TryBuildCalcOff-Center Point Load Beam Calculator (Bending Moment, Shear & Reactions)
Calculate beam bending moment, shear, and reactions.
Calculate bending moment, shear force, and unequal support reactions for a beam with an off-center point load. 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 the concentrated load
ℹ️Distance from the left support. Defaults to mid-span — move it to model an off-center load (e.g. a column or equipment load that isn't centered).
Maximum Bending Moment
93.75 kN·m
Occurs at 3 m from the left support
Scenario: Simply Supported, Point Load at 3 m from the left support
Shear Force & Reactions
Maximum Shear Force: 31.25 kN
Left Support Reaction: 31.25 kN
Right Support Reaction: 18.75 kN
Reactions are unequal because the load isn't centered — the shear force above is the larger of the two.
Design Notes
A simply supported beam's maximum bending moment location shifts toward whichever support is closer to the load — dead-center only when the load itself is centered.
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.
8 m span, 50 kN load at 3 m from the left support
When a point load isn't centered, the two support reactions split unevenly and the maximum bending moment shifts to sit directly under the load, not at mid-span. For an 8 m span with a 50 kN load 3 m from the left support (5 m from the right): the left reaction is 31.25 kN, the right reaction is 18.75 kN, and the maximum moment is 93.75 kN·m at the load's own position.
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, load: 50 kN at 3 m from the left support.
- Left reaction 31.25 kN, right reaction 18.75 kN — unequal.
- Max moment 93.75 kN·m directly under the load, not mid-span.
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 | Point Load |
| Load | 50 kN |
| Load Position | 3 m from the left support |
Step 1 — Maximum Bending Moment
| Calculation | Substitution | Result |
|---|---|---|
| M = (P × a × b) / L | (50 × 3 × 5.00) / 8 | 93.75 kN·m |
Step 2 — Maximum Shear Force & Reaction(s)
| Calculation | Substitution | Result |
|---|---|---|
| max(Pb/L, Pa/L) or wL/2 | max((50 × 5.00) / 8, (50 × 3) / 8) | 31.25 kN |
| Left Support Reaction | (50 × 5.00) / 8 | 31.25 kN |
| Right Support Reaction | (50 × 3) / 8 | 18.75 kN |
Therefore, this beam has a maximum bending moment of 93.75 kN·m (at 3 m from the left support) and a maximum shear force of 31.25 kN — the 31.25 kN left and 18.75 kN right reactions split unevenly since the load isn't centered.
Cross-check against the Beam Load Formula Reference table in the complete Beam Load Calculator.