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

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Homework Help Overview

The discussion revolves around a buckling problem related to determining the maximum allowable length for a column under a load. Participants are examining the implications of column length on critical load and stability.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are exploring the reasoning behind the proposed solution of 10.74m and questioning the impact of increasing the column length to 11m on its stability. There is also a focus on the distinction between elastic and inelastic buckling and how it affects allowable lengths.

Discussion Status

The discussion is active, with participants providing feedback on each other's reasoning and identifying potential errors in calculations. There is acknowledgment of the need to consider different types of buckling, and some participants are seeking clarification on specific details of the formulas used.

Contextual Notes

There is mention of a solution manual, indicating that the problem may be part of a structured assignment or textbook exercise. The discussion highlights a specific typo in the formula that could affect the interpretation of the problem.

theBEAST
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Homework Statement


Here is the problem with the solution:
cWx5bja.png


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?
 
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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.
 
paisiello2 said:
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
 
KL^2 should be (KL)^2 when you made the substitution.
 

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