Engineering & Analysis Methods > Panel Buckling

Plate Buckling Approach for Non-Uniform and/or Biaxial Loads

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stress_geek:
Hello,
        For a laminated rectangular plate (Unstiffened) with uniaxial compression (Nx) Hyperizer uses the general orthotropic equation to calculate the Nxcr. But in a case where a moment about z axis is applied on the edges then Nx would be non uniformaly distributed along the edges in order to obtain the proper resultant moment. Hypersizer assumes this as uniformly distributed along the edges and uses the classical buckling equation in calculating Nxcr. My question is: 1.) Isn't this approach too conservative?

2.) In the case of biaxial loading with Nx being positive and Ny being negative I understand that Nxcr is calculated taking into account the +ve Nx. But is the stress ratio Rx calculated based on the compressive stress in the Y direction i.e; Rx= Nxcr/Ny

Thanks

Phil:

--- Quote from: stress_geek on September 12, 2008, 11:19:07 AM ---Hello,
        For a laminated rectangular plate (Unstiffened) with uniaxial compression (Nx) Hyperizer uses the general orthotropic equation to calculate the Nxcr. But in a case where a moment about z axis is applied on the edges then Nx would be non uniformaly distributed along the edges in order to obtain the proper resultant moment. Hypersizer assumes this as uniformly distributed along the edges and uses the classical buckling equation in calculating Nxcr. My question is: 1.) Isn't this approach too conservative?

--- End quote ---

For the first case you describe, assume that half the plate is in compression and half is in tension.  (see the attached image at the bottom of this post - you must be signed it to see it)

HyperSizer does two things. 

First, it averages just the compressive stress, therefore the tensile stress is ignored completely.  Also, the load applied is not the maximum compressive stress, but the average.

Second, it takes into account the fact that the buckling length should be adjusted such that only the compressive part of the panel should be included in the buckling length.  So if half of the panel is in compression and half in tension, then the buckling length should be modified to approximately one-half the entered buckling length.  To see this effect, generate a stress report with sample calculations for panel buckling, and look at the panel buckling sample calculation.  The adjusted buckling lengths should be presented. 

These two operations should give reasonable buckling results that will match a buckling analysis that takes the actual load gradient into account and not be over-conservative.


--- Quote from: stress_geek on September 12, 2008, 11:19:07 AM ---2.) In the case of biaxial loading with Nx being positive and Ny being negative I understand that Nxcr is calculated taking into account the +ve Nx. But is the stress ratio Rx calculated based on the compressive stress in the Y direction i.e; Rx= Nxcr/Ny

Thanks

--- End quote ---

HyperSizer doesn't really calculate the critical Nxcr directly, rather given the Nx and Ny load, it calculates the eigenvalue for buckling.  From the eigenvalue, you can get the critical Nx and Ny by multiplying Nx_cr = Eigv * Nx_applied; Ny_cr = Eigv * Ny_applied.

Example,

Nx_applied = +300
Ny_applied = -1000

Eigv = 1.3

Nx_critical = Eigv * Nx_applied = +300 * 1.3 = +390
Ny_critical = Eigv * Ny_applied = -1000 * 1.3 = -1300

So the critical buckling load is:
Nx = +390
Ny = -1300

Note:  The margin of safety reported on the Failure tab is:
MS = Eigv - 1

Please let me know if you need further clarification.

stress_geek:
Thanks for your reply. For buckling of flat panel where the panel is subjected to non uniform compressive load (Nx-Bending+Direct Compression) and a uniform compressive load (Ny), I generated a report and the report contains the following data:
1.) Object load which is the average of all negative compressive load in x (Nx), y (Ny) direction and average of negative shear (Nxy)
2.) Based on the report it seems like it calculates the critical Nxcr using the general orthotropic equation in which the effect of Ny is taken into account
3.) Then it calculates the stress ratio Rx= Nxcr/Ny
4.) Finally the report lists the interaction equation used to calculate the margin of safety.

What you explained is true for curved panels i.e; the report shows that a eigen value is calculated and the margin is based on the calculated eigen value. But this is not true for flat panels.

On the other hand, looking at the image you attached it seems that hypersizer breaks the load into pure bending and direct compression in case of compression and tension load on one edge. But the report calculates the object load as noted in Point 1 above. Can you please clarify?

Phil:
I did a test on my own and I see the confusion.  The Rb listed in the stress report is shown as

Rb = Nx / Nx, cr,

however in reality, it is using the Eigenvalue from the from the biaxial solution.  So you could look at it as the following:

If Ny is controlling

     Rb = Ny / Ny,cr

If Nx is controlling

     Rb = Nx / Nx,cr

In reality, the eigenvalue is

     Eigv = Ny,cr / Ny = Nx,cr / Nx

So

     Rb = 1 / Eigv

Hopefully that makes sense.  I think the documentation can be changed to reflect this.

This is actually easier to see if you turn on the biaxial and the shear margins in addition to the interaction margin.  By definition, both of these two margins should be higher than the interaction margin, so there should be no danger of one of them controlling instead of the interaction.  However, if you turn these two margins on, you will get details of how these two margins are calculated.   If you do this, then you can more easily see where the Nx and Nx,cr in the biaxial calculation comes from. When you only have the interaction margin turned on, the details for the biaxial or shear buckling are not presented in the stress report.

When you turn on the biaxial buckling, you should see the updated buckling lengths.

garyjh:
Can you please clarify what the "entered buckling length" is. Is it the X & Y buckling spans in the sizing form buckling tab? Do these have to be changed manually or does hypersizer determine the edge length of the panel that is in compression? Is the average compression load applied to the full edge span by default?

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