DESIGN OF SHAFTS

PURE TORSION

when the shaft is subjected to pure torsional load,the diameter of the shaft may be obtained by using torsion equation


                              τ = T r / J

where,
τ=  torsional shear stress
T= torque acting upon the shaft
r = radial distance of the outermost fibre
J = polar moment of inertia

Note:-

The "Polar Moment of Inertia of an Area" is a measure of a beam's ability to resist torsion. The "Polar Moment of Inertia" is defined with respect to an axis perpendicular to the area considered. It is analogous to the "Area Moment of Inertia" - which characterizes a beam's ability to resist bending - required to predict deflection and stress in a beam.

"Polar Moment of Inertia of an Area" is also called "Polar Moment of Inertia", "Second Moment of Area", "Area Moment of Inertia", "Polar Moment of Area" or "Second Area Moment".


        τ=16T/πd^3

∵      J= (π/32)*d^4

         r=d/2




FOR HOLLOW SHAFT JUST REPLACE D^4 WITH [d⁴₀-dᵢ⁴]

where ,

d⁴₀ =outer dia
dᵢ⁴ = inner dia