You're designing a bridge where the beam is simply supported at both ends. You need to calculate the maximum deflection in the middle of the beam when a load (e.g., a vehicle) is placed on it.

Calculation:

For a simply supported beam with a point load in the center, the deflection is given by:

Example Values:

• F = 10000 N (1000 kg vehicle weight)
• L = 10 meters
• E = 210 GPa (Steel)
• I = 5 × 10⁻⁶ m⁴ (Rectangular cross-section)

Using these values in the formula:

δ = (10000 × 10³) / (48 × 210 × 10⁹ × 5 × 10⁻⁶) = 0.019 m (19 mm)

So, the maximum deflection in the middle of the beam is 19 mm, which should be within acceptable limits for bridge design.