# Homework Help: Buckling of a short structure

1. Jun 2, 2010

### n707jt

1. The problem statement, all variables and given/known data

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
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.
2. Relevant 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]

3. 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?

Last edited by a moderator: Apr 25, 2017
2. Jun 2, 2010

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