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Session 2666

Elementary Limit Analysis in Mechanical and Civil Engineering Sophomore Curricula

Kenneth Sawyers Department of Mechanical Engineering and Mechanics Lehigh University Bethlehem, PA 18015

Abstract: The customary Mechanics of Materials / Strength of Materials courses for Civil and Mechanical Engineering sophomores do not include a unit on limit analysis (presumably) due to its absence from textbooks. All the same, background required for limit analysis - uniaxial elastoplastic deformation and plastic hinge - is routinely included in the course. Thus, students are prepared to learn elementary limit analysis and extend their understanding of “plastic hinge” into a usable basis for beam design.

The author has prepared and taught a two lecture unit on limit analysis within a Strength of Materials course. This material is based on and reinforces plasticity topics already addressed in the course and includes examples of increasing complexity involving concentrated and distributed loadings. It is similar in spirit to Chapter 13 of Nash’s summary [1]. However, the method of virtual work is employed here as an alternative to static analysis.

Limit analysis offers students a new design methodology and sharpens their geometrical / analytical skills through postulating collapse mechanisms and applying virtual work techniques. They acquire a basis for comparing the relative merits of using limit loads instead of traditional elastic analysis of statically indeterminate beams.

Introduction

It might be worthwhile asking whether exposing sophomores to limit analysis has pedagogical value.

Except for a brief introduction to elastic-plastic material behavior in a mechanics of materials course, our students live in a linearly elastic world. Further, based on the dominant theme of homework problems, this world is also statically determinate. Analysis of statically indeterminate beams is usually accompanied by multiple variables and simultaneous equations1. Reactions at supports must be determined. While locating maxima in a moment diagram is straightforward for statically determinate cases, it can be difficult otherwise. Elastic beam design, based on maximum moment, Mmax, is impeded by static indeterminacy.

1 The degree of difficulty depends on the method used to handle the indeterminacy.—integration, superposition, or Castigliano’s Theorem.

Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education

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Sawyers, K. (2005, June), Elementary Limit Analysis In Mechanical / Civil Engineering Sophomore Curricula Paper presented at 2005 Annual Conference, Portland, Oregon. 10.18260/1-2--15284