We were discussing the basic concept
of spring in strength of material, various
definitions and terminology used in springs, importance of
spring index, expression
for maximum bending stress, deflection developed in the plate of leaf spring and basic difference between open coiled and closed coiled helical spring in our previous posts.

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

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**
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 10

^{0}. 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

Ï„ = 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 = (ÐŸ/16) Ï„ d

^{3}
Therefore, we can say that torque or twisting moment
on spring wire could also be expressed as

T = (ÐŸ/16) Ï„ d

^{3}
And we can say here

W x R = (ÐŸ/16) Ï„ d

^{3}
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