Configure a simply supported or cantilever beam with any combination of uniform distributed load and up to 3 point loads. Instantly see shear and moment diagrams, reactions, and max deflection.
Interactively plot shear force and bending moment diagrams for simply supported and cantilever beams with uniform distributed loads and up to three point loads. Instantly visualize the free-body diagram, reactions, and maximum deflection with live canvas charts that update as you adjust loads.
Configure the beam span, support type, UDL, and up to three point loads using sliders. The simulator applies static equilibrium (ΣFy = 0, ΣM = 0) to solve reactions, then numerically integrates across 200 segments to build the shear V(x) and moment M(x) diagrams. Deflection is computed by superposition of analytical formulas for UDL and each point load, then checked against L/360 and L/240 serviceability limits.
Simply supported UDL: RA = RB = wL/2, Mmax = wL²/8 at midspan, δmax = 5wL⁴/(384EI). Point load P at a from left: RA = Pb/L, RB = Pa/L, Mmax = Pab/L under the load, δmax = PL³/(48EI) for central load. Cantilever with tip load P: RA = P, MA = PL, δtip = PL³/(3EI).
The shear diagram is the integral of the load diagram; the moment diagram is the integral of the shear diagram. Points of zero shear coincide with local moment maxima or minima. The maximum moment location is critical for sizing beam depth and reinforcement. The L/Δ ratio (e.g., L/360) is a dimensionless measure of deflection relative to span used for serviceability checks.
A shear force diagram (SFD) plots the internal transverse shear force V(x) along the beam length. It jumps at point loads by the load magnitude and has a constant slope equal to the distributed load w under UDL. Maximum shear typically occurs at the supports.
A bending moment diagram (BMD) plots the internal bending moment M(x). For a simply supported beam with UDL, the BMD is parabolic with maximum value wL²/8 at midspan. For a cantilever with tip load P, the BMD is linear with maximum PL at the fixed end.
Positive shear means the left face of the cut section moves upward. Positive moment (sagging) causes tension on the bottom fiber — the beam smiles upward. Cantilever moment is shown as negative (hogging) by convention, causing tension on the top fiber.
L/360 is the IBC Chapter 16 live load deflection limit: maximum allowable deflection = span/360. For a 20 ft span, this is 240/360 = 0.67 in. The total load limit L/240 is less restrictive. Exceeding these limits does not mean the beam fails structurally, but may cause cracking of finishes or ponding.