Torsion of a cylinder, Mechanical Engineering

Torsion of a Cylinder

Let a cylinder of length l and radius R be clamped at one end and twisted at the other end by applying a torque τ about the axis of the cylinder. Each cross-section of the cylinder is rotated about the axis by an amount proportional to its distance from fixed end; hence the twist is maximum at the free end.


Consider the fig. let the cylinder be divided into a large number of thin co-axial cylindrical shells. Consider a shell of radius rand thickness dr. When the cylinder is twisted, a generating line PQ of this shell is displaced to position PQ'. The angle θrepresents angle of shear, while angle Ø (Q O' Q') is called angle of twist. From geometry, we have

QQ' = l θ = r Ø

Or, θ = rθ/l

The angle of shear θ is same on the entire surface of the shell. It increases linearly with r and hence the shearing strain is maximum at the outermost surface of the cylinder.

Let F be the tangential force acting on the lower face of the given shell; then the shearing stress is given by

Stress = F/(2 π r dr)

where, 2 π r dr is the face area of the shell. Now modulus of rigidity η, by definition is

η = (F/(2 π r dr))/θ

or, F = 2 π η θ rdr

= (2 π η Ø )/l r2 dr

The torque applied by this force about the axis OO' of the cylinder is,

d τ = Fr = (2 π η Ø )/l r3 dr

The above is the torque required to twist a thin cylindrical shell of radius r by an angle Ø. The torque required to twist the entire cylinder is therefore,

149_download (6).png 

The quantity τ/Ø is called torsional rigidity of the cylinder. It is equal to torque required to twist the cylinder by one radian (Ø = 1).

Posted Date: 9/18/2012 1:20:00 AM | Location : United States







Related Discussions:- Torsion of a cylinder, Assignment Help, Ask Question on Torsion of a cylinder, Get Answer, Expert's Help, Torsion of a cylinder Discussions

Write discussion on Torsion of a cylinder
Your posts are moderated
Related Questions
Neutra l Layer and Neutral Axis In the beam or cantilever, there is one layer which retains the original length of it even after bending. So in this layer tensile stress and c


draw the projection of pentagonal pyramid have 30 mm edge and axis 50 mm long having base on hp and an edge of the box parallel to vp

Our sir asked us to design a knuckle joint...they gave us only the tensile force applied on the joint as 50kn...and told us to find the appropriate material..so what can we use???

please share some basic theory material

Fourth Gear Position: When gear M4 on the main shaft is in mesh with gear C4 on the countershaft then this is known as fourth gear position. The free gear M4 rotates with the

Figure shows a Warren girder consisting of seven members each of 3 m length freely supported at its end points. The girder is loaded at B and C as given. Determine the forces in al

The Circular Orbits The bounded motion of a particle in a central force is in general an ellipse given by   where eccentricity e is related to semi-major and minor axes a

(a) Describe a vector and scalar ? (b) What is meant by line of action of vector ? (c) What are displacement vectors and position vector ? (d) Calculate the component of t

What is ignition angle offset