When a simply supported reinforced concrete beam with three surfaces exposed to high temperature is acted by a positive bending moment (i.e., tension zone on its section exposed to high temperature), the bending moment–curvature ( M − 1/ ρ) relation under the path of loading at constant temperature is shown in Fig.
However, the thermal–mechanical behavior of the structure, especially the mechanical condition of the plastic hinge at elevated temperatures, is complicated, and this should be considered carefully during the plastic limit analysis. The plastic limit analysis of a statically indeterminate reinforced concrete structure under common actions of temperature and load are the same as that of the structure at room temperature, if the influence of the heating–loading path is not taken into account. Zhenhai Guo, Xudong Shi, in Experiment and Calculation of Reinforced Concrete at Elevated Temperatures, 2011 13.5.2 Characteristics of Plastic Hinges at Elevated Temperatures It concludes with a note on the optimal plastic design problems. Furthermore, it provides a general description of the discrete plane frame problem with a view to its eventual computer implementation as a MATLAB script. Following this, it introduces the solutions of some simple examples through application of the LP capability of the popular Microsoft Excel spreadsheet software. It focuses on the application of static theorem.
It begins with brief statements concerning the dual pair of bound theorems of limit analysis that clearly suggest associated formulations as constrained optimization problems. This chapter aims to fill the gap between the mathematical programming methods and the classical and often tedious techniques involving, for instance, upper bound approximations to the collapse load using an approach based on identification and combination of basic mechanisms. Plastic collapse factor represents one of the most important outcomes of a plastic structural analysis, as it is useful for the reliable and economical safety assessment and design of ductile structures. Plastic collapse takes place when the structure is converted into a mechanism by the development of a suitable number and disposition of plastic hinges.
It estimates the factor by which the live load component needs to be amplified so that a structural crisis, which takes the form of plastic collapse, occurs. Plastic limit analysis is concerned with the problem of finding how “strong” a given structure is. Tin-Loi, in Plastic Analysis and Design of Steel Structures, 2009 Publisher Summary
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