Torsion
Nash, Mech of Mat by Beer
Torsion
• Consider a bar rigidly clamped at one end and twisted at
the other end by a torque (twisting moment)
T = Fd
• Applied in a plane perpendicular to the axis of the bar.
Such a bar is in torsion.
• An alternative representation of the torque is
the curved arrow shown in the figure.
TORSION
• Torsion is the twisting of a straight bar when it is loaded
by twisting moments or torques that tend to produce
rotation about the longitudinal axes of the bar.
• For instance, when we turn a screw driver to produce
torsion our hand applies torque ‘T’ to the handle and
twists the shank of the screw driver.
Torsional Stresses & Strains
•
• A circular shaft 50 mm of diameter is required to transmit
torque from one shaft to another. Find the safe torque,
which the shaft can transmit, (if the shear stress is not to
exceed to 40 MPa).
• A solid steel shaft is to transmit a torque of 10 kN-m, If the
shear stress is not to exceed to 45 MPa, find the maximum
diameter of the shaft.
Strength of a Hollow Shaft
•
• A hollow shaft of external and internal diameter of 80 mm
and 50 mm is required to transmit torque from one end to
the other. What is the safe torque it can transmit, if the
allowable shear stress is 45 MPa.
Power Transmitted by a Shaft
•
• A circular shaft of 60 mm diameter is running at 150 r.p.m. if the
shear stress is not to exceed 50 MPa, find the power which can be
transmitted by the shaft.
• A hollow shaft of external and internal diameter of 100 mm and 40
mm transmitting power at 120 r.p.m. find the power the shaft can
transmit, if the shearing stress is not to exceed 50 MPa.
• A solid circular shaft of 100 mm diameter is transmitting 120 kW at
150 r.p.m. Find the intensity of shear stress in the shaft.
• A hollow shaft is to transmit 200 kW at 80 r.p.m. If the shear stress is
not to exceed 60 Mpa and internal diameter is 0.6 of the external
diameter, find the diameters of the shaft.
• A solid steel shaft has to transmit 100kW at 160 r.p.m. Taking
allowable shear stress as 70 MPa, find the suitable diameter of the
shaft. The maximum torque transmitted in each revolution exceeds
the mean by 20%.
Polar Moment on Inertia
•
• Calculate the maximum torque that a shaft of 125 mm
diameter can transmit, if the maximum angel of twist is 1o
in a length of 1.5 m. Take G as 70 GPa.
• Find the angel of twist per meter length of a hollow shaft
of 100 mm external and 60 mm internal diameter, if the
shear stress is not to exceed 35 MPa. Take G as 85 GPa.
• A solid shaft of 120 mm diameter is required to transmit
200 kW at 100 r.p.m. If the angel of twist not to exceed 2o,
find the length of the shaft. Take modulus of rigidity for
the shaft material as 90 GPa.
• Find the maximum torque, that can be safely applied to a
shaft of 80mm diameter. The permissible angel of twist is
1.5o in a length of 5 m and shear stress not to exceed 42
MPa. Take G as 84GPa
• A solid shaft is subjected to a torque of 1.6 kN-m. find the
necessary diameter of the shaft, if the allowable shear
stress is 60 Mpa. The allowable twist is 1o for every 20 mm
diameters length of the shaft. Take G as 80 Gpa.
Replacing a Shaft
• Sometime, we required to replace a solid shaft by a hollow
one, or vice versa.
• In such cases the torque transmitted by the new shaft
should be equal to that by the replacing shaft.
• A solid steel shaft of 60 mm diameter is to be replaced by a
hollow steel shaft of the same material with internal
diameter equal to half of the external diameter. Find the
diameters of the hollow shaft and saving in material, if the
allowable shear stress is same for both shafts.
• A solid shaft of 80 mm diameter is to be replaced by a
hollow shaft of external diameter 100 mm. determine the
internal diameter of the hollow shaft if the same power is
to be transmitted by both the shafts at the same angular
velocity and shear stress.
