Inputs
Enter span, loads, and a query position. Units: kN, kN/m, and meters.
Example data table
| Case | Span (m) | Loads | Rleft (kN) | Rright (kN) | Max |V| (kN) |
|---|---|---|---|---|---|
| 1 | 12 | UDL 18 kN/m (0–12), Point 120 kN at 5 m | ≈ 156.000 | ≈ 180.000 | ≈ 180.000 |
| 2 | 8 | Point 90 kN at 3 m, Point 60 kN at 6 m | ≈ 71.250 | ≈ 78.750 | ≈ 78.750 |
| 3 | 6 | Cantilever: UDL 10 kN/m (0–6) | ≈ 60.000 | 0.000 | ≈ 60.000 |
Formula used
1) Resultant loads
Point loads add directly: W = ΣP. A UDL segment becomes a resultant force W = w·(b−a) acting at its centroid x̄ = a + (b−a)/2.
2) Support reactions
For a simply supported girder: Rright = (ΣMleft)/L and Rleft = W − Rright.
For a cantilever fixed at left: Rleft = W and fixed-end moment M = Σ(P·x) + Σ(w·len·x̄).
3) Shear at a section
Simply supported: V(x) = Rleft − ΣP(≤x) − Σ[w·overlap], where overlap is UDL length from its start to x.
Cantilever: internal shear magnitude equals the load to the right of the cut.
How to use this calculator
- Enter the girder span and select the support model.
- Add point loads and their positions from the left end.
- Define UDL segments with start and end coordinates.
- Optionally include self-weight as a full-span UDL value.
- Set a query position to read shear at that location.
- Press Calculate shear to view results and the table.
- Use the export buttons to download CSV or PDF records.
Shear force meaning in girder design
Shear force is the internal action that transfers vertical loads through the web of a girder to its supports. It governs web thickness, stiffener spacing, seat angles, and bearing details. Tracking shear along the span also highlights where sudden load changes can trigger local yielding, web buckling, or connection distress near supports and openings. Support reactions also drive bearing pad and seat checks.
Load entry and modelling options
This calculator models up to three point loads and two UDL segments, plus optional self-weight as a full-span UDL. Enter loads in kN and kN/m, and positions in meters from the left support or fixed end. Downward loads are entered as positive. UDL segments are converted to equivalent resultants at their centroids, while shear varies linearly within each UDL length. Query point outputs left and right shear.
Reaction checks for fast QA
For a simply supported girder, equilibrium provides reactions: the right reaction comes from moment balance about the left support, and the left reaction is the remaining force balance. As a quick check, the sum of reactions should match the total applied load within rounding. For a cantilever, the vertical reaction equals the total load and the fixed-end moment equals the sum of load moments about the fixed end. Use this as a sanity check.
Finding critical sections for detailing
Shear usually peaks at supports and immediately after point loads, so review the maximum |shear| location and the “shear at x” values for cuts near bearings, splices, penetrations, and connection groups. UDL start and end points change the slope of the shear diagram, making them important event points. High shear demand may require web stiffeners, thicker webs, closer weld patterns, or larger bolt groups, alongside bearing and web-crippling checks. Check shear at connections and bearings.
Documenting results with exports
Use the export buttons to keep calculations traceable. The CSV supports design registers, comparison across load cases, and independent review. The PDF is convenient for site submissions and QA packs. Record the girder mark, span, load case name, and assumptions such as self-weight inclusion so results stay audit-ready during construction changes.
FAQs
1) What does “shear at x (left/right)” mean?
The left value is the internal shear just before the cut at x, and the right value is just after any point load located at x. This helps you see the jump caused by concentrated loads.
2) Which units should I use for accurate results?
Use meters for all positions and span length, kN for point loads, and kN/m for UDL intensity. Keep one unit system across the inputs to avoid equilibrium and reaction errors.
3) Can I model uplift or upward loads?
Yes. Enter an upward point load or UDL as a negative value. The calculator will include it in reactions and shear, so the output sign reflects net loading at each section.
4) How are UDL segments handled between start and end?
Only the portion of the UDL that overlaps the section contributes to shear at that x. Within the segment, shear changes linearly with distance because the distributed load accumulates gradually along the span.
5) Why is the right reaction zero for a cantilever?
The cantilever model assumes the girder is fixed at the left end and free at the right end. All vertical support action is taken at the fixed end, along with the fixed-end moment.
6) Does the maximum shear always occur at a support?
Often, but not always. It commonly occurs at supports or immediately after a large point load. The calculator checks key event positions, but you should also review sections near major load changes and connections.