5 Replies Latest reply on Mar 1, 2010 4:20 PM by Andy Krispie

    Euler Buckling using NL Analysis

    Andy Krispie

      I've been doing some buckling analysis using simulation NL analysis, and after a bit of initial rigging have been quite pleased with the results.

       

      I wanted to verify that my boundary conditions were behaving as expected, so I decided to conduct a basic buckling analysis of a W-Section (ie I-Beam) and compare it to the critical Euler buckling load.  I used a W150x30 section (Iy=5.56e6 mm^4, ry=38.2mm).  Assuming a slenderness ratio of kL/r=200, L=7640mm.  Plugging that into the Euler critical buckling equation, Pc~188kN.  I'm using 350W steel (E=200000MPa, Fy=350MPa) as a material.

       

      I applied a constant lateral load of 2kN to create some initial displacement that would instigate buckling (worked out to ~3mm in this case).  Attached are some images of my setup.

       

      While I'm pleased with the buckling shape (visually K~1.0), the failure load of 547kN (+/- 5kN) is well above the critical buckling load.  I've tried creating a very stiff material to use as the rocker component and increasing the lateral load but the failure results were within 5%.  I would think simulating Euler buckling should be fairly simple, and I'm making a silly mistake.  I thought someone out there might have some suggestions from past experience.

       

      Thanks!

        • Re: Euler Buckling using NL Analysis
          Andy Krispie
          As a side note, I also attempted a more fundemetnal version of the same problem using a simple 50x50 solid-steel-square bar & rocker assemply.  Results were similar with a failure load well in excess of the critical Euler buckling load.
            • Re: Euler Buckling using NL Analysis
              Bill McEachern
              I have done verification on Euler buckling before and it was right on the money. I don't think you need to do it in an NL study. You need BC's that allow axial freedom & a allow rotations  or you won't get the right numbers. Using the remote load (restraint) would be the simplest way to get it done in a linear buckling study. I would put one together for you but I just don't have the time today.
            • Re: Euler Buckling using NL Analysis
              Bill McEachern
              here is  verification and the problem set up. Good luck.
              • Re: Euler Buckling using NL Analysis
                Anthony Botting
                Hi Andy: Yes, I have to concur with Bill on this. I have witnessed the Euler Buckling problem gets it right-on, in Simulation. I suspect the difference you see is because the Euler Buckling problem is being solved in Simulation as a plain Eigenvalue/Eigenvector problem, whereas a nonlinear approach will likely produce a path-dependent answer. I have learned the Euler Buckling solution is non-conservative, but certainly useful for design. Moreover, actual test data for buckling problems have characteristically wide scatter. It is just too sensitive to minute variations in load, load position/offsets, load rate, temperature, material variations, geometry variations from manufacturing, boundary conditions, etc., as can be seen when trying to column-buckle an unopened beer or soda can.  That last example I am particularly fond of the experiment in school and we all got different answers in a controlled compression test machine - but it was really fun.
                • Re: Euler Buckling using NL Analysis
                  Andy Krispie
                  Excellent - definetely a boundary condition issue on my part.  Thanks for the clarification and sample setup - much appreciated!