Chapter 10 Torsion Tests

Mechanical properties in torsion
• Consider a cylindrical bar subjected to a torsional moment at one end.
• The twisting moment is resisted by shear stresses set up in the cross
section of the bar. (zero at centre, max at surface)
M
T
= = r a
∫
∫ dA
r=
0
τ
τrdA
=
r
∫
o
a
r
2
dA
r
But is the polar moment
of inertia of the area with respect
to the axis of the bar. Thus,
2
M
T
τ J
= , or τ =
r
M
J
T
r
Eq.3
Eq.2
Where ττττ = shear stress, Pa
M T = torsional moment, Nm
r = radial distance measured
from centre of bar, m
J = polar moment of inertia, m 4
Torsion of a solid bar
Suranaree University of Technology May-Aug 2007
Tapany Udomphol