Stiffness of Cantilever Beam Calculator

Stiffness Formula:

\[ \kappa = \frac{3 \times E \times I}{L^3} \]

Stiffness (κ):

1. What is Stiffness of Cantilever Beam?

Definition: The stiffness of a cantilever beam represents its resistance to deflection under load, measured as the force required to produce unit displacement.

Purpose: This calculation is essential in structural engineering to ensure beams can withstand expected loads without excessive deflection.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \kappa = \frac{3 \times E \times I}{L^3} \]

Where:

\( \kappa \) — Stiffness (N/m)
\( E \) — Young's Modulus (Pa)
\( I \) — Moment of Inertia (m⁴)
\( L \) — Beam length (m)

Explanation: The stiffness increases with material stiffness (E) and cross-section stiffness (I), but decreases dramatically with beam length (L³).

3. Importance of Stiffness Calculation

Details: Proper stiffness calculation ensures structural integrity, prevents excessive vibrations, and maintains serviceability of cantilever structures.

4. Using the Calculator

Tips: Enter Young's Modulus, Moment of Inertia, and Total Length. All values must be > 0. The ±5% indicates typical tolerance ranges.

5. Frequently Asked Questions (FAQ)

Q1: What affects cantilever beam stiffness most?
A: Length has the greatest effect (cubed relationship), followed by moment of inertia and material properties.

Q2: Why is Young's Modulus important?
A: It quantifies the material's inherent stiffness - higher values mean stiffer materials.

Q3: How do I find Moment of Inertia?
A: It depends on cross-section shape - use standard formulas or engineering tables.

Q4: What units should I use?
A: Consistent SI units (Pa, m⁴, m) will give stiffness in N/m.

Q5: Does this account for large deflections?
A: No, this is linear theory valid for small deflections only.