Beam and Loading Details
Example Data Table
| Case | Support | Load | E | L | Section | Output (k) |
|---|---|---|---|---|---|---|
| Steel beam | Simply supported | P = 10 kN at midspan | 200 GPa | 6 m | Rect 300×500 mm | Computed by k = P/δ |
| Concrete member | Fixed–fixed | w = 2 kN/m | 30 GPa | 5 m | Rect 250×600 mm | Computed by k = (wL)/δ |
| Cantilever arm | Cantilever | P = 2 kN at free end | 210 GPa | 2 m | Circular d = 100 mm | Computed by k = P/δ |
Formula Used
This calculator uses classic Euler–Bernoulli beam relationships, where deflection is inversely proportional to flexural rigidity E·I. The equivalent translational stiffness is defined as:
k = F / δ
Point load (P)
- Cantilever, end load: δ = P·L³ / (3·E·I) ⇒ k = 3·E·I / L³
- Simply supported, midspan load: δ = P·L³ / (48·E·I) ⇒ k = 48·E·I / L³
- Fixed–fixed, midspan load: δ = P·L³ / (192·E·I) ⇒ k = 192·E·I / L³
Uniform distributed load (w)
For distributed load, the calculator uses an equivalent resultant force W = w·L, then computes k = W/δ.
- Cantilever, uniform load: δ = w·L⁴ / (8·E·I)
- Simply supported, uniform load: δ = 5·w·L⁴ / (384·E·I)
- Fixed–fixed, uniform load: δ = w·L⁴ / (384·E·I)
End moment (M) on a cantilever
- Rotation: θ = M·L / (E·I) and rotational stiffness kθ = M/θ = E·I/L
- Tip deflection from moment: δ = M·L² / (2·E·I)
How to Use This Calculator
- Select a unit system that matches your project documents.
- Choose the support condition that matches the real beam.
- Pick the load type and enter the magnitude in proper units.
- Enter elastic modulus for the material being evaluated.
- Define the section by dimensions or input the I value directly.
- Press Calculate to view stiffness, deflection, and E·I results.
- Use the export buttons to attach results to reports.
Beam Stiffness in Construction Practice
1) Why stiffness matters on site
Beam stiffness controls serviceability: vibration, cracking, ceiling alignment, door operation, and finishes. Even when strength checks pass, excessive deflection can trigger rework, callbacks, or premature damage. Tracking stiffness early helps coordinate structural, architectural, and MEP constraints without late changes.
2) What this calculator reports
The tool computes maximum deflection for the chosen load case and converts that response into an equivalent translational stiffness k = F/δ. It also reports E·I, the flexural rigidity, so you can separate material effects (E) from geometry effects (I) when comparing options.
3) Material data you should verify
Elastic modulus values vary with grade, curing, and moisture. Structural steel is commonly near 200 GPa, while normal-weight concrete is often 25–35 GPa for short-term response. Timber can vary widely by species and direction. Use project specifications or verified design references, not generic averages, when accuracy matters.
4) Section geometry drives I
The second moment of area is strongly affected by depth: for rectangles, I = b·h³/12. Doubling depth increases I by eight times, which typically improves deflection performance more than modest material upgrades. When using composite sections, confirm the effective I about the bending axis you are evaluating.
5) Support conditions change deflection
End fixity significantly alters stiffness. A fixed–fixed beam under midspan point load deflects far less than a simply supported beam of the same E·I and span. Field reality may fall between idealized cases due to connection slip, bearing deformation, or staged construction. Model supports conservatively when the boundary behavior is uncertain.
6) Load case selection and “equivalent k”
Point loads represent concentrated reactions from frames, posts, or equipment. Uniform load approximates slab tributary weight or continuous façade line loads. For uniform load, the calculator uses the resultant W = w·L to define an equivalent stiffness, making comparisons straightforward across span changes and alternative layouts.
7) Serviceability limits as a decision guide
Many projects check deflection limits such as L/360 or L/480 depending on occupancy, finishes, and vibration sensitivity. Use the calculated δ to assess whether the beam meets the chosen criterion under relevant load combinations. If δ is high, consider increasing depth, improving fixity, or reducing span with intermediate support.
8) Reporting, QA, and coordination benefits
Exportable results help document assumptions and support design reviews. Store the CSV with your calculation package and include the PDF in submittals when comparing alternates. Consistent reporting improves QA checks, enables quick peer review, and helps teams align on design intent across disciplines.
FAQs
1) What does “beam stiffness” mean here?
It is an equivalent translational stiffness defined as load divided by maximum deflection for the selected case. It lets you compare beam options quickly using a single, consistent metric.
2) Why do my results change when I switch supports?
Support conditions control how bending and rotation develop. Fixed ends reduce rotation and deflection, so stiffness increases. Real connections can be semi-rigid, so results are an idealized reference.
3) Can I use this for continuous multi-span beams?
This calculator covers common single-span ideal cases. For continuous beams, use a frame analysis method or software, then you may still compare spans by evaluating local E·I and deflection targets.
4) What if I already know the second moment of area?
Select “Use I directly” and enter the value with its unit. This is useful for rolled sections, built-up members, or when you obtain I from manufacturer tables and design catalogs.
5) How should I pick E for concrete?
Use the value specified by your design standard or project documents. Concrete modulus depends on strength, density, and age; short-term and long-term effects differ. For critical checks, follow code guidance.
6) Why is the moment case limited to cantilevers?
The implemented moment formulas correspond to a fixed–free beam with an end moment. Other support configurations require different boundary conditions and coefficients; they can be added if you have a target case.
7) Are shear deformations included?
No. The model uses Euler–Bernoulli beam theory, which neglects shear deformation. For deep beams, short spans, or soft materials, consider Timoshenko methods or consult a structural engineer.