Combined Bending, Direct And Torsional Stresses In Shafts

In this article, I will describe combined bending and direct and torsional stresses in shafts.

For example, on a ship’s propeller shaft, it happens that the shaft is subjected to direct thrust in addition to bending moments and torsion. In this case, the forward and axial forces due to the bending moment must be combined into one result.

a) Direct stress

Direct stress in shaft

where P = axial thrust

A = area of cross-section

b) Bending stress

Bending stress in shaft

where M = bending moment

y- a distance of fiber from the neutral axis

I = moment of inertia.

c) Torsional Stress (shear)

Torsional Stress in shaft

where T = torque

r = radius of the shaft

J = polar moment of inertia

Combined Stresses:

Under the combination of these stresses,

(d) Principle Stress

Principle Stress in shaft

(e) Maximum shear stress

Maximum shear stress in shaft

Equivalent Moment and Torque:

The equivalent bending moment Me can be defined as the bending moment that produces forward stress equal to the torque acting independently of the bending moment. Similarly, the equivalent torque Te can be defined as the torque that produces the maximum shear stress equal to the torque acting independently of the bending moment.

For a circular shaft of diameter, d = 2r

Equivalent Moment and Torque in Shaft

Power transmitted by a shaft:

Power transmitted by a shaft

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