# Beam Reaction Force Calculator (Simply Supported) Calculate support reactions of a simply supported beam via static equilibrium. UDL: RA=RB=q·L/2. Center point load: RA=RB=P/2. Off-center point load at a: RA=P·b/L, RB=P·a/L. Also returns max shear Vmax and max moment Mmax. > Canonical page: https://elysiatools.com/en/tools/beam-reaction-force - **Category:** Math & Numbers - **Keywords:** beam reaction, support reaction, simply supported beam, static equilibrium, shear force, bending moment, structural analysis, mechanics of materials, civil engineering ## Overview The Beam Reaction Force Calculator (Simply Supported) computes the support reactions, maximum shear force, and maximum bending moment for a simply supported beam under static equilibrium. It supports uniformly distributed loads (UDL), center point loads, and off-center point loads, providing structural engineers, students, and builders with instant, accurate calculations. ## Inputs - **Load Type** (select) - **Span L (m)** (number): e.g. 6 - **Uniformly Distributed Load q (kN/m)** (number): Required for UDL. - **Point Load P at Position a (kN)** (number): Point load magnitude. Required for center/point modes. - **Load Position a from Left (m)** (number): Distance from left support to the point load. Required for point mode. 0 ≤ a ≤ L. - **Decimal Places** (number) ## When to use - When designing structural framing and needing to determine the reaction forces transmitted to columns or foundations. - When calculating the maximum shear force and bending moment to select appropriate beam sizes or verify structural capacity. - When verifying manual structural analysis calculations for homework, exams, or engineering design checks. ## How it works - Select the load type: Uniformly Distributed Load (UDL), Center Point Load, or Point Load at a specific position. - Enter the span length of the beam in meters and the corresponding load values (load magnitude and position, if applicable). - Specify the desired decimal precision and click calculate to solve the static equilibrium equations. - Review the calculated left and right support reactions, total load, maximum shear force, and maximum bending moment. ## Use cases - Determining foundation or column load requirements by calculating the reaction forces transmitted from supported beams. - Sizing steel or timber beams by identifying the maximum bending moment and shear force under design loads. - Teaching or learning structural mechanics principles by comparing manual equilibrium calculations with instant digital results. ## Frequently asked questions ### What load types does this calculator support? It supports Uniformly Distributed Loads (UDL), Center Point Loads, and off-center Point Loads. ### How are the reaction forces calculated for an off-center point load? They are calculated using static equilibrium equations: RA = P * b / L and RB = P * a / L, where b is the distance from the load to the right support. ### What units are used for the inputs and outputs? Span and positions are in meters (m), loads are in kilonewtons (kN) or kilonewtons per meter (kN/m), and bending moment is in kilonewton-meters (kN·m). ### Does this calculator support multiple loads on a single beam? No, this calculator is designed for a single load configuration (either one UDL, one center point load, or one off-center point load) at a time. ### Does the calculator account for the self-weight of the beam? 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