We were discussing the Torsion
or twisting moment, Shear stress produced in a circular shaft subjected to torsion and Torque transmitted by a circular solid shaft in our previous
posts.

Now we are going further to start a new topic i.e. Torque
transmitted by a circular hollow shaft with the help of this post.

###
**So,
what is torsion or twisting moment?**

A shaft will said to be in torsion, if it will be
subjected with two equal and opposite torques applied at its two ends.

When a shaft will be subjected to torsion or
twisting moment, there will be developed shear stress and shear strain in the
shaft material.

We will discuss here one case of a hollow circular
shaft which will be subjected to torsion and we will secure here the expression
for maximum torque transmitted by a hollow circular shaft.

####
*We
have following information from above figure*

*We have following information from above figure*

Ro = Outer radius of the hollow circular shaft

Ri = Inner radius of the hollow circular shaft

Do = Outer diameter of the hollow circular shaft

Di = Inner diameter of the hollow circular shaft

dr = Thickness of small elementary circular ring

r = Radius of the small elementary of circular ring

q = Shear stress at a radius r from the centre of
the hollow circular shaft

Ï„ = Maximum shear stress at outer surface of shaft

dA = Area of the small elementary of circular ring

dA = 2ÐŸ x r x dr

Shear stress, at a radius r from the centre, could
be determined as mentioned here

q/r = Ï„ / Ro

q = Ï„ x r/ Ro

Turning force due to shear stress at a radius r from
the centre could be determined as mentioned here

dF = q x dA

dF = Ï„ x r/ Ro x 2ÐŸ x r x dr

dF = Ï„/ Ro x 2ÐŸ r

^{2}dr
Twisting moment at the circular elementary ring
could be determined as mentioned here

dT = Turning force x r

dT = Ï„/ Ro x 2ÐŸ r

^{3}dr
Do you have suggestions? Please write in
comment box.

We will now discuss the Principal
planes and principal stresses, in the category of strength of material, in our
next post.

###
**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google