Optimum seismic design of concentrically braced steel frames: concepts and design procedures

A methodology is presented for optimization of the dynamic response of concentrically braced steel frames subjected to seismic excitation, based on the concept of uniform distribution of deformation. In order to obtain the optimum distribution of structural properties, an iterative optimization procedure has been adopted. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. This process is continued until a state of uniform deformation is achieved. It is shown that the seismic performance of such a structure is optimal, and behaves generally better than those designed by conventional methods. In order to avoid onerous analysis of the frame models, an equivalent procedure is introduced for performing the optimization procedure on the modified reduced shear-building model of the frames, which is shown to be accurate enough for design purposes.     

Tensile forces for seismic design of braced frame connections — Experimental results

Experimental results from seventeen large scale tests on bracing members are presented within the context of tensile force demands on connections during seismic loading. The bracing members are subjected to three cyclic loading histories consistent with expected axial deformation demands during seismic loading in concentrically braced frames. The experiments feature commonly used cross-sections including HSS, Pipe and Wide-flanged beams. The test data suggests that the current approach of designing bracing connections based on the expected yield strength of the brace is somewhat unconservative, since it does not incorporate the effect of strain hardening. This trend is observed across all the cross-section types and loading histories. On average, the current approach underestimates the maximum forces transferred to connections by 9%-11%, depending on the level of deformation expected in the brace. To reduce this unconservatism, an alternate approach, based on the average of the expected yield and ultimate strength is proposed. This approach provides significantly improved estimates of the forces that may be transferred to bracing connections. Limitations of the study and future work are outlined.     

Buckling-restrained braced frame connection performance

Large-scale experimental studies of buckling-restrained braced frames (BRBFs) have shown that although they display good overall seismic performance, they may have limitations due to connection failure modes that do not allow the braces to realize their full ductility capacity. These experimental results motivate further investigation of BRBF connection behavior. In this study, nonlinear finite element models are used to study BRBF beam–column–brace connections. The models focus on a one-story subassembly extracted from a previously-tested, four-story BRBF. After the baseline finite element analysis results are verified with experimental data, parametric studies varying the connection configuration are used to assess the key factors influencing performance. Connection configuration is shown to have a significant impact on global system response and localized connection demands.     

A balanced design procedure for special concentrically braced frame connections

Concentrically braced frames (CBFs) are stiff, strong structures that are suitable for resisting large lateral loads. Special CBFs (SCBF) are used for seismic design and are designed and detailed to sustain relatively large inelastic deformations without significant deterioration in resistance. Current AISC Seismic Design Provisions aim to ensure the brace sustains the required inelastic action, but recent research showed that current SCBF design requirements lead to variable seismic performance, unintended failure modes, and limited deformation capacity. To improve the seismic response of SCBFs, a balanced design procedure was proposed. The premise of the design methodology is to balance the primary yield mechanism, brace buckling and yielding, with other, complementary ductile yielding mechanisms, such as gusset plate yielding. This balance process maximizes ductile yielding in the frame thereby maximizing the drift capacity of the frame. Further, the undesirable failure modes are balanced with the yield mechanisms and the preferred failure mode, brace fracture, to ensure that the frame fails in the desired manner. To achieve the objectives of the design methodology namely maximum drift capacity, and adherence to a desired yield and failure hierarchy, rational resistance checks and appropriate balance factors (β factors) are used to balance each yield mechanism and failure mode. These factors were developed, validated, and refined using the measured results from an extensive test program. An SCBF connection design example to illustrate the application of the balanced design method and to demonstrate differences from the current AISC design method is presented in an appendix.     

Progressive collapse analysis of seismically designed steel braced frames

The progressive collapse resistance of seismically designed steel braced frames is investigated using validated computational simulation models. Two types of braced systems are considered: namely, special concentrically braced frames and eccentrically braced frames. The study is conducted on previously designed 10-story prototype buildings by applying the alternate path method. In this methodology, critical columns and adjacent braces, if present, are instantaneously removed from an analysis model and the ability of the model to successfully absorb member loss is investigated. Member removal in this manner is intended to represent a situation where an extreme event or abnormal load destroys the member. The simulation results show that while both systems benefit from placement of the seismically designed frames on the perimeter of the building, the eccentrically braced frame is less vulnerable to progressive collapse than the special concentrically braced frame. Improvement in behavior is due to improved system and member layouts in the former compared to the latter rather than the use of more stringent seismic detailing.     

Recent research on eccentrically braced frames

Recent research developments on eccentrically braced steel frames for seismic design are reviewed. The emphasis is placed on the design of links, which are short sections of beams between columns and braces, and similar elements at eccentric joints. The review includes some highlights of the latest experiments with one-third scale models employing different eccentric bracing schemes, an updated classification of links, and special design requirements for different types of links. Some results are given on recent cyclic tests of full-size links.     

Seismic response of stainless steel braced frames

The present paper investigates the feasibility of the application of stainless steel (SS) in the seismic design of braced frames, either concentrically (CBFs) or eccentrically (EBFs) braced. A sample of regular multi-storey CBFs and EBFs was designed in compliance with modern seismic standards based on capacity-design rules. The results of pushover and inelastic response history analyses demonstrate that systems employing SSs exhibit enhanced plastic deformations and excellent energy absorbing capacity with respect to mild steel braced frames. The augmented strain hardening of SS, which is nearly twice that of carbon steels, is beneficial to prevent local buckling in steel members, especially those subjected to high axial compression. The performed analyses also demonstrate that in CBFs with SS braces and columns the increase in overstrength is about 40% with respect to the configuration in mild steel. For EBFs, the use of SS in the diagonals or in braces and links increases the global overstrength of the lateral resisting system by 20%. When the EBFs employ braces and columns in SS the increase can be as high as 50%.     

Seismic response of steel braced frames with shape memory alloy braces

In this paper, the seismic performance of steel frames equipped with superelastic SMA braces was investigated. To do so, buildings with various stories and different bracing configurations including diagonal, split X, chevron (V and inverted V) bracings were considered. Nonlinear time history analyses of steel braced frames equipped with SMA subjected to three ground motion records have been performed using OpenSees software. To evaluate the possibility of adopting this innovative bracing system and its efficiency, the dynamic responses of frames with SMA braces were compared to the ones with buckling restrained braces. After comparing the results, one can conclude that using an SMA element is an effective way to improve the dynamic response of structures subjected to earthquake excitations. Implementing the SMA braces can lead to a reduction in residual roof displacement and peak inter-story drift compare to the buckling restrained braced frames.     

Analytical expressions for preliminary design of dissipative bracing systems in steel frames

In this paper a direct displacement-based design (DDBD) method for seismic design of steel frames equipped with dissipative braces is proposed. Attention is focused on concentric braced steel frames with pinned beam-to-column joints in which the bracing system (with viscoelastic or elastoplastic dissipative devices) is the main seismic resistant component. The proposed design method uses an equivalent continuous model where flexural deformability and shear deformability are related respectively to columns and diagonals of the bracing system. In this way, analytical expressions of the required flexural and shear stiffness distributions are obtained. These expressions are quite simple and can be conveniently used in preliminary design of dissipative diagonal braces and columns. Examples are shown for steel frames with dissipative braces based on elastomeric dampers (viscoelastic devices) and steel frames with buckling-restrained braces (elastoplastic devices). Results of time history analyses are illustrated and discussed in order to evaluate the effectiveness of the proposed DDBD procedure.     

Experimental investigation of link-to-column connections in eccentrically braced frames

The design of link-to-column connections in seismic-resistant eccentrically braced frames remains a largely unresolved problem. In order to address this problem, twenty-four large-scale specimens were tested under cyclic loading. The test parameters included the connection detail, link length, link section, and cyclic loading protocol. The test results suggest that link-to-column connections are susceptible to fracture at the link flange welds, regardless of the link length. A large number of specimens failed prematurely, before meeting the plastic link rotation requirement in US code provisions. However, two promising link-to-column connection details were developed as an outcome of this research. The new connection details include a detail using all-around fillet welds between the link and the column flange, and a reinforced connection detail that welds a pair of stiffeners in the first link web panel next to the column, parallel to the link web. Test specimens using either of these two details were able to exceed the plastic link rotation requirement.     

Stochastic optimisation of buckling restrained braced frames under seismic loading

A stochastic optimisation procedure is proposed for the design of low- and mid-rise buckling restrained braced frames subject to seismic loading. The seismic excitation is represented as a zero-mean nonstationary filtered white noise. The Bouc–Wen model is chosen to represent the hysteretic behaviour of the buckling restrained braces. The equivalent linearisation method is employed to determine the second-order statistics of structural responses from the non-linear system. Three seismic intensity levels are considered in this study, which are associated to earthquakes with different probability of occurrence during the building’s lifecycle. It was observed that the optimal design that minimises the maximum ductility demand produces a more uniform distribution of energy dissipation and avoids soft-storey mechanisms; therefore, this design objective is considered to be a more reasonable optimisation objective for the design of buckling restrained braced frames. For higher rise structures, buckling restrained braces may experience over-dimensioning in the top stories, which means that dissipation will not occur. Thus, an upper bound constraint for the stiffness design of the buckling restrained braces is taken into account.     

偏心支撑钢框架的设计

简述了偏心支撑钢框架结构的工作原理及特点,介绍了偏心支撑钢框架的设计计算方法,其中重点介绍了各杆件的内力计算：耗能梁段设计、非耗能梁段设计、支撑设计和框架柱设计,为工程设计人员提供了指导。     

防屈曲支撑钢框架结构中被撑柱抗震设计探讨

通过3个算例,对采用人字形和V字形的无粘结内藏钢板支撑剪力墙(即人字形和V字形防屈曲支撑)的防屈曲支撑钢框架结构的抗震性能进行分析。重点考察大震下,支撑的轴力分布和对被撑柱所受轴力的影响。分析表明,采用结构在一阶振型下的支撑轴力分布来设计被撑柱的做法,适用于多层的防屈曲支撑钢框架结构;而对于高层的防屈曲支撑钢框架结构,高振型影响较显著,上述设计方法对被撑柱的设计较保守,有必要考虑高振型参与下的支撑轴力分布来设计被撑柱。     

An investigation on the accuracy of pushover analysis for estimating the seismic deformation of braced steel frames

This paper investigates the potentialities of the pushover analysis to estimate the seismic deformation demands of concentrically braced steel frames. Reliability of the pushover analysis has been verified by conducting nonlinear dynamic analysis on 5, 10 and 15 story frames subjected to 15 synthetic earthquake records representing a design spectrum. It is shown that pushover analysis with predetermined lateral load pattern provides questionable estimates of inter-story drift. To overcome this inadequacy, a simplified analytical model for seismic response prediction of concentrically braced frames is proposed. In this approach, a multistory frame is reduced to an equivalent shear-building model by performing a pushover analysis. A conventional shear-building model has been modified by introducing supplementary springs to account for flexural displacements in addition to shear displacements. It is shown that modified shear-building models have a better estimation of the nonlinear dynamic response of real framed structures compared to nonlinear static procedures.     

Evaluation of the residual capacity of a structure in performance-based seismic design (PBSD) through seismic hazard analysis

In this paper through the concept of seismic hazard assessment and the damage index criterion, a new approach to assess the performance of a structure with respect to the level of earthquake excitation is developed. Using Fajfar's hysteretic energy model and the damage index of Park and Ang, damage-related hazard curves are generated. The parameters to be considered in these hazard curves include capacity and demand of system ductility, hysteretic dissipation energy capacity of the structural system, and structural period. Similarly, through the concept of dissipated energy during a sequence of earthquakes and the proposed damage consistent hazard curves, the residual energy capacity of a ‘pre-damaged’ structure can also be estimated. Re-estimation on the performance objective after a series of earthquake excitations can be conducted. Seismic ground motion data collected from Taiwan were used to generate the regression model in this study.     

Influence of masonry infill on the seismic performance of concentrically braced frames

This paper presents an experimental and analytical study to investigate the effect of masonry infill on the seismic performance of special Concentrically Braced Frames (CBFs). Cyclic lateral load tests are conducted on three half-scale specimens including two special CBFs with and without masonry infill and a moment resisting steel frame with masonry infill for comparison purposes. Companion analyses are performed to study the influence of masonry infill on the potential rupture of gusset plates and top-seat angle connections by using detailed FE models validated with experimental results. It is shown that the presence of masonry infill could increase the lateral stiffness and load carrying capacity of the special CBF by 33% and 41%, respectively. However, the interaction between masonry infill and the frame significantly increased the strain demands and failure potential of the connections. The results of the experimental tests and analytical simulations indicate that ignoring the influence of masonry infill in the seismic design process of CBFs results in a premature fracture of the connection weld lines and a significant reduction in the deformation capacity and ductility of the frame. This can adversely influence the seismic performance of the structure under strong earthquakes. The results of this study compare well with the damage observations after the 2003 earthquake in Bam, Iran.     

砌体填充墙RC框架结构平面内抗震性能有限元模拟

砌体填充墙RC框架结构是我国建筑结构中普遍采用的结构形式,历次地震震害表明填充墙的刚度效应和约束效应改变了主体结构的传力机理,导致整体结构的严重破坏。为了分析其砌体填充墙RC框架侧向承载力和刚度,研究砌体填充墙与RC框架之间的相互协同工作机理和砌体填充墙的开裂模式以及砂浆层的滑移,该文利用三维实体单元和基于表面的粘性接触面模型和摩擦原理,建立一种能够较好地模拟其平面内抗震性能的分离式有限元模型。对一个已有试验分别建立普通有限元模型和分离式有限元模型,二者的分析结果与试验结果的对比表明,分离式有限元模拟方法可以更加准确地预测砌体填充墙RC框架结构的侧向承载力和刚度,并且可以有效地模拟出砌体填充墙的开裂模式,通过塑性应变可以判断出RC构件的失效。     

Y型偏心支撑钢框架受力性能有限元分析

建立了四种Y型偏心支撑钢框架有限元模型,对平面模型框架和三种空间模型框架进行了单向加载和循环加载试验,并对比分析了模型框架的屈服强度、极限承载力、侧向刚度、延性和耗能能力等方面的受力性能差异,得到的结果为工程设计提供了参考。     

A simplified analytical story drift evaluation of steel moment frames with radius-cut reduced beam section

A simplified analytical procedure is presented to estimate the elastic story drift of steel frames with the radius-cut RBS (reduced beam section) moment connections. Due to the geometric configuration of the radius-cut RBS, the mathematical formulation is complicated when applying the conjugate beam method to compute the component of story drift contributed by the beam. In this study, the problem is circumvented by replacing the original radius-cut RBS with an equivalent beam of constant width. The equivalence between the two is established by imposing the equal flange elongation criterion over the RBS region. This approach is justified by a finite element analysis. The story drift components contributed by the column, the panel zone, and the beam are then formulated into a closed form solution for a typical beam-column subassembly. The derived results can readily be used by designers to estimate the magnitude of RBS frame story drift and the effect of the stiffness variations.     

Plastic design of eccentrically braced frames, II: Failure mode control

A design methodology aiming at the development of a collapse mechanism of a global type for eccentrically braced frames is presented in this paper. This result is of primary importance in earthquake resistant design, because partial and local failure modes are responsible of the worsening of the energy dissipation capacity leading to an increased risk of collapse under destructive ground motions.The proposed method is based on the assumption that horizontal member sections are known, as they are designed to resist internal actions due to vertical loads and design horizontal forces. Conversely, column and diagonal sections constitute the unknowns of the design problem. In particular, the presented approach also includes the influence of second order effects which are accounted for by means of the concept of mechanism equilibrium curve. The design requirements are derived by means of the kinematic theorem of plastic collapse. Column and diagonal sections are obtained by imposing that the mechanism equilibrium curve corresponding to the global mechanism has to lie below those corresponding to the undesired mechanisms within a displacement range compatible with the local ductility supply. Moreover, the introduction of the equivalent moment concept presented in a companion paper provides the proposed method with the ability to deal with short, intermediate and long links in the same manner.Aiming at the evaluation of the accuracy of the presented procedure, the inelastic performances of eccentrically braced frames designed by means of the proposed method are investigated, by means of static and dynamic non-linear analyses, in terms of collapse mechanism typology, available ductility and energy dissipation capacity.