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
For fan installation detail and indicate correct structural components, drip pan, acoustical and thermal insulation. Provide special acoustical curbs for critical areas. Chec

Q. Why we use Nickel Alloys in welding? Nickel weld metals have high creep-rupture strength but often have lower stress-rupture ductility and lower mechanical and thermal fatig

a.The closest point to discharge treated effluent is a lake, but the pipeline is extended so it discharges into the river draining the lake. This allows a conventional secondary tr

Lubrication Complaints If the engine oil level is too low, check for the following things: External oil leaks Worn out piston rings Worn out valve guide and/o

a) What do ypu understand by production Planning and Control Function. Briefly mention the objective of PPC. b) There are 8 job in an auxiliary unit requiring processing on mach

Ott o Cycle (1876): This cycle consists of the two reversible adiabatic processes and the two constant volume processes as shown in the figure given below on P - V and T -

A square column 410 x 410 mm (along with 4 No. 16 mm bars) carries a dead load of 1020 kN and an imposed load of 410 kN. The foundation soil has a safe bearing capacity of 200 kPa.

Q. Define the Moving boat method? Moving boat method has been more recently evolved and tested in the U.S.A. and holds promise in measurement of discharge of big rivers and tid

determine the vertical deflection at end A neglecting shear

Clutch cable model: Ensure the cables fitted are of the respective model and not interchanged with other model. Also ensure that the cable is genuine.