Calculate Bending Moment Of Beam

Bending Moment Equation:

\[ M(x) = \frac{w L x}{2} - \frac{w x^2}{2} \]

Bending Moment M(x):

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1. What is Bending Moment?

Bending moment is a measure of the bending effect that occurs when an external force is applied to a structural element, causing it to bend. It's a crucial parameter in structural engineering for designing beams and other load-bearing elements.

2. How Does the Calculator Work?

The calculator uses the bending moment equation for a simply supported beam with uniform load:

\[ M(x) = \frac{w L x}{2} - \frac{w x^2}{2} \]

Where:

\( M(x) \) — Bending moment at distance x (Nm)
\( w \) — Uniform load (N/m)
\( L \) — Beam length (m)
\( x \) — Distance from left support (m)

Explanation: This equation calculates the internal bending moment at any point along a simply supported beam carrying a uniformly distributed load.

3. Importance of Bending Moment Calculation

Details: Accurate bending moment calculation is essential for structural design, ensuring beams have sufficient strength to resist applied loads without excessive deflection or failure.

4. Using the Calculator

Tips: Enter uniform load in N/m, beam length in meters, and distance from support in meters. All values must be valid (positive numbers, x between 0 and L).

5. Frequently Asked Questions (FAQ)

Q1: What is maximum bending moment for this loading condition?
A: Maximum bending moment occurs at the center of the beam (x = L/2) and equals \( \frac{w L^2}{8} \) Nm.

Q2: What are the support reactions for this beam?
A: Both support reactions equal \( \frac{w L}{2} \) N for a symmetrically loaded simply supported beam.

Q3: Does this equation work for other beam types?
A: No, this specific equation applies only to simply supported beams with uniform load. Other support conditions require different equations.

Q4: What units should I use?
A: Consistent units are important. Use Newtons for force, meters for length, and Newton-meters for bending moment results.

Q5: How does bending moment relate to beam stress?
A: Bending moment is directly related to bending stress through the formula \( \sigma = \frac{M y}{I} \), where y is distance from neutral axis and I is moment of inertia.