The maximum shear stress occurs on the outermost fibres of a circular shaft under torsion. In a close coiled helical spring, the maximum shear stress occurs on the _______.

Explanation:

The simple torsion equation is written as

$\frac{T}{J}=\frac{\tau }{r}=\frac{G\theta }{L}or\tau =\frac{G\theta r}{L}$

This states that the shearing stress varies directly as the distance ‘r' from the axis of the shaft and the following is the stress distribution

Hence the maximum shear stress occurs on the outer surface of the shaft where r = R and at the centre the shear stress is zero.

For Closed coil fibre:

The major stresses in a helical spring are of two types, shear stress due to torsion and direct shear due to applied load. It is observed that for both tensile load as well as compressive load on the spring, maximum shear stress always occurs at the inner side of the spring. Hence, failure of the spring, in the form of crake, is always initiated from the inner radius of the spring.

Alternate MethodThe correct option is 3 innermost fiber

In close coiled helical springs,:

τ_max = τ_transverse ± τ_torsion

τtorsion will be maximum at outermost fiber of wire.

At inner side,

τmax = τtorsion + τtransverse

$=\frac{16PR}{\pi d^3}+\frac{4P}{\pi d^2}$

$=\frac{16PR}{\pi d^3}\left(1+\frac{d}{4R}\right)$$$$$