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Beam Load Calculator (Bending Moment, Shear & Reactions)

Calculate beam bending moment, shear force, and reactions.

Inputs

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ℹ️Simply Supported has a pin support at each end. Cantilever is fixed at one end and free at the other — it carries the full load through a single support and develops its maximum moment at the fixed end.

ℹ️The effective span, center-to-center of the two supports.

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ℹ️UDL applies over the full beam length. Point Load lets you place a single concentrated load anywhere along the span.

💡Enter load per meter length

Maximum Bending Moment

22.5 kN·m

Occurs at mid-span

Scenario: Simply Supported, Uniformly Distributed Load (UDL)

Shear Force & Reactions

Maximum Shear Force: 15 kN

Left Support Reaction: 15 kN

Right Support Reaction: 15 kN

Design Notes

A simply supported beam under a full-span UDL always develops its maximum bending moment at mid-span, since the load is symmetric along the entire length.

This is a single-load-case estimate for one span only — it does not combine multiple loads, account for the beam's own self-weight automatically, or model continuous (multi-span) beams. Always confirm with a qualified structural engineer before finalizing beam design.

Approximate results for planning only. Verify with a professional.

Beam Load VisualizationLength: 6 mUDL (kN/m)Max MBending Moment DiagramDiagram simplified for clarity (not to scale)

What is the purpose of this Beam Load Calculator?

This beam load calculator determines the maximum bending moment, maximum shear force, and support reaction(s) for a single-span beam — Simply Supported (a pin support at each end) or Cantilever (fixed at one end, free at the other) — carrying either a uniformly distributed load (UDL) across its full length or a point load placed anywhere along the span, not just the center.

In real construction, beams carry slab loads, wall loads, and sometimes off-center concentrated loads from a column above, equipment, or a water tank. Understanding where the maximum bending moment and shear force occur — and how they change when a load isn't centered, or when a beam is cantilevered instead of simply supported — is essential for safe preliminary sizing.

Using this calculator helps you:

  • Estimate maximum bending moment and shear force quickly, for either support condition
  • Model a point load at its actual position, not just the center
  • Understand how support reactions split when a load is off-center
  • Verify manual calculations before detailed structural design
  • Plan preliminary beam sizing before involving a structural engineer

This calculator follows standard statics formulas for single-span beams. It is suitable for quick estimation and educational purposes, not final structural design — see Limitations below.

How does this beam load calculator work?

The bending moment, shear force, and reactions all depend on the support type, load type, and — for a point load — exactly where along the span it's applied.

Step 1 — Simply Supported, UDL

M = (w × L²) / 8 at mid-span · R₁ = R₂ = (w × L) / 2

Maximum shear force equals the reaction at either support, since they're equal.

Step 2 — Simply Supported, Point Load (at distance a from the left support, b = L − a)

R₁ = (P × b) / L · R₂ = (P × a) / L · M = (P × a × b) / L at the load point

At a = L/2 (centered) this reduces to the familiar R₁ = R₂ = P/2 and M = PL/4. Off-center, the reactions split unevenly and the maximum moment shifts to sit directly under the load, not at mid-span.

Step 3 — Cantilever, UDL

M = (w × L²) / 2 at the fixed support · R = w × L

Step 4 — Cantilever, Point Load (at distance a from the fixed support)

M = P × a at the fixed support · R = P

A cantilever has only one support, so the full load reaction — and the full bending moment — concentrate at the fixed end. At a = L (load at the free tip), this reduces to the familiar M = PL.

Worked Example

This example uses the active inputs above and follows the same steps as the Formula section.

Input Values Used

InputValue
Support TypeSimply Supported
Beam Length6 m (6 m)
Load TypeUniformly Distributed Load (UDL)
Load5 kN/m

Step 1 — Maximum Bending Moment

CalculationSubstitutionResult
M = wL² / 8(5 × 6²) / 822.5 kN·m

Step 2 — Maximum Shear Force & Reaction(s)

CalculationSubstitutionResult
max(Pb/L, Pa/L) or wL/2(5 × 6) / 215 kN
Left Support Reaction(5 × 6) / 215 kN
Right Support Reaction(5 × 6) / 215 kN

Therefore, this beam has a maximum bending moment of 22.5 kN·m (at mid-span) and a maximum shear force of 15 kN — the 15 kN left and 15 kN right reactions are equal since the load is centered.

Cross-check against the Beam Load Formula Reference table below.

Essential Checklist+

Complete these critical checks before approving the work or proceeding to the next construction stage.

✓17 Inspection Points
✓3 Verification Categories
✓Load Identification & Input+
  • Dead load (self-weight of beam, slab, finishes) correctly calculated
  • Live load selected per IS 875 Part 2 for the actual occupancy type
  • Wall load included where masonry walls sit on the beam
  • Load combination applied — 1.5 (DL + LL) for IS 456:2000 limit state design
  • Tributary width (load width contributing to the beam) correctly identified
  • Point loads (columns above, equipment, water tanks) identified and included
  • Point load position measured from the actual support, not assumed to be centered
  • Support type (Simply Supported vs Cantilever) confirmed against the actual detail
  • Beam span measured as effective span — centre to centre of supports
  • Beam self-weight included — 25 kN/m³ × beam width × beam depth
✓Bending Moment & Shear+
  • Correct bending moment formula applied for loading and support type
  • Maximum shear force identified — occurs at supports for simply supported beams
  • All loads in consistent units throughout — kN and metres, or kN/m²
✓Beam Size & Adequacy+
  • Beam effective depth adequate for applied bending moment
  • Beam width adequate — minimum 200mm, 230mm standard in residential construction
  • Beam checked for shear — shear stress within permissible limit or stirrups designed
  • Beam load calculation reviewed by qualified structural engineer before construction
Full QC Checklist+

Verification checklist for beam load calculation and structural assessment — covering load identification, load combination, beam sizing, deflection, and safety. Use the Essential Checklist for critical checks before finalising beam design; expand to Full QC Checklist for complete structural verification.

✓27 Inspection Points
✓3 Verification Categories
✓Load Identification & Input+
  • Dead load (self-weight of beam, slab, finishes) correctly calculated
  • Live load selected per IS 875 Part 2 for the actual occupancy type
  • Wall load included where masonry walls sit on the beam
  • Load combination applied — 1.5 (DL + LL) for IS 456:2000 limit state design
  • Tributary width (load width contributing to the beam) correctly identified
  • Point loads (columns above, equipment, water tanks) identified and included
  • Point load position measured from the actual support, not assumed to be centered
  • Support type (Simply Supported vs Cantilever) confirmed against the actual detail
  • Beam span measured as effective span — centre to centre of supports
  • Beam self-weight included — 25 kN/m³ × beam width × beam depth
  • Wind and seismic loads assessed — applied to beam if applicable
  • Load diagram drawn showing beam span, support type, and all applied loads
  • Support conditions correctly identified — simply supported, fixed, or continuous
  • Superimposed dead loads (SDL) confirmed — floor finishes, screed, partition allowance
✓Bending Moment & Shear+
  • Correct bending moment formula applied for loading and support type
  • Maximum shear force identified — occurs at supports for simply supported beams
  • All loads in consistent units throughout — kN and metres, or kN/m²
  • Support reactions checked — sum of reactions equals total applied load
  • For continuous beams — hogging moments at supports checked, not just mid-span
  • Deflection checked — span/depth ratio or calculated deflection within IS 456 limit
  • Bending moment diagram drawn and reviewed — critical section identified
✓Beam Size & Adequacy+
  • Beam effective depth adequate for applied bending moment
  • Beam width adequate — minimum 200mm, 230mm standard in residential construction
  • Beam checked for shear — shear stress within permissible limit or stirrups designed
  • Beam load calculation reviewed by qualified structural engineer before construction
  • Bearing length at supports adequate — minimum 150mm on masonry, per drawing on RCC
  • Pre-camber specified for beams spanning more than 6m

Beam Load Formula Reference

Support TypeLoad TypeMax MomentMax Moment LocationReaction
Simply SupportedUDLwL²/8Mid-spanwL/2 each
Simply SupportedPoint LoadPab/LAt the loadPb/L and Pa/L
CantileverUDLwL²/2Fixed supportwL
CantileverPoint LoadPaFixed supportP

w = load per unit length (kN/m) · P = point load (kN) · L = span (m) · a, b = distances from left/fixed support (a + b = L for Simply Supported).

How to Use This Beam Load Calculator

  1. Select Support Type — Simply Supported (a pin support at each end) or Cantilever (fixed at one end, free at the other).
  2. Enter the beam length — the effective span for Simply Supported, or the span from the fixed support to the free end for Cantilever.
  3. Select Load Type — Uniformly Distributed Load (UDL) across the full span, or a Point Load at a specific position.
  4. Enter the load value — kN/m for UDL, kN for a point load.
  5. For a point load, adjust the Load Position if it isn't centered (Simply Supported) or not at the free tip (Cantilever) — the default assumes the common governing case.
  6. Review the maximum bending moment, maximum shear force, and support reaction(s), and cross-check against the Verification Checklist before finalizing a preliminary size.

Beam Load Tips & Best Practices

  • Always include the beam's own self-weight (25 kN/m³ × width × depth) as an additional UDL on top of the loads from above — it's the single most commonly forgotten load.
  • Use the effective span (center-to-center of supports), not the clear span between column/wall faces — the difference (typically 150-300mm) can meaningfully underestimate the moment.
  • For a transfer beam carrying a column load that isn't centered, use the Point Load position input to place it accurately — the maximum moment shifts to sit under the actual load location, not mid-span.
  • Cantilevers should almost always be checked with the point load at the free tip (the default here) — that's the governing worst case for bending moment.
  • Cross-check the reaction values against a simple equilibrium check: the sum of all reactions must equal the total applied load.
  • Compare your result against the Beam Load Verification Checklist before finalizing a preliminary size.

Common Mistakes to Avoid

  • Assuming every point load is centered. A column, water tank, or equipment load off to one side produces unequal reactions and a moment that peaks under the load, not at mid-span — using the centered formula there under-designs one side of the beam.
  • Modeling a cantilever as simply supported (or vice versa). A cantilever's maximum moment is at the fixed support, not mid-span, and is typically much larger for the same span and load than a simply supported beam would show.
  • Forgetting the beam's own self-weight. For a typical 230mm × 450mm beam this is roughly 2.6 kN/m — easily larger than some superimposed loads, and this calculator does not add it automatically.
  • Ignoring shear force and only checking bending moment. Maximum shear force governs stirrup/shear reinforcement design and can control the design even when the moment looks comfortable.
  • Using the clear span instead of the effective span. This understates bending moment by roughly 5-10% for typical residential spans.
  • Combining multiple loads by simply adding their individual maximum moments. When more than one load acts on the same beam, the true combined maximum moment doesn't always occur at the same location as either individual load's peak — this calculator handles one load case at a time; see Limitations.

Limitations of beam load calculation

This calculator handles one span, one support condition, and one load case at a time. It does not account for:

  • Fixed-fixed or continuous (multi-span) beams
  • Combined loads (UDL and point load together, or multiple point loads) on the same beam
  • A partial-length UDL that doesn't span the full beam
  • Beam self-weight — add it manually as an additional UDL
  • Shear reinforcement design, deflection calculation, or section adequacy checks

For detailed structural design, including reinforcement design, deflection verification, and safety checks, always refer to structural drawings and consult a qualified structural engineer.

Related Calculators

Use the Concrete Beam Calculator to estimate concrete volume once the beam is sized.

The Beam Steel Calculator sizes the reinforcement for the bending moment calculated here.

For a short-span beam over an opening, see the Lintel Calculator.

FAQ

It's a statics calculator for a single-span beam that outputs the maximum bending moment, maximum shear force, and support reaction(s) for a chosen support type (Simply Supported or Cantilever) and load type (UDL or Point Load). These three outputs — moment, shear, and reactions — are the starting point for sizing the beam's depth/width and reinforcement, and for checking that the supports themselves (walls, columns) can carry the load.
Simply Supported means the beam rests on a support at each end (each providing an upward reaction, neither resisting rotation) — most floor and roof beams are this type. Cantilever means the beam is rigidly fixed at one end and completely free at the other, carrying the entire load through that single fixed connection — balconies, canopies, and staircase overhangs are common examples. For the same span and load, a cantilever's maximum bending moment (wL²/2 for a UDL) is 4 times larger than the same beam simply supported (wL²/8), and it occurs at the fixed support instead of mid-span — modeling a cantilever as simply supported (or vice versa) produces a badly wrong answer, not just a slightly different one.
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