Free Online Beam Calculator
Analyze simply supported, cantilever, and overhanging beams. Plot exact Shear Force Diagrams (SFD), Bending Moment Diagrams (BMD), and evaluate maximum elastic deflection in seconds.
EI · d⁴v/dx⁴ = q(x) ⟹ M(x) = -EI · d²v/dx²
Beam Master handles any combination of point loads, uniform distributed loads (UDL), varying loads (UVL), and applied moments with instant SFD, BMD, and deflection curves.
How to Calculate Beam Reactions & Diagrams
Structural beam analysis begins with creating a Free Body Diagram (FBD), resolving boundary reactions via equations of static equilibrium, and integrating internal shear and bending equations across every segment of the span.
Shear Force (V)
Clockwise shearing action (upward force on the left segment, downward on the right segment) is defined as positive (+).
Bending Moment (M)
Sagging moment (compression in top fibers, tension in bottom fibers) is defined as positive (+).
Engineering Formulas & Governing Equations
Static Equilibrium (Vertical Forces)
Equation 01Sum of all upward vertical reaction forces equals the sum of applied downward forces.
Static Equilibrium (Moments about A)
Equation 02Moment equilibrium allows direct solution of support reactions for statically determinate systems.
Shear Force Differential Relation
Equation 03The slope of the shear force diagram at any point equals the negative of the distributed load intensity.
Bending Moment Differential Relation
Equation 04The slope of the bending moment diagram equals the shear force. Moment peaks occur where V(x) = 0.
Calculation Details & Clarifications
Solve in Beam Master
Need to add internal hinges, multiple supports, or export a professional PDF report? Open the complete web application.
Open Beam Master Free414/414 regression tests passing • No install needed