Buckling Analysis Control

 

1. A buckling analysis process requires static analysis results to formulate the initial geometric stiffness matrix. Accordingly, enter the load cases to be applicable for the buckling analysis following the procedure for static analysis.

 

2. Invoke the dialog box of the Analysis > Buckling Analysis Control menu and enter the required number of modes and data necessary for convergence and assign the load combination to be applied to the buckling analysis.

 

3. Select the Analysis > Perform Analysis menu or click Perform Analysis to carry out the analysis.

 

4. Once the analysis is successfully completed, use either the Results > Buckling Mode Shapes function or the Results > Result Tables > Bucking Mode Shape function to review the buckling mode shapes and critical load factors for each mode shape.

 

5. To calculate buckling loads, enter the self-weight (Constant) and additional loads (Variable) and then perform the analysis. The Eigenvalue resulting from the analysis is the critical load factor. Accordingly, the buckling load = critical load factor X additional load (Variable) + self-weight (Constant).

A1. In midas Gen, both flexural buckling and lateral torsional buckling of the beam elements are considered in buckling analysis. After that, local second order effect and imperfection can be considered as per Cl.6.3 in EN1993-1-1 during Steel Code Checking in midas Gen. It is according to the Cl.5.2.2(3)b. In Steel Code Checking, LTB check is also verified for steel I-shape section.

However, if the user wants to consider the local second order effect and imperfection as per Cl.5.2.2(3)a, we can use buckling analysis. In midas Gen, both flexural buckling and lateral torsional buckling are considered in Buckling Analysis.

For this verification, I had a test as below.

The report below is generated from "LTB.mgb" model file, which considers Cl.5.2.2(3)b.

 

By performing buckling analysis, we can see the 1st buckling factor, which is LTB, is determined as 1.3618. "My" value is 250kNm. Therefore lateral torsional buckling moment is 1.3618*250 = 340.45kNm.

We can see this value is very similar to Mcr above.

After checking buckling load, we can update the geometry of model with the buckling mode 1 in order to consider local imperfection using the Results > Buckling Mode Shape function. This model can be used for the verification of buckling force by performing geometric nonlinear analysis. Here, maximum eccentricity was entered as 0.015m.

   *Why 0.015m is determined?

       e0/L for buckling curve a  = 1/300

       L=10m

       e=0.03m

       For LTB, k=0.5

      Therefore, eccentricity is 0.5*0.03 = 0.015m

In the updated model with 1st mode imperfection, if we check the value of My, it is shown as 362kNm which is also similar to Mcr.