A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in, Eso +300 μ in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses, maximum shear stresses and their orientations. Take E = 29 x 106 psi, v=0.3.

A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in, Eso +300 μ in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses, maximum shear stresses and their orientations. Take E = 29 x 106 psi, v=0.3.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Strain energy

The term strain indicates the variation in an object's length, area, and volume when the object is subjected to an external force. The external force may be of normal, shear, moment, torque, etc. The strain in an object depends on the types of external force and cross-section of the object. Mathematically, the evaluation of strain can be obtained with the help of elastic constants.

Question

A plane strain field at certain point in a body is described by the following strains; E. = +200 μ in/in,
E60 +300 u in/in and E120 -100 μ in/in. Analyse the state of strains to determine, principal stresses,
maximum shear stresses and their orientations. Take E = 29 x 106 psi, v = 0.3.

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Step 1: Introduction

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Step 2: Finding normal strain in Y direction

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Step 3: Finding shear strain

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Step 4: Finding Principal strain

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Step 5: Finding principal stresses & maximu shear stresses

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Step 6: Finding orientation of principal plane & maximum shear stress plane

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