Energy-based design optimization of steel building frameworks using nonlinear response history analysis

Presented in this paper is a design optimization method for steel building frameworks subjected to seismic loading using a nonlinear response history analysis procedure. Minimum weight, minimum seismic input energy and maximum hysteretic energy of fuse members are identified as the three design objectives. Design constraints include the limits on inter-story drift and plastic rotation of member sections. The design optimization method employs a multi-objective genetic algorithm to search for optimal member section sizes from among commercially available steel section shapes. The design method is illustrated for a moment-resisting steel frame of a three-story building. It is concluded the proposed optimization methodology is an effective and efficient application of the capacity-design principle to building frameworks under earthquake loading.     

Seismic optimal design of 3D steel frames using cuckoo search algorithm

The present article is concerned with optimization of real size 3D steel structures under seismic loading based on response spectral and equivalent static analyses. The effect of lateral seismic loading distribution on the achieved optimum designs is investigated. An integrated optimization procedure with the objective of minimizing the self‐weight of frame is simply performed interfacing SAP2000 and MATLAB® software in the form of parallel computing. The meta‐heuristic algorithm chosen here is the cuckoo search (CS) algorithm recently developed as a type of population‐based algorithm inspired by the behavior of some cuckoo species in combination with the Lévy flight behavior. The CS algorithm performs suitable selection of sections from the American Institute of Steel Construction (AISC) wide‐flange (W) shapes list. Strength constraints of the AISC load and resistance factor design specification, geometric limitations, and displacement constraints are imposed on the considered frames. Results show similar weights for optimum designs using spectral and equivalent static analyses; however, different material distribution and seismic behaviors are observed. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimum design of steel frames using Cuckoo Search algorithm with Lévy flights

In the last two decades, many researchers have implemented various kinds of meta‐heuristic algorithms in order to overcome the complex nature of the optimum design of structures. In this paper, the optimum design of two‐dimensional steel frames for discrete variables based on the Cuckoo Search (CS) algorithm is developed. The CS is one of the recently developed population‐based algorithms inspired by the behavior of some cuckoo species in combination with the Lévy flight behavior of some birds and insects. The design algorithm is supposed to obtain minimum weight frame through suitable selection of sections from a standard set of steel sections such as the American Institute of Steel Construction (AISC) wide‐flange (W) shapes. Strength constraints of AISC load and resistance factor design specification and displacement constraints are imposed on frames. In order to demonstrate the effectiveness and robustness of the CS, low‐weight design and performance comparisons are made between the CS and other algorithms for some benchmark frames. Copyright © 2011 John Wiley & Sons, Ltd.     

Topology optimization and seismic collapse assessment of shape memory alloy (SMA)-braced frames: Effectiveness of Fe-based SMAs

This paper presents a seismic topology optimization study of steel braced frames with shape memory alloy (SMA) braces. Optimal SMA-braced frames (SMA-BFs) with either Fe-based SMA or NiTi braces are determined in a performance-based seismic design context. The topology optimization is performed on 5- and 10-story SMA-BFs considering the placement, length, and cross-sectional area of SMA bracing members. Geometric, strength, and performance-based design constraints are considered in the optimization. The seismic response and collapse safety of topologically optimal SMA-BFs are assessed according to the FEMA P695 methodology. A comparative study on the optimal SMA-BFs is also presented in terms of total relative cost, collapse capacity, and peak and residual story drift. The results demonstrate that Fe-based SMA-BFs exhibit higher collapse capacity and more uniform distribution of lateral displacement over the frame height while being more cost-effective than NiTi braced frames. In addition to a lower unit price compared to NiTi, Fe-based SMAs reduce SMA material usage. In frames with Fe-based SMA braces, the SMA usage is reduced by up to 80%. The results highlight the need for using SMAs with larger recoverable strains.     

Performance-based seismic design of steel frames using ant colony optimization

In this paper, a performance-based optimal seismic design of frame structures is presented using the ant colony optimization (ACO) method. This discrete metaheuristic algorithm leads to a significant improvement in consistency and computational efficiency compared to other evolutionary methods. A nonlinear analysis is utilized to arrive at the structural response at various seismic performance levels, employing a simple computer-based method for push-over analysis which accounts for first-order elastic and second-order geometric stiffness properties. Two examples are presented to illustrate the capabilities of ACO in designing lightweight frames, satisfying multiple performance levels of seismic design constraints for steel moment frame buildings, and a comparison is made with a standard genetic algorithm (GA) implementation to show the superiority of ACO for the discussed optimization problem.     

Optimal placement of steel plate shear walls for steel frames by bat algorithm

Layout optimization of steel frames with steel plate walls (SPWs) using a meta‐heuristic search algorithm is the main aim of the present study. SPWs are lateral load‐resisting systems, especially against earthquake excitation. These systems offer significant advantages in terms of cost, performance and ease of design compared with other systems. In this study, orthotropic membrane model is used to model the behaviour of steel plate shear walls. The newly developed bat algorithm, which is based on the echolocation behaviour of bats, is employed as the present study optimizer. Design variables of the optimization problem consist of the cross sections of beams and columns of the frame, the web plate thicknesses of SPWs and the placement of SPW in the frame. The bat algorithm performs suitable selection of sections from the AISC wide‐flange (W) shapes list. Strength constraints of the American Institute of Steel Construction Load and Resistance Factor Design and displacement constraints are checked during the optimization process. The results reveal the effectiveness of the proposed method for optimization of steel frames with SPWs. Copyright © 2014 John Wiley & Sons, Ltd.     

高强螺栓端板连接钢梁-方钢管混凝土框架结构抗震性能研究

通过一榀高强螺栓端板连接的2层1跨半4∶7比例组合梁-方钢管混凝土模型框架的拟动力试验、拟静力试验和静力推覆试验,运用子结构方法,模拟了一榀10层3跨的平面框架,研究了钢管混凝土框架结构的破坏形态、位移响应、滞回特性和耗能等抗震性能。拟动力试验中,多遇烈度地震时,框架刚度降低很小;基本设计烈度地震时,框架刚度降低约13%;罕遇烈度地震时,框架刚度降低20%,框架层间位移角小于2.0%。拟静力试验中,最大层间位移角超过1.6%,部分构件出现初始局部屈曲,框架整体未出现强度退化。在静力推覆试验中,即使层间位移角超过6.0%,框架承载力仍未发生下降。高强螺栓端板连接节点能够满足抗震设计要求,在规范限定的按弹塑性设计的层间位移角限值范围内,经过合理设计的螺栓端板连接可视为刚性连接。试验结果验证采用螺栓连接的钢梁-方钢管混凝土框架具有良好的抗震性能,可在抗震设防区结构中推广使用。     

Prevention of story drift amplification in a 20‐story steel frame structure by tension‐rod displacement–restraint bracing

This paper proposes an application of tension‐rod displacement–restraint bracing to prevent story drift amplification in tall steel moment frames. Seismic response analyses of a 20‐story bare steel frame are performed first, revealing that story drift amplification occurs in the upper and lower stories at different times. Characteristics observed for the seismic response of the bare frame suggest the efficacy of the delay action of bracing. Subsequently, seismic response analyses of the 20‐story braced frame with tension‐rod displacement–restraint bracings reveals that the increment of the column axial force by addition of bracing is reduced dramatically by the delay action of bracing. The story rotation angles within partial stories where the story drift amplification occurs in the bare frame are also reduced efficiently by the displacement–restraint bracing. The delay action of bracing influences the floor response acceleration and the residual displacement. Finally, parametric analysis results indicate an appropriate value of the story rotation angle at which the brace action starts.     

Equivalent viscous damping in direct displacement‐based design of steel braced reinforced concrete frames

Performance‐based design method, particularly direct displacement‐based design (DDBD) method, has been widely used for seismic design of structures. Estimation of equivalent viscous damping factor used to characterize the substitute structure for different structural systems is a dominant parameter in this design methodology. In this paper, results of experimental and numerical investigations performed for estimating the equivalent viscous damping in DDBD procedure of two lateral resistance systems, moment frames and braced moment frames, are presented. For these investigations, cyclic loading tests are conducted on scaled moment resisting frames with and without bracing. The experimental results are also used to calibrate full‐scale numerical models. A numerical investigation is then conducted on a set of analytical moment resisting frames with and without bracing. The equivalent viscous damping and ductility of each analytical model are calculated from hysteretic responses. On the basis of analytical results, new equations are proposed for equivalent viscous damping as a function of ductility for reinforced concrete and steel braced reinforced concrete frames. As a result, the new equation is used in direct displacement‐based design of a steel braced reinforced concrete frame. Copyright © 2012 John Wiley & Sons, Ltd.     

Efficient semi-analytical generator of initial stiffness designs for steel frames under seismic loading. Part 1: Fundamental frame

The purpose of this paper is to propose a new efficient semi-analytical generator of initial stiffness designs for a moment-resisting steel building frame under seismic loading. Requirements on interstory drift under seismic loading are often active constraints in the usual structural design practice for steel building frames and simple methods of design and analysis are needed especially in the preliminary design stage. Interstory drifts and ratios of the angles of nodal rotation to the angles of column member rotation are selected as key parameters and specified based upon the designer's intention. A practical design formula for a frame with design variable grouping is proposed as well as one for a basic frame without design variable grouping. A recursive technique is introduced to evaluate the design story shear forces under a set of design-spectrum-compatible earthquakes. Numerical examples are presented to disclose the characteristics of member stiffness distributions and the response characteristics of frames designed by the present method. In the present paper (Part 1), a fundamental design formula is proposed for a simple frame without column elongation. A more practical design formula for a slender frame with column elongation will be presented in the companion paper. (Part 2). © 1997 John Wiley & Sons, Ltd.     

Optimal damper placement based on base moment in steel building frames

A new damper optimization method for finding optimal size and location of the added viscous dampers is proposed based on the elastic base moment in planar steel building frames. A Fourier Transform is applied to the equation of the motion and the transfer function in terms of the fundamental natural frequency of the structures is defined. The transfer function amplitude of the elastic base moment evaluated at the first natural circular frequency of the structure is chosen as a new objective function in the minimization problem. The damper coefficients of the added viscous dampers are taken into consideration as design variables in a steel planar building frame. The transfer function amplitude of the elastic base moment is minimized under an active constraint on the sum of the damper coefficients of the added dampers and the passive constraints on the upper and lower bounds of the added dampers. The optimal damper design presented in this paper is compared with other optimal damper methods based on top displacement, top absolute acceleration and base shear. A ten-storey steel planar building frame is chosen to be rehabilitated with the optimal dampers. The optimal damper allocation is obtained for the transfer function amplitude of the elastic base moment then compared with the other damper optimization methods in terms of the transfer function response. The results of the proposed method show that the method can also be beneficial to decrease both the base moment and the interstorey drift ratios in some frequency regions.     

Seismic performance of low-rise intermediate steel moment frame buildings in South Korea

The seismic performance of low-rise intermediate steel moment frame buildings following design practices of South Korea was investigated and its benefit was presented in comparison with those of customary design practice in the United States. The major features in the design and construction practices in South Korea are that the entire frames of the building are designed to resist the lateral load and beam-to-column connections are fabricated in factories. In contrast, in the United States, only exterior frames resist the lateral load and the entire beam-to-column connections are welded at the construction site. To investigate the effects of distinctive design practices on seismic performance, the example buildings were designed and evaluated with the procedure in FEMA 355F. The effect of panel zone deformation in addition to story drift was considered in performance evaluation. The evaluation results showed that the seismic performance of the buildings designed in accordance with the practice in South Korea were not significantly different from those in the United States. Therefore, design and construction practices in South Korea are a competitive way for intermediate steel moment frame buildings.     

钢框架抗震改造的支撑系统研究

评估了不同支撑系统改造的抗弯钢框架的抗震性能。采用3种结构形式:中心支撑框架、防屈曲支撑框架和巨型支撑框架。设计了一横向刚度不足的9层钢框架,满足规范对高地震灾害区域结构的侧移要求。用中心支撑、防屈曲支撑和巨型支撑改造框架,进行非弹性时程分析,评估地震作用下的结构性能。以局部变形(杆件转角)和整体变形(层间及屋顶侧移)为参数,比较改造框架非弹性性能的不同。结果表明:巨型支撑框架是最有效率的支撑系统,其最大层间侧移比抗弯框架低70%,比中心支撑框架低50%。侧移的减小量与地震特性有关,尤其是频率。防屈曲支撑的抗震性能仅稍优于巨型支撑框架,但其总质量更大。巨型支撑框架的杆件和节点用钢量比中心支撑框架低20%,既降低了费用又体现了抗震优势。     

钢框架抗震改造的支撑系统研究

评估了采用不同支撑系统改造的抗弯钢框架的抗震性能。共采用3种结构形式:中心支撑框架、防屈曲支撑框架、巨型支撑框架。设计了一横向刚度不足的9层钢框架,满足规范对高地震灾害区域结构的侧移要求。用中心支撑、防屈曲支撑和巨型支撑改造框架。进行非弹性时程分析,评估地震作用下的结构性能。以局部变形(杆件转角)和整体变形(层间及屋顶侧移)为参数,比较改造框架非弹性性能的不同。结果表明:巨型支撑框架是最有效率的支撑系统,其最大层间侧移比抗弯框架低70%,比中心支撑框架低50%。侧移的减小量与地震特性有关,尤其是频率。防屈曲支撑的抗震性能仅稍优于巨型支撑框架,但其总质量更大。巨型支撑框架的杆件和节点用钢量比同心支撑框架低20%,既可降低费用又具有抗震优势。     

Damage‐controlled performance‐based design optimization of steel moment frames

In the present paper, performance‐based design of steel moment‐resisting frames (SMRFs) is implemented to minimize total cost of the structures. The total cost is summation of the initial construction cost and the seismic damage cost in operational lifetime of the structures subjected to seismic loading. In order to evaluate the seismic damage cost, Park–Ang damage index (DI), as one of the most realistic measures of structural seismic damage, is utilized. To calculate the DI, nonlinear time‐history response of the structure needs to be evaluated during the optimization process. As the computational burden of the process is very high, neural network techniques are utilized to predict the required nonlinear time‐history structural responses. As the design constraints, besides the drift checks at immediate occupancy and collapse prevention performance levels, the global DI is also checked at collapse prevention level to control the amount of seismic damage. In order to achieve the optimization task, a sequential enhanced colliding bodies optimization II is proposed. Numerical studies are conducted to demonstrate the efficiency of the proposed methodology involving 2 illustrative examples of a 6‐story SMRF and a 12‐story SMRF.     

Seismic performance of Y‐type eccentrically braced frames combined with high‐strength steel based on performance‐based seismic design

In the Y‐type eccentrically braced frame structures, the links as fuses are generally located outside the beams; the links can be easily repairable or replaceable after earthquake without obvious damage in the slab and beam. The non‐dissipative member (beams, braces, and columns) in the Y‐type eccentrically braced frames are overestimated designed to ensure adequate plastic deformation of links with dissipating sufficient energy. However, the traditionally code design not only wastes steel but also limits the application of eccentrically braced frames. In this paper, Y‐type eccentrically braced steel frames with high‐strength steel is proposed; links and braces are fabricated with Q345 steel (the nominal yield stress is 345 MPa); the beams and columns are fabricated with high‐strength steel. The usage of high‐strength steel effectively decreases the cross sections of structural members as well as reduces the construction cost. The performance‐based seismic design of eccentrically braced frames was proposed to achieve the ideal failure mode and the same objective. Based on this method, four groups Y‐type eccentrically braced frames of 5‐story, 10‐story, 15‐story, and 20‐story models with ideal failure modes were designed, and each group includes Y‐type eccentrically braced frames with ordinary steel and Y‐type eccentrically braced frames with high‐strength steel. Nonlinear pushover and nonlinear dynamic analyses were performed on all prototypes, and the near‐fault and far‐fault ground motions are considered. The bearing capacity, lateral stiffness, story drift, link rotations, and failure modes were compared. The results indicated that Y‐type eccentrically braced frames with high‐strength steel have a similar bearing capacity to ordinary steel; however, the lateral stiffness of Y‐type eccentrically braced frames with high‐strength steel is smaller. Similar failure modes and story drift distribution of the prototype structures designed using the performance‐based seismic design method are performed under rare earthquake conditions.     

Optimum design of steel sway frames to BS5950 using harmony search algorithm

Harmony search method based optimum design algorithm is presented for the steel sway frames. The harmony search method is a numerical optimization technique developed recently that imitates the musical performance process which takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The optimum design algorithm developed imposes the behavioral and performance constraints in accordance with BS5950. The member grouping is allowed so that the same section can be adopted for each group. The combined strength constraints considered for a beam-column take into account the lateral torsional buckling of the member. The algorithm presented selects the appropriate sections for beams and columns of the steel frame from the list of 64 Universal Beam sections and 32 Universal Column sections of the British Code. This selection is carried out so that the design limitations are satisfied and the weight of steel frame is the minimum. The number of design examples considered to demonstrate the efficiency of the algorithm is presented.     

基于屈服点谱法的中心支撑钢框架抗震性态评估

屈服点谱(Yield Point Spectra,YPS)是以位移-加速度表述的反应谱形式。YPS可以用于对现有结构进行抗震评估,确定结构在给定地震作用下的峰值位移和延性。本文按照我国设计规范分别设计了6层、9层、12层3个人字形中心支撑钢框架结构,利用YPS对3个结构进行非线性静力分析,得到结构在设防地震和罕遇地震下的峰值位移和层间位移角,并与SAP2000动力时程分析得到的结果进行对比,评估人字形中心支撑钢框架在设防地震和罕遇地震下的抗震性态,评价了YPS方法用于中心支撑钢框架抗震性态评估的可靠性。     

水平双向加载下钢筋混凝土柱抗震性能试验研究

针对双向水平地震作用下钢筋混凝土框架柱的抗震性能,开展了9个钢筋混凝土框架柱的水平双向拟静力试验研究,考察轴压比、体积配箍率、纵筋配筋率以及加载路径对柱抗震性能的影响,对双向加载下柱的受力特点、承载力变化、位移延性和极限侧移角等指标进行分析。结果表明：相对于水平单向加载,双向加载对柱的抗震性能存在显著不利影响：柱的抗弯承载力及极限位移均明显减小,损伤程度明显加重;随加载方式由单向-十字-菱形-方圈变化,相同位移下柱的强度退化与抗弯承载力下降幅度均有所增加。考虑双向受力后,典型技术标准给出的RC框架结构极限层间侧移角限值的安全冗余度显著降低。基于试验结果初步提出结构设计及分析建议：考虑双向水平地震动影响时,框架柱的抗震设计宜适当降低轴压比、增加约束箍筋、适当折减柱的抗弯承载力;采用层间侧移角进行结构倒塌判别时,可取双向地震动作用下结构最大层间侧移矢量的大小作为判别位移,并根据分析性质（结构设计或既有结构分析）选取恰当的极限层间侧移角判断标准。     

Seismic design, performance, and behavior of composite-moment frames with steel beam-to-concrete filled tube column connections

Concrete filled steel tube (CFT) columns have been widely used in composite-moment frames (C-MFs) both in non-seismic and in high seismic zones. The objective of this research is to develop a design methodology of such moment resisting frame structures designed with CFT columns in achieving ductile behavior and high strength. These composite-moment frames mostly constructed around the perimeter of the building provide the enough stiffness to withstand the lateral displacement due to wind or seismic loads. In this research, three sets of prototype composite frame models were designed on the basis of the proposed design examples as 3-, 9-, and 20-story post-Northridge SAC buildings with composite-special moment frame (C-SMF) systems designed for the western US area. The exact moment-rotational behavior of steel beam-to-CFT column connections including the strength degradation was simulated using the 2D joint model with the rigid boundary element. Nonlinear pushover analyses were conducted on the numerical frame models so as to evaluate the over-strength, inelastic deformation, and P-Delta effect for the entire structure. The statistical investigation was introduced to nonlinear dynamic analyses under 40 SAC ground motions corresponding to a seismic hazard level of 2% probability of exceedence in 50 years in order to efficiently examine seismic performance and behavior of entire composite frame structures. All frame models meet the allowable limit for safe designs. In addition, the entire frame design becomes conservative as the number of stories increases. The distribution of interstory drift ratios (ISDRs) as well as the over-strength ratio also demonstrates this conservative design of low to high-rise CMF structures.