Calculator Inputs
Example Data Table
| Parameter | Example Value |
|---|---|
| Layer count | 3 |
| Span length | 4.0 m |
| Composite interaction factor | 0.95 |
| Load case | Simply Supported - Center Point Load |
| Load value | 8.0 kN |
| Layer 1 | Steel, 210 GPa, 200 mm width, 20 mm thickness |
| Layer 2 | Timber, 12 GPa, 200 mm width, 80 mm thickness |
| Layer 3 | CFRP, 70 GPa, 150 mm width, 10 mm thickness |
Formula Used
1) E-weighted neutral axis
ȳ = Σ(Eᵢ Aᵢ yᵢ) / Σ(Eᵢ Aᵢ)
2) Layer area and centroidal inertia
Aᵢ = bᵢ tᵢ and Iᵢ = bᵢ tᵢ³ / 12
3) Transformed section inertia
nᵢ = Eᵢ / Eref
Itr = Σ[nᵢ (Iᵢ + Aᵢ dᵢ²)]
4) Effective flexural rigidity
EIeff = η × Σ[Eᵢ (Iᵢ + Aᵢ dᵢ²)] = η × Eref × Itr
5) Maximum deflection by load case
Simply supported, point load: δmax = P L³ / (48 EI)
Simply supported, uniform load: δmax = 5 w L⁴ / (384 EI)
Cantilever, tip load: δmax = P L³ / (3 EI)
Cantilever, uniform load: δmax = w L⁴ / (8 EI)
Fixed-fixed, point load: δmax = P L³ / (192 EI)
Fixed-fixed, uniform load: δmax = w L⁴ / (384 EI)
6) Equivalent beam stiffness
k = Weq / δmax
Here, η represents partial interaction or connection efficiency. A value of 1.0 means fully composite action, while lower values reduce the effective rigidity.
How to Use This Calculator
- Select how many layers your beam has, from one to three.
- Enter the span length in meters and the interaction factor η.
- Choose the support and loading condition that matches your beam.
- Enter the load value. Use kN for point loads and kN/m for uniform loads.
- For each layer, enter its name, elastic modulus, width, and thickness.
- Press Calculate Stiffness to display the results under the header and above the form.
- Review the neutral axis, transformed inertia, flexural rigidity, maximum deflection, and equivalent stiffness.
- Use the CSV and PDF buttons to export the result summary.
Frequently Asked Questions
1) What does composite beam stiffness mean?
It describes how strongly a layered beam resists bending. Higher stiffness means smaller deflection under the same loading and span conditions.
2) Why does the calculator use a transformed section method?
Different materials have different elastic moduli. Transforming them to a reference material lets the layered beam be combined into one equivalent section for bending calculations.
3) What is the interaction factor η?
η represents how effectively the layers act together. Perfect shear transfer is close to 1.0, while slip or weak connectors reduce the effective composite action.
4) Does the order of layers matter?
Yes. The stacking order changes the neutral axis position and the distance of each layer from it, which strongly affects the section’s bending stiffness.
5) What units should I use?
Use GPa for elastic modulus, millimeters for width and thickness, meters for span, kN for point loads, and kN/m for distributed loads.
6) What is the difference between EI and k?
EI is flexural rigidity of the section itself. k is the beam’s overall load-deflection stiffness for a chosen span, support condition, and loading case.
7) Can I use one material only?
Yes. Set the layer count to one. The calculator will then behave like a standard rectangular beam stiffness tool for the selected load case.
8) Is this suitable for final design checks?
It is useful for estimation, comparison, and quick studies. Final design should also consider shear deformation, local buckling, code rules, connection details, and safety factors.