Simply Supported Beam Calculator

Analyze beam response from point and distributed loading cases. Get reactions, moments, shears, and deflection. Plot diagrams, save reports, and verify structural assumptions easily.

Beam Input Form

Load Case

Span Length (m)

Point Load (kN)

Point Load Position from Left (m)

Uniformly Distributed Load (kN/m)

Elastic Modulus E (GPa)

Section Input Method

Section Width b (mm)

Section Depth h (mm)

Second Moment of Area I (mm⁴)

Deflection Limit

Reset Form

Example Data Table

Parameter	Example Value	Output
Span	8 m	Load case: Combined
Point Load	18 kN at 3 m	Reaction A: 35.250 kN
UDL	6 kN/m over full span	Reaction B: 30.750 kN
Material Stiffness	200 GPa	Max moment: 78.750 kN·m
Section	250 mm × 450 mm	Max deflection: -1.306 mm
Inertia	1,898,437,500 mm⁴	Serviceability: Pass

Formula Used

This calculator combines equilibrium equations with Euler–Bernoulli beam theory.

ΣV = 0 and ΣM = 0 are used to find support reactions.

R_A = P(L-a)/L + wL/2

R_B = Pa/L + wL/2

V(x) = R_A - wx - P·H(x-a)

M(x) = R_Ax - wx²/2 - P·(x-a) for x ≥ a

EI·y''(x) = M(x)

Deflection is found by numerically integrating curvature across the beam while enforcing zero deflection at both supports.

How to Use This Calculator

Choose the load case: point load, full-span UDL, or combined loading.
Enter the beam span in meters.
Provide point load magnitude and position when that load case is active.
Enter the distributed load in kN/m for UDL or combined cases.
Enter the elastic modulus in GPa.
Select rectangular section input or enter a custom second moment of area.
Pick a serviceability limit such as L/240, L/360, or L/480.
Press Calculate Beam Response to view reactions, maximum values, and the Plotly graph above the form.
Use the CSV and PDF buttons to export the calculated report.

FAQs

1. What does a simply supported beam mean?

A simply supported beam rests on two supports. One support usually resists vertical movement, while the other allows horizontal movement. The beam carries load without fixed-end restraint, so end moments are normally zero.

2. Which loads can this calculator handle?

This version handles a single point load, a full-span uniformly distributed load, or both together. It then computes reactions, shear, bending moment, and deflection from the combined loading condition.

3. Why is the point load position important?

Load position changes the support reactions and the peak bending moment location. An off-center point load shifts force toward the nearest support and changes where the beam experiences its highest stress and deflection.

4. What is the second moment of area?

The second moment of area, often called I, measures how strongly a section resists bending. Larger values reduce deflection for the same material and loading. It depends on the section shape and dimensions.

5. Why does the calculator ask for elastic modulus?

Elastic modulus describes material stiffness. Steel, concrete, and timber have different stiffness values. A higher modulus produces smaller deflections when the same beam geometry and loading are used.

6. What does the serviceability check show?

The serviceability check compares calculated maximum deflection with an allowable limit such as L/360. Passing does not prove full structural safety, but it helps assess whether beam movement stays within common practical limits.

7. Are the graph results enough for final design?

They are useful for preliminary sizing, checking, and learning. Final design should still consider code requirements, load combinations, self-weight, lateral stability, bearing, shear capacity, and material-specific design checks.

8. Can I use custom inertia instead of section dimensions?

Yes. Choose the custom inertia option when you already know the section property from a handbook, design sheet, or manufacturer table. That method is helpful for standard rolled or built-up sections.