Maximum allowable length for a column under a load (buckling question)

[theBEAST]

Homework Statement

Here is the problem with the solution:

I feel like the solution should be 10.74m. The maximum allowable length should be the lower one. This is because, for example, if we make the column 11m in length. The Pcr in the zy plane would decrease and since we are applying the same load, it would fail.

Does anyone else agree that the solution is wrong?

 

[paisiello2]

I think your reasoning is sound. Only one small typo in your formula that you didnt carry through, so you're good still.

As a side note, the problem only considers elastic buckling and doesn't take inelastic buckling into account which would reduce the allowable length.

 

[theBEAST]

I think your reasoning is sound. Only one small typo in your formula that you didnt carry through, so you're good still.

As a side note, the problem only considers elastic buckling and doesn't take inelastic buckling into account which would reduce the allowable length.

Sweet, but what small typo are you referring to? PS: this is from the solution manual

 

[paisiello2]

KL^2 should be (KL)^2 when you made the substitution.