Beam Stiffness Calculator

Model span behavior, flexural rigidity, and stiffness instantly. Review support choices and load cases clearly. Plan safer members using formulas, charts, tables, and exports.

Calculator form

Use direct inertia when a supplier, engineer, or section table already provides I.

Example data table
Beam case Span E I Load Typical use
Simply supported, center load 6.0 m 200 GPa 5.40 × 109 mm⁴ 25 kN Steel floor beam check
Simply supported, UDL 5.0 m 11 GPa 1.82 × 109 mm⁴ 8 kN/m Timber joist screening
Cantilever, end load 2.4 m 200 GPa 8.90 × 108 mm⁴ 6 kN Canopy bracket estimate
Fixed-fixed, UDL 4.8 m 30 GPa 3.10 × 109 mm⁴ 12 kN/m Concrete transfer strip
Formulas used
Flexural rigidity: EI, where E is elastic modulus and I is second moment of area.
Rectangular section: I = b h³ / 12
Solid circular section: I = π d⁴ / 64
Hollow circular section: I = π (D⁴ − d⁴) / 64
Cantilever, end load: δmax = PL³ / (3EI), so k = 3EI / L³
Cantilever, UDL: δmax = wL⁴ / (8EI), with equivalent stiffness k(eq) = W / δmax and W = wL
Simply supported, center load: δmax = PL³ / (48EI), so k = 48EI / L³
Simply supported, UDL: δmax = 5wL⁴ / (384EI), with equivalent stiffness based on total load W = wL
Fixed-fixed, center load: δmax = PL³ / (192EI), so k = 192EI / L³
Fixed-fixed, UDL: δmax = wL⁴ / (384EI), with equivalent stiffness based on total load W = wL
How to use this calculator
  1. Choose the beam case that best matches the real support and load arrangement.
  2. Enter span length and select the correct length unit.
  3. Enter the material elastic modulus using GPa, MPa, or Pa.
  4. Choose a section mode, then either enter dimensions or provide moment of inertia directly.
  5. Enter the point load or distributed load using the matching unit.
  6. Press the calculate button to show stiffness, deflection, rigidity, and the graph above the form.
  7. Use the CSV or PDF buttons to save the result summary for review or sharing.
  8. Check the span-deflection screen, then verify final design decisions against your governing code and a qualified engineer.
FAQs

1. What does beam stiffness mean?

Beam stiffness describes how strongly a member resists bending under load. Higher stiffness means less deflection for the same span, support condition, material, and section geometry.

2. Why is EI important?

EI combines material stiffness and section geometry into one value. A larger elastic modulus or a larger moment of inertia increases flexural rigidity and reduces beam deflection.

3. Why do support conditions change the answer so much?

Restraint changes the beam curvature pattern. A fixed-fixed beam usually deflects much less than a simply supported beam, while a cantilever is often the most flexible case.

4. Can I use this for steel, timber, or concrete members?

Yes. Enter the correct elastic modulus and a realistic section moment of inertia. The calculator then applies the selected beam formula using consistent units.

5. For a distributed load, what load value should I enter?

Enter the load intensity per unit length, such as kN/m. The calculator internally converts it to total load where needed for equivalent stiffness output.

6. What if I already know the moment of inertia?

Use the direct inertia mode. That is useful when you already have section properties from a catalog, software model, or manufacturer table.

7. Is the L/360 result enough for final design?

No. It is only a quick screen. Final design should also check bending, shear, vibration, local stability, creep, connection behavior, and your governing code requirements.

8. Can this replace a full structural analysis?

No. It is best for fast preliminary checks and education. Complex framing, multiple spans, unusual loads, or nonlinear behavior need fuller analysis.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.