A differential element on the bracket as shown in Figure Q1 is subjected to plane strain that has the following components: ex = 150µ, ey = 200µ, yxy = -700µ. By using the strain transformation equations, determine:- (i) The equivalent in-plane strains on an element oriented at an angle 0 = 60° counterclockwise from the original position. (ii) Sketch the deformed element within the x' – y' plane due to these strains. (iii) The stresses on the oriented planes in (i) where the value of elasticity, E = 200 GPa and Poisson's ratio, v = 0.32.

A differential element on the bracket as shown in Figure Q1 is subjected to plane strain that has the following components: ex = 150µ, ey = 200µ, yxy = -700µ. By using the strain transformation equations, determine:- (i) The equivalent in-plane strains on an element oriented at an angle 0 = 60° counterclockwise from the original position. (ii) Sketch the deformed element within the x' – y' plane due to these strains. (iii) The stresses on the oriented planes in (i) where the value of elasticity, E = 200 GPa and Poisson's ratio, v = 0.32.

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

(b)
A differential element on the bracket as shown in Figure Q1 is subjected to plane
strain that has the following components: ex = 150µ, ey = 200µ, yxy = -700µ.
By using the strain transformation equations, determine:-
(i)
The equivalent in-plane strains on an element oriented at an angle 0 = 60°
counterclockwise from the original position.
(ii)
Sketch the deformed element within the x' – y' plane due to these strains.
(iii)
The stresses on the oriented planes in (i) where the value of elasticity, E =
200 GPa and Poisson's ratio, v = 0.32.

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