1. What is Beam Stiffness?

Beam stiffness (k) is a measure of a beam's resistance to deflection under load. For a cantilever beam, the stiffness constant is calculated using the formula \( k = \frac{3EI}{L^3} \), where E is the elastic modulus, I is the moment of inertia, and L is the length of the beam.

2. How Does the Calculator Work?

The calculator uses the beam stiffness formula:

Where:

• \( k \) — Beam stiffness (N/m)
• \( E \) — Elastic modulus (Pa)
• \( I \) — Moment of inertia (m⁴)
• \( L \) — Length of the beam (m)

Explanation: The formula shows that beam stiffness is directly proportional to the elastic modulus and moment of inertia, and inversely proportional to the cube of the beam length.

3. Importance of Beam Stiffness

Details: Calculating beam stiffness is crucial for structural engineering applications, ensuring beams can withstand expected loads without excessive deflection, and for designing stable and safe structures.

4. Using the Calculator

Tips: Enter elastic modulus in Pascals (Pa), moment of inertia in meters to the fourth power (m⁴), and length in meters (m). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is elastic modulus (E)?
A: Elastic modulus is a material property that measures its stiffness or resistance to elastic deformation under stress.

Q2: What is moment of inertia (I)?
A: Moment of inertia is a geometric property that quantifies how a beam's cross-sectional area is distributed relative to its neutral axis.

Q3: Why is beam length cubed in the denominator?
A: The cubic relationship shows that beam stiffness decreases rapidly as length increases, making longer beams much more flexible.

Q4: What types of beams does this formula apply to?
A: This formula specifically applies to cantilever beams with a point load at the free end.

Q5: How does material selection affect beam stiffness?
A: Materials with higher elastic modulus (like steel vs. wood) will produce stiffer beams for the same geometric dimensions.