A 35mmdiameter solid shaft is subjected to axial transverse

A 35-mm-diameter solid shaft is subjected to axial, transverse, and torsional loadings. Determine the normal and shear stresses at H and K, which are L = 110 mm down the shaft from the loading location. For each point, show these stresses on a stress element.

Solution

Normal and shear stresses are a sum of the individual contributions due to the normal axial force, the sideways force and the torque.

a) contribution due to 5KN force -- stress is 4* 5000/(pi*.035^2) N/m^2

b) contribution due to sideways force, introduces sideways bending ( in x-z plane). the stress at K is maximum and is given by Mc/I where M is the moment at K, c is the radius ( .035/2 m) and I is the area moment of Inertia equal to ( pi*c^4)/4

c) stress due to torsion, this is T*c/J where c as above, J = polar moment of Inertia = (pi/2)*c^4

d )At H which passes through the centre of the rod, there is no bending stress as c =0, however torsional stress is there as is normal stress.