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. %3D 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)
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Author:Barry J. Goodno, James M. Gere
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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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Figure Q1
Transcribed Image Text:Figure Q1
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, o = 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.
Activ
Transcribed Image Text: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, o = 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. Activ
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