Torsion of Hollow and Rigid shaft
Objective
Determination of angle of twist and shear strain in a shaft subjected to torsion
Apparatus
The apparatus (Fig.1) setup consists of fixtures for holding the specimen and is
provided with a lever arm and weighing pans for loading the shaft in pure torsion. The
telescope and scale arrangement is to measure the twist of the shaft. The lamp is used
for clear vision of the readings in the telescope
Fig .1 Experimental setup
Theory
A slender member subjected primarily to twist is usually called a shaft. Shafts are used
in the transfer of mechanical power from one point two another. In such an application,
one is primarily interested in the twisting moment, which can be transmitted by the shaft
without damage to the material. Knowledge of stresses that develop due to twisting (and
its variation in the cross section) is necessary to be known. In certain applications
twisted shafts are act as a spring with prescribed stiffness with respect to rotation. In
such a case, one I interested primarily in the relation between the applied twisting
moment and the resulting angular twist of the shaft. For a circular shaft of constant
diameter transmitting a uniform torque
M G∅ τ
J
=
L
=
r
Where M is the twisting moment applied, J is the polar moment of inertia of the cross-
section τ is the shear stress developed due to torsion, r is the radius of the element
considered, G is the shear modulus of the material, ∅ is angle of twist and L is the
length of the uniform shaft.
Procedure
1) Measure the cross sectional details of the shaft.
2) Fix the hollow aluminium shaft in the setup
3) Adjust the telescope in such a way that the image of the scale can be seen
through the mirror on the shaft.
4) Measure the length of the shaft (L), distance from the fixed end to the center of
the mirror (L1) and distance from the center of the mirror to the scale (L2).
5) Note down the initial readings (X1) of the telescope without applying any load.
6) Figure out how pure torsion is applied to the shaft. Apply a load of 200 g in the
pan. Note: Loads should be applied simultaneously on both the weighing pans
so that the setup does not get disturbed during loading.
7) Due to loading the shaft is twisted. Note down the corresponding reading (X2)
by mirror and telescope arrangements. Also make the strain measurements.
8) Figure out how to find out the angle of twist from these readings.
9) Load the shaft in steps of 200g until 1 kg and note down the readings as
above’
10) Unload the weights in steps of 200g and record your readings.
Analysis of Results
1) Draw the free body diagram of the loaded specimen.
2) Plot a graph showing the torque versus angle of twist
Table
Hollow shaft dimensions r0 = r1 = L=
Telescope reading (X1)= (X2) =
Distance of mirror from scale (L1)
SL Load Torque Telescope Readings(X2) (X2)- (X1) Angle of
No N N-m mm twist
(Radians)
Loading Unloading Average
mm mm mm
G for Aluminium =26 GPa
Discussion
1) How is shear Modulus related to Young’s modulus?
