# How do you determine weights from CG when there are more than two locations

On the internet they list ways to calculate weights based on CG when there is a weight on the left and on the right of your CG.

Most of the examples show a box truck for determining the weight on the axles.

How would you determine weight when there are 3 points rather than two. I tried looking up how to determine the weights on the axles of a semi-tractor and trailer, but the weight of the front axle seems to always be known.

I would like to suspend this load using springs. So points A, B, and C would be springs in this case. How can I determine the weight on each spring?

The internet seems to have almost nothing beyond the simple A/B example.

The top example is statically determinate. With knowledge of the distances from A and B to the CG you can take the the sum of the moments of A and B about the CG and set to 0. Then sum of the vertical forces $$-CG+F_A+F_B=0$$ gives you two equations and two unknowns to enable you to solve for the forces at A and B.

For the bottom example, the additional reaction force at C gives you a redundant reaction force to the CG and makes the problem statically indeterminate. It becomes a mechanics of materials problem requiring analysis of the deformations of the three springs and information on the distances between A, B and C with respect the CG and some assumptions about the truck body (e.g., is it rigid, is it to remain level).

Hope this helps.

Consider converting a simple two-support problem to a mysterious three-support problem.

Suppose you have the load in your diagram supported by $$A$$ and $$B$$. The solution is simple: $$A+B$$ must equal the load, and the total moment of the three forces ($$A$$, $$B$$, and $$\text{Load}$$) about any point must be zero. Two equations, two unknowns, no problem: a single, unique solution.

Now suppose you decide that the two supports may not be up to the task, and decide to shove another support, $$C$$, in to help.

So you stick $$C$$ in, and use jacks or wedges to raise it up to take part of the load. But you can stop wherever you want!

You can just lightly wedge $$C$$ in, or you can keep pounding away until $$B$$ is relieved of almost all of its load.

Both of these extremes, and everything in between constitutes a valid solution to the question of the value for $$A$$, $$B$$ and $$C$$.

Two equations, three unknowns: no unique solution.

In the real world, the bed of the truck will flex, the three supports will compress slightly and the load will be shared. But a simple change in temperature with the attendant thermal expansion of the three load-bearing points, would change this.