1. What is the Bending Moment Formula?

The bending moment formula \( M = \frac{E I}{\rho} \) relates the bending moment in a beam to its material properties and geometry. It describes how much a beam will bend under applied loads based on its elastic modulus, moment of inertia, and radius of curvature.

2. How Does the Calculator Work?

The calculator uses the bending moment formula:

Where:

• \( M \) — Bending moment (Nm)
• \( E \) — Elastic modulus (Pa)
• \( I \) — Moment of inertia (m⁴)
• \( \rho \) — Radius of curvature (m)

Explanation: The formula calculates the moment required to produce a specific curvature in a beam based on its material stiffness and cross-sectional properties.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for structural design, ensuring beams can withstand applied loads without excessive deformation or failure.

4. Using the Calculator

Tips: Enter elastic modulus in Pascals, moment of inertia in meters to the fourth power, and radius of curvature in meters. All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is elastic modulus (E)?
A: Elastic modulus is a measure of a material's stiffness - its resistance to elastic deformation under stress.

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

Q3: What does radius of curvature represent?
A: Radius of curvature describes how sharply a beam is bending - smaller values indicate sharper bends.

Q4: When is this formula applicable?
A: This formula applies to beams undergoing pure bending within their elastic limit (Hooke's law valid).

Q5: What are typical values for these parameters?
A: Steel E ≈ 200 GPa, aluminum E ≈ 70 GPa. I depends on cross-section shape and size. ρ varies with loading conditions.