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.     

Optimal lateral stiffness design of composite steel and concrete tall frameworks

This paper presents the optimal lateral stiffness design of composite steel and concrete tall frameworks subject to overall and interstorey drift constraints as well as member sizing limits using an efficient numerical approach developed based on the Optimality Criteria (OC) method. Taking into account the composite interaction between the structural steel and concrete materials, the stiffness-based optimal design problem is first formulated according to the European Code 4 (EC4). The necessary optimality criteria are then derived for the design followed by the construction of an iterative scheme to satisfy these optimality conditions while indirectly optimizing the design problem with multiple constraints. The recursive OC process is then carried out with the initial member sizes obtained from a closed-form solution developed for the similar problem with a single drift constraint. The effectiveness and practicality of the developed optimization approach is further illustrated through a series of framework examples.     

Stiffness optimization technique for 3D tall steel building frameworks under multiple lateral loadings

Although today's engineering computer technology allows for precise analysis of the structural response of a building, it does not readily provide insight for economical design. Due to the complex nature of a modern tall building consisting of thousands of structural members, the traditional design method is generally highly iterative and time consuming. This paper describes an efficient computer-based technique for least-weight design of three-dimensional (3D) tall steel building frameworks under multiple lateral loading conditions. Stiffness constraints in terms of interstorey drifts are considered and optimum discrete member sizes are automatically selected from databases of commercial standard steel sections. The technique is remarkably efficient and the optimum design generally converges in a few cycles. The designs of two 3D lateral-load resisting building frameworks are presented as illustrations. The effectiveness and suitability of the technique for the design of large-scale tall steel building frameworks are discussed.     

A multi-objective structural optimization method for serviceability design of tall buildings

Structural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi-hazard scenario. This study proposes a multi-objective serviceability design optimization methodology for buildings in multi-hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA-II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural-network-based surrogate model with self-updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50-story frame-tube building and was compared against the general genetic algorithm and general NSGA-II to verify the feasibility and effectiveness.     

基于层次分析OC-GA算法的钢骨混凝土框架柱优化设计

在工程结构优化理论的基础上,将钢骨混凝土框架柱的工程造价最小化和斜截面抗剪承载力最大化定为优化目标。根据型钢混凝土的受力特性,在多遇烈度地震下,应用最优性准则K-T条件对钢骨混凝土构件的混凝土截面尺寸进行优化设计;在基本烈度地震下应用层次分析遗传(GA)算法对钢骨混凝土构件中的型钢进行优化设计,从而建立层次分析OC-GA算法。综合考虑各种约束条件,运用层次分析OC-GA算法实施钢骨混凝土框架柱的优化设计,并通过优化设计实例证实所采用优化方法和设计思路的有效性和可行性。     

Microcomputer-Based Optimization of Steel Structures in Professional Practice

The paper concerns the computer-automated design of least-weight structural steel frameworks, where members are automatically sized using commercial standard steel sections in full conformance with steel design code provisions for strength/stability and stiffness. The necessary features and functions of such a design system are first identified. Two alternative approaches to the optimal design of steel frameworks are then discussed. Finally, a microcomputer software system is applied for the least-weight design of a steel framework comprised of a variety of member types and subject to a number of load effects. A number of alternative designs of the framework are conducted to illustrate differing optimization strategies and corresponding outcomes.     

考虑整体稳定的单层网壳截面优化设计

整体稳定性是单层网壳结构设计中的一个关键问题.在进行此类结构的优化时,必须考虑整体稳定性的影响才能得到符合规程要求的设计.本文综合考虑了位移、应力和杆件稳定以及结构整体稳定性条件,提出了基于最优准则法的优化设计方法,可按照钢结构设计规范和网壳结构规程的要求,对单层网壳结构进行杆件截面设计.     

高层建筑钢结构基于风振响应和动力特性的优化设计

高层建筑的风致响应和等效静力荷载虽然可以通过风洞试验和动力分析有效的加以确定,在结构设计的整个过程中这些等效风力却往往被当作常数来应用。本文提出了一个结合气动风力分析和结构刚度优化的自动化技术。在结构设计中利用这个技术,可以在优化结构刚度和最小化结构造价的同时,实时检查和更新作用在建筑结构上的等效风荷载。一个几何尺度与航空研究共同顾问理事会(CAARC)建议的建筑模型一致的钢框架结构被用来进行风力分析和结构优化的例子。结果表明这个技术不但能在满足位移设计要求的情况下优化结构刚度降低造价,而且也降低了作用在结构上的等效风力。     

Integrated aerodynamic load determination and stiffness design optimization of tall buildings

Modern tall steel buildings are wind sensitive and are prone to dynamic serviceability problems. Although wind tunnel techniques have emerged as valuable tools in providing reliable prediction of the wind‐induced loads and effects on tall buildings, current design practice normally considers the wind tunnel‐derived loads as constant static design loads. Such practice does not take into account the change in wind‐induced structural loads while the dynamic properties of a building are modified during the design synthesis process. This paper presents a computer‐based technique that couples together an aerodynamic wind tunnel load analysis routine and an element stiffness optimization method to minimize the cost of tall steel buildings subject to the lateral drift design criteria, while allowing for instantaneous prediction and updating of wind loads during the design synthesis process. Results of a full‐scale steel building framework with the same geometric shape of the Commonwealth Advisory Aeronautical Research Council (CAARC) standard building indicate that not only is the proposed technique able to produce the cost‐effective element stiffness distribution of the structure satisfying the serviceability wind drift design criteria, but a potential benefit of reducing the design wind loads can also be achieved by the stiffness optimization method. Copyright © 2007 John Wiley & Sons, Ltd.     

Progressive collapse design of seismic steel frames using structural optimization

This paper uses structural optimization techniques to cost-effectively design seismic steel moment frames with enhanced resistance to progressive collapse, which is triggered by the sudden removal of critical columns. The potential for progressive collapse is assessed using the alternate path method with each of the three analysis procedures (i.e., linear static, nonlinear static, and nonlinear dynamic), as provided in the United States Department of Defense United Facilities Criteria (UFC) Design of Buildings to Resist Progressive Collapse. As a numerical example, member sizes of a two-dimensional, nine-story, three-bay regular steel immediate moment frame are optimally determined such that the total steel weight is minimized while the design satisfies both AISC seismic provisions and UFC progressive collapse requirements. Optimization results for the example frame reveal that the traditional minimum weight seismic design, which does not explicitly consider progressive collapse, fails to meet the UFC alternate path criteria associated with any analysis procedure. Progressive collapse design optimization using the linear static procedure produces the most conservative and consequently heaviest design against progressive collapse. In contrast, the more accurate nonlinear static and dynamic procedures lead to more economical designs with UFC-acceptable resistance to progressive collapse, at the expenses of considerable modeling and computing efforts.     

半刚性钢框架优化设计研究

推导了考虑连接柔性和几何非线性的局部坐标下的单元刚度矩阵,并对半刚性连接单元的固端力进行了修正;其次,采用增量加载法,给出了考虑连接柔性、框架的几何非线性和单元内力与连接之间耦合效应的半刚性钢框架结构分析计算机流程;按照GB50017-2003《钢结构设计规范》和实际施工的要求,建立了考虑构件和连接最小费用问题的半刚性钢框架优化数学模型;然后,在遗传算法和半刚性钢框架结构分析流程的基础上,给出了半刚性钢框架优化设计步骤;根据算例,对半刚性钢框架优化设计做了初步的探讨。     

Optimal placement of steel diagonal braces for upgrading the seismic capacity of existing structures and its comparison with optimal dampers

In this study, the optimal placement of X steel diagonal braces (SDBs) is presented to upgrade the seismic response of a planar building frame. The optimal placement is defined as the optimal size and location of the SDBs in a frame structure. Steady state response of the structure evaluated at the undamped fundamental natural frequency is defined by means of transfer functions that are independent of initial values and the input excitation. The objective functions are chosen as the amplitude of transfer function of the top displacement and the amplitude of transfer function of the base shear force evaluated at the undamped fundamental natural frequency of the structure. In the optimization procedure, the stiffness parameters of the added braces are described as the design variables. Principal optimality criteria are derived using Lagrange Multipliers Procedure. The obtained nonlinear equations are solved with “Steepest Direction Search Algorithm”. Sensitivities of the objective functions are determined analytically. A simplified algorithm for the state of the base shear force as the objective function is also proposed. The response of the structure is examined for both of the objective functions in terms of the transfer function. Seismic rehabilitation with SDBs is compared to the rehabilitation with viscous dampers. Therefore, a total equivalent stiffness parameter is defined so that the transfer function amplitude of the top displacement of building structure with SDB attains the same value with the transfer function amplitude of the top displacement of building structure with optimal dampers based on the top displacement. The time history analysis is performed using El Centro earthquake ground motion records to demonstrate the validity of the proposed design method. The results of the numerical procedure point out that the proposed procedure based on the transfer function of the base shear force and the top displacement can also be beneficial in the rehabilitation of seismic response of the structures.     

Optimal drift design of tall reinforced concrete buildings with non‐linear cracking effects

This paper presents an efficient, computer‐based technique for the optimum drift design of tall reinforced concrete (RC) buildings including non‐linear cracking effects under service loads. The optimization process consists of two complementary parts: an iterative procedure for the non‐linear analysis of tall RC buildings and a numerical optimality criteria (OC) algorithm. The non‐linear response of tall RC buildings due to the effects of concrete cracking is obtained by a series of linear analyses, the so‐called direct effective stiffness method. In each linear analysis, cracked structural members are first identified and their stiffness modified based on a probability‐based effective stiffness relationship. Stiffness reduction coefficients are introduced as measures of the remaining stiffness for structural elements after cracking. A rigorously derived OC method is developed to solve for the minimum weight/cost design problem subject to multiple drift constraints and member sizing requirements. A shear wall‐frame example is presented to illustrate the application of this optimal design method. The design results of the optimized structure with cracking effects are compared to those of the linear‐elastic structure without concrete cracking. Copyright © 2005 John Wiley & Sons, Ltd.     

Integrated wind‐induced response analysis and design optimization of tall steel buildings using Micro‐GA

This paper presents an integrated procedure for wind‐induced response analysis and design optimization for rectangular steel tall buildings based on the random vibration theory and automatic least cost design optimization technique using Micro‐Genetic Algorithm (GA). The developed approach can predict wind‐induced drift and acceleration responses for serviceability design of a tall building; the technique can also provide an optimal resizing design of the building under wind loads to achieve cost‐efficient design. The empirical formulas of wind force spectra obtained from simultaneous measurements of surface pressures on various rectangular tall building models in wind tunnel tests are verified testified using a published example. Upon the known wind force spectra, the equivalent static wind loads for every storey, such as along‐wind, across‐wind and torsional loads, are then determined and applied for structural analysis including estimation of wind‐induced responses. An improved form of GAs, a Micro‐GA, is adopted to minimize the structural cost/weight of steel buildings subject to top acceleration and lateral drifts constraints with respect to the discrete design variables of steel section sizes. The application and effectiveness of the developed integrated wind‐induced response analysis and design optimization procedure is illustrated through a 30‐storey rectangular steel building example. Copyright © 2009 John Wiley & Sons, Ltd.     

Frequency-constrained optimization of space frames having general cross-sectional relationships∗

An optimality criteria (OC) method is presented for weight optimization of space frames having general cross-sectional relationships. The space frames support a sizeable amount of non-structural mass, while multiple natural frequency constraints, and minimum and maximum gauge restrictions are imposed on their design. The iterative design method involves alternately satisfying the constraints (scaling) and applying the Kuhn-Tucker (optimality) condition (resizing). The primary sizing variables (cross-sectional areas), and indirectly the secondary ones (two principal moments of inertia and a torsional constant), are uniformly scaled to the constraint surfaces using a nonlinear closed-form formulation. No exact scaling formulation for this class of problem has been proposed and tested in the optimization literature hitherto. The closed-form scaling procedure is united with an adaptable design strategy in which linear extrapolates of past-scaled design vectors are coupled with automatically-tuned OC recursive methods. Elementary design examples are presented to demonstrate the method. On average, the method achieves a stable upper-bound convergence of weight minima, as it quickly dissolves the (sometimes violent) oscillations of scaled weights in the iteration history. Most of all, the present design strategy eliminates the need for adjustments of internal parameters during the redesign phase.     

Life‐cycle cost assessment of mid‐rise and high‐rise steel and steel–reinforced concrete composite minimum cost building designs

The traditional trial‐and‐error design approach is inefficient to determine an economical design satisfying also the safety criteria. Structural design optimization, on the other hand, provides a numerical procedure that can replace the traditional design approach with an automated one. The objective of this work is to propose a performance‐based seismic design procedure, formulated as a structural design optimization problem, for designing steel and steel–reinforced concrete composite buildings subject to interstorey drift limitations. For this purpose, eight test examples are considered, in particular four steel and four steel–reinforced concrete composite buildings are optimally designed with minimum initial cost. Life‐cycle cost analysis (LCCA) is considered as a reliable tool for measuring the damage cost due to future earthquakes that will occur during the design life of a structure. In this study, LCCA is employed for assessing the optimum designs obtained for steel and steel–reinforced concrete composite design practices. Copyright © 2011 John Wiley & Sons, Ltd.     

Lateral drift constrained structural optimization of an actual supertall building acted by wind load

Recent trends towards constructing taller and increasingly slender buildings imply that these structures are more sensitive to wind excitation. This paper presents a technique for the wind‐resistant optimal design of supertall buildings with a complex structural system including concrete‐filled steel tube columns, shear walls, and various types of beams and columns. In each optimal design cycle, the dynamic wind load acting on a building is transformed into a set of multiple‐oriented equivalent static wind loads, which converts the optimal design for a building acted by dynamic loads into a simpler optimal design problem that considers only static loads. The objective function and constraint functions are explicitly formulated for various types of frame and area members, and consequently, the optimal design problem is mathematically modeled. The optimality criteria method is employed to seek a solution to the optimal design problem. A 68‐story actual supertall building with a height of 303 m is considered for a case study. The obtained results show that the presented technique is capable of giving a good numerical optimal solution for practical use. The technique and results obtained from this study are valuable for academic and professional engineers involved in wind engineering and structural design.     

Optimization layout of viscous dampers and its application in retrofitting of a high-rise steel structure

阻尼器优化布置是结构减震设计过程中的重要环节，通常需要通过多次动力响应计算来完成。为此，提出了一种通过结构静力分析确定阻尼器合理布置位置的方法，并能够快速计算出优化方案的附加阻尼比。将该方法应用于一栋位于日本东京都新宿区29层钢结构建筑的减震加固设计中，分析了该建筑的强震观测系统在日本“311地震”中采集到的部分楼层加速度时程数据，并基于分析结果验证了所建立的非线性数值分析模型的可靠性。采用所提方法对结构进行减震加固，得到双向共64个阻尼器的优化布置方案及其附加阻尼比，并通过动力方法对结果进行了验证。同时针对长周期及长持时特性的地震波，对减震结构进行动力弹塑性时程分析，评估其抗震性能。分析结果表明：减震优化方案的减震效果明显，结构整体地震反应和构件损伤较非减震方案都大大减小；减震优化方案有效改善了高层钢结构楼层变形不均匀的情况，层间位移角均满足小于1/100的性能要求；通过减震优化后大部分钢支撑和钢梁的塑性率都降低至小于1。     

黏滞阻尼器的优化布置及其在高层钢结构加固中的应用

阻尼器优化布置是结构减震设计过程中的重要环节,通常需要通过多次动力响应计算来完成。为此,提出了一种通过结构静力分析确定阻尼器合理布置位置的方法,并能够快速计算出优化方案的附加阻尼比。将该方法应用于一栋位于日本东京都新宿区29层钢结构建筑的减震加固设计中,分析了该建筑的强震观测系统在日本“311地震”中采集到的部分楼层加速度时程数据,并基于分析结果验证了所建立的非线性数值分析模型的可靠性。采用所提方法对结构进行减震加固,得到双向共64个阻尼器的优化布置方案及其附加阻尼比,并通过动力方法对结果进行了验证。同时针对长周期及长持时特性的地震波,对减震结构进行动力弹塑性时程分析,评估其抗震性能。分析结果表明：减震优化方案的减震效果明显,结构整体地震反应和构件损伤较非减震方案都大大减小;减震优化方案有效改善了高层钢结构楼层变形不均匀的情况,层间位移角均满足小于1/100的性能要求;通过减震优化后大部分钢支撑和钢梁的塑性率都降低至小于1。     

Progressive-Failure Analysis of Buildings Subjected to Abnormal Loading

Abstract: This article presents a progressive‐failure analysis procedure to evaluate the performance of a building framework after it has been damaged by unexpected abnormal loading, such as an impact or blast load caused by a natural, accidental, or deliberate event, or as a result of human error in design and construction. To begin with, it is assumed that some type of short‐duration abnormal loading has already caused some form of local damage to the structure. The residual load‐carrying capacity of the remaining framework is then analyzed by incrementally applying the prevailing long‐term loads and any impact debris loads, and progressively tracing the strength deterioration of the structure until either a globally stable state is reached or progressive collapse occurs for part or all of the structure. The computer‐based procedure is based on the displacement method of analysis. The effect of both axial force and shear deformation on member and structure stiffness is accounted for in this article (Liu, 2004; Xu et al., 2004). The stiffness matrices for framework members account for elastic–plastic bending, shearing, and axial deformations, and are progressively updated under incrementally increasing loads through the use of degradation factors that characterize stiffness deterioration. The computational model allows the incremental analysis to proceed beyond loading levels at which structural instabilities occur, including the formation of plastic collapse mechanisms and the disengagement of members from the building superstructure. The progressive‐failure analysis procedure is quite general and, with the appropriate choice of material constitutive model, may be applied to building frameworks of any type (concrete, steel, composite, etc.). Herein, a constitutive model for structural steel is adopted to account for elastic–plastic behavior under single or combined forces, and the progressive‐failure analysis procedure is illustrated for two example planar steel moment frames.