Tutorial: Torsion
Problem 1 (br141)
A hollow cylindrical steel shaft is 1.5m long
and has inner and outer diameters
respectively of 40 and 60mm. (a) What is the
largest torque that can be applied to the shaft
if the shearing stress is not to exceed
120MN/m2 (b) What is the corresponding
angle of twist. T  4084Nm   0.075rad (4.3)
Problem 2 (hrn8.0)
A shaft 20mm diameter and 500mm long carries a torque of 400Nm
determine shear stress and angle of twist (G=80GN/m2) [254.6MN/m2, 9.11o]
Determine the diameter necessary in order to halve the stress. [25.2mm]
Determine the diameter necessary in order to halve the angle of twist. [23.8]
Problem 3 (hrn8.1)
A solid steel shaft A of 50mm diameter rotates at 250rev/min. Find the
greatest power that can be transmitted for a limiting shearing stress of 60
MN/m2 in the steel. … It is proposed to replace A by a hollow shaft B, of the
same external diameter but with a limiting shearing stress of 75 MN/m 2.
Determine the internal diameter of B to transmit the same power at the same
speed.
[38.6 kW, 33.4 mm]
Problem 4 ()
A solid shaft of diameter 40mm used to transmit power between one point and
another. If the limiting shear stress is 120MN/m2 and the speed of rotation is
300RPM. Calculate the max power which may be transmitted. [ 47.4kW].
If the shaft is replaced by a hollow shaft 50mm external diameter and of equal
weight (same CSA), calculate the new power which may be transmitted if
limited to the same maximum shear stress. [80.5kW].
Problem 5 (Hib5-74 p220)
A rod is made from two segments: AB is steel
and BC is brass. It is fixed at its ends and a
torque of 800Nm is applied at the interface B.
If the steel portion AB has a diameter of 30mm
and the brass section has a diameter of 40mm
determine the reaction torques at A and C, the
Gst = 80GN/m2
shear stress in each section and the angle of
Gbr = 40GN/m2.
twist at B. [ 1  86.7  2  27.1MN / m2 1,2  3.1 ]
Problem 6 ()
The rod shown is gripped tightly at one
end and twisted by applying a torque at
the other end. Determine the diameter
of B so that its shear stress will be
Gst = 80GN/m2.
double that in A. [ d  15.87mm ]
If the free end is turned to an angle of 5 degrees determine, the twist ratio, the
torque required and the stresses induced in each section.
[ B  1.081 A ; T  75.2Nm ;  A  47.87MN / m2 ;  B  95.82MN / m2 ]
29 November 2010
Tutorial: Torsion
29 November 2010