What equations are used to calculate RA and RB?

The calculator uses the two static equilibrium equations: (1) Sum of moments about B = 0, which gives RA = (sum of each load times its distance from B) / L. (2) Sum of vertical forces = 0, which gives RB = total load − RA. A UDL of intensity w over a length a is replaced by its resultant force w×a acting at the centroid of the loaded segment.

What is a simply supported beam?

A simply supported beam rests on two supports — a pin at A (left) and a roller at B (right). The pin prevents horizontal and vertical movement; the roller prevents only vertical movement. Both supports provide a vertical reaction but zero moment reaction, making the beam statically determinate with exactly two unknowns (RA and RB).

What is a UDL (uniformly distributed load)?

A uniformly distributed load (UDL) is a load spread evenly along a portion of the beam, measured in kN/m or kN per unit length. For equilibrium calculations a UDL of intensity w (kN/m) over length a (m) is equivalent to a single point load of magnitude w×a (kN) applied at the midpoint of the loaded region.

Can I add both point loads and UDLs in the same calculation?

Yes. The calculator superimposes all loads — any combination of point loads and UDLs — and sums the moment contributions of each one to compute RA and RB through a single equilibrium solution.

Why must all loads be within the beam span?

The equilibrium model assumes all loads act on the beam between the two supports (0 ≤ position ≤ L). Loads outside the span would create overhanging conditions requiring a different structural model (propped cantilever or continuous beam).

Does this account for the self-weight of the beam?

No. Self-weight is not included automatically. To account for it, add a UDL running the full span length (0 to L) with intensity equal to the beam self-weight in kN/m (e.g. a W200×100 steel section weighs approximately 1.0 kN/m).

Beam Reaction Calculator

Name: Beam Reaction Calculator
Availability: InStock
Author: Nham Vu

Enter beam length, point loads, and distributed loads to instantly calculate support reactions RA and RB using sum of moments equilibrium.

Beam Span

Total Span Length, L (m)

Distance between the two supports A (left) and B (right).

Point Loads

No point loads added yet.

Distributed Loads (UDL)

No distributed loads added yet.

Reaction at A (left support)

—

R_A — from moment about B = 0

Reaction at B (right support)

—

R_B — from ΣF_y = 0

Enter beam span and at least one load, then click Calculate.

Equilibrium Equations

ΣM_B = 0 ⇒ R_A × L = Σ(P_i × d_Bi)

ΣF_y = 0 ⇒ R_A + R_B = ΣP_i

d_B = distance of each load from support B (= L − position from A)

Summary

Enter beam length, point loads, and distributed loads to instantly calculate support reactions RA and RB using sum of moments equilibrium.

How it works

Enter the total beam span length L in meters.
Add one or more point loads by specifying the magnitude (kN) and position from the left support (m).
Optionally add uniformly distributed loads (UDL) by entering the load intensity (kN/m), the start position, and the end position along the beam.
Click Calculate to apply moment equilibrium about each support and compute RA and RB.
Review the reaction values and the load summary table to verify input.
Use the Reset button to clear all inputs and start a new calculation.

Use cases

Preliminary structural analysis of floor beams, roof beams, and bridge girders.
Verifying hand calculations against equilibrium equations in structural engineering.
Teaching statics and mechanics of materials — beam reactions and free body diagrams.
Quick reaction checks when sizing beam sizes before detailed analysis.
Checking reactions for simply supported timber, steel, or concrete beams.
Identifying unbalanced loads or incorrect positioning in beam designs.
Comparing reactions for alternative load patterns on the same span.
Educational demonstrations of how load position affects reaction magnitude.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu