Simply Supported Beam Calculator

Enter Beam Data

Span length L (m)

Point load P (kN)

Point load position a (m)

Full uniform load w (kN/m)

Partial uniform load wp (kN/m)

Partial load start x1 (m)

Partial load end x2 (m)

Elasticity E (GPa)

Second moment I (million mm⁴)

Section modulus Z (thousand mm³)

Allowable bending stress (MPa)

Deflection limit ratio L / n

Analysis sample points

Formula Used

Equilibrium is used first. The vertical reactions satisfy RA + RB = total downward load.

For a point load P at distance a from the left support, b = L - a. The reactions are RA = P b / L and RB = P a / L.

For a full uniform load w over span L, the reactions are RA = RB = wL / 2. The common maximum moment for only that load is wL² / 8.

For a partial uniform load, the resultant load equals wp(x2 - x1). It acts at the loaded length centroid. Reactions are then found by taking moments about each support.

At each sample station, shear is summed as V(x). Moment is integrated from shear using M(x). Curvature is M / EI. Numerical integration estimates deflection, with zero deflection enforced at both supports.

Bending stress is estimated by σ = M / Z. Deflection is checked against L / n, using the entered limit ratio.

How to Use This Calculator

Enter the clear span of the simply supported beam.
Add any point load and its position from the left support.
Enter a full span uniform load when the load covers the whole beam.
Use the partial load fields for a load that starts and ends inside the span.
Enter material stiffness and section inertia for deflection results.
Add section modulus and allowable stress for a simple stress check.
Press calculate. The result appears below the header and above the form.
Use the CSV or PDF buttons to save the beam report.

Example Data Table

Case	Span	Point Load	Position	Full UDL	E	I
Steel floor beam	6 m	20 kN	3 m	5 kN/m	200 GPa	80 million mm⁴
Timber joist check	4.2 m	4 kN	2.1 m	1.8 kN/m	11 GPa	22 million mm⁴
Patch load review	8 m	0 kN	0 m	2 kN/m	200 GPa	150 million mm⁴

Practical Beam Review

A simply supported beam is one of the most common structural models. It rests on two supports. One support is usually pinned. The other support is usually a roller. This arrangement lets the member rotate at the ends. It also keeps vertical movement restrained. The model is useful for floor joists, lintels, small bridges, platforms, and temporary works.

What the Numbers Mean

The first values to check are support reactions. They show how much load each bearing point must carry. Shear values help locate zones where web capacity or connection strength may control. Bending moment values show where the beam wants to sag most. Deflection estimates show service performance. A beam may be strong enough, yet still feel weak when it bends too much.

Good Input Practice

Use one consistent set of units. This calculator uses metres, kilonewtons, gigapascals, and millimetres. Moment output is shown in kilonewton metres. Deflection is shown in millimetres. Enter a realistic modulus of elasticity for the material. Steel is often near 200 GPa. Timber and concrete may be much lower. Enter the correct second moment of area from the section table.

Combined Loading

Real beams often carry more than one load. A point load can represent a machine, column, or wheel. A full uniform load can represent deck weight or distributed storage. A partial uniform load can represent a wall, patch load, or stacked material. The calculator combines these effects by equilibrium. It then samples the span to find critical shear, moment, and deflection positions.

Using Results Wisely

The output is a preliminary design aid. It does not replace a code check. Real projects may need lateral stability, bearing, vibration, buckling, load factors, and connection checks. Support settlement can also change forces. Use conservative loads. Keep a record using the CSV or PDF tools. Ask a qualified engineer when safety, public use, or unusual loading is involved.

Review Tips

Check the reported critical position before selecting a section. High moment usually occurs near midspan, but offset point loads and partial loads can move it. Also compare the deflection ratio with the project limit. Common limits include span over 240, 360, or 480. Stricter finishes need smaller movement. Always document your assumptions clearly.

FAQs

What is a simply supported beam?

It is a beam supported at two ends. One support resists vertical movement. The other allows horizontal movement. This model is common for quick bending, shear, and deflection checks.

Can I combine point and uniform loads?

Yes. Enter values in multiple load fields. The calculator adds point load, full uniform load, and partial uniform load effects using static equilibrium and span sampling.

What units should I use?

Use metres for span, kilonewtons for point loads, kilonewtons per metre for uniform loads, gigapascals for elasticity, and million mm⁴ for inertia.

Why is section inertia required?

Deflection depends on flexural stiffness, which is E multiplied by I. A larger I usually means the beam bends less under the same load.

What does the deflection ratio mean?

The ratio sets the allowed deflection as span divided by a number. For example, L/360 allows less movement than L/240.

Is the stress check final design?

No. It is a simple bending stress check. Final design may need code factors, shear strength, buckling, bearing, vibration, and connection checks.

Why are sample points included?

Sampling helps find critical locations for combined loading. More points improve location accuracy, but very high values may slow page processing.

Can this calculator handle upward loads?

This version assumes downward loads. For uplift, prestress, or support settlement, use a more detailed structural model with signed loading options.