Machine Design
The stiffness of a closely coiled helical spring subjected to an axial load W is equal to (where G = Modulus of rigidity, and n = Number of active coils)

Gd⁴/ 8D3n
Gd⁴/ 8D²n
Gd3/ 8D3n
Gd⁴/ 4D3n

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Machine Design
When a machine member is subjected to torsion, the torsional shear stress set up in the member is

Maximum at the centroidal axis and zero at the outer surface of the member
Zero at the centroidal axis and maximum at the outer surface of the member
Maximum at both the centroidal axis and outer surface of the member
Zero at both the centroidal axis and outer surface of the member

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