1. What is the Cantilever Beam Bending Moment Equation?

The cantilever beam bending moment equation calculates the internal bending moment at any point along a cantilever beam with an end load. This is fundamental in structural engineering for designing beams that can withstand applied loads without failure.

2. How Does the Calculator Work?

The calculator uses the bending moment equation:

Where:

• \( M(x) \) — Bending moment at distance x from fixed end (Nm)
• \( P \) — Applied load at the free end (N)
• \( L \) — Total length of the beam (m)
• \( x \) — Distance from the fixed end (m)

Explanation: The equation shows that the bending moment decreases linearly from the fixed end (where it's maximum) to the free end (where it's zero).

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for determining the required beam size and material, ensuring structural integrity, and preventing beam failure under load.

4. Using the Calculator

Tips: Enter the applied load in Newtons, beam length in meters, and distance from the fixed end in meters. All values must be positive, and x cannot exceed the beam length.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is a rigid structural element that extends horizontally and is supported at only one end.

Q2: Where is the maximum bending moment in a cantilever beam?
A: The maximum bending moment occurs at the fixed end (x = 0) and equals P × L.

Q3: What are the units for bending moment?
A: Bending moment is typically measured in Newton-meters (Nm) in the SI system.

Q4: Does this equation account for distributed loads?
A: No, this specific equation is for a concentrated end load. Different equations are used for distributed loads.

Q5: How does beam material affect bending moment capacity?
A: Different materials have different yield strengths, which determine how much bending moment a beam can withstand before failing.