Example 1:

A solid shaft is designed to carry a maximum torque of 286 Nm. Find the shaft diameter if the shaft is made of steel EN3, with a required safety factor of 5.

D = 30 mm

Given:

            T = 422 Nm = 286 000 N mm

             Material EN3 (t_u = 270 N/mm²)

             SF = 5

Req:

             D = ?

Solution:

                t_all  = t_u / SF                          …………..…….(1)

                 t_all  = (T r) /  [(p/32) D⁴] = (T D/2) /[(p/32) D⁴]

                 t_all  = 16 T / (p D³)                             ………..(2)

From eqn. (1):

                 t_all  = 270/5 = 54 N/mm²

From eqn. (2):

                  54 = (16 x 286 000) / (p D³)

                  D³ = (16 x 286 000) / (p x 54) = 26 973.815 mm³

                  D = 29.99 mm = 30 mm (Ans)

1) If the above shaft is made hollow with the same outer diameter and with a thickness of 2 mm. Find:

A) The shaft torque capacity. (124.77 Nm)

B) The reduction of the shaft weight, if the shaft length is 1 m. (4.14 kg)