductility moment‐resisting frames. Slip response between the concrete slab and the beams was taken into account. A fibre representation was adopted for the concrete slab to accurately capture the non‐uniform stress distribution and progressive crushing of the concrete at the interface between the concrete slab and the column flange. The model is validated against results from full‐scale subassemblages monotonic physical tests performed at the University of Pisa, Italy. A parametric study is presented to illustrate the capabilities of the model and the behaviour of the joints examined. Copyright © 2006 John Wiley & Sons, Ltd.     

Minimal‐disturbance seismic rehabilitation of steel moment‐resisting frames using light‐weight steel elements

This paper presents a rehabilitation technique developed under a design and construction scheme, termed minimal‐disturbance seismic rehabilitation. This scheme pursues enhancing the seismic performance of buildings with the intention of improving the continuity of business while minimizing obstruction of the visual and physical space of building users and the use of heavy construction equipment and hot work (welding/cutting). The developed rehabilitation technique consists of light‐weight steel elements and aims to decrease demands to beam‐ends of steel moment‐resisting frames. The behavior of the baseline model was verified through numerical analysis and proof‐of‐concept testing. Furthermore, the effectiveness of rehabilitation is studied through retrofitting a four‐story steel moment‐resisting frame originally designed with Japanese design guidelines. Copyright © 2015 John Wiley & Sons, Ltd.     

Rocking damage‐free steel column base with friction devices: design procedure and numerical evaluation

Earthquake‐resilient steel frames, such as self‐centering frames or frames with passive energy dissipation devices, have been extensively studied during the past decade, but little attention has been paid to their column bases. The paper presents a rocking damage‐free steel column base, which uses post‐tensioned high‐strength steel bars to control rocking behavior and friction devices to dissipate seismic energy. Contrary to conventional steel column bases, the rocking column base exhibits monotonic and cyclic moment–rotation behaviors that are easily described using simple analytical equations. Analytical equations are provided for different cases including structural limit states that involve yielding or loss of post‐tensioning in the post‐tensioned bars. A step‐by‐step design procedure is presented, which ensures damage‐free behavior, self‐centering capability, and adequate energy dissipation capacity for a predefined target rotation. A 3D nonlinear finite element (FE) model of the column base is developed in abaqus . The results of the FE simulations validate the accuracy of the moment–rotation analytical equations and demonstrate the efficiency of the design procedure. Moreover, a simplified model for the column base is developed in OpenSees . Comparisons among the OpenSees and abaqus models demonstrate the efficiency of the former and its adequacy to be used in nonlinear dynamic analysis. A prototype steel building is designed as a self‐centering moment‐resisting frame with conventional or rocking column bases. Nonlinear dynamic analyses show that the rocking column base fully protects the first story columns from yielding and eliminates the first story residual drift without any detrimental effect on peak interstory drifts. The study focuses on the 2D rocking motion and, thus, ignores 3D rocking effects such as biaxial bending deformations in the friction devices. The FE models, the analytical equations, and the design procedure will be updated and validated to cover 3D rocking motion effects after forthcoming experimental tests on the column base. Copyright © 2017 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.     

Effective periods and seismic performance of steel moment resisting frames designed for risk categories I and IV according to IBC2009

In current seismic design, structures that are essential for post‐disaster recovery, and hazardous facilities are classified as risk category IV and are designed with higher importance factors and stringent drift limits. These structures are expected to perform better in an earthquake event because a larger base shear and more stringent drift limit are used. Although this provision has been in the seismic design code over the last three decades, few studies have investigated the performance of essential structures. The aim of this study is to quantify the impact of higher importance factors and stringent drift limits on the seismic performance of steel moment resisting frames. A total of 16 steel structures are designed for Los Angeles and Seattle. Different risk categories are used for the design. The effects of the risk categories on the structural periods, and thus on the seismic force demand, are investigated. A suite of inelastic time history analyses are carried out to understand the probability of exceeding a specified limit state when the structures are subjected to different levels of earthquake events. The results show that the periods of the structures in risk category IV decrease by a factor of 0.5 to 0.8, and the strengths increase by a factor of 1.5 to 3.2. Seismic fragility analysis shows that the structures in risk category IV generally satisfy the probabilistic performance objectives. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal seismic design of moment‐resisting steel frames with hysteretic passive devices

The effectiveness of hysteretic passive devices to protect and mitigate the response of a structure under seismic loading is well established by both analytical and experimental research. Nevertheless, a systematic and well‐established methodology for the topological distribution and size of these devices in order to achieve a desired structural response performance does not exist. In this paper, a computational framework is proposed for the optimal distribution and design of yielding metallic buckling restrained braces (BRB) and/or friction dampers within steel moment‐resisting frames (MRF) for a given seismic environment. A Genetic Algorithm (GA) is used to solve the resulting discrete optimization problem. Specific examples involving two three‐story, four‐bay steel MRFs and a six‐story, three‐bay steel MRF retrofitted with yielding and/or friction braces are considered. The seismic environment consists of four synthetic ground motions representative of the west coast of the United States with 5% probability of exceedance in 50 years. Non‐linear time‐history analyses are employed to evaluate the potential designs. As a result of the evolutionary process, the optimal placement, strength and size of the dampers are obtained throughout the height of the steel MRF. Furthermore, the developed computational approach for seismic design based upon GAs provides an attractive procedure for design of MRFs with hysteretic passive dampers. Copyright © 2009 John Wiley & Sons, Ltd.     

Local deformation‐based design of minimal‐disturbance arm damper for retrofitting steel moment‐resisting frames

This paper presents a design approach for seismic rehabilitation of frames having a beam‐collapse mechanism using a technique termed minimal‐disturbance seismic rehabilitation. This technique pursues enhancing the seismic performance of buildings with the intention of improving the continuity of business. It minimizes obstruction of the visual and physical space of building users and the use of heavy construction equipment and work requiring fire permit (welding/cutting). The developed design approach is simple to use. Yet it leads to designs that limit the beams' plastic rotations to allowable values, while minimizing the number of locations where devices are installed and the devise dimensions. Furthermore, the effectiveness of the design approach and the rehabilitation technique is numerically studied through retrofitting a four‐story steel moment‐resisting frame. Copyright © 2017 John Wiley & Sons, Ltd.     

Identification of the hysteretic behaviour of a partial‐strength steel–concrete moment‐resisting frame structure subject to pseudodynamic tests

In low‐rise steel‐concrete composite structures, moment‐resisting frames can be designed to develop a ductile response in beam‐to‐column joints and column bases by activating flexural yielding of beams and end plates, shear yielding of column web panel zones and yielding of anchors. To evaluate the performance of these components under differing earthquake intensities, a series of pseudodynamic, quasistatic cyclic and vibration tests were carried out on a two‐storey two‐bay moment resisting structure. The performance‐based seismic design and control of these structures requires that stiffness degradation, strength deterioration and slip are properly modelled. In this context, compact hysteretic models can play a key role and must therefore be striven for. Nonetheless, relevant techniques, like nonlinear system identification, are far from representing standard and reliable tools for the dynamic characterization of full‐scale structural systems. With this objective in mind, we present a restoring force surface‐based technique applied to pseudodynamic test data, in view of the nonlinear identification of multistorey frames. The technique is developed by means of a parametric approach, where a time‐variant stiffness operator is coupled to a modified Bouc–Wen model that allows both for slip and for degradation in stiffness. Strength deterioration is indirectly taken into account too. We also show how model‐based parameters can be correlated to the damage process progressively observed both in the structure and in its components. Finally, the predictive capabilities of the identified model are highlighted. Copyright © 2012 John Wiley & Sons, Ltd.