Beam Shear And Moment Calculator

Beam Shear and Moment Formulas:

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

Shear Force (V):

Maximum Moment (M):

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1. What is Beam Shear and Moment Calculation?

Beam shear and moment calculation determines the internal forces in a simply supported beam under uniform load. Shear force (V) represents the internal force parallel to the beam's cross-section, while bending moment (M) represents the internal moment that causes bending.

2. How Does the Calculator Work?

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

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

Where:

\( w \) — Uniform load (lb/ft)
\( L \) — Beam length (ft)
\( V \) — Maximum shear force (lb)
\( M \) — Maximum bending moment (lb-ft)

Explanation: For a simply supported beam with uniform load, the maximum shear occurs at the supports and equals half the total load. The maximum moment occurs at the midspan and equals wL²/8.

3. Importance of Shear and Moment Calculation

Details: Accurate shear and moment calculations are essential for structural design, ensuring beams can safely support applied loads without failure due to shear or bending stresses.

4. Using the Calculator

Tips: Enter uniform load in lb/ft and beam length in ft. Both values must be positive numbers. The calculator provides maximum shear force and bending moment.

5. Frequently Asked Questions (FAQ)

Q1: What types of beams does this calculator apply to?
A: This calculator applies specifically to simply supported beams with uniformly distributed loads.

Q2: What are typical units for these calculations?
A: Common units are lb/ft for load, ft for length, lb for shear, and lb-ft for moment. Metric units (N/m, m, N, N-m) can also be used with appropriate conversions.

Q3: Where does maximum shear occur in a simply supported beam?
A: Maximum shear occurs at the supports for a uniformly loaded simply supported beam.

Q4: Where does maximum moment occur in a simply supported beam?
A: Maximum bending moment occurs at the midspan (center) of a uniformly loaded simply supported beam.

Q5: Can this calculator be used for other loading conditions?
A: No, this calculator is specifically designed for uniformly distributed loads on simply supported beams. Other loading conditions require different formulas.