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# Thin-walled tube theory

#### glemieux

##### New member
I'm trying to model various static load responses for a short, thin walled, cantelevered aluminum tube. The length to diameter ratio is approx. 3 and the wall is 0.030 in thick. I've used shell and beam idealizations on seperate occasions and the results are within an order of magnitdue of each other. However, the Pro/Mech values are of an order-of-magnitude difference when compared to hand calculations. Any thoughts? The hand calculations are determine from beam theory that has been modified through experimentation. The reference is Roarke's Formula's for Stress and Strain by Warren Young, 1989, pg 201-2. Any thoughts?

#### JHardy

##### New member
glemieux,

You should be able to get the same overall results as the shell and beam idealisations, and the same as the classic solutions. Sounds like you have a modeleing error. What differences are you getting - stresses, strains, deflections, or all of the above?

A few things to check:

Are you units correct?

Have you got the right total load (eg have you applied an end load thinking you are applying a total load of x Newtons, but you have actually apllied an end pressure of x Pa?

Are all your material properties correct?

Have you applied the appropriate boundary conditions (fully fixed end versus free ends, etc.)

Have you tried to apply concentrated force or moment loads to a continuum solid element model?

#### Luis Aguirre

##### New member
Hello Glemieux,

Another thing you may take in consideration is the spand and over all section of your model. The ratio of 3 between the spand and the section diameter makes me think that you have a very short beam. IF this is the case most books do not take in cosideration the shear energy. Make sure Roaks is taking in to cosideration this info. You may try to use Castiglianos second method with shear include in the solution to get a better hand approximation. By the way Mechanica takes in cosideration the shear factor with all elements ( shells solids and beams). Mechanica beams uses Timoshenko beam formulation which takes into consideration the shear factor.

Also make sure that the over all displacement of the model is less that 20% of the total spand or 10% of the total tickness which ever is less. This is a rule of tumb in thin membranes whe using finite element analysis. If it is more than that you model may start going geometrically non linear. IF this is the case use solid element and turn on the non linear analysis option in the static analysis window. I hope this information helps!

Luis