Pipe Thickness

Do you need to design to a pressure code?

If there is no pressure code to design to, then carry out a theoretical slice through the pipe in several planes, and do a force balance. Keep the calculations lest they need to be scrutinised for burst and collapse indemnity insurance reasons.

In your case the problem is the loss of stability not only the "resistance".

For the axial force you should consider the pipe as a column and verify depending on the conditions at the ends how big can be the force before collapsing.

For the wall the problem is similar but on an other scale, the wall will collapse if the stress reaches the elasticity limit so that a "hinge" can build up. You may look at the colapse loads for rings or use the simplifed equation σ= pext*dext/(2* t) = Re.

t is the wall thickness. In stability computing the safety coefficents have to be important since there are several variable parameters as thickness, Re and manufacturing deviations.

Hope it will help.