How a beam acts under a load depends on how it is supported and how its ends are attached to the supports. It can be supported on one or both ends (roots). The amount of force applied to the root depends on the load size and the distance from the root. This is called the bending moment.
Make up an equation for this last statement, using variables of your choice and then compare them to the formula that is used:
M = P L
Bending moment (M) = load (P) x distance from root (L)
The bending moment is zero at the end supports and maximum in the middle.
A lower strength material can be used in a beam that is made greater in height.
The strength of a beam, simply supported and loaded in the middle, to resist sagging/bending is a function of its height squared, span, width, and E. Simply said:
1. if you the double the height, the strength is quadrupled and the stresses reduced by a factor of 4.
2. if you double the length of a span, the strength is cut in half.
3. if you double the width, the strength is doubled.
4. if the modulus of elasticity is doubled, then the strength is doubled.