NRI INSTITUTE OF INFORMATION SCIENCE & TECHNOLOGY BHOPAL (M.P) COMPILED BY AMIT SINGH 9827740442 ([email protected]) Page 1 TORSION OF CIRCULAR SHAFT When a circular shaft is subjected to torsion, shear stresses are set up in the material of the shaft. To determine the magnitude of shear stress at any point on the shaft, consider a shaft fixed at one end AA and free at the end BB as shown. Let CD is any line on the outer surface of the shaft. Now let the shaft is subjected to a torque T at the end BB as shown. As a result of this torque T, the shaft at the end BB will rotate clockwise and every cross-section of the shaft will be subjected to shear stresses. The point D will shift to D’ and hence line CD will be deflected to CD’ and the line OD’ will be shifted to OD’. R = Radius of the shaft. L = Length of the shaft. T = torque applied at the end BB. τ= Shear stress induced at the surface of the shaft due to torque T. C = Modulus of rigidity of the material of the shaft. Also equal to shear strain. And is also called angle of twist. If is very small than
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When a circular shaft is subjected to torsion, shear stresses are set up in the
material of the shaft. To determine the magnitude of shear stress at any point onthe shaft, consider a shaft fixed at one end AA and free at the end BB as shown.
Let CD is any line on the outer surface of the shaft. Now let the shaft is subjected
to a torque T at the end BB as shown. As a result of this torque T, the shaft at the
end BB will rotate clockwise and every cross-section of the shaft will be subjected
to shear stresses. The point D will shift to D’ and hence line CD will be deflected to
Total strain energy in the hollow shaft due to torsion
COMBINED BENDING & TORSION
When a shaft is transmitting torque or power, it is subjected to shear stresses. At
the same time the shaft is also subjected to bending moment due to gravity or
inertia loads. Due to bending moment, bending stresses are also set up in the
shaft. Hence each particle in a shaft is subjected to shear stress and bending
stress. For design purpose it is necessary to find the principal stresses, maximumshear stresses and strain energy. The principal stresses and maximum shear stress
when a shaft is subjected to bending and torsion, are obtained as
Consider any point on the cross-section of a shaft
Let
The torque T will produce shear stress at the point whereas the B.M. will produce
bending stress.
Let q = Shear stress at the point produced by the torque T and