TORQUE TRANSMITTED BY A CIRCULAR SOLID SHAFT

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.

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

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

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 r²dr

Twisting moment at the circular elementary ring could be determined as mentioned here

dT = Turning force x r

dT = τ/R x 2П r³dr

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 D³

Do you have suggestions? Please write in comment box.

We will now discuss the another topic, Torque transmitted by a hollow circular shaft, in the category of strength of material, in our next post.

Reference:

Strength of material, By R. K. Bansal

Image Courtesy: Google

Also read

Bending stress in beams

Basic concept of shear force and bending moment

Strain energy stored in body Stress analysis of bars of composite sections

Stress and strain in strength of materials, Strain energy stored due to impact loading