ENGR 220Section 5.1-5.3

Torsional Deformation of a Circular Shaft

Torsional Deformation of a Circular Shaft

max

c

The Torsional Formula• If the material is elastic then Hooke’s Law

applies.

max

c

G

Derivation of the Torsional Formula

Torsional Equation

44

4

max

2Shaft Tubular

2Shaft Solid

io ccJ

cJ

J

Tc

Lecture Example: Plot the torque on the shaft as a function of position from E to B. The smooth bearings at A and B do not resist torque.

Lecture Example: Plot the shear stress distribution acting along a radial line lying in the region EA of the shaft. The smooth bearings at A and B do not resist torque.

Shaft ID = 1 inShaft OD = 1.25 in

Power Transmission

TfP

Tdt

dTP

2

Lecture Example: The gear motor can develop 1/10 hp when it turns at 80 rev/min. If the allowable stress for the shaft is τallow = 4 ksi determine the smallest diameter shaft to the nearest 1/8 in that can be used.