**COMBINED BENDING, DIRECT AND TORSIONAL STRESSES IN SHAFTS**

Cases arise such as in propeller shafts of ships where a shaft is subjected to direct thrust in addition to bending moment and torsion. In such cases the direct stresses due to bending moment and the axial thrust have to be combined into a single resultant.

**a) Direct stress, **

where P = axial thrust

A = area of cross-section

**b) Bending stress, **

where M = bending moment

y- distance of fibre from neutral axis

I = moment of inertia.

**c) Torsional Stress (shear), **

where T = torque

r = radius of shaft

J = polar moment of inertia

**Combined Stresses:**

Under combination of these stresses,

(d) Principle Stress

(e) Maximum shear stress

**Equivalent Moment and Torque**

Equivalent bending moment

For a circular shaft of diameter, d = 2r

(f)

(g)

If P = 0

(h)

**Power transmitted by a shaft **

Torque** = **

Where power is measured in watts and n is the speed in rpm.