Above picture is from my lecture notes. It deals with a column subject to axial load, which follows Euler buckling theory. The material is nonlinear, approximated by two lines as seen in the stress-strain diagram. The two elastic moduli, $E_1$ and $E_2$ are calculated. Then the buckling stresses corresponding to both moduli are calculated.
It is then noted that neither of the buckling stresses are located in the range where the material follows the corresponding elastic modulus.
It is then stated:
Application of Euler's theory becomes problematic when the elastic modulus changes significantly. The buckling now happens when the material reaches the lower limit, which is also when its modulus changes.
Why does the bolded sentence hold true? Why is the buckling now assumed to happen at the limit of the first line? I cannot picture in my head what happens in the situation when neither of the buckling stresses are inside the ranges where their corresponding elastic moduli are defined. And if we are able to somehow conclude that the buckling happens at this lower limit (240MPa) why is the application of Euler's theory "problematic"? Didn't we just get an answer?
Another thing is said:
In design norms there are often limitations to the slenderness and deformations due to the theoretical variety of the buckling event.
What does this last sentence mean? What kind of limitations are there and what is meant by the "theoretical variety of the buckling event"? (please note that these lecture notes are not in English, but this is the closest translation that I could come up with)