# How much weight can a cardboard of size $n \times m$ hold? [closed]

I am interested in knowing how much weight a piece of cardboard can hold in proportion to it's size.

Suppose we have independent variables $$x$$ and $$y$$ corresponding to length and width and that these two vectors are in $$\mathbb{R}^2$$. Then I think (could be wrong) the formula would be

$$f(x,y) = \lambda_1 x + \lambda_2 y$$ where $$\lambda_1 = \lambda_2$$ if the piece of cardboard has square dimension.

However I am kind of stuck from here because I don't know how to get the $$\lambda$$ scalars to complete the formula. I tried looking online and there doesn't appear to be a general formula (surprised because cardboard is so common in our lives). Does anyone have any insight into figuring out this problem?

edit: the weight is assumed to be evenly distributed

• Your best would be to run trials with varying $x$ and $y$ then interpolate to get a multivariable function $f$
– user28616
Mar 19 at 18:27
• You still need to account for how the load is distributed in the cardboard. A 12" x 12" square could hold a 5 lbs plate no problem, but put a tack on the bottom of the plate it will cut through your cardboard. Are you evenly loading the entire surface or part of it? Then it becomes a question of shear stress.
– jko
Mar 19 at 18:32
• oh I forgot to mention it, the weight is assumed to be evenly distributed. I added that to my post, thanks! Mar 19 at 18:35
• And how is the box supported? All around, or just on two ends (like a person carrying with two hands)?
– Wasabi
Mar 19 at 18:52
• Two cardboard layers with a wavy filling? Spacing? Filling angles? Mar 19 at 18:59