Von Mises Stress Calculation for Internally Pressurized Pipe

In summary, the problem at hand is to compare the Finite Element Von Mises stress with a hand-calculated value for an internally pressurized pipe elbow with open ends. The formulae being used are the Hoop Stress formula, the Radial Stress formula, and the Von Mises Stress formula. There is uncertainty about whether or not to include axial stress in the calculation of the Von Mises Stress. The individual believes that axial stress should be included but is unsure about the inclusion of radial stress.
  • #1
aidansully01
1
0
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..
 
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  • #2
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.
 

1. What is Von Mises stress calculation for internally pressurized pipe?

Von Mises stress calculation for internally pressurized pipe is a method used to determine the maximum stress that a pipe will experience when subjected to internal pressure. It takes into account both the axial and hoop stresses caused by the internal pressure, and provides a more accurate representation of the stress distribution in the pipe compared to other methods.

2. How is the Von Mises stress calculated?

The Von Mises stress is calculated using the formula σVM = √(σx^2 + σy^2 - σxσy + 3τxy^2), where σx and σy are the axial and hoop stresses, and τxy is the shear stress. This formula is based on the principle of maximum distortion energy and is commonly used in the analysis of complex stress states.

3. What are the assumptions made in Von Mises stress calculation for internally pressurized pipe?

The assumptions made in Von Mises stress calculation for internally pressurized pipe include: the pipe is made of a homogeneous and isotropic material, the pipe is thin-walled, and the internal pressure is uniform. These assumptions may not hold true in all cases, so it is important to consider the limitations of the method when using it for analysis.

4. Why is Von Mises stress calculation important for pipe design?

Von Mises stress calculation is important for pipe design because it helps engineers determine the maximum stress that a pipe can withstand before failure. This information is crucial in ensuring the safety and reliability of the pipe in different operating conditions. It also helps in selecting the appropriate material and wall thickness for the pipe to prevent failure.

5. Are there any limitations to the Von Mises stress calculation method?

Yes, there are some limitations to the Von Mises stress calculation method. It may not accurately predict the failure of ductile materials, as it does not take into account the material's strain hardening behavior. It also assumes that the stresses are distributed uniformly across the pipe wall, which may not be the case in some scenarios. Additionally, this method may not be suitable for pipes with complex geometry or loading conditions.

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