GATE ME 2026 Set 1 — Question 52
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Strength of Materials → Stress, Strain & Elastic Constants → Mohr's Circle
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Question
A welded square plate of is subjected to biaxial state of stress of magnitude and , as shown in the figure below. The ratio of the normal stress acting in the perpendicular direction of the weld to the shear stress of the weld is ________ (rounded off to 2 decimal places).
Correct answer
0.57 to 0.61
Solution
Given:
(horizontal tension)
(vertical tension)
Angle of the weld with the horizontal, (since it is a diagonal of a square plate).The normal stress () and shear stress () on a plane inclined at an angle are given by the transformation equations:In this case, there is no applied shear stress, so . For the weld plane, .The ratio of the normal stress to the shear stress is:Rounding off to 2 decimal places, we get .
(horizontal tension)
(vertical tension)
Angle of the weld with the horizontal, (since it is a diagonal of a square plate).The normal stress () and shear stress () on a plane inclined at an angle are given by the transformation equations:In this case, there is no applied shear stress, so . For the weld plane, .The ratio of the normal stress to the shear stress is:Rounding off to 2 decimal places, we get .
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