Simply Supported Beam Analysis

This quiz tests your understanding of bending moment calculations for simply supported beams under uniform distributed loads.

Key Concepts

For a simply supported beam with uniform distributed load:

• The maximum bending moment occurs at midspan
• The formula for maximum moment is: $M_{max} = -\frac{wL^2}{8}$
• Where:
  • $w$ = uniform distributed load (kN/m)
  • $L$ = beam length (m)

Sign Convention

In this problem, we use the convention where:

• Positive moments cause compression in the top fiber
• Negative moments cause tension in the top fiber
• For a simply supported beam with downward load, the moment at midspan is negative

Solution Steps

1. Identify the beam parameters: $L = 6$ m, $w = 4$ kN/m
2. Apply the formula: $M = -\frac{4 \times 6^2}{8}$
3. Calculate: $M = -\frac{4 \times 36}{8} = -\frac{144}{8} = -18 \times 4 = -72$ kN·m

Important Notes

Remember to include the negative sign in your answer, as it indicates the direction of the bending moment according to our sign convention.