Von Mises Stress Calculation for Internally Pressurized Pipe

[aidansully01]

Problem Description:
Internally pressurised pipe elbow with open ends.

I have to compare the Finite Element Von Mises stress with that calculated by hand.

I am having issues calculating this.

The formulae that I am using are:

Hoop Stress: σ_1 = \frac{P*d}{2*h}
Where: P is pressure; d is mean diameter; h is thickness of pipe

Radial Stress: σ_2 = \frac{-P*(r_i)^2*((r_o)^2-(r)^2)}{(r)^2((r_o)^2-(r_i)^2)
Where: P is pressure; r_i is inner radius; r_o is outer radius; r is radius of curvature

Von Mises Stress: σ_Y = \sqrt{\frac{1}{2}*[σ_1^2_σ_1*σ_2+σ_2^2]}
Note: neglecting σ_3

Could someone please point me in the right direction with this problem? I am not sure if I should be including axial stress in calculating the Von Mises Stress..

 

[Chestermiller]

In my judgment, the axial principal stress should also be included in this, but I don't think it is necessary to include the radial principal stress.