Free structural engineering tool. Calculate instant deflection, slope, and support reactions for simply supported beams with formulas. Support for point and distributed loads.
Enter the beam length, the Young's Modulus (E) of the material, and the Moment of Inertia (I). For steel, E is typically 200-210 GPa.
Input the applied load (Point load or Uniformly Distributed Load - UDL). Select the support condition: Simply Supported, Cantilever, or Fixed-Fixed.
The tool outputs the maximum deflection (δ) and rotation (θ). Ensure the deflection is within the limits set by building codes (e.g., L/360 for floor beams).
For the same total load W on a span L, a single central point load produces M = WL/4, while spreading that same total as a uniform load halves the peak to wL²/8 = WL/8. Concentrating the load at midspan is therefore the more demanding case, which is why a point load at the center is the usual worst-case check.
A central point load deflects by δ = PL³/48EI; a uniform load by δ = 5wL⁴/384EI. For example, a 6 m steel beam (E = 200 GPa) with I = 8.36×10⁷ mm⁴ under 10 kN/m deflects about 10.1 mm at midspan — an L/594 ratio that passes the L/360 floor limit.
The reactions split a point load inversely with distance: R₁ = Pb/L and R₂ = Pa/L, where a and b measure from each support. The support nearer the load carries the larger share, and the two reactions always sum to the applied load by vertical equilibrium.
Building codes cap live-load deflection of floor members at L/360 — 16.7 mm on a 6 m span — to prevent cracked finishes and a springy feel underfoot. Roof and total-load limits are usually looser (L/240 or L/180); compare the calculated δ against the ratio your application requires.