Test: Helical Springs - 2 - Mechanical Engineering MCQ

From the equation of torsion

The deflection of a close coil helical spring subjected to axial  force ‘W’ is 

Where δ = Deflection of spring θ = angle of twist
= TL/GJ
∴  

Spring constant or stiffness factor is defined as the axial force required to produce unit deflection

∴ 

∴  
⇒ 

When axial load is applied to the spring stress are 3etup due to:
(i) Torsion
(ii) Direct shear and
(iii) Bending
Where ever the stresses due to direct shear and bending are very small and may be neglected.

When a closed coil helical spring, fixed at one end is subjected to a twisting couple about the central axis of the spring, then bending moment will be produced at every cross-section of the spring. The twisting couple will try to wind up or unwind the spring.

Stiffness of the spring will be same in each case

Angular twist in spring is

Where,
d is diameter of wire of spring
G is modulus of rigidity
W is axial pull on spring
R is mean radius of coil
L is length of spring
∴ 

Wire diameter, d = 10 mm
Spring index = 5 = D/d
D = 5d; D = 50 mm
Number of turns n = 10
Length of wire = πD x n = π x 50 x 10 = 3.14 x 500 = 1570 mm