Beam Reaction Calculator

Calculate support reactions, maximum shear, and moment for simple beams.

Structural Mechanics
1

Design Parameters

Beam Span Length (m or ft) must be entered.

Quick Presets

UDL simple beam (5m)
Simple beam with UDL load of 10 kN.

Calculated Outputs

Reaction Left (R1)
0.00
Reaction Right (R2)
0.00
Maximum Bending Moment
0.00

Beam Statics: Reactions & Moments

A simply supported beam carries forces loaded along its length and transfers them to support columns at both ends. Determining reactions at these supports is essential.

This calculator computes reaction forces and maximum bending moments for simply supported beams carrying uniform distributed loads (UDL) or concentrated point forces.

Simply Supported Beam Diagram Diagram of a beam with point load and UDL.

Reactions Calculations

By solving the equations of static equilibrium (ensuring the sum of vertical forces is zero, and the sum of moments about any point is zero), we calculate the reaction forces loaded onto the left support (R1) and the right support (R2).

Point Load: R1 = P × (L - a) ÷ L,   R2 = P × a ÷ L
Uniform Load (UDL): R1 = w × L ÷ 2,   R2 = w × L ÷ 2
Example Calculation (Point Load at Mid-Span):

1. Beam Span Length (L): 5.0 meters.

2. Point Load Magnitude (P): 10.0 kN.

3. Load Position (a from Left): 2.5 meters (center).

4. Left Support Reaction (R1): 10.0 × (5.0 - 2.5) ÷ 5.0 = 5.0 kN.

5. Right Support Reaction (R2): 10.0 × 2.5 ÷ 5.0 = 5.0 kN.

6. Maximum Bending Moment: (10.0 × 2.5 × 2.5) ÷ 5.0 = 12.5 kNm.

Result: Supports carry 5.0 kN each, and the beam must resist a peak bending moment of 12.5 kNm at mid-span.
Warning: This calculator is for preliminary estimation and educational purposes only. It is NOT a replacement for structural analysis by a licensed professional engineer (PE) or architect. Always verify loads, material properties, and deflection criteria with local building codes (e.g., IBC, Eurocodes).

Equilibrium Equations in Statics

Simply supported beams are statically determinate structure members. The support reaction forces are solved by satisfy two main static equilibrium equations:

  1. Sum of Vertical Forces = 0: R1 + R2 - Total Loads = 0.
  2. Sum of Moments about Support = 0: The rotational forces about either support must balance out. This allows us to solve for one reaction directly, then solve for the other.

Frequently asked questions

What is UDL?

UDL stands for Uniformly Distributed Load, representing a load spread evenly along the length of the beam (e.g., slab self-weight).

Where does maximum bending moment occur?

For simply supported beams, maximum bending moment occurs at the center of the span under a uniform distributed load or directly under the point of load application for a concentrated force.

What is the unit of bending moment?

Bending moment is measured in force times distance, such as kilonewton-meters (kNm) in metric or pound-feet (lb-ft) in imperial.