We were discussing the various assumptions made in the theory of simple bending, Thermal stress in composite bars, Centroid and centre of gravity and Elasticity and elastic limit in our previous posts.

Now we are going further to start a new topic i.e. Maximum
torque transmitted by a circular solid shaft with the help of this post. We
recommend to first review the recent post “Torsion or twisting moment” for
having basic information about the concept of torsion or twisting moment.

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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 circular shaft
which will be subjected to torsion and we will secure here the expression for maximum
torque transmitted by a circular solid shaft.

*We have following information from above figure*
R = Radius of the circular shaft

D = Diameter of the 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 circular shaft

τ = Shear stress at outer surface of shaft

dA = Area of the small elementary of circular ring

dA = 2П x r x dr

q/r = τ /R

q = τ x r/R

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

dF = q x dA

dF = τ x r/R x 2П x r x dr

dF = τ/R x 2П r

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

dT = Turning force x r

dT = τ/R x 2П r

^{3}dr
Total torque could be easily determined by
integrating the above equation between limits 0 and R

Therefore total torque transmitted by a circular
solid shaft

**T = (П/16) τ D**

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

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**Reference:**

Strength of material, By R. K. Bansal

Image Courtesy: Google