Shear stress distribution on the cross-section of the coil wire in a helical compression spring is shown in the figure. This shear stress distribution represents
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In helical springs, the combined effects of direct shear and torsional shear are crucial in determining the total shear stress distribution. The shear stress varies across the cross-section and is typically higher at the outer edges.
direct shear stress in the coil wire cross-section
torsional shear stress in the coil wire cross-section
combined direct shear and torsional shear stress in the coil wire cross-section
combined direct shear and torsional shear stress along with the effect of stress concentration at inside edge of the coil wire cross-section
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The Correct Option isC
Solution and Explanation
The shear stress distribution shown in the figure represents a typical stress distribution in the cross-section of a helical compression spring under load. The cross-section of the spring undergoes both direct shear and torsional shear due to the combined effects of axial load and the torsion created by the winding of the spring.
Direct Shear Stress:
Direct shear stress is generated when the load is applied axially along the length of the spring. This force is distributed across the cross-section of the wire and varies depending on the location within the cross-section. Typically, the shear stress is higher at the center of the wire and decreases toward the outer edge.
Torsional Shear Stress:
Torsional shear stress is generated due to the twisting of the spring. The spring’s helical shape leads to a torsional load that causes shear stress along the length of the wire. This torsional stress varies with the distance from the center of the wire, being zero at the center and increasing as you move outward.
Combined Shear Stress:
In the given figure, both types of shear stress are combined. The diagram shows the variation in shear stress from the center to the outer edges of the cross-section, with the magnitude increasing toward the outer regions. This combined effect of direct shear and torsional shear stress is what the diagram represents. The presence of both shear stresses makes this problem a case of combined shear stress. Therefore, the correct answer is (C), which indicates the combination of both types of shear stress in the coil wire cross-section.
Why Other Options Are Incorrect:
- Option (A): This only refers to the direct shear stress, which does not account for the torsional shear stress present in the system.
- Option (B): This refers to only the torsional shear stress, which is also incorrect since the figure shows both types of shear stress.
- Option (D): While the diagram does account for both shear stresses, it does not explicitly show stress concentration effects at the inside edge, so this option is not fully correct.
Thus, the correct answer is (C).
