Beam Load Calculator
Calculate support reactions, total applied load, maximum shear force, and maximum bending moment for a simply supported beam carrying a full-span uniform distributed load and an optional point load.
Enter Beam Loads
Simply supported beam with UDL and one point load.
What Is a Beam Load Calculator?
A beam load calculator applies basic static-equilibrium formulas to an idealized beam and its applied loads. This calculator is designed for a simply supported beam with a uniform distributed load across the full span and one optional concentrated point load.
The tool calculates vertical reactions at the left and right supports. It then evaluates the internal shear force and bending moment along the beam to identify their maximum values.
What Is a Simply Supported Beam?
A simply supported beam is an idealized beam with support at both ends that allows rotation while preventing vertical translation at the support locations. It is commonly represented using a pin support and roller support.
How to Use the Beam Load Calculator
Enter Beam Span
Enter the distance between the left and right beam supports using meters or feet.
Enter Applied Loads
Enter a full-span uniform load, a downward point load, or both. Also specify the point-load position from the left support.
Calculate Results
The calculator determines support reactions, total load, maximum shear, maximum bending moment, and moment location.
How Are Beam Support Reactions Calculated?
The total distributed load from a full-span UDL is equal to the load intensity multiplied by beam span: W = wL . This equivalent load acts at the midpoint of the beam.
For a downward point load P located a distance a from the left support, the left and right vertical support reactions are: RA = wL/2 + P(L−a)/L and RB = wL/2 + Pa/L .
The sum of the two vertical reactions should equal the total downward applied load: RA + RB = wL + P .
What Is Beam Shear Force?
Internal shear force represents the vertical force transferred through a cross-section of the idealized beam. Immediately to the right of the left support, the shear starts at the left reaction.
A uniform distributed load causes shear to change linearly along the span. A concentrated point load produces an immediate jump in the shear diagram equal to the magnitude of that point load.
The calculator checks important shear values immediately before and after the concentrated load and at both ends of the span to report the largest absolute shear magnitude.
How Is Maximum Bending Moment Found?
For a section located before the point load, bending moment is: M(x) = RAx − wx²/2 . After passing the point load, its additional moment effect must also be included: M(x) = RAx − wx²/2 − P(x−a) .
A local maximum bending moment generally occurs where the shear force crosses zero. The calculator checks the possible zero-shear locations as well as the point-load position and supports to find the largest positive bending moment.
Common Simply Supported Beam Formulas
| Load Case | Maximum Moment | Location |
|---|---|---|
| Full-span UDL only | wL² / 8 | Midspan |
| Center point load only | PL / 4 | Midspan |
| Point load at distance a | Pa(L−a) / L | At point load |
Metric and Imperial Beam Load Units
In metric mode, span is entered in meters, point loads are entered in kilonewtons, and distributed loads are entered in kilonewtons per meter. Bending moment is therefore displayed in kilonewton-meters.
In imperial mode, span is entered in feet, point loads are entered in pounds, and distributed loads are entered in pounds per foot. The resulting bending moment is displayed in pound-feet.
Beam Analysis Is Not the Same as Beam Design
Support reactions and bending moments are only part of structural beam design. A real beam may also need checks for bending stress, shear stress, deflection, vibration, bearing, buckling, connections, load combinations, lateral restraint, material properties, and other conditions.
This calculator does not recommend beam dimensions and should not be used by itself to decide how much load a real structural beam can safely support.