The beam can't stand on these supports. Give it two pinned supports, or one fixed support.
What This Beam Calculator Does
This beam calculator analyzes a beam you draw: one span or several, on pinned or fixed supports or with a free end, carrying any mix of point loads, uniform and partial uniform loads, triangular or trapezoidal loads and applied moments. It finds the reaction at each support and draws the shear, bending moment and deflection along the whole beam. Results update as you edit.
Continuous beams and beams with a fixed end are statically indeterminate, so their reactions depend on how the beam bends. The calculator solves them with the stiffness method, the same way frame analysis programs do, so you don't need a table for each case.
It works for any material. Pick a steel or wood size from the shape library, or enter the modulus of elasticity, E, and the moment of inertia, I, yourself. They only change the deflection; the reactions, shear and moment of a beam with the same E and I along its length don't depend on them.
How to Use It
- Click Material or Shape and pick a steel W, C, HSS or pipe shape, sawn lumber, LVL or glulam from the shape library; the calculator takes its E and I. Or type E and I yourself: the table below lists typical E values, and the cross-section calculator finds I for other sections.
- Click Add Spans to set the span lengths, or add spans to the left or right for a continuous beam or an overhang.
- Click a support on the drawing to change it between pinned, fixed and free. A fixed support with a free end is a cantilever.
- Click Add Loads to add uniform, linear and point loads and moments.
- Read the reactions under the drawing and the deflection, shear and moment diagrams below it.
Switch between US units (feet, kips, psi) and metric units (meters, kN, GPa) with the buttons above the
drawing. You can also type a value with its unit in either system, such as 3.5 m,
12' 6" or 20 kN.
| Material | Typical E (psi) | Typical E (GPa) |
|---|---|---|
| Structural steel | 29,000,000 | 200 |
| Aluminum | 10,000,000 | 69 |
| Concrete, 4,000 psi | 3,600,000 | 25 |
| Douglas fir-larch No. 2 lumber | 1,600,000 | 11 |
Sign Convention
Loads entered as positive act downward. Bending moment is positive when the beam sags (tension on the bottom), so the moment over an interior support of a continuous beam, and at the support of a cantilever, is negative. Shear is the slope of the moment diagram, so the shear just right of a support jumps by that support's reaction.
Common Beam Formulas
To check the calculator by hand, here are the four cases engineers use most, for a span L, uniform load w or point load P, and stiffness EI. The beam deflection formulas page has 19 cases, including fixed-end and propped cantilever beams.
| Beam and load | Reactions | Maximum moment | Maximum deflection |
|---|---|---|---|
| Simply supported, uniform load | wL/2 each end | wL²/8 at midspan | 5wL⁴/(384EI) at midspan |
| Simply supported, point load at midspan | P/2 each end | PL/4 at midspan | PL³/(48EI) at midspan |
| Cantilever, uniform load | wL at the support | wL²/2 at the support | wL⁴/(8EI) at the free end |
| Cantilever, point load at the free end | P at the support | PL at the support | PL³/(3EI) at the free end |
For two equal spans L with a uniform load w on both, the end reactions are 3wL/8 and the middle reaction is 5wL/4. The moment over the middle support is −wL²/8. The shear and moment diagram examples work five beams through by hand.
Beam Calculator or Beam Designer?
This calculator tells you how a beam behaves: its reactions, moments, shears and deflections. It doesn't pick a beam size or check the beam against a design code.
To size a steel or wood beam, click Check this beam to AISC or NDS under the diagrams. It opens the same beam in the WebStructural Beam Designer, with the loads as dead load and the shape you picked, if any. There you split the loads into dead, live, roof and snow load, choose an AISC steel shape or sawn or engineered lumber, and the designer checks bending, lateral-torsional buckling, shear and deflection under the LRFD or ASD load combinations. The steel beam design guide walks through those checks by hand.
Frequently Asked Questions
Is the beam calculator free?
Yes, for beams of up to two spans, with no account or sign-up. More spans need a WebStructural subscription.
Can it analyze continuous or multi-span beams?
Yes. Add spans to the left or right of the first one. Each support can be pinned or fixed, and either end can be free for an overhang.
Does it work in metric units?
Yes. Click m, kN above the drawing to enter spans in meters, loads in kN and kN/m and E in GPa, and to read the reactions, shear, moment and deflection in metric units.
Does it show the support reactions?
Yes. The reaction at each support is listed under the drawing and updates as you edit the beam.
Does it include the beam's own weight?
Not automatically. Add the self weight as a uniform load over the whole beam, for example 26 lb/ft for a W16X26 steel beam.
Is there a table of the deflection formulas?
Yes. The beam deflection formulas page lists the largest deflection, moment and reactions for 19 standard cases.