Analogies for magazine article related to structural engineering

[JackDuVal]

Homework Statement

Hi all, I'm writing an article for a scouting magazine. It is a short column to inform people about the danger of using long -badly supported - horizontal poles. I'd like to compare the situation of using a short beam and a long beam, and then able to tell a rough percentage how much worse the long beam is over the short one.

Homework Equations

Bending moment (UDL) = WL^2/8 (Kg-mm or Kg-m)
Bending moment (point load) = Force x Distance ( This is actually for a horizontal beam with load acting is a point load) (Kg-mm or Kg-m)

The Attempt at a Solution

"Image you're building a simple swing. Supports on either side, horizontal pole on top, attach plank with 2 ropes, done! If you made a normal sized swing, using a top pole of 2 meters, you can put Charlie and 3 other friends on it and it'll hold. But if you use a top pole of 4 meters, maybe you can just put Charlie in it."

Idea:
ASSUME: the relation between the length of the pole and the stress is L^2
Swing with 4 meter pole can hold 1 kid, causing stress 1 kid * 4^2 meters = 16
Swing with 2 meter pole can hold 4 kids, causing stress 4 kids * 2^2 meters = 16
This article will be read by people barely able to do vector math, so I have to keep things easy :)

To summarize what I'm looking for: to correct what I put behind ASSUME, with some background info. An article that clarifies it will do as well, I've looked around but couldn't get it clear enough.

Thank you very much!

 

[Valkarie]

The relationship between the length of the pole and the stress is not necessarily linear. The factors that contribute to the bending moment (which determines the stress) depend on the type of loading applied to the beam. For example, if a uniform distributed load (UDL) is applied, the bending moment is calculated as WL^2/8 (where W is the load and L is the length of the beam). On the other hand, if a point load is applied, the bending moment is calculated as Force x Distance. Additionally, the material properties of the beam, such as its Young's modulus, also play an important role in determining the stress.