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.
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.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Figure Q1
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 , γχν = -700μ.
By using the strain transformation equations, determine:-
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.
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