The way we load a beam really affects how much it bends. Let's break it down:

1. Point Loads:

   • When you put a load right in the middle of a beam that is only supported at the ends, it bends the most. We can use this formula to understand how much it bends:
     $\delta = \frac{PL^3}{48EI}$
     Here,
   • $P$ is the weight you put on,
   • $L$ is how long the beam is,
   • $E$ is a measure of how strong the material is,
   • and $I$ is about how the shape of the beam affects bending.

2. Uniformly Distributed Loads (UDL):

   • If the load is spread evenly across the whole beam, the bending can be described using another formula:
     $\delta = \frac{5wL^4}{384EI}$
     In this case,
   • $w$ is the load per unit length, meaning how heavy the beam feels along its length.

3. Effects of Load Magnitude:

   • If you double the load on a point load, the bending increases by eight times.
   • For a UDL, if you double the load, the bending increases by sixteen times.
     This shows that as you add more weight, the bending gets much bigger in a way that isn’t just straight-forward.

Knowing how loading works is really important for picking materials and designing structures.