## Sunday, 29 October 2017

Today, we will find out here the expression for maximum shear stress developed in wire of spring with the help of this post.

### Let us brief here first helical spring

Helical springs are usually used in number of applications due to their shock absorption and load bearing properties. There are two types of helical spring i.e. Open coiled helical spring and closed coiled helical spring. We will be concentrated here on closed coil helical spring.

### Closed coiled helical spring

Closed coiled helical springs are also termed as tension springs as such springs are designed to resist the tensile load and twisting load. In simple, we can say that closed coiled helical springs are those springs which are used in such applications, where tensile or twisting loads are present.

In case of closed coiled helical spring, spring wires are wound tightly. Hence such springs will have very small pitch. Closed coiled helical springs wires are very close to each other and hence, spring turns or coils will lie in same plane.

In case of closed coiled helical spring, turns or coils of such spring will be located at right angle to the helical axis.

Closed coiled helical spring, as displayed here, carrying an axial load W. In case of closed coiled helical spring, helix angle will be small and it will be less than 100. Therefore, we will neglect the bending effect on spring and we will only consider the effect of torsional stresses on the coils of closed coiled helical spring.
Let us consider the following terms from above figure of closed coil helical spring.
d = Diameter of spring wire or coil
p = Pitch of the helical spring
D = Mean diameter of spring
R = Mean radius of spring
n = Number of spring coils
W = Load applied on spring axially
C = Modulus of rigidity
τ = Maximum shear stress developed in the spring wire

Twisting moment on spring wire could be expressed as mentioned here
T = W x R

We can consider the spring wire as solid shaft with diameter d and as we know that torque or twisting moment transmitted by a solid shaft is given as
T = (П/16) τ d3

Therefore, we can say that torque or twisting moment on spring wire could also be expressed as
T = (П/16) τ d3
And we can say here
W x R = (П/16) τ d3
Do you have suggestions? Please write in comment box.

We will now discuss another topic, Derive the expression for deflection and stiffness in closed coil helical spring, in the category of strength of material, in our next post.

### Reference:

Strength of material, By R. K. Bansal