How Beam Deflection Works
When you put a load on a beam, it bends. The bigger the load, the more it bends. The longer the beam, the more it bends. Deflection is how much the beam droops from its straight shape.
What Affects Deflection?
Four things change how much a beam bends. The load (P), the length (L), the material stiffness (E), and the cross-section shape (I). Length matters most. Doubling the length increases deflection by eight times. Doubling the height of a rectangle cuts deflection by eight times.
Beam Types
A cantilever beam is fixed at one end and free at the other. A simply supported beam sits on two supports. A fixed-fixed beam is clamped at both ends. Each type has its own formula because the supports change how the beam bends.
Pro tip: A fixed-fixed beam deflects four times less than a simply supported beam with the same load. If you can clamp both ends, your beam gets much stiffer.
Moment of Inertia
Moment of inertia (I) tells you how stiff the cross-section is. A tall thin beam has more I than a short wide beam with the same area. That is why I-beams are shaped the way they are. Most of the material is at the top and bottom where it does the most good.
Bending Stress
Bending stress is the tension and compression in the beam. The top fibers squeeze together. The bottom fibers stretch apart. The biggest stress is at the outside surfaces. Compare this stress to the material yield strength to check if the beam is safe.