(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.
(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.
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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![(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.
(iv) Give your comments on those stresses in (iii) in terms of elastic limit/failure
if the material's yield strength in tension/compression is 250 MPa and in
shear is 90 MPa.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0f1eddb-28da-4f24-b7ef-3a955fb0be65%2F09de8100-7b7c-444a-b5b4-f3d132f57367%2F4g9559_processed.png&w=3840&q=75)
Transcribed Image Text:(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.
(iv) Give your comments on those stresses in (iii) in terms of elastic limit/failure
if the material's yield strength in tension/compression is 250 MPa and in
shear is 90 MPa.
![Figure Q1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0f1eddb-28da-4f24-b7ef-3a955fb0be65%2F09de8100-7b7c-444a-b5b4-f3d132f57367%2F9y7nih_processed.png&w=3840&q=75)
Transcribed Image Text:Figure Q1
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