Consider a circular shaft of length 1 and diameter d subjected to torque T, as shown in Fig. 5.1 (a). One end of the shaft is rigidly fixed. A line AB on the surface of the shaft, which is parallel to the axis before twisting, takes up the form of a helix AC after twisting. Let 4’ be the angle of shear strain on the surface. Then
Therefore, we find that the shear stress in the shaft is proportional to the radius of the shaft, as shown in Fig. 5.2. Hence
Now consider the elementary ring of the shaft at a radius x and of thickness dx, as shown in Fig. 5.1 (c).
This is the well known torsion formula for a circular shaft. The SI units of various quantities are:
No comments:
Post a Comment