TryBuildCalcBeam Moment Calculator (Bending Moment, Shear & Reactions)
Calculate beam bending moment, shear, and reactions.
Calculate maximum beam moment for UDL or point load with editable span and load value. Adjust support type, span, load type, load value, and (for a point load) its position for preliminary structural checks.
🕒 Last updated: August 3, 2026
Inputs
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.
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
72 kN·m
Occurs at mid-span
Scenario: Simply Supported, Uniformly Distributed Load (UDL)
Shear Force & Reactions
Maximum Shear Force: 36 kN
Left Support Reaction: 36 kN
Right Support Reaction: 36 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.
Looking for the verification checklist, reference tables, tips, or common mistakes?See the complete Beam Load Calculator.
Beam moment calculation
This page provides a moment-focused setup for preliminary beam analysis.
The calculator is pre-filled for this beam load use case. Change any input and the example updates from the active values.
- Default span: 8 m.
- Default UDL: 9 kN/m.
- Outputs maximum moment.
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
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)
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
Step 4 — Cantilever, Point Load (at distance a from the fixed support)
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
| Input | Value |
|---|---|
| Support Type | Simply Supported |
| Beam Length | 8 m (8 m) |
| Load Type | Uniformly Distributed Load (UDL) |
| Load | 9 kN/m |
Step 1 — Maximum Bending Moment
| Calculation | Substitution | Result |
|---|---|---|
| M = wL² / 8 | (9 × 8²) / 8 | 72 kN·m |
Step 2 — Maximum Shear Force & Reaction(s)
| Calculation | Substitution | Result |
|---|---|---|
| max(Pb/L, Pa/L) or wL/2 | (9 × 8) / 2 | 36 kN |
| Left Support Reaction | (9 × 8) / 2 | 36 kN |
| Right Support Reaction | (9 × 8) / 2 | 36 kN |
Therefore, this beam has a maximum bending moment of 72 kN·m (at mid-span) and a maximum shear force of 36 kN — the 36 kN left and 36 kN right reactions are equal since the load is centered.
Cross-check against the Beam Load Formula Reference table in the complete Beam Load Calculator.