Clarification on buckling formula needed

[franc11HD]

Hi,

I have been reading a lot theses days on the buckling subject. I have gone through many references and design manual, and a lot of web sites about when to use which formulas for buckling. For long colmun, I think it is clear that Euler is applicable. That is for the other formulas that it seems neboulus to me. I think I have an explanation, but wanted to have some of your experienced input about it.

It is for short and intermediary column that it gets my confuse. I guess that Euler-johnson (with critical crippling stress Fcc) is good for interaction between buckling and crippling.

1) In the case where Fcc is above Fcy, then I guess the cut off is Fcy and use Euler-Johnson with yield properties.

2) Then my second question is about Engesser formula. It is said in many textbooks and design manuals (quite franckly seems taken from Bruhn) that this should be used when applied stress is above yield. When does this happens? Euler-Johnson limits to yield point, how can the stress be above yield?

Unless the "applied" stress here does not reference the average stress over the cross-section (P/A) but the actual stress including some bending stress du to the deformation of the column. Because when I used Bruhn fig. C2.17, I get a critical stress below Fcy. So how can I get a critical stress below Fcy if this criteria applies to stresses above Fcy? Unless it refers now to the average stress. Am I missing something or understand it correct.

When should we use Engesser, because I hardly see any use of it.

Thanks.

 

[rb1957]

1) Fcc is never above Fcy ... it might equal Fcy, but even then most solutions for Fcc have cut-offs at something like 0.8*Fcy.

2) Engesser uses Et as a means to correct Euler for short columns. The assumption with both Euler and Engesser is that the X-section is stable, ie doesn't cripple, and doesn't account for crippling. also, i'd suggest that the texts are saying (possibly meaning) to use Engesser when the allowable Euler stress is above yield.

Engesser has a better theoretical basis than Johnson; that said, Johnson is much easier to apply and "near enough". Satellite design, where reducing the structure to the minimum (every gram is important) might be somewhere where i'd use Engesser.

 

[franc11HD]

1) I did a quick check with my structure with Gerard Method (even if I am no thin and t is not constanct) and it gave me Fcc higher than Fcy, but I cut it off at Fcy.

2) I think you are right. The more I re-read the more I think it refers that if the allowable Euler is higher than proportional limit, to use Engesser. That is why you could have an allowable higher than the proprotional limit, but lower than Fcy.