1. What is Shear Distribution in Cantilever Beams?

A cantilever beam is a rigid structural element that extends horizontally and is supported at only one end. The shear distribution describes how internal shear forces vary along the length of the beam when subjected to external loads.

2. How Does the Calculator Work?

The calculator uses the shear distribution formula:

Where:

• \( V(x) \) — Shear force at position x (N)
• \( P \) — Applied force at the free end (N)
• \( x \) — Position along the beam from fixed end (m)
• \( L \) — Total length of the beam (m)

Explanation: This formula calculates the internal shear force at any point along a cantilever beam with a point load applied at the free end.

3. Importance of Shear Force Calculation

Details: Understanding shear distribution is crucial for structural design, ensuring beams can withstand applied loads without failure, and determining appropriate dimensions and materials.

4. Using the Calculator

Tips: Enter the applied force in Newtons, position along the beam in meters, and total beam length in meters. All values must be positive, and position cannot exceed beam length.

5. Frequently Asked Questions (FAQ)

Q1: What is a cantilever beam?
A: A cantilever beam is fixed at one end and free at the other, commonly used in construction, bridges, and various engineering applications.

Q2: How does shear force vary along the beam?
A: Shear force is maximum at the fixed end (equal to P) and decreases linearly to zero at the free end.

Q3: What are the limitations of this formula?
A: This formula applies specifically to a single point load at the free end. Different load configurations require different formulas.

Q4: How is this different from bending moment?
A: Shear force represents internal forces perpendicular to the beam's axis, while bending moment represents internal moments that cause bending.

Q5: What units should I use?
A: Use consistent units - typically Newtons for force and meters for distance, though any consistent unit system will work.