# Interaction of buckling modes

I'm reading this paper on structural members subject to both bending and compression.

In the first paragraph, in context of the equations 6.61 and 6.62, it is said:

The second two terms are modified by factors that allow for the interaction between the different modes of buckling.

What is meant by the interaction between different modes of buckling? How do buckling modes "interact"? I tried searching online but couldn't really find a good source. Checking a member against buckling I've understood that only the first mode is usually checked, with $$N=1$$ in Euler buckling equation.

\begin{align} \frac{N_{Ed}}{N_{b, y, Rd}} + k_{yy}\frac{M_{y, Ed}}{M_{b, Rd}} + k_{yz}\frac{M_{z, Ed}}{M_{c, z, Rd}} &\leq 1 \\ \frac{N_{Ed}}{N_{b, z, Rd}} + k_{zy}\frac{M_{y, Ed}}{M_{b, Rd}} + k_{zz}\frac{M_{z, Ed}}{M_{c, z, Rd}} &\leq 1 \\ \end{align}

• answered here: engineering.stackexchange.com/a/39979/10902 Commented Jan 27, 2021 at 14:22
• @SolarMike It's not the same question. Now I'm asking about the interaction of buckling modes, as in the quote "..second two terms are modified by factors that allow for the interaction between the different modes of buckling." Commented Jan 27, 2021 at 14:33
• But the answer does talk about bending and then combining tension... which is the interaction you seem to be needing. Commented Jan 27, 2021 at 14:37
• @SolarMike I don't see how. The equation in the previous question does not have those factors in front of the moment terms. That equation seems to be about simply combining compression the stresses caused by moments, not about buckling. In this one we seem to include buckling somehow, and its interactions. Commented Jan 27, 2021 at 14:50