Barlow vs. Roark Pressure Vessel EQs 1

[DBCox]

Hello everyone,

I am working on some thick walled pressure vessels and would like to apply the Roark equation for a thick walled for this case and noticed something odd.

Until now, we have always used the Barlow equation with a hefty safety factor, thick walled or not, but now we are moving on to more advanced methods. It is my understanding that the Barlow equation assumes a uniform hoop stress (or an average stress through the thin wall). The Roark eq does not and can be used to find the stress at any point, so I assumed the Roark equation result for max hoop stress would be greater since the sum of all the stresses would need to equal the Barlow result (or be close). This is not the case. The Roark resultant stress is around 3/4 that of the barlow equation for a thick walled tube.

What is wrong here? Are my assumptions and theory wrong, or am I making an algebraic mestake?

Thanks!

 

[BarryEng]

For simplicity, if there are only biaxial stresses, the reference stress (Huber-Hencky-von Mises) is: -
Ref stress = sqrt(f1^2 + f2^2 - f1f2)
If f1 is the hoop stress, it is still correct (as per Troitsky in my thread above) to use the Barlow formula for this stress.
Obviously the reference stress depends on the combination in the formula above. The reference to Troitsky (re Barlow above), hoop stress was definitely one dimensional.