GATE ME 2026 Set 1 — Question 19
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Question
A closely coiled helical compression spring of mean coil diameter and wire diameter , is loaded by an axial force . The maximum shear stress developed in the wire is
Correct answer
(A) (8FD)/(π d³) + (4F)/(π d²)
Solution
The maximum shear stress in a closely coiled helical spring is the result of two components: torsional shear stress and direct shear stress.
1.Torsional Shear Stress (): The axial force creates a torque on the wire cross-section. The torque is given by . The resulting torsional shear stress is:
2.Direct Shear Stress (): The axial force also causes a direct shear stress across the wire cross-section. It is calculated as the force divided by the area of the wire:
3.Total Maximum Shear Stress: The maximum shear stress is the sum of these two components (neglecting the curvature effect/Wahl factor for this specific representation):
Comparing this with the given options, option (A) is the correct representation.Continue learning with Success Tracker
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