Calculate support reactions on a simply supported beam by entering your beam span, number of point loads, and each load's magnitude and position. You get back Reaction A (R_A) and Reaction B (R_B) at each support, plus a visual breakdown of how the loads distribute across the beam.
Reaction at Support A (R_A)
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Reaction at Support B (R_B)
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Total Applied Load
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Equilibrium Check (R_A + R_B)
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A support reaction is the force (or moment) that a structural support exerts on a beam to keep it in static equilibrium. According to Newton's third law, every applied load on the beam produces an equal and opposite reaction at the supports. For a simply supported beam, there are two vertical reaction forces — one at each end.
A simply supported beam is a structural element that rests on two supports — one at each end — where one support is a pin (resisting vertical and horizontal forces) and the other is a roller (resisting only vertical force). This configuration is statically determinate, meaning the reactions can be found using only the equilibrium equations.
Use two static equilibrium equations: the sum of all vertical forces equals zero (ΣFy = 0), and the sum of moments about any point equals zero (ΣM = 0). Take moments about support A to find R_B = Σ(Fᵢ × xᵢ) / L, then find R_A = ΣFᵢ − R_B, where xᵢ is each load's distance from A and L is the beam span.
Taking moments about A: R_B × 6 = 25 × 2, so R_B = 8.333 kN. Then R_A = 25 − 8.333 = 16.667 kN. You can verify this by entering these values into the calculator above with beam span = 6 m, 1 load of 25 kN at 2 m.
Support reactions are the foundation of any structural beam analysis. They are the first step in determining internal shear forces and bending moments along the beam, which are required to check whether the beam will safely carry the applied loads without yielding or deflecting excessively. Getting reactions wrong will invalidate all downstream design checks.
Yes. A load positioned closer to support B generates a higher reaction at B and a lower reaction at A, and vice versa. If a load sits exactly at the midspan, it contributes equally to both reactions. The calculator automatically accounts for each load's position when computing R_A and R_B.
The equilibrium check confirms that R_A + R_B equals the total applied load (ΣFᵢ). If these values match, the beam is in vertical static equilibrium and the calculation is correct. Any discrepancy would indicate an input error or a calculation issue.
This calculator is designed for vertical point loads on simply supported beams. For uniformly distributed loads, you can approximate a UDL by converting it to an equivalent point load equal to (w × L) acting at the midspan. For more complex loading scenarios including UDLs, triangular loads, and trapezoidal loads, a more advanced beam analysis tool would be required.