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.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter7: Analysis Of Stress And Strain

Section: Chapter Questions

Problem 7.7.13P: An clement of material in plane strain (see figure) is subjected to strains ex= 480 × 10-6, Ey= 70 ×...

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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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