Cylinders : frequently asked questions

1. Which failure theory to use ?
2. Why doesn't compound cylinder equation ( 4) agree with other texts ?

Question 1
Doug,   I have been working through the 'Cylinders' problems and was wondering why for questions 9 and 11 you have used the maximum shear stress design equation rather than distortion energy. Neither question specified which design criteria to use, so is there a reason for choosing maximum shear stress both times or was it just a random selection? (or does it have something to do with steel being used in both questions?)

Answer
You'll see from the chapter on Stress Strength & Safety that either the distortion energy or the maximum shear stress failure theory can be used for ductiles such as steel. Maximum shear is useful as you can often get a result very quickly ( s_max - s_min ) however distortion is considered to be slightly more accurate. It's a matter of choice (unless a Code eg. specifies that you must use a certain one).
Distortion is less conservative then maximum shear, and when you're designing a thick cylinder very occasionally distortion is the only theory which gives a meaningful result - see Error of thin cylinder approximation and note the difference in OD given by the two theories in the subsequent worked example.
If you're dealing with a brittle material then you have no choice, you've got to use the modified Mohr theory.

Question 2
Doug,   Your equation ( 4) for the interface pressure of a compound cylinder doesn't agree with any of the textbooks I've consulted.

Answer
No, it won't agree if the textbook's model differs from the one I used. All the texts I've looked at consider only the contribution due to interference on assembly - you must additionally and separately superimpose the contribution of internal and external pressures if they're present.
Since these pressures DO occur in the majority of practical cases it seems easier to include them in the model   ab initio - which is what the three terms on the RHS of ( 4) are all about.
You may remember that when we first analysed indeterminate assemblies you were advised to include ALL load components in the final loaded state. That's what we're doing here - interference, internal pressure and external pressure in general.