Optimal seismic design of steel frame buildings based on life cycle cost considerations

A multi‐objective optimization procedure is presented for designing steel moment resisting frame buildings within a performance‐based seismic design framework. Life cycle costs are considered by treating the initial material costs and lifetime seismic damage costs as two separate objectives. Practical design/construction complexity, important but difficult to be included in initial cost analysis, is taken into due account by a proposed diversity index as another objective. Structural members are selected from a database of commercially available wide flange steel sections. Current seismic design criteria (AISC‐LRFD seismic provisions and 1997 NEHRP provisions) are used to check the validity of any design alternative. Seismic performance, in terms of the maximum inter‐storey drift ratio, of a code‐verified design is evaluated using an equivalent single‐degree‐of‐freedom system obtained through a static pushover analysis of the original multi‐degree‐of‐freedom frame building. A simple genetic algorithm code is used to find a Pareto optimal design set. A numerical example of designing a five‐storey perimeter steel frame building is provided using the proposed procedure. It is found that a wide range of valid design alternatives exists, from which a decision maker selects the one that balances different objectives in the most preferred way. Copyright © 2003 John Wiley & Sons, Ltd.     

Direct displacement-based seismic design of steel eccentrically braced frame structures

This paper details a direct displacement-based design procedure for steel eccentrically braced frame (EBF) structures and gauges its performance by examining the non-linear dynamic response of a series of case study EBF structures designed using the procedure. Analytical expressions are developed for the storey drift at yield and for the storey drift capacity of EBFs, recognising that in addition to link beam deformations, the brace and column axial deformations can provide important contributions to storey drift components. Case study design results indicate that the ductility capacity of EBF systems will tend to be relatively low, despite the large local ductility capacity offered by well detailed links. In addition, it is found that while the ductility capacity of EBF systems will tend to reduce with height, this is not necessarily negative for seismic performance since the displacement capacity for taller EBF systems will tend to be large. To gauge the performance of the proposed DBD methodology, analytical models of the case study design solutions are subject to non-linear time-history analyses with a set of spectrum-compatible accelerograms. The average displacements and drifts obtained from the NLTH analyses are shown to align well with design values, confirming that the new methodology could provide an effective tool for the seismic design of EBF systems.     

Earthquake response of a steel frame building

A study has been made of the response, during the San Fernando earthquake 9 February 1971, of the nine-storey steel frame Building 180, located at the California Institute of Technology, Jet Propulsion Laboratory, Pasadena. The analysis throws light on the actual dynamical properties of the building during the earthquake, and also demonstrates that it is possible, when the ground motion is specified, to make accurate predictions of building motions during moderate earthquakes by using a linear viscously damped model. Methods of evaluating the lower mode periods and damping ratios from the earthquake records are described and the values obtained are compared with results from dynamic testing before and after the earthquake and with the periods computed from computer models of the building. Although no structural damage occurred and computed stresses in the steel frame were less than yield stresses, the periods measured by an ambient vibration test after the earthquake were of the order of 10 per cent higher than the pre-earthquake values. The maximum periods during the earthquake were found to be about 30 per cent higher than the post-earthquake periods.     

钢框架结构直接基于位移抗震性能设计的非迭代法

为使直接基于位移的抗震性能设计方法更加简便准确,本文采用一种直接基于位移的非迭代抗震设计方法对钢框架结构进行设计。该方法首先考虑结构的非弹性反应确定等效弹性反应谱和弹塑性反应谱,并建立了使用Newmark-Hall变形折减系数的能力谱的明确表达式。采用能力-需求图方法,确定了结构需要的目标位移与延性、谱位移和谱加速度之间关系的明确表示式,得到结构的刚度和设计基底剪力,进而确定构件截面,完成结构设计。对五层两跨平面钢框架结构进行了直接基于位移的抗震性能设计,设计过程简便,无需迭代程序,不需画出反应谱,通过时程分析验证了设计结果的精确性。本文研究表明:直接基于位移的非迭代抗震设计方法是一种简便、高效、精确的抗震性能设计方法。     

Optimal design of a base isolated system for a high‐rise steel structure

In a previous study (Kaplan H, Seireg A., Int. J. Comput. Appl. Technol., 2000; 13 (1/2): 25–41), the authors proposed a base isolation system for earthquake protection of structures.The system incorporates spherical supports for the base, a specially designed spring‐cam system to keep the base rigidly supported under normal conditions and to allow it to move for the duration of the earthquake under the constraint of a spring with optimized stiffness characteristics. A single‐degree‐of‐freedom structure was considered to investigate the feasibility of the concept. The simulation of the system response shows a 20 times reduction of the transmitted force as a result of using the proposed design in the considered case. This paper extends the previous study to the case of a 40‐storey steel structure subjected to the Taft as well as El Centro earthquakes. A 7.5 and 6 times reduction of the maximum transmitted force was achieved for the considered disturbances, respectively, without any adverse effects due to the tilting moment which is inherent in this type of base isolation. Copyright © 2001 John Wiley & Sons, Ltd.     

Simplified seismic design approach for steel portal frame piers with hysteretic dampers

A simplified seismic design procedure for steel portal frame piers installed with hysteretic dampers is proposed, which falls into the scope of performance‐based design philosophy. The fundamental goal of this approach is to design a suite of hysteretic damping devices for existing and new bridge piers, which will assure a pre‐defined target performance against future severe earthquakes. The proposed procedure is applicable to multi‐degree‐of‐freedom systems, utilizing an equivalent single‐degree‐of‐freedom methodology with nonlinear response spectra (referred to as strength‐demanded spectra) and a set of formulae of close‐form expressions for the distribution of strength and stiffness produced in the structure by the designed hysteretic damping devices. As an illustrative example, the proposed procedure is applied to a design of a simple steel bridge pier of portal frame type with buckling‐restrained braces (one of several types of hysteretic dampers). For the steel portal frame piers, an attempt is made to utilize not only the displacement‐based index but also the strain‐based index as pre‐determined target performance at the beginning of design. To validate this procedure, dynamic inelastic time‐history analyses are performed using the general‐purpose finite element program ABAQUS. The results confirm that the proposed simplified design procedure attains the expected performance level as specified by both displacement‐based and strain‐based indices with sufficient accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Seismic design and shake table tests of a steel post‐tensioned self‐centering moment frame with a slab accommodating frame expansion

Post‐tensioned (PT) self‐centering moment frames were developed as an alternative to welded moment‐resisting frames (MRFs). Lateral deformation of a PT frame opens gaps between beams and columns. The use of a composite slab in welded MRFs limits the opening of gaps at the beam‐to‐column interfaces but cannot be adopted in PT self‐centering frames. In this study, a sliding slab is used to minimize restraints to the expansion of the PT frame. A composite slab is rigidly connected to the beams in a single bay of the PT frame. A sliding device is installed between the floor beams and the beams in other bays, wherever the slab is allowed to slide. Many shaking table tests were conducted on a reduced‐scale, two‐by‐two bay one‐story specimen, which comprised one PT frame and two gravitational frames (GFs). The PT frame and GFs were self‐centering throughout the tests, responding in phase with only minor differences in peak drifts that were caused by the expansion of the PT frame. When the specimen was excited by the 1999 Chi‐Chi earthquake with a peak ground acceleration of 1.87g, the maximum interstory drift was 7.2% and the maximum lateral force was 270 kN, equal to 2.2 times the yield force of the specimen. Buckling of the beam bottom flange was observed near the column face, and the initial post‐tensioning force in the columns and beams decreased by 50 and 22%, respectively. However, the specimen remained self‐centering and its residual drift was 0.01%. Copyright © 2011 John Wiley & Sons, Ltd.     

The vibrational characteristics of a twelve-storey steel frame building

The Ralph M. Parsons World Headquarters building, a twelve-storey steel frame structure, was subjected to a series of forced vibration tests. The natural frequencies, three-dimensional mode shapes and damping coefficients of nine modes of vibration were determined. Other features of this investigation included the study of non-linearities associated with increasing levels of response, detailed measurements of the deformation of the first floor and the ground surrounding the structure, and measurements of strain in one of the columns of the structure during forced excitation. The dynamic characteristics of the building determined by these tests are compared to those predicted by a finite element model of the structure. The properties of primarily translational modes are predicted reasonably well, but adequate prediction of torsional motions is not obtained. The comparison between measured and predicted strains suggests that estimates of stress determined from finite element analyses of buildings might be within 25 per cent of those experienced by the structure for a known excitation.     

Multiobjective optimization for performance‐based seismic design of steel moment frame structures

The performance‐based seismic design of steel special moment‐resisting frame (SMRF) structures is formulated as a multiobjective optimization problem, in which conflicting design criteria that respectively reflect the present capital investment and the future seismic risk are treated simultaneously as separate objectives other than stringent constraints. Specifically, the initial construction expenses are accounted for by the steel material weight as well as by the number of different standard steel section types, the latter roughly quantifying the degree of design complexity related additional construction cost; the seismic risk is considered in terms of maximum interstory drift demands at two hazard levels with exceedance probabilities being 50% and 2% in 50 years, respectively. The present formulation allows structural engineers to find an optimized design solution by explicitly striving for a desirable compromise between the initial investment and seismic performance. Member sizing for code‐compliant design of a planar five‐story four‐bay SMRF is presented as an application example using the proposed procedure that is automated by a multiobjective genetic algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Hybrid testing and modeling of a suspended zipper steel frame

An analytical and experimental study has been conducted to evaluate the seismic performance of a three‐story suspended zipper steel frame. The frame was concentrically braced and had zipper struts to transfer the unbalanced forces induced on the beams due to the buckling of the lower‐story braces. The experimental study was conducted with the hybrid test technique, in which only the bottom‐story braces of the three‐story frame were physically tested, while the behavior of the rest of the frame was modeled using a general structural analysis software. The paper discusses issues pertinent to the calibration of the computer model for the analytical substructure as well as for the entire frame, including the selection of an appropriate damping matrix, and the modeling of the buckling behavior of the braces and bracing connections. The analytical model of the entire frame was validated with the hybrid tests and was able to accurately capture the material and geometric nonlinearities that developed when the braces yielded and buckled. This study has demonstrated the usefulness of hybrid testing in improving analytical models and modeling assumptions and providing information that cannot be obtained from an analytical study alone. The results have shown that the suspended zipper frame can distribute the brace nonlinearity over the first two stories as intended in the design and will not have catastrophic failure under the design‐level earthquakes considered in this study, despite the significant inelastic deformations. Copyright © 2009 John Wiley & Sons, Ltd.     

多层钢结构基础隔震性能研究

本文用算例按基底剪力法,振型反应谱法和时程分析法分析了多层基础隔震钢结构和多层钢筋混凝土结构及其对应的非隔震结构的地震力和层间剪力。     

足尺钢框架振动台试验及动力弹塑性数值模拟

本文通过有限元分析程序OpenSees对一足尺四层钢框架结构进行静力及动力弹塑性分析,结构构件采用自由度较少的纤维模型模拟。在振动台试验之前,预测足尺钢框架结构连续在小震、中震及大震作用下的响应,将预测分析结果与振动台试验结果进行对比,结果显示该数值模拟方法能很好地反映结构的弹塑性行为及破坏机制,准确预测结构的地震响应及大震下结构倒塌时间。这进一步说明基于纤维模型的整体结构弹塑性分析方法,由于自由度数少,适用于整体结构抗震分析。     

型钢混凝土框架pushover分析

Pushover分析方法是逐渐得到广泛应用的一种评估结构抗震性能的简化方法。由于型钢混凝土（SRC）构件塑性铰属性确定方面的原因,SRC构件难以直接应用于pushover分析方法,而常采用按“等刚度”原则转化为钢筋混凝土构件（RC）进行计算。本文从理论上给出了SRC压弯构件N-M相关曲线、Mx-My相关曲线的形成方法,提出了SRC构件M-φ曲线的确定及转化为塑性铰曲线的原则,并研究了SRC构件塑性铰区等效长度的计算方法,可为SRC结构进行pushover分析提供参考数据。按照本文方法,采用pushover方法对两跨三层SRC框架进行分析,结果与该结构模型振动台实验吻合较好。在此基础上,对10层SRC框架和采用刚度等效的3层、10层的钢筋混凝土（RC）框架进行了对比分析,结果表明,随着层数的增加,SRC结构相对于RC结构表现出更优越的抗震耗能能力。     

合理确定梁端塑性铰弯矩值及改进钢框架梁连接设计

多次强震震害表明,梁破坏时梁端截面并未能形成理想塑性铰,而是在梁柱连接处发生脆性破坏。提出了改进钢框架梁连接设计的具体作法,即局部加大梁端焊缝截面的同时,在梁端一定距离处又适当削弱梁翼缘尺寸,合理确定梁端塑性铰弯矩,按梁两端出现同向塑性铰求出钢框架梁柱连接、梁的拼接处的内力(M、V)作为多遇地震作用下的调整内力设计值,改进梁柱连接、梁拼接的设计,供工程设计和修订相应规范作参考。     

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.     

钢框架-带缝钢板剪力墙结构受力性能分析

本文对4种钢框架、6种带缝(两排)钢板剪力墙片(四周与构件无连接)和6种固接的钢框架-带缝钢板剪力墙结构在3种不同竖向荷载作用下的抗侧能力和往复荷载下的滞回性能进行了研究,并对比分析。结果表明:前两种结构的侧移刚度、抗侧能力相对较低,屈曲后刚度退化快;钢框架-带缝钢板剪力墙结构的侧移刚度、抗侧能力和耗能能力比前两种结构有明显的提高,说明钢框架与带缝钢板剪力墙片固接后工作协调性能良好。带缝钢板剪力墙片与钢框架-带缝钢板剪力墙结构的整体设计参数宽高比W/H,开缝设计参数开缝墙肢的高宽比h/b、宽厚比b/t、开缝墙肢与剪力墙的高宽比h/H对结构的抗侧能力和滞回性能有很大影响。W/H增大,结构的抗侧能力增强,滞回性能降低;h/b、b/t、h/H增大,结构的抗侧能力降低,滞回性能提高。     

薄弱层设置耗能阻尼器支撑的钢框架模型振动台试验

设计制作了一个五层钢框架模型,在其第一层、第三层和第五层薄弱层分别设置摩擦阻尼器、粘弹性阻尼器和粘弹性-摩擦阻尼器等三种耗能阻尼器支撑,进行了罕遇地震和多遇地震下的振动台试验。试验结果表明,耗能阻尼器支撑能够有效地控制结构的地震反应。     

基于损伤部位向量法的钢框架损伤识别研究

对损伤部位向量(DLV)法作了简单介绍,并用该方法对钢框架进行了损伤识别和损伤定位。该方法假定结构损伤前后为线性,对结构损伤前后柔度矩阵差进行奇异值分解,将奇异值为零所对应的向量,作为静荷载施加在无损结构的测点位置,则应力为零的单元为可能损伤的单元。对3种不同工况的钢框架进行了振动模态试验,用前3阶模态参数构造框架的柔度矩阵,按照DLV法对其进行了损伤识别,识别结果与已知损伤情况相一致。从测试自由度不完备、噪声和振型质量归一化系数这3个方面对识别效果进行了分析,结果表明:当损伤使结构动力特性有微小改变时,使用该方法不易定位损伤,应结合局部损伤识别方法进行判定;当损伤使结构动力特性有较大改变时,该方法能有效识别损伤的单元。DLV方法概念简单,理论明确,不受结构类型的限制,不需要结构的数学模型和模型缩聚或扩展技术,只需获得结构损伤前后的前几个低阶模态参数,即可识别结构一处或多处损伤,实际应用时可操作性强。