# Simply Supported Beam Calculator Calculate the maximum bending moment M_max, maximum shear force V_max and support reactions for a simply supported beam under a uniformly distributed load, a mid-span point load, or a point load at an arbitrary position. UDL: M_max = qL²/8; mid-span: M_max = PL/4; offset: M_max = P·a·b/L. > Canonical page: https://elysiatools.com/en/tools/simply-supported-beam-calculator - **Category:** Math & Numbers - **Keywords:** simply supported beam, bending moment, shear force, reaction, UDL, point load, M_max = qL²/8, PL/4, strength of materials, mechanics of materials, structural, civil engineering ## Overview The Simply Supported Beam Calculator is a structural engineering tool designed to compute support reactions, maximum shear forces, and maximum bending moments for beams under various loading conditions. It supports uniformly distributed loads (UDL), mid-span point loads, and offset point loads, providing instant analytical solutions based on standard mechanics of materials formulas. ## Inputs - **Load Type** (select) - **Uniformly Distributed Load q (N/mm)** (number): Used in 'Uniformly Distributed Load' mode. - **Point Load P (N)** (number): Used in 'Mid-span Point Load' and 'Point Load at a' modes. - **Span Length L (mm)** (number): e.g. 4000 - **Load Position a (mm)** (number): Used only in 'Point Load at a' mode. Must satisfy 0 < a < L. - **Decimal Places** (number) ## When to use - When designing structural beams and needing to quickly determine the maximum bending moment and shear force for sizing steel or timber sections. - When verifying hand calculations for simply supported beams under uniform or concentrated loads during civil engineering coursework or professional design. - When calculating support reactions to design columns, foundations, or connections that support the beam ends. ## How it works - Select the load type: Uniformly Distributed Load (UDL), Mid-span Point Load, or Point Load at an arbitrary offset. - Enter the span length (L) and the corresponding load values (q or P), along with the load position (a) if using an offset load. - Specify the desired decimal precision and click calculate to generate the reactions, maximum shear force, and maximum bending moment. ## Use cases - Sizing structural joists by calculating the maximum bending moment under uniform floor loads. - Determining reaction forces at beam supports to design bearing plates and anchor bolts. - Analyzing shear and moment demands for a beam supporting a heavy piece of localized machinery. ## Frequently asked questions ### What load types does this calculator support? It supports Uniformly Distributed Loads (UDL), mid-span point loads, and point loads placed at any arbitrary position along the span. ### What units should I use for inputs? Input span lengths and positions in millimeters (mm), uniformly distributed loads in Newtons per millimeter (N/mm), and point loads in Newtons (N). ### How is the maximum bending moment calculated for an offset point load? It uses the formula M_max = (P * a * b) / L, where 'a' is the distance from support A, 'b' is the distance to support B (L - a), and 'L' is the total span. ### Does this calculator account for the self-weight of the beam? No, the calculator only computes forces based on the external loads you input. You must add the beam's self-weight as a UDL if you wish to include it. ### Where does the maximum shear force occur? 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