Steel multistorey 3D frames are commonly used in business and residential buildings, industrial sheds, warehouses, etc. The design optimization of tall steel buildings is usually governed by horizontal loadings, such as, wind load, as well as its dynamic behavior, for which the structure must have the stiffness and stability in accordance with the safety criteria established by codes. This chapter deals with sizing structural optimization problems, concerning weight minimization of 3D steel frames, considering natural frequencies of vibration as well as allowable displacements as the constraints of the optimization problem. The discrete design variables are to be chosen from commercial profiles tables. A differential evolution (DE) is the search algorithm adopted coupled to an adaptive penalty method (APM) to handle the constraints. Three different 3D frames are optimized, presenting very interesting results.

This book presents the application of new techniques in analyzing truss and frame structures. The book contains two main sections: Numerical Analysis of Structures and Mass-Saving in Structures. Under each section, different approaches on the topic are given. Covered in these sections are dynamic stability analysis, design optimization considering vibration, FEM analysis, topology optimization methods, and recommendations to build lightweight structures. It is believed that this book will be helpful to its readers for new perspectives on the analysis of structures.

Optimal design of structures leads, as a rule, to slender and thin-walled shapes of the elements, and such elements are subject to the loss of stability. Hence the constraints of structural optimization usually include stability constraints, expressed by some eigenvalues. Optimal design under vibration constraints belongs also to optimization with respect to eigenvalues. The present volume gives a short introduction to structural optimization and then pays particular attention to multimodal optimization under stability and vibration constraints, both in elastic and inelastic range. One part is devoted to thin-walled bars optimized for interactive buckling with imperfections taken into account. The volume is of interest both to researchers and design engineers: it covers the most recent results of multimodal and interactive optimization, allowing for inelastic behaviour of structures, and the constraints discussed appear in almost all problems of engineering design.

The contributions in this book discuss large-scale problems like the optimal design of domes, antennas, transmission line towers, barrel vaults and steel frames with different types of limitations such as strength, buckling, displacement and natural frequencies. The authors use a set of definite algorithms for the optimization of all types of structures. They also add a new enhanced version of VPS and information about configuration processes to all chapters. Domes are of special interest to engineers as they enclose a maximum amount of space with a minimum surface and have proven to be very economical in terms of consumption of constructional materials. Antennas and transmission line towers are the one of the most popular structure since these steel lattice towers are inexpensive, strong, light and wind resistant. Architects and engineers choose barrel vaults as viable and often highly suitable forms for covering not only low-cost industrial buildings, warehouses, large-span hangars, indoor sports stadiums, but also large cultural and leisure centers. Steel buildings are preferred in residential as well as commercial buildings due to their high strength and ductility particularly in regions which are prone to earthquakes.

This study proposes a seismic design optimization method for steel building frameworks following the capacity design principle. Currently, when a structural design employs an elastic analysis to evaluate structural demands, the analysis results can be used only for the design of fuse members, and the inelastic demands on non-fuse members have to be obtained by hand calculations. Also, the elastic-analysis-based design method is unable to warrant a fully valid seismic design since the evaluation tool cannot always capture the true inelastic behaviour of a structure. The proposed method is to overcome these shortcomings by adopting the most sophisticated nonlinear dynamic procedure, i.e., Nonlinear Time- (or Response- ) History Analysis as the evaluation tool for seismic demands. The proposed optimal design formulation includes three objectives: the minimum weight or cost of the seismic force resisting system, the minimum seismic input energy or potential earthquake damage and the maximum hysteretic energy ratio of fuse members. The explicit design constraints include the plastic rotation limits on individual frame members and the inter-story drift limits on the overall performance of the structure. Strength designs of each member are treated as implicit constraints through considering both geometric and material nonlinearities of the structure in the nonlinear dynamic analysis procedure. A multi-objective Genetic Algorithm is employed to search for the Pareto-optimal solutions. The study provides design examples for moment resisting frames and eccentrically braced frames. In the examples some numerical strategies, such as integrating load and resistance factors in analysis, grouping design variables of a link and the beams outside the link, rounding-off the objective function values, are introduced. The design examples confirm that the proposed optimization formulation is able to conduct automated capacity design of steel frames. In particular, the third objective, to maximize the hysteretic energy ratio of fuse members, drives the optimization algorithm to search for design solutions with favorable plastic mechanisms, which is the essence of the capacity design principle. For the proposed inelastic-analysis-based design method, the seismic performance factors (i.e., ductility- and overstrength-related force reduction factors) are no longer needed. Furthermore, problem-dependent capacity design requirements, such as strong-column-weak-beam for moment resisting frames, are not included in the design formulation. Thus, the proposed design method is general and applicable to various types of building frames.