Engineering Calculator
Professional engineering calculations for pressure, torque, stress, force, and more. Precision tools for engineers and technical professionals.
Calculates the maximum vertical deflection of a beam under load. Serviceability design limits deflection to span/300–span/500 to prevent cracking of finishes and user discomfort.
Simply supported, mid-point load: δ_max = FL³/(48EI). Cantilever, tip load: δ_max = FL³/(3EI). Distributed load (UDL), simply supported: δ_max = 5wL⁴/(384EI).
The Roman Pantheon's unreinforced concrete dome (built ~125 AD) was the world's largest for 1,300 years. Modern structural analysis confirms it operates almost perfectly under compression — the only load concrete naturally handles well.
Using the mid-span formula for a distributed load. The UDL formula (5wL⁴/384EI) differs from the point-load formula (FL³/48EI) — substituting one for the other gives a 5/8 = 62.5% error in deflection.