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.

 

[HalfLostAndSearching]

I cannot provide an opinion on the correctness of a solution without examining the specific problem and its context. However, I can offer some insights on the concept of maximum allowable length for a column under a load.

The maximum allowable length for a column under a load is determined by its critical buckling load, also known as the Euler buckling load. This is the maximum load that the column can withstand before it buckles under compressive stress. The critical buckling load is affected by various factors such as the material properties, cross-sectional area, and end conditions of the column.

In order to determine the maximum allowable length, we need to consider the critical buckling load and the applied load. If the applied load exceeds the critical buckling load, the column will buckle and fail. Therefore, the maximum allowable length should be below the critical buckling length to ensure the safety and stability of the column.

In the given problem, the solution of 10.74m may be the correct maximum allowable length based on the critical buckling load and applied load. However, it is important to note that the solution may vary depending on the specific details of the problem. As a scientist, it is important to carefully analyze the problem and consider all relevant factors before determining a solution.