What this calculator does
Shear force is the internal force that resists one part of a beam sliding vertically past the part next to it, and it is one of the two internal forces, alongside bending moment, that any beam design has to be checked against. Its value along the beam depends entirely on how the beam is supported and how the load is applied.
Rather than attempt a single formula that covers every possible support and loading arrangement, which would either be too narrow to be useful or misleadingly oversimplified, this calculator covers the two most common textbook cases for a simply supported beam: a single point load at mid-span, and a uniformly distributed load along the full span.
The formula
For a simply supported beam carrying a single point load at the centre of the span, each support carries half the load, and the maximum shear force equals half the point load: V_max = P ÷ 2. For a uniformly distributed load spread evenly along the span, the total load is the load per metre multiplied by the span length, and again each support carries half of that total, giving V_max = (w × L) ÷ 2.
| Term | Meaning |
|---|---|
| Shear force | The internal force acting parallel to a beam's cross-section, tending to shear one side past the other. |
| Simply supported beam | A beam resting on two supports, free to rotate at each end, with no fixed moment connection. |
| Uniformly distributed load (UDL) | A load spread evenly along the length of a beam, measured as force per unit length. |
The inputs explained
| Field | What to enter |
|---|---|
| Loading type | Choose whether the beam carries a single central point load or a uniformly distributed load. |
| Point load, P (N) | The magnitude of the point load, if that is the loading case selected. |
| Distributed load, w (per metre of span) (N/m) | The distributed load per metre of span, if that is the loading case selected. |
| Span length, L (m) | The full length of the beam between its two supports. |
When to use it
Sizing a simple support beam
For a straightforward beam carrying a single central load, such as a point load from a column above, the maximum shear force at the supports is a quick first check before a full structural design.
Checking a beam under its own weight and a floor load
A beam carrying a fairly even load along its length, such as its self-weight plus an evenly loaded floor, is well approximated by the uniformly distributed load case.
Comparing point load and distributed load cases
The same total load produces a different maximum shear force depending on whether it acts at one point or is spread along the span, which is worth checking before assuming one case can stand in for the other.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How maximum shear force changes with span, for a fixed point load
A fixed 5,000 N point load at mid-span, across a range of span lengths.
How maximum shear force changes with span, for a fixed distributed load rate
A fixed 2,000 N/m distributed load, across a range of span lengths.
| Span length | Maximum shear force | Total load on the beam |
|---|---|---|
| 2 m | 2,000 N | 4,000 N |
| 3 m | 3,000 N | 6,000 N |
| 4 m | 4,000 N | 8,000 N |
| 5 m | 5,000 N | 10,000 N |
| 6 m | 6,000 N | 12,000 N |
| 8 m | 8,000 N | 16,000 N |
Questions
Why does span length not affect shear force for a point load, but it does for a distributed load?
For a point load, the support reactions only depend on the size of that one load and where it sits, not on the beam's length. For a distributed load, a longer span accumulates more total load at the same rate per metre, so the reactions, and therefore the maximum shear force, grow with span.
What if the point load is not at the centre of the span?
The support reactions become uneven, split according to how far the load sits from each support rather than exactly in half, and the maximum shear force calculation needs that off-centre position as an input, which is outside this calculator's single central-load case.
Does this calculator cover multiple loads or multiple spans?
No. It covers a single simply supported span carrying either one central point load or one uniform distributed load. A beam with several loads, overhangs or continuous spans needs a full shear force and bending moment analysis for that specific arrangement.
How does shear force relate to bending moment?
They are the two internal forces used to check a beam is not going to fail: shear force resists vertical sliding across a section, while bending moment resists the beam bending. Both are checked against the beam's material and cross-section, but they are calculated separately.
For related structural sizing tools, see the other calculators in the Home & build and Physics categories on the site.