We were
discussing the various Theories of failure in machine design, Concept of eccentric loading and Concept of direct and bending stresses in our previous
posts.

Now we are
going further to start a new topic i.e. Power 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 power 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

Ï„ = 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„ /R

q = Ï„ 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 = Ï„ x
r/R x 2ÐŸ x r x dr

dF = Ï„/R 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„/R x
2ÐŸ 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
= (ÐŸ/16) Ï„ D**^{3}

^{3}

Let us
consider that N is the R.P.M of the shaft and Ï‰ is the angular velocity of the
shaft. We have already secured here the torque transmitted by circular solid
shaft and it is mentioned above. Now we will find here the expression for power
transmitted by solid circular shaft as mentioned here.

Do you
have suggestions? Please write in comment box.

We will
now discuss the topic, Power 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

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