# How do I properly scale down a force for scale-down model testing?

I am designing structural frame for a shipping container that would have 8000 lbs of weight stacked on top of it. Of course, i don't access to real size container. I have built a model whose scale is 1:8 of the real one (same material, steel). How do I scale down the force so that the stress generated in model structure is equivalent of that in the real size one? Can anyone refer me to some good materials? Thank you.

• For stress analysis only - if the load is uniformly distributed,, scale down the actual uniform load by 8. For concentrated load, scale the concentrated force by 64.
– r13
Oct 5 '21 at 17:41

TL;DR: you need to prioritize which behaviour is important and scale the load to investigate this behavior. It is very difficult to scale the load and expect to obtain the full behaviour of the structure.

IMHO it is very difficult to scale the load and expect to obtain the full behaviour of the structure. Different loading conditions have different dependencies from the loads.

For the following analysis I will assume that only the normal loads play a role. I.e. the structure will fail when the operating stress ($$\sigma$$) exceeds the allowable stress $$\sigma_{all}$$.

e.g. take buckling of a column and bending of a beam. (I intentionally take buckling and bending because they both have similar quantities. If I compared axial loading cases - compression/tension- to bending that might have left more doubts)

representation
beam breadth $$b$$ $$b$$
beam thickness $$h$$ $$h$$
beam cross-section $$bh$$ $$bh$$
(moment area) I $$\frac{b\; h^3}{12}$$ $$\frac{b\; h^3}{12}$$
load at failure $$P_{buck} = \frac{\pi^2 EI}{L^2}$$ $$P_{bend}=q\cdot L$$
stress at failure $$\frac{\pi^2 EI}{A\cdot L^2}$$ $$\frac{PL}{4\cdot I}\frac{h}{2}$$
operating stress at failure after simplification $$\frac{h}{L^2}\frac{\pi^2 E }{12}$$ $$\frac{3 PL}{ 2b\; h^2}$$

Notice that at the end I separate the material properties from the cross-section properties.

stress at failure after simplification $$\frac{h}{L^2}\frac{\pi^2 E }{12}$$ $$\frac{L}{ b\; h^2} \cdot \frac{3}{2}\cdot P$$
factors affected by dimensional scaling $$\frac{h}{L^2}$$ $$\frac{L}{ b\; h^2}$$
reduction to scale 1:8 $$\frac{h/8}{(L/8)^2}= 8\frac{h}{L^2}$$ $$\frac{(L/8)}{ (b/8)\; (h/8)^2} = 8^2 \frac{L}{ b\; h^2}$$
So this means that the operating stress for buckling ($$8^2$$)will increase at a different rate that the operating stress for buckling ($$8^1$$). So - IMHO- you expect that you can scale the load and obtain the same behaviour for all loading conditions of the model (you need to tune other parameters also).