Eigenvalue buckling due to horizontal load 3

[MrKnightyKnight]

All textbooks I found explains how to formulate matrices for columns under axial loads, and the results matches the analysis of commercial software like Ansys.

However, I found that Ansys can calculate "Eigenvalue" buckling load for a column loaded with a horizontal force only! I wonder if anyone can give me a hint about how this is done.

Thanks.

 

[gravityandinertia]

I'm confused, are you looking for a way to calculate this horizontal load buckling in Ansys, or a way to calculate this by hand to compare to Ansys?

 

[MrKnightyKnight]

I am looking for a way to calculate it by hand.

 

[rb1957]

the eigenvalue is a result of the stiffness matrix.

a simple compression column isn't going to react to transverse loads.

A column with bending stiffness will react transverse loads (in bending) and the column can buckle under compression stresses. I don't know if that is hand calc-able.

another day in paradise, or is paradise one day closer ?

 

[GPapazafeiropoulos]

Provided that no material or geometric nonlinearities exist, the buckling load is a function of only the axial load of a member, and not any lateral load. This results from the definition of the geometric stiffness matrix.

George Papazafeiropoulos

 

[jean15paul]

It would be interesting to use the eigenvalue for the buckling under horizontal load and determine your critical buckling load. (Just multiply the eigenvalue by the applied load.) Then use that load to calculate stress values. My suspicion is that those stresses will exceed the material capability, because I would expect a bending or shear failure to happen before a buckling failure under a horizontal load. This would imply that this linear buckling failure would never actually happen because the column would experience a strength failure first.

 

[NRP99]

Refer attached screenshot for simple buckling problem of cylinder 100mm dia*2000mm length with 1 N force applied horizontally. Obtained eigenvalues are massive indicating that the failure mode for horizontal force is not buckling but by bending/shear as suggested by the rb1957, GPapazafeiropoulos, jean15paul. Loads will be less for the bending strength and shear strength than the critical buckling load obtained here.

 

[jean15paul]

Thanks NRP99.

Regarding the OP's question about trying to recreate the horizontal buckling solution with a hand calculation. I don't think there is any traditional hand calculation to arrive at a similar solution. This was implied by a few replies here, but I don't think it's be said directly. But this isn't a failure mode that you should need to worry about because a horizontal load on a column would produce a bending or shear failure before any buckling would occur.

That being said. Buckling isn't just a pure compression phenomenon, depending on the type of structure. For example thin plates can experience local buckling under bending or shear loads. See the excerpt from Bruhn's "Analysis & Design of Flight Vehicle Structures" focusing on Fig. C5.12 and Fig. C5.14. (This small except is shared for educational use only. #FairUse)

Bruhn is a REALLY good book for anyone analyzing mechanical structures. Highly recommended purchase.