Shear Force Bending Moment Diagram Calculator

Fundamental Relationships:

\[ V = \frac{dM}{dx} \quad \text{(opposite sign convention)} \]

Calculated Shear Force (V): N

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1. What is a Shear Force Bending Moment Diagram Calculator?

Definition: This calculator helps determine the relationship between shear force (V) and bending moment (M) at a given distance (x) along a beam.

Purpose: Essential for structural engineering to analyze beam behavior under various loads and design safe structures.

2. How Does the Calculator Work?

The calculator uses the fundamental relationship:

\[ V = \frac{dM}{dx} \quad \text{(with opposite sign convention)} \]

Where:

\( V \) — Shear force (N)
\( M \) — Bending moment (N·m)
\( x \) — Distance along beam (m)

Explanation: The shear force is equal to the negative of the slope of the bending moment diagram at any point.

3. Importance of Shear and Moment Calculations

Details: Proper analysis ensures beams can withstand applied loads without excessive deflection or failure.

4. Using the Calculator

Tips: Enter known values for any two parameters to calculate the third. Distance must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: Why the opposite sign convention?
A: This follows the standard engineering convention where positive shear causes clockwise rotation and positive moment causes compression on top.

Q2: What units should I use?
A: Consistent units are critical - N for force, N·m for moment, and m for distance.

Q3: How accurate is this calculation?
A: It provides a point estimate. For complete analysis, consider distributed loads and multiple points.

Q4: Can I calculate bending moment from shear?
A: Yes, by integrating the shear diagram, though this requires boundary conditions.

Q5: What about point loads?
A: Point loads create discontinuities in the shear diagram and slope changes in the moment diagram.