1. What is the Bending Moment Equation?

The bending moment at any point along a beam is equal to the integral of the shear force from the start of the beam to that point. This relationship is fundamental in structural analysis and beam design.

2. How Does the Calculator Work?

The calculator uses the bending moment equation:

Where:

• \( M(x) \) — Bending moment at position x (Newton-meters)
• \( V(t) \) — Shear force function (Newtons)
• \( x \) — Position along the beam (meters)
• \( t \) — Integration variable (meters)

Explanation: The equation calculates the accumulated bending effect by integrating the shear force distribution along the beam's length.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is crucial for determining beam deflections, stress distributions, and ensuring structural integrity in engineering designs.

4. Using the Calculator

Tips: Enter the shear force function in terms of t (e.g., "5*t^2 + 3*t + 2"), the position x along the beam in meters. All values must be valid (position > 0).

5. Frequently Asked Questions (FAQ)

Q1: What units should be used?
A: Use consistent units - Newtons for force and meters for length. The bending moment will be in Newton-meters.

Q2: How accurate is this calculation?
A: The accuracy depends on correctly inputting the shear force function and position. The calculator performs symbolic integration of the given function.

Q3: What types of beams can this be used for?
A: This can be used for any statically determinate beam where the shear force function is known.

Q4: Can this handle point loads?
A: Yes, but the shear force function must properly represent any discontinuities from point loads.

Q5: What about distributed loads?
A: Distributed loads should be included in the shear force function input.