Seismic response of unbraced steel frames

In the analysis and design of unbraced steel frames various models are employed to represent the behaviour of beam-to-column connections. In one such model, termed here as ‘Simple Construction’, pinned connections are assumed when resisting gravity loads, whereas the same connections are assumed to be moment-resistant rigid connections when resisting lateral loads due to an earthquake or wind. Such connections are designed for moments due to lateral loads only; thus, they are not only flexible but may yield when the gravity and lateral loads act concurrently. This paper establishes the seismic performance of two (one 5-storey and the other 10-storey) unbraced steel building frames designed based on the ‘Simple Construction’ technique and on limit state principles. The first part of the paper describes briefly the design of such frames and compares their static responses with the corresponding responses of frames designed based on the ‘Continuous Construction’ assumption. Using realistic moment-rotation behaviour for flexible beam-to-column connections and realistic member behaviour, the non-linear dynamic responses of such frames for the 1940 El Centro record and 2 times the 1952 Taft record have been established using step-by-step time-history analyses. Floor lateral displacement envelopes, storey shear envelopes and cumulative inelastic rotations of beams, columns and connections are presented. The results indicate that the ‘Simple Construction’ frames experience larger lateral deflections while attracting lesser storey shears. During a major earthquake, the columns and connections of the ‘Simple Construction’ frames experience yielding, whereas in ‘Continuous Construction’ frames the beams and columns experience yielding. The cyclic plastic rotations in the connections and in the columns associated with ‘Simple Construction’ frames are found to be considerably higher.     

A deformation-based seismic design method for 3D R/C irregular buildings using inelastic dynamic analysis

A new deformation-based design method concerning 3D reinforced concrete (R/C) buildings is presented, which involves the use of advanced analysis tools, i.e. response-history analysis for appropriately scaled input motions, for multiple levels of earthquake action. The critical issues concerning the inelastic response-history analysis used for the design, namely the definition of the appropriate input, the set up of the analytical model that should account for post-yield behaviour of plastic hinge zones, and the direction of loading, are discussed. The proposed method is based on a partially inelastic model, while the design of structural members is carried out for different performance levels related to their inelastic behaviour. The aforementioned method builds on previous proposals by the first author and his co-workers, nevertheless a new procedure for the design of members that are expected to develop inelastic behaviour for the serviceability earthquake is proposed; its aim is the reduction of member design forces and the a-priori definition of their inelastic performance, by exploiting the deformation limits for the specific performance level, which are related to the damage level of the structural members. The proposed method was applied to irregular multistorey R/C 3D frame buildings with setbacks, and their performance for several levels of earthquake action was assessed using a fully inelastic model and additional ground motions not used at the design phase. The same buildings were designed according to the provisions of Eurocode 8. Comparison of the two methods of seismic design, revealed the advantages of the proposed design method, in particular the more economic detailing of transverse reinforcement in the members that develop very little inelastic behaviour even for very strong earthquakes.     

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.     

基于变轴力柱恢复力模型的钢框筒地震反应分析

建立了考虑轴力变化影响的钢结构杆件的恢复力模型,介绍了模型构成和经试验比较得到的模型的适用性,采用这一模型,对钢框筒结构进行了多维地震作用下的非线性分析,对这类结构的弹塑性特征进行了考察。     

Effects of column axial force – bending moment interaction on inelastic seismic response of steel frames

It is well known that axial force – bending moment interaction (N–M interaction) affects to a large extent the cyclic inelastic behaviour of structural elements, especially columns in framed structures, with reduction in bending capacity and loss of available ductility. A few studies have also shown that significant inelastic axial shortening affects the response of column elements subjected to medium–high levels of axial loads and cyclic bending. This paper is primarily aimed at evaluating the effects of column N–M interaction on the inelastic seismic response of steel frames. By considering the contemporaneous action of vertical loads, due to gravity, and of horizontal seismic excitation, it is shown that the progressive axial shortening of adjacent columns may differ substantially, thus inducing significant relative settlements at the ends of the connecting beams and, then, remarkable amplifications in beam plastic rotations. An evaluation of additional beam plastic rotations induced by column N–M interaction is carried out for real structures by investigating the inelastic response of steel frames designed according to European standards under horizontal and vertical earthquake excitations. Copyright © 2003 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.     

Maximum seismic displacements evaluation of steel frames from their post-earthquake residual deformation

The maximum seismic displacements of a structure can be used for the assessment of its post-earthquake performance. In this paper, a simple and efficient procedure is proposed for determining maximum seismic displacements of planar steel frames from their residual deformation. More specifically, the inelastic behaviour of 36 moment resisting steel frames and 36 concentrically X-braced steel frames under one hundred strong ground motions is investigated. Thus, on the basis of extensive parametric studies for these structures and seismic records, empirical equations are constructed for simple and effective prediction of maximum seismic displacements from residual deformation, which can be measured in-situ after strong seismic events. It is found that the usage of residual deformation can be effectively utilized to evaluate the post-earthquake performance level of steel structures.     

Estimation of seismic drift and ductility demands in planar regular X‐braced steel frames

This paper summarizes the results of an extensive study on the inelastic seismic response of X‐braced steel buildings. More than 100 regular multi‐storey tension‐compression X‐braced steel frames are subjected to an ensemble of 30 ordinary (i.e. without near fault effects) ground motions. The records are scaled to different intensities in order to drive the structures to different levels of inelastic deformation. The statistical analysis of the created response databank indicates that the number of stories, period of vibration, brace slenderness ratio and column stiffness strongly influence the amplitude and heightwise distribution of inelastic deformation. Nonlinear regression analysis is employed in order to derive simple formulae which reflect the aforementioned influences and offer a direct estimation of drift and ductility demands. The uncertainty of this estimation due to the record‐to‐record variability is discussed in detail. More specifically, given the strength (or behaviour) reduction factor, the proposed formulae provide reliable estimates of the maximum roof displacement, the maximum interstorey drift ratio and the maximum cyclic ductility of the diagonals along the height of the structure. The strength reduction factor refers to the point of the first buckling of the diagonals in the building and thus, pushover analysis and estimation of the overstrength factor are not required. This design‐oriented feature enables both the rapid seismic assessment of existing structures and the direct deformation‐controlled seismic design of new ones. A comparison of the proposed method with the procedures adopted in current seismic design codes reveals the accuracy and efficiency of the former. Copyright © 2007 John Wiley & Sons, Ltd.     

Experimental and numerical studies on buckling restrained braces with posttensioned carbon fiber composite cables

There has been an increasing interest in using residual deformation as a seismic performance indicator for earthquake resistant building design. Self-centering braced structural systems are viable candidates for minimizing residual deformations following a major earthquake. Hence, this study proposes an alternative type of buckling restrained brace (BRB) with externally attached posttensioned (PT-BRB) carbon fiber composite cables (CFCCs). The steel core of the brace is used as an energy dissipator, whereas the CFCCs provide the self-centering force for minimizing residual story drifts. Three proof-of-concept specimens are designed, fabricated, and cyclically tested at different posttensioning force levels. The CFCC behavior to obtain cyclic response, including the anchorage system, is examined closely. A parametric study is also conducted to show the effect of the different configurations of PT-BRBs on the inelastic response. Furthermore, optimal brace parameters are discussed to realize design recommendations. The results indicated that the implementation of partially self-centering BRBs in building frames can lead to the target residual displacements. A stable behavior is obtained for the proposed PT-BRBs when subjected to the loading protocol specified in the American Institute of Steel Construction (AISC) 2016 Seismic Provisions.     

A displacement‐based seismic design procedure for RC buildings and comparison with EC8

A procedure for displacement‐based seismic design (DBD) of reinforced concrete buildings is described and applied to a 4‐storey test structure. The essential elements of the design procedure are: (a) proportioning of members for gravity loads; (b) estimation of peak inelastic member deformation demands in the so‐designed structure due to the design (‘life‐safety’) earthquake; (c) revision of reinforcement and final detailing of members to meet these inelastic deformation demands; (d) capacity design of members and joints in shear. Additional but non‐essential steps between (a) and (b) are: (i) proportioning of members for the ULS against lateral loads, such as wind or a serviceability (‘immediate occupancy’) earthquake; and (ii) capacity design of columns in flexure at joints. Inelastic deformation demands in step (b) are estimated from an elastic analysis using secant‐to‐yield member stiffnesses. Empirical expressions for the deformation capacity of RC elements are used for the final proportioning of elements to meet the inelastic deformation demands. The procedure is applied to one side of a 4‐storey test structure that includes a coupled wall and a two‐bay frame. The other side is designed and detailed according to Eurocode 8. Major differences result in the reinforcement of the two sides, with significant savings on the DBD‐side. Pre‐test calculations show no major difference in the seismic performance of the two sides of the test structure. Copyright © 2001 John Wiley & Sons, Ltd.     

Statistical insight into constant-ductility design using a non-stationary earthquake ground motion model

A recently developed earthquake ground motion model non-stationary in both intensity and frequency content is validated at the inelastic Single-Degree-Of-Freedom (SDOF) structural response level. For the purpose of this study, the earthquake model is calibrated for two actual earthquake records. The objective of a constant (or target) displacement ductility used in conventional earthquake-resistant design is examined from the statistical viewpoint using this non-stationary earthquake model. The non-linear hysteretic structural behaviour is modelled using several idealized hysteretic SDOF structural models. Ensemble-average inelastic response spectra corresponding to various inelastic SDOF response (or damage) parameters and conditioned on a constant displacement ductility response are derived from the two identified stochastic ground motion models. The effects of the type of hysteretic behaviour, the structural parameters, the target displacement ductility factor, and the ground motion model on the statistics of the inelastic response parameters are thoroughly investigated. The results of this parametric study shed further light on the proper interpretation and use of inelastic response or damage parameters in earthquake-resistant design in order to achieve the desirable objective of ‘constant-damage design’. © 1997 by John Wiley & Sons, Ltd.     

不同支撑形式高强钢组合偏心支撑抗震性能研究

耗能梁段作为偏心支撑结构的耗能元件,在大震作用下通过弹塑性变形吸收地震能量,保护主体结构处于弹性受力状态。现行规范基于强度的设计理论,为了保证耗能梁段进入塑性或破坏,梁柱构件需要进行放大内力设计,导致截面过大,而且基于强度的设计方法很难保证结构的整体破坏状态。目前,抗震设计越来越重视基于性能的设计思想,该方法能够评估结构的弹塑性反应。对于高强钢组合偏心支撑,其中耗能梁段和支撑采用Q345钢,框架梁柱采用Q460或者Q690高强度钢材,高强钢不仅带来良好的经济效益,而且能够推广高强钢在抗震设防区的应用。利用基于性能设计方法设计了4种不同形式的高强钢组合偏心支撑钢框架,包括K形、Y形、V形和D形,考虑4层、8层、12层和16层的影响。通过Pushover分析和非线性时程分析评估该结构的抗震性能,研究结果表明:4种形式的高强钢组合偏心支撑钢框架具有类似的抗震性能,在罕遇地震作用下,几乎所有耗能梁段均参与耗能,而且层间侧移与耗能梁段转角沿高度分布较为均匀。其中:D形偏心支撑具有最大的抗侧刚度,但延性较差,而Y形偏心支撑的抗侧刚度最弱,但延性最佳。     

The seismic behaviour of cross-braced steel frames

Analytical studies on the inelastic behaviour of concentrically braced steel frames for low-rise buildings are described in this paper. The bracing members which provide energy dissipation were used to provide information on the ductility levels that are likely to occur under differing levels of earthquake excitation. An indication of the relative performance of cross bracing is provided in terms of suitable SM values for use in the seismic provisions of New Zealand loadings code NZS 4203.     

轻质砌块填充墙对钢框架地震反应影响分析

本文根据现有的填充墙钢框架结构试验和理论研究成果,提出了一种适用于结构整体分析的框架填充墙有限元模型。采用杆系模型并编制了相应的弹塑性地震反应分析程序。通过对空框架和带填充墙钢框架的地震反应分析,研究了轻质砌块填充墙的存在对钢框架顶层位移反应、底层柱弯矩及柱轴力反应的影响,得出了有益的结论。为进一步完善钢结构抗震设计提供了理论基础。     

Simplified procedure for the estimation of local inelastic deformation demands for seismic performance assessment of buildings

The implementation of performance‐based design and assessment procedures in seismic codes leads to the need for an accurate estimation of local component demands. According to Part 3 of Eurocode 8 safety checks should be always conducted in terms of plastic rotations, even when linear elastic methods of analysis are used. This paper demonstrates that linear analysis fails to predict inelastic deformation demands at the member level. Therefore, a simplified procedure that allows for the estimation of beam inelastic deformation demands using linear elastic methods of analysis in a simple and conservative way is presented herein. A number of moment‐resisting steel frames designed according to different criteria and exhibiting different column‐to‐beam strength ratios were analysed and used for the derivation of the proposed procedure. A comparative study between alternative methods of quantifying inelastic deformation demands using linear analysis is also carried out. The results obtained allow concluding about the efficiency and conservativeness of the proposed procedure which makes it attractive to be employed in engineering practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Influence of connection typology on seismic response of MR‐Frames with and without ‘set‐backs’

The work presented is aimed at the investigation of the influence of beam‐to‐column connections on the seismic response of MR‐Frames, with and without ‘set‐backs’, designed according to the Theory of Plastic Mechanism Control. The investigated connection typologies are four partial strength connections whose structural details have been designed to obtain the same flexural resistance. The first three joints are designed by means of hierarchy criteria based on the component approach and are characterized by different location of the weakest joint component, leading to different values of joint rotational stiffness and plastic rotation supply and affecting the shape of the hysteresis loops governing the dissipative capacity. The last typology is a beam‐to‐column connection equipped with friction pads devoted to the dissipation of the earthquake input energy, thus preventing the connection damage. An appropriate modelling is needed to accurately represent both strength and deformation characteristics, especially with reference to partial‐strength connections where the dissipation of the earthquake input energy occurs. To this aim, beam‐to‐column joints are modelled by means of rotational inelastic springs located at the ends of the beams whose moment‐rotation curve is characterized by a cyclic behaviour which accounts for stiffness and strength degradation and pinching phenomena. The parameters characterizing the cyclic hysteretic behaviour have been calibrated on the base of experimental results aiming to the best fitting. Successively, the prediction of the structural response of MR‐Frames, both regular frames and frames with set‐backs, equipped with such connections has been carried out by means of both push‐over and Incremental Dynamic Analyses. Copyright © 2016 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.     

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.     

PLASTIC DESIGN OF SEISMIC RESISTANT STEEL FRAMES

A new method for designing moment resisting steel frames failing in a global mode is presented in this paper. Starting from the analysis of the typical collapse mechanisms of frames subjected to horizontal forces, the method is based on the application of the kinematic theorem of plastic collapse. The beam section properties are assumed to be known quantities, because they are designed to resist vertical loads. As a consequence, the unknowns of the design problem are the column sections. They are determined by means of design conditions expressing that the kinematically admissible multiplier of the horizontal forces corresponding to the global mechanism has to be the smallest among all kinematically admissible multipliers. In addition, the proposed design method includes both the influence of distributed loads acting on the beams and the influence of second-order effects. In particular, the influence of second-order effects, which can play an important role in the seismic design of steel frames, is accounted for by the mechanism equilibrium curves of the analysed collapse mechanisms. Moreover, in order to show the practical application of the proposed design procedure, a worked example is presented. Finally, the inelastic behaviour of the designed frame is compared to that obtained when the simple member hierarchy criterion or a similar rule is applied. © 1997 by John Wiley & Sons, Ltd.