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
State the Planning the foundation for reciprocating engines i)  The eccentricity of  the common centre of gravity of machine and foundation referred to the centroid of base are

Define the term Engineering Mechanics Sol.: Engineering mechanics is the branch of science, which deals the action of forces on the rigid bodies. Everywhere we feel applicat

Explain the Laws of Thermodynamics Usually thermodynamics contains four laws; a. Zeroth law:  this law deals with thermal equilibrium and establishes an idea of temperature.

Classification Two categories of plastics are identified. Those are: thermosetting plastics and thermoplastics. Plastics generally cannot stand higher temperatures. They becom

Q. What is Injection moulding? An important industrial method of producing articles of thermoplastics is injection moulding. The moulding material is loaded into a hopper from

what is relation between tool life and cutting speed?


Application of group technology point wise

Applications of spot welding As spot welding can be employed for Al, Cu, Ni and Mg alloys. It is not advisable to spot weld steels with carbon content greater than 0.25 % unles

Spinal fluid Collection:    Spinal fluid is usually obtained from lumbar region, although may be obtained during surgery from the cervical region or from the cistern or ventri