Chapter 3 Torsion

Engr. Othman A. Tayeh

DEFORMATIONS IN A CIRCULAR SHAFT

Φ the angle of twist

STRESSES IN THE ELASTIC RANGE

τ: shear stressT: applied torqueC: outer diameter ρ: any distanceJ= polar moment of inertia

The shearing stress in the shaft varies linearly with the distance ρ from the axis of the shaft.

The polar moment ofinertia J

For hollow section

For solid section

ANGLE OF TWIST

G: is the modulus of rigidity or shear modulus of the material.This equation can be used only if the shaft is homogeneous (constant G), has a uniform cross section, and is loaded only at its ends.

If the shaft is subjected to torques at locations other than its ends, or if it consists of several portions with various cross sections and possibly of different materials, we must divide it into component parts that satisfy individually the required conditions for the application of previous formula