Predicting Buckling Load for Thin-Walled Structures Using ANSYS/Nastran

[n707jt]

Homework Statement

Finding the critical buckling load of a really short column with wide cross section (is it still considered a column?)

E = 22 GPa
Yield: 300 MPa
Load: 28N
thickness: 0.226 mm
I = 670706.51 mm^4 (is this right?)
Load Applied Area (as indicated by white arrows): 190400 mm²

I understand from http://www.engineersedge.com/column_buckling/column_ideal.htm that I should be applying Johnson's Formula.

Homework Equations

Euler Buckling :

[URL]http://172.31.254.243/www.engineersedge.com/column_buckling/image/column1.gif[/URL]

Johnson's Formula

[URL]http://172.31.254.244/www.engineersedge.com/column_buckling/image/johnson.gif[/URL]

The Attempt at a Solution

Using Johnson's formula, I've found out the Critical Buckling Load (Pcr) is 57119986 N

I know this is a really short structure with a wide cross sectional area so naturally the Pcr will be bigger but could someone please verify my method?

 

[minger]

I don't think that will work. Typical buckling problems assume a deflected shape, which you won't get.

The issue is not that it is short, but that it is thin-walled. Roark gives an idea for thin-cylindrical tubes, but not thin-rectangular tubes. I will quote his paragraph, 12.3 Columns and other Compressions Members

For a thin cylindrical tube, the theoretical formula for the critical stress at which buckling occurs is
$$\sigma' = \frac{E}{\sqrt{3}\sqrt{1-\nu^2}}\frac{t}{R}$$
when R denotes the mean radius of the tube. Tests indicate that the critical stress actually developed is usually only 40-60% of this theoretical value.

Much recent work has been concerned with measuring initial imperfections in manufactured cylindrical tubes and correlating these imperfections with measured critical loads.

My best guess would be to perhaps run a really good buckling model in ANSYS/Nastran and give it a good safety factor.