EXPERIMENT # 08
TO VERIFY EXPERIMENTALLY TORSION FORMULA
AND MODULUS OF RIGIDITY BY TESTING A
MEMBER WITH CIRCULAR CROSS SECTION
OBJECTIVE:
To verify torsional formula
To verify modulus of rigidity
THEORY:
TORSION:
Torsion is the twisting of an object caused by a moment acting about the
object’s longitudinal axis. Torsion is the deformation that a torque tends
to produce when applied in the along the longitudinal axis of an object.
Transmission shafts, like drive shaft in axle, are used to transmit power
by rotation.
Tρ
τ=
J
WHERE:
τ = TORSIONAL STRESS
T = TORQUE
J = POLOR MOMENT OF INERTIA
ρ = DISTANCE FROM THE CENTRE
The maximum torsional stress in a circular cross section is given by:
TR
(τ) max= WHERE R = d/2
J
Moreover, for circular shaft the moment of inertia is given by:
J = π D4 / 32
So the value of max-torsion will become:
(τ) max = 16T / πD^3
MODULUS OF RIGIDITY:
Shear modulus also known as Modulus of rigidity is the measure of the
rigidity of the body, given by the ratio of shear stress to shear strain.
Often denoted by G
G = 𝜏/ γ
σ = -K ε
Where,
K=proportionality constant
σ = stress
ε =strain
Moreover, from above equation it can also be written as:
G = TL / G φ
POLAR MOMENT OF INERTIA:
Polar Moment of Inertia is a measure of an object's capacity to oppose or
resist torsion when some amount of torque is applied to it on a specified
axis. If the polar moment of inertia is of higher magnitude then the
torsional resistance of the object will also be greater.
ANGLE OF TWIST:
Angle of twist: For a shaft under torsional loading, the angle through
which fixed end of a shaft rotates with respect to the free end is called the
angle of twist.. As the torque is increased, the outer region of the shaft
behaves like a plastic material while the inner core is still linear elastic.
φ = TL/JG
Where the angle is always in radians.
APPARATUS AND EQUIPMENT:
Torsion Testing Machine
Dial Gauge
Vernier Calliper
Ruler
Weight
PROCEDURE:
FOR TORSIONAL FORMULA
Measure the length of the specimen by measuring tape
Measure the diameter of the specimen by Vernier caliper
Calculate the polar moment of inertia of the sample
Insert the specimen into the jaws of the torsion testing machine
Apply the torque and increase it by appropriate increments
Record the applied torque and the angle of twist
Plot the torque versus angle graph
GJ T
Calculate the value of L and θ
Compute the percentage error
FOR MODULUS OF RIGIDITY
Measure the diameter of test specimen using vernier callipers.
Measure the gauge length of the specimen.
Hold the specimen in between the plates with a dog holder.
Adjust the circular scale with zero of the vernier scale.
Torque reading show the value in digital indicator.
Fracture occurs.
Plot a graph of torque vs angle of twist and determine the Modulus
of Rigidity.
OBSERVATION:
S.no length diameter torque Angle of
twist
ft in Kip/ft degree
1 3 4 15 1.23
L = 36in d = 4in T = 150 kip-in τ = 0.02 rad
CALCULATIONS:
Maximum torsion stress is given by = 16T / πD^3
= 14.33 ksi
Modulus of rigidity is given by = G = TL / G φ
By putting the values in above equation, we get
G = 12903.5 ksi RESULTS:
S NO (τ)max G (ksi)
1 14.33 12903.5
CONCLUSION:
The above results shows the required values of torsional stress and modulus of
rigidity.
