TORSION OF RECTANGULAR BARS
TORSION OF RECTANGULAR BARS
The analysis of circular shafts was based upon the assumption that plane cross sections
remain plane and undistorted. If the cross section of the shaft is not circular,
experiments showed that the cross section distort and do not remain plane. Therefore,
the formulas for shear distribution and torsional rigidity derived for circular shafts can
not be applied to noncircular members.
Figure 3.10 shows the distortion of a rectangular bar caused by the torque T. The two
significant features of the deformation are:
• The cross sections become distorted.
• The shear strain (and thus the shear stress) is zero at the edges of the bar and
largest at the middle of the sides.
For the rectangular bar in Fig. 3.12 that carries the torque T, results obtained by
numerical methods determine that the maximum shear stress τ and the angle of twist θ
are given by: