Bending Moment Shear Force Calculator

Formulas:

\[ M = \frac{w L^2}{8} \] \[ V = \frac{w L}{2} \]

Bending Moment (M):

Shear Force (V):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Bending Moment and Shear Force?

Bending moment (M) and shear force (V) are fundamental concepts in structural engineering that describe the internal forces and moments in beams under load. The bending moment represents the moment that causes bending, while shear force represents the force that causes sliding.

2. How Does the Calculator Work?

The calculator uses the standard formulas for a simply supported beam with uniform load:

\[ M = \frac{w L^2}{8} \] \[ V = \frac{w L}{2} \]

Where:

\( w \) — Uniform load (N/m)
\( L \) — Length of the beam (m)
\( M \) — Maximum bending moment (N·m)
\( V \) — Maximum shear force (N)

Explanation: These formulas calculate the maximum bending moment at the center of the beam and the maximum shear force at the supports for a simply supported beam with uniform distributed load.

3. Importance of Bending Moment and Shear Force Calculation

Details: Accurate calculation of bending moment and shear force is crucial for structural design, ensuring beams can safely support applied loads without excessive deflection or failure.

4. Using the Calculator

Tips: Enter uniform load in N/m and beam length in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams do these formulas apply to?
A: These formulas are specifically for simply supported beams with uniform distributed load across the entire span.

Q2: How do point loads affect bending moment and shear force?
A: Point loads create different moment and shear diagrams. The formulas would be different for point load conditions.

Q3: What are typical units for these calculations?
A: Common units include N/m for load, meters for length, N·m for bending moment, and N for shear force.

Q4: How does beam material affect these calculations?
A: The material properties (strength, elasticity) determine if the calculated moments and forces are within safe limits, but don't affect the basic calculations shown here.

Q5: Are there limitations to these formulas?
A: Yes, these are simplified formulas for ideal conditions. Real-world applications may require more complex analysis considering factors like support conditions, load combinations, and safety factors.