Cantilever & Load: Explaining Physics Intuition

[bjgawp]

Intuitively, if we have a beam nailed down to a box of some sort on one side and have the other side of the beam stick out (with an object on it), we would expect the beam to bend to an extent. However, when I tried to apply the knowledge of physics that I have, I had a bit of trouble explaining why it is so. Of course, the amount it bends depends on how much of the beam sticks out and how much mass there is on the beam sticking out. Is there a formal explanation for this or do we just assume it to be something intuitive?

 

[FredGarvin]

This is classical beam theory. The cantillever beam with a load at the end is day one mechanics. Take a look here:

http://www.efunda.com/formulae/solid_mechanics/beams/casestudy_display.cfm?case=cantilever_endload

 

[bjgawp]

Thanks a lot for the link. It has certainly helped me. However, another question came to my head when delving more into the world of elastic bending. Why is it that the greater the length of the cantilever sticking out, the more flexion will occur? This is evident by the equation y = FL³ / 2EI but I cannot conceptually describe it with physics. Is it because the force of gravity have a larger amount of the beam to "work" on without the beam interfering? Thanks again.

 

[FredGarvin]

The longer the beam, the more moment you apply to it by using the same force. Think of it this way, what puts more torque on a bolt, a wrench with a short handle or a wrench with a long handle? Same thing here. The same force but at a longer distance produces a greater moment (torque).