The reliable sequence
Quick start: solve a beam from beginning to end
Follow this order for a new model. Each step links to the full explanation below.
- 1Set the working units
Choose Metric or Imperial and confirm every displayed length, force, stress, and section-property unit.
- 2Enter the beam length
Use one positive span. Locations start at x = 0 on the left and increase to the right.
- 3Add supports
Place pinned, roller, end-fixed, or spring supports so the beam is stable and matches the intended idealization.
- 4Apply signed loads
Add point, distributed, and applied-moment loads using the Beam Calculator sign convention.
- 5Assign section regions
Enter E and I for stiffness. Add A and extreme-fibre distances when the corresponding stress result is needed.
- 6Run and inspect results
Review reactions, shear, bending moment, slope, deflection, and stress. Query important locations directly.
- 7Verify, save, and report
Check equilibrium and behavior independently, then save the reviewed model and export a fresh PDF.
Read the complete Beam Calculator sign convention before entering loads or interpreting signed reactions.
When to use this workspace
One straight beam under in-plane bending
Use Beam Calculator for simply supported, cantilever, fixed, overhanging, and continuous beams with one or more section regions.
Screenshot note: These annotated guide images focus on the control locations and workflow. Minor visual details can differ as the interface is refined.
Inputs
Build the beam model
Add inputs in sequence, then use the Model Inputs and Section Properties tables to verify, edit, or remove them.
Choose the unit system
Use the Metric/Imperial switch, then choose the displayed length and force units. Imperial models start in ft and kip by default, while in and lb remain available. Section-property units appear beside each property.
- Changing working units converts existing model inputs and results; it does not only relabel them.
- Spring stiffness converts with the selected force and beam-length units. See spring units; section properties and deflections retain their own displayed units.
- Re-check every value after a switch, especially A, I, and extreme-fibre distances.
- Do not enter an imperial property while a metric label is active, or the reverse.
Enter the beam length
Enter a positive length and commit the field. The left end is x = 0; x increases to the right.
After shortening a beam: Supports, loads, or section limits beyond the new right end may be removed. Re-check the input tables.
Add supports
Select a support, enter its x-location, then choose Add or Add Another. Edit or delete it in the model table. Compatible restraints can share a location, but the same vertical or rotational degree of freedom cannot be restrained twice.
For a flexible support, select the slim Spring support… button below Pinned, Roller, and Fixed. Its dialog offers Vertical, Rotational, and Both. See spring setup and shared-location rules.
Stability: The restraint pattern must prevent rigid vertical movement and uncontrolled rotation.
Spring supports
A spring develops a reaction as the beam moves or rotates at its location. Its finite stiffness allows movement; an ideal pinned, roller, or fixed restraint prevents the corresponding movement.
- Select Spring support… below the three common support types.
- Choose Vertical, Rotational, or Both, and enter the location from the left end.
- Enter a positive, finite stiffness for each selected direction in the units beside its field.
- Define positive E and I in section regions covering the full beam, then select Run.
Both adds independent vertical and rotational springs at the same location. They appear as separate rows in the model table, where each stiffness can be edited or removed.
Stiffness and units
Vertical stiffness, kᵥ
Force per unit vertical displacement. Defaults: kN/m in metric and kip/ft in imperial.
For example, 1000 kN/m gives a reaction magnitude of 1 kN for 1 mm of displacement. Convert the displacement to metres when checking that relationship.
Rotational stiffness, kθ
Moment per unit rotation. Defaults: kN·m/rad in metric and kip·ft/rad in imperial.
For example, 100 kN·m/rad gives a moment magnitude of 1 kN·m for 0.01 rad of rotation, about 0.573°. Slope results are displayed in degrees; stiffness is always per radian.
Stiffness units follow your selected force and beam-length units: choosing N and mm gives N/mm and N·mm/rad. Changing units converts the stored stiffness automatically. The desktop model table and PDF place the spring unit beside its value; mobile rows include it in the field label.
Sharing a support location
- Allowed: a rotational spring with a pin, roller, or vertical spring. These act on different degrees of freedom.
- Not allowed: two vertical restraints or two rotational restraints at the same location. For example, a vertical spring cannot share with a pin or roller.
- A fixed support already restrains both directions, so no additional support or spring can share its location.
Stability: One vertical spring alone leaves free rotation, and one rotational spring alone leaves free vertical movement. Provide two separated vertical restraints, or a vertical restraint together with a rotational restraint.
Springs are linear and act in both directions relative to a stationary support. Rotational springs resist rotation in the beam’s bending plane. Compression-only contact, uplift release, nonlinear stiffness, and torsion about the beam axis are not modeled.
Apply loads
- Equal distributed intensities create a uniform load.
- One zero intensity creates a triangular load.
- Unequal nonzero intensities create a trapezoidal load.
- Distributed-load start and end values must act in the same direction; change both signs to reverse it.
Example: Enter +8 for an 8 kN downward point load or −8 for an 8 kN upward point load.
Define section and material properties
Open Section Properties. Choose a standard or saved section, or enter properties directly. Set the start and end of the beam interval, then choose Add to beam.
Under Standard Sections, choose a region, optionally narrow the list by shape, and select a section. If you know its designation, choose Search by name to search across libraries. The picker uses the same catalog as Steel Beam Sizes. Select a result to fill its area, x-axis moment of inertia, and top and bottom fibre distances in your current units. Your material, modulus E, and beam interval stay as entered.
Saved models and stored personal sections retain their saved property values, including older or custom sections. Catalog updates do not change those values when you reopen a model. To use updated catalog properties, explicitly select a section and update the model's section.
| Property | Meaning | Used for |
|---|---|---|
E | Modulus of elasticity | Flexural stiffness, slope, and deflection |
I | Second moment of area about the bending axis | Flexural stiffness, slope, and deflection |
A | Cross-sectional area | Average shear-stress output |
y-top | Neutral axis to top extreme fibre | Top-fibre bending stress |
y-bottom | Neutral axis to bottom extreme fibre | Bottom-fibre bending stress |
- Section regions cannot overlap; use adjacent limits for a stepped beam.
- Cover every span region that needs stiffness, slope, deflection, or stress results.
- For any spring model, positive E and I must cover the full beam without gaps or overlaps, even when you only need reactions or internal forces.
- Confirm I and y-values use the intended bending axis.
Analyze and interpret
Run and read Beam Calculator results
Review the input tables, select Run, and resolve any validation message before using the results.
Support reactions
Support reactions retain their signed values, with arrows and direction labels to clarify how they act on the beam. Spring Force is a vertical spring reaction; Spring Moment is a rotational spring reaction. Include both when checking equilibrium.
Shear diagram
Signed internal shear along x. Point forces create jumps; distributed loading changes the diagram slope.
Moment diagram
Positive is sagging and negative is hogging. Local moment peaks commonly occur where shear crosses zero.
Slope
Rotation of the beam centreline, displayed in degrees. A rotational spring can rotate while developing a moment; an ideal fixed support has zero rotation.
Deflection
Transverse displacement based on flexural stiffness. Check support displacement and whether the shape matches the loading.
Stress
Bending stress uses M, I, and extreme-fibre distance. Average shear stress uses V and A and is not a detailed through-depth distribution.
Extreme-value summaries identify governing signed values; a location query is better for a support face, splice, connection, or other point of interest.
Beam Calculator reference
Sign conventions
Use this table for every signed Beam Calculator input and result.
Position x starts at the left end and increases to the right.
| Quantity | Positive (+) | Negative (−) |
|---|---|---|
| Point load | Downward | Upward |
| Distributed-load intensity | Downward | Upward |
| Applied moment | Clockwise | Counter-clockwise |
| Signed force reaction, including Spring Force | Downward | Upward |
| Signed moment reaction, including Spring Moment | Clockwise | Counter-clockwise |
| Internal bending moment | Sagging | Hogging |
| Diagram ordinate | Signed positive value | Signed negative value |
For example, −20 kN is shown with ↑ Upward. The signed value remains consistent with the load convention; the arrow and wording clarify its physical direction on the beam.
Keep a calculation record
Save, reopen, and export a beam model
Save and reopen
- Use Save to name a new model or update the currently open model.
- Use Save As before exploring a separate design or load variation.
- Use Open to search models and folders.
- Check the unsaved-change indicator before replacing the current model.
Saving, model counts, and folders depend on the account plan.
PDF calculation report
- Run the current model so the results are fresh.
- Select PDF Export.
- Add the available project, author, notes, and branding details.
- Download and inspect every page before sharing the report.
Check that inputs, section regions, units, reactions, diagrams, assumptions, and revision information match the intended model. Spring stiffness units appear beside the spring values in the PDF; spring reactions include their physical directions.
Assisted setup
Use Optimal AI as a model draft
Describe the working units, beam length, support types and locations, and every signed load. The proposed inputs can speed up setup, but section requests and generated values still require manual confirmation.
Example prompt: “Create a 6 m simply supported beam with a pin at 0 m, a roller at 6 m, and a 12 kN downward point load at 2 m.”
Review every support, location, load sign, and property in the input tables. Then run the deterministic solver and complete the normal checks.
Know the idealization
Assumptions and limits
Included
- One straight beam under in-plane, static transverse loading.
- Linear-elastic stiffness based on entered E and I.
- Ideal pinned, roller, and fixed restraints, plus linear vertical and rotational springs.
- Determinate and indeterminate response using stiffness-based analysis.
- Piecewise section properties along the span.
Not included
- Code resistance, load factors, or a serviceability acceptance decision.
- Connection, bearing, bracing, lateral-torsional buckling, or local-buckling design.
- Torsion, lateral loading, dynamics, construction stages, or nonlinear behavior.
- A detailed through-depth shear-flow calculation.
- Support or connection behavior beyond the entered linear spring stiffness, including compression-only or nonlinear response.
For the calculation method, see Beam theory and the matrix stiffness method.
Before relying on results
Beam review checklist
Fix common problems
Beam Calculator troubleshooting
The beam is unstable or cannot be solved+
Confirm the support pattern prevents rigid vertical movement and rotation. Check for duplicate restraints on the same degree of freedom, locations outside the beam, or an unintended free beam. Compatible restraints may share a location; see spring support rules.
A spring model will not run+
Each spring stiffness must be a positive, finite number. Define positive E and I over the full beam with no section gaps or overlaps, even for a reaction-only calculation. Check the shared-location rules and overall stability. To remove a restraint, delete its row rather than enter zero stiffness.
A spring support has nonzero deflection or rotation+
This is expected for finite spring stiffness. Check the displacement or rotation at the spring’s location and its reaction. Use consistent displacement units for a vertical spring; convert the displayed slope from degrees to radians before checking a rotational spring’s stiffness.
A load or reaction points the wrong way+
For load inputs, positive force is downward, negative force is upward, positive applied moment is clockwise, and negative applied moment is counter-clockwise. Reaction values use the same signs, with arrows and words showing their physical direction on the beam.
Slope or deflection is missing+
Assign positive E and I over every beam region where stiffness results are needed, confirm region limits do not overlap, and run the model again.
A stress result is missing+
Bending stress needs M, I, and the relevant y-top or y-bottom distance. Average shear stress needs shear force and area A. Add the missing properties and rerun.
Results do not reflect the latest edit+
Select Run after changing length, supports, loads, or section properties. Export reports only after the latest analysis finishes.
A section region is rejected or results stop at a location+
Confirm each start is less than its end, all limits lie on the beam, and regions do not overlap. Use adjacent boundaries to describe a stepped beam and cover all required locations.
A result is many orders of magnitude too large or small+
Check E and I first. Confusing mm⁴, m⁴, and in⁴ changes flexural stiffness enormously. Also confirm load intensity units and the beam length unit.
The model cannot be saved+
Confirm you are signed in, the model has a valid name, and the current plan permits another model or revision. Use Save As only when you intend to create a separate copy.
The PDF is blank, incomplete, or fails to export+
Run the model, wait for results, and retry with default branding. Replace any invalid logo and confirm the browser allows the download. If it persists, contact support with the browser and exact error.
Quick reference
Beam symbols and terms
- x
- Location along the beam, measured from the left end.
- E
- Modulus of elasticity describing linear-elastic material stiffness.
- I
- Second moment of area about the bending axis.
- A
- Cross-sectional area.
- V
- Internal shear force.
- M
- Internal bending moment; positive sagging and negative hogging.
- kᵥ
- Vertical spring stiffness: force per unit displacement.
- kθ
- Rotational spring stiffness: moment per radian of rotation.
- rad
- Radian, the angle unit used for rotational stiffness. One radian is approximately 57.296°.
- Slope
- Rotation of the beam centreline, displayed in degrees.
- Deflection
- Transverse displacement of the beam centreline.
- Reaction
- Support force or moment required to satisfy equilibrium and compatibility.
- Section region
- A beam interval assigned one set of material and geometric properties.
Responsible use
Analysis supports judgment; it does not replace it.
The user remains responsible for the beam idealization, inputs, load combinations, code requirements, interpretation, independent checks, and decisions affecting safety or construction.