Ways to Calculate Beam Deflection with Point Loads

When beams are pushed down by point loads, we can figure out how much they bend. Here are some methods to do that:

1. Euler-Bernoulli Beam Theory:

   • For beams that are supported at both ends, the biggest bend (or deflection) right in the middle due to a load (let's call it P) can be calculated using this formula: $y_{max} = \frac{PL^3}{48EI}$
   • Here, $L$ is the length of the beam, $E$ is a measure of the beam's stiffness, and $I$ is related to how the beam's shape affects its bending.

2. Superposition Method:

   • This method adds together the effects of each load on the beam to find out how much the whole beam bends.

3. Numerical Methods:

   • One common way to get pretty accurate results for beams with complicated shapes or loads is called Finite Element Analysis (FEA).

4. Integration of Load Function:

   • We can also find out how much a beam bends by working out the math behind its curve as it bends.

5. Moment-Area Theorem:

   • This method is helpful when dealing with beams that have many loads and supports. It helps to calculate the deflection easily.

By using these methods, engineers can understand how much a beam bends under different loads.