I think I am making this harder than necessary but hopefully someone can help clear this up for me:
Radius of gyration is the square root of the ratio of the moment of inertia to the area
r=√(I/A)
Slenderness ratio is the unbraced length (L) X the end condition factor (k) / radius of gyration (r)
SR = (kL)/r
Question 1:
The inverse relationship between the two is confusing me. I understand (by these equations) that the LARGER the RoG, the SMALLER the SR - so larger radius of gyration leads to lower SR, leads to less likelihood of buckling.
But then, if the area of the cross section goes UP, the RoG goes down; if the RoG goes down, the SR goes UP. How can a larger area lead to a larger SR? Seems like it would be less likely to buckle with a larger area?
Question 2:
See attached image. Is the cross-sectional area in the equation for RoG the surface area or the overall area (i.e., would the area be the same on these top vs bottom images, or would the tubes be larger "areas" (A) because of the holes in the middle spreading their area further)?
THANKS in advance! (I'm totally going to dream in equations again tonight...)