Beam Load Calculator

Frequently Asked Questions

How are reactions calculated on a simply supported beam?

For a uniformly distributed load (UDL) of w over span L, each reaction = wL/2. For a point load P at distance a from the left support: R_left = P × (L − a) ÷ L, R_right = P × a ÷ L. The reactions must always sum to the total applied load.

Where is maximum bending moment on a simply supported beam?

For a UDL, max moment is at the center: M = wL²/8. For a single center point load: M = PL/4. For an off-center point load at distance a: max moment = R_left × a (occurs at the load). Maximum shear is always at the support nearest the heavier reaction.

What is the difference between dead load and live load?

Dead load is the permanent self-weight (beams, joists, drywall, flooring) - typically 10–15 psf for residential floors. Live load is occupancy/movable load: 40 psf for residential rooms, 60 psf for assembly areas, 100 psf for office corridors. Building codes require both to be combined per ASCE 7 load combinations.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

This tool analyzes a simply supported beam - one resting on a pin at the left end and a roller at the right, free to rotate but not translate. It solves the static equilibrium equations (ΣF = 0 and ΣM = 0) to find support reactions, then derives the peak internal shear force and bending moment for the load case you select:

Uniform distributed load (UDL): with intensity w over span L, each reaction is wL ÷ 2, peak shear is wL ÷ 2 at the supports, and the maximum moment is wL² ÷ 8 at midspan.

Point load at center: reactions are P ÷ 2 each, and the maximum moment is PL ÷ 4 under the load.

Point load at distance a: with b = L − a, the left reaction is Pb ÷ L, the right is Pa ÷ L, and the maximum moment is Pab ÷ L beneath the load.

The output is unit-agnostic - use a consistent system (e.g. N and m, or lb and ft) and shear/moment come out in those units.

From Moment to Member Size

The maximum bending moment is only step one. To size a beam you compare the demand against the section's capacity using the flexure formula σ = M × c ÷ I, or more practically the section modulus relation S_required = M ÷ σ_allow. For a steel wide-flange (A992, F_y = 50 ksi) the allowable bending stress under ASD is roughly 0.66F_y ≈ 33 ksi; for dimensional lumber it is far lower, typically 900–1,500 psi depending on species and grade. Pick the lightest section whose published S exceeds the required value, then check deflection separately.

Deflection Usually Governs

For everyday spans, serviceability - not strength - often controls the design. A simply supported beam under UDL deflects δ = 5wL⁴ ÷ (384EI) at midspan; under a central point load it is PL³ ÷ (48EI). Common code limits are L/360 for floors carrying plaster or live load and L/240 for roof members. A beam can pass the stress check comfortably yet still feel bouncy or crack finishes if I is too small, so always verify deflection against span-based limits.

Loads You Must Not Forget

Self-weight: the beam's own mass acts as an additional UDL - add it to the applied load once you choose a trial section.

Load combinations: real codes (ASCE 7, Eurocode) apply factors such as 1.2D + 1.6L; this calculator uses raw service loads, so factor inputs yourself.

Tributary width: a floor beam carries load from half the bay on each side - convert area pressure (psf or kPa) to a line load w before entering it.

Dynamic and impact loads: moving, vibrating, or suddenly applied loads can effectively double the static value.

Limits of This Model

Results assume an ideal, linearly elastic, prismatic beam with frictionless supports and no axial force. It does not cover continuous or cantilevered spans, fixed/moment connections, lateral-torsional buckling, web crippling, shear-deflection in deep beams, or composite action. It is a fast estimating and learning aid - any beam in a real structure should be designed and stamped by a licensed structural engineer to the governing building code.

Beam Load Calculator

Frequently Asked Questions

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