GATE ME 2016 Set 3 — Question 18
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Strength of Materials → Stress, Strain & Elastic Constants → Mohr's Circle
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Question
The state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b). 
The components are given by
Correct answer
(B) (0, 0, p)
Solution
Figure (a) shows an element rotated by relative to the horizontal. The normal stresses on these planes are (tensile) and (compressive). This represents a state of pure shear when viewed in the coordinate system.Using stress transformation equations to find stresses in the system (where is the rotation from to ):
Substituting , , and :
Adding the two equations gives . Subtracting them gives .
Since there are no other external loads, and .
In the notation of the question, , , and . Thus, the components are .
Substituting , , and :
Adding the two equations gives . Subtracting them gives .
Since there are no other external loads, and .
In the notation of the question, , , and . Thus, the components are .
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