Beam Load Calculator — Support Reactions & Bending Moment
Enter the beam span, load magnitude and type (point load or UDL) to instantly get the left and right support reactions, maximum bending moment, and the bending moment diagram along the beam.
Load type
kN
m
m
Moment at the load position
- 1
Left support reaction (R_A)
10 × (4 − 2) ÷ 4 = 5 - 2
Maximum bending moment
5 × 2 = 10Bending moment peaks directly under the point load.
How does this calculator work?
For a simply supported beam: point load P at position a from left → R_A = P(L−a)/L, R_B = Pa/L, M_max = R_A·a. UDL of w kN/m → R_A = R_B = wL/2, M_max = wL²/8. The bending moment diagram is triangular for a point load and parabolic for a UDL. These are static equilibrium results for a weightless beam.
Formula
How this is calculated
A simply supported beam is the most common structural element: it rests on two supports, one pinned (no horizontal movement) and one on a roller (free to slide horizontally). The support reactions — the upward forces R_A and R_B — are found from static equilibrium: the sum of forces equals zero and the sum of moments about any point equals zero. For a point load P at distance a from the left support, summing moments about the right support gives R_A = P(L−a)/L, and by subtraction R_B = Pa/L. For a uniform distributed load w (kN/m) the beam is symmetric, so R_A = R_B = wL/2.
The bending moment at any cross-section equals the algebraic sum of moments of all forces to the left (or right) of that section. For a point load the moment diagram is triangular, peaking at M_max = R_A·a directly under the load. For a UDL the diagram is parabolic, peaking at midspan with M_max = wL²/8. The shear force equals R_A just inside the left support and drops to −R_B just inside the right support.
These are the foundational static-equilibrium formulas and assume a rigid, perfectly supported beam with no self-weight. Real designs must add the beam's own weight as a UDL and apply appropriate safety factors to the loads — consult a structural engineer for load-bearing structural work.
Frequently asked questions
Take moments about one support to find the reaction at the other. For point load P at distance a from support A: ΣM_B = 0 → R_A·L = P(L−a) → R_A = P(L−a)/L. Then R_B = P − R_A = Pa/L. For a UDL of intensity w, symmetry gives R_A = R_B = wL/2.
For a central point load P: M_max = PL/4 (at midspan). For a load at arbitrary position a: M_max = Pa(L−a)/L (at the load). For a UDL of intensity w: M_max = wL²/8 (at midspan).
Enter loads in kN (or kN/m for UDL) and span in metres. Reactions appear in kN and bending moments in kNm, which are the standard SI units used in structural engineering. Multiply by 1 000 to convert kN to N or kNm to Nm.
TG we-Calculate Editorial Team. (2026). Beam Load Calculator — Support Reactions & Bending Moment [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/beam-load-calculator
TG we-Calculate Editorial Team. "Beam Load Calculator — Support Reactions & Bending Moment." TG we-Calculate. 2026. https://we-calculate.com/calculator/beam-load-calculator.
TG we-Calculate Editorial Team, "Beam Load Calculator — Support Reactions & Bending Moment," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/beam-load-calculator
@misc{wecalculate_beam_load_calculator, title = {Beam Load Calculator — Support Reactions & Bending Moment}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/beam-load-calculator}}, year = {2026}, note = {TG we-Calculate} }
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