The plastic method has been used extensively by engineers for the design of steel structures, including simple beams, continuous beams, and simple portal frames. Traditionally, the analysis is based on the rigid-plastic theory whereby the plastic collapse load is evaluated through virtual work formulation in which elastic deflection is ignored. For more complex frames, specialist computer packages for elastoplastic analysis are usually employed. Current publications on plastic design method provide means of analysis based on either virtual work formulation or sophisticated plastic theory contained in specialist computer packages.
This book aims to bridge this gap. The advent of computers has enabled practicing engineers to perform linear and nonlinear elastic analysis on a daily basis using computer programs widely available commercially. The results from computer analysis are transferred routinely to tools with automated calculation formats such as spreadsheets for design. The use of this routine procedure is commonplace for design based on elastic, geometrically nonlinear analysis. However, commercially available computer programs for plastic analysis are still a rarity among the engineering community.
This book emphasizes a plastic analysis method based on the hinge by hinge concept. Frames of any degree of complexity can be analyzed plastically using this method. This method is based on the elastoplastic analysis procedure where a linear elastic analysis, performed either manually or by computers, is used between the formation of consecutive plastic hinges. The results of the linear elastic analysis are used in a proforma created in a spreadsheet environment where the next plastic hinge formation can be predicted automatically and the corresponding culmulative forces and deflections calculated. In addition, a successive approximation method is described to take account of the effect of force interaction on the evaluation of the collapse load of a structure.
This method can be performed using results from analysis obtained from most commercially available computer programs. The successive approximation method is an indirect way to obtain the collapse load of structures using iterative procedures. For direct calculation of the collapse load without using iterative procedures, special formulations, possibly with ad-hoc computer programming, according to the plastic theory must be used. Nowadays, the stiffness method is the most popular and recognized method for structural analysis. This book provides a theoretical treatment for derivation of the stiffness matrices for different states of plasticity in an element for the stiffness method of analysis.
The theory is based on the plastic flow rule and the concept of yield surface is introduced. An introduction to the use of the linear programming technique for plastic analysis is provided in a single chapter in this book. This powerful and advanced method for plastic analysis is described in detail using optimization procedures. Its use is important in an automated computational environment and is particularly important for researchers working in the area of nonlinear structural plastic analysis.
This chapter was written by Professor Francis Tin-Loi, a prominent researcher in the use of mathematical programming methods for plastic analysis of structures. In this book, new insights into various issues related to plastic analysis and design are given, such as the effect of high temperature on plastic collapse load and the use of plastic rotation capacity as a limit state for plastic design. Based on the elastoplastic approach, an interpolation procedure is introduced to calculate the design forces and deflections at the design load level rather than at the collapse load level. In the final chapter of this book, a comparison among design codes from Australia, Europe, and the United States for plastic design method is given. This comparison enables practicing engineers to understand the issues involved in the plastic design procedures and the limitations imposed by this design method.
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