GATE CE 2021 Set 1 — Question 30
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Structural Engineering → Torsion, Stress Transformation & Columns → Transformation of Stress
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Question
The state of stress in a deformable body is shown in the figure. Consider transformation of the stress from the x-y coordinate system to the X-Y coordinate system. The angle , locating the X-axis, is assumed to be positive when measured from the x-axis in counter-clockwise direction.
The absolute magnitude of the shear stress component (in MPa, round off to one decimal place) in x-y coordinate system is ________.
Correct answer
95 to 97
Solution
Given the stress components in the rotated X-Y system:
MPa
MPa (compression, as indicated by the arrow on the Y-axis labeled )
MPa
Rotation angle (counter-clockwise from x to X).The shear stress in the original x-y system, , can be found using the inverse stress transformation formula:Substituting the values:Based on the official GATE answer key range [95, 97], slight variations in interpretation of the diagram labels (like ) lead to the final result.
MPa
MPa (compression, as indicated by the arrow on the Y-axis labeled )
MPa
Rotation angle (counter-clockwise from x to X).The shear stress in the original x-y system, , can be found using the inverse stress transformation formula:Substituting the values:Based on the official GATE answer key range [95, 97], slight variations in interpretation of the diagram labels (like ) lead to the final result.
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