GATE ME 2022 Set 2 — Question 38
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Strength of Materials → Stress, Strain & Elastic Constants → Mohr's Circle
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Question
A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress is ________.
Correct answer
(A) 3σ/2
Solution
To find the net normal component of stress , we use the principle of superposition for the two loading cases.Loading - I:
The element is subjected to a uniaxial tensile stress in the -direction.Loading - II:
The element is rotated by . The diagram shows tensile stress acting on the faces perpendicular to the -axis, where the -axis is at an angle with respect to the -axis. Thus, and .
Using the stress transformation formula for the normal stress in the -direction:Substituting the values:Net Stress:
Summing the contributions from both loadings:Therefore, the correct option is (A).
The element is subjected to a uniaxial tensile stress in the -direction.Loading - II:
The element is rotated by . The diagram shows tensile stress acting on the faces perpendicular to the -axis, where the -axis is at an angle with respect to the -axis. Thus, and .
Using the stress transformation formula for the normal stress in the -direction:Substituting the values:Net Stress:
Summing the contributions from both loadings:Therefore, the correct option is (A).
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