If the A36 steel pipe has an outer and inner diameter of 30

If the A-36 steel pipe has an outer and inner diameter of 30 mm and 20 mm, respectively. The material is homogeneous and isotropic, and in a tension test it yields at a stress Y - 250 MPa. Determine the factor of safety at point A according to Maximum shear stress theory (Tresca) Distortion energy theory (Von Mises) Show your results on small material elements. Neglect weights of the members.

Solution

a) Torque acting on the pipe = 2 * 900 * 0.2 = 360 Nm

     Shear stress = 16 * T / pi (do^3 - di^3)  

                         = 16 * 360 / pi * (0.03^3 - 0.02^3)

                         = 96.5 MPa

     For Tresca criterion

     shear stress = sigma_yield / 2*FS

     96.5 = 125 / FS      => FS = 1.29533

b) For Von mises criterion

     shear stress = sigma_yield / sqrt(3)*FS

     96.5 = 250 / sqrt(3) * FS        =>   FS = 1.4957