A loaded beam bends, and two questions decide whether that's acceptable: how far does it deflect, and is the bending stress within the material's limit. Both depend on the support and load arrangement, the span, the load magnitude, and — crucially — the beam's cross-section through its moment of inertia. The diagrams above stack the load, shear, bending moment, and deflected shape so you can see where the worst values occur along the span.
A simply-supported beam carrying a uniform load deflects most at mid-span, following δ = 5wL⁴ / 384EI. Because span enters to the fourth power, doubling the length increases deflection sixteen-fold for the same load per unit length.
Bending stress is σ = M / Z, where M is the maximum moment and Z the section modulus. A deeper section raises Z quickly, which is why beams are tall rather than wide — depth is far more effective than width at resisting bending.
Either can. A beam might be plenty strong (low stress) but still deflect too much to feel solid, or vice versa. Both are checked independently against their own limits.
Stiffness depends on the moment of inertia, which grows with the cube of depth. Adding height to a section buys far more bending resistance than adding the same amount of width.
Span/360 is a common reference for floor beams under live load, but acceptable limits vary by code, application, and what the beam supports. Treat any single number as a starting point.
No — it's for estimation and learning. Real structural design accounts for load factors, combinations, buckling, connections, and code requirements this tool doesn't model. Verify against proper methods.