The following compression beam is fixed at one end and subjected to load according to Euler case 1. The profile and system dimensions are illustrated below. The beam is made of construction steel St 37. The load is applied at the center of mass.
For the system detailed above, the FEM calculation delivers the following results for the
first 4 buckling eigenmodes. Influences such as shear strain and warping are taken into account.
Buckling Eigenmodes of a Column
The illustrated structure was analyzed by Rubin and Aminbagai .
The stability analysis delivers, in complete agreement with the above publication, the following buckling eigenmodes and results:
Buckling Eigenmode of a Shell Structure
This example addresses slab buckling. The illustrated slab is supported flexibly all around. The slab thickness is 0.005 m, the material is construction steel St 37. Two load cases will be analyzed.
Uniformly Distributed Load
The theoretical buckling stress according to Petersen is sKi = 1.18625 MN/m².
Given the above system setup, this is approximated by 1.186 < sKi < 1.188 MN/m².
The theoretical buckling stress according to Petersen is sKi = 2.3132 MN/m².
Given the above system setup, this is approximated by 2.322 < sKi < 2.324 MN/m².
 Petersen, C.
Statik und Stabilität der Baukonstruktionen (Statics and Stability of Constuctions). Vieweg Verlag, Braunschweig 1980.
 Rubin, H.; Aminbaghai, M.
Ein Stabilitätsproblem mit Überraschungen (A Stability Problem with Surprises).
Stahlbau 66, Issue 5, pp. 271 - 276. Verlag Ernst & Sohn, Berlin 1997.