Imagine you're designing a balcony supported by a cantilever beam. The beam is fixed at one end (attached to the building) and free at the other. You need to ensure that the deflection of the beam is within safe limits to prevent structural issues and ensure the safety of the occupants.

Calculation:

Let's calculate the deflection at the free end of the beam using the formula:

Example Values:

• F = 5000 N (500 kg balcony weight)
• L = 3 meters
• E = 200 GPa (Steel)
• I = 8 × 10⁻⁶ m⁴ (Rectangular cross-section)

Using these values in the formula:

δ = (3 × 5000 × 3³) / (200 × 10⁹ × 8 × 10⁻⁶) = 0.014 m (14 mm)

So, the deflection at the free end of the beam is 14 mm, which should be checked against allowable deflection limits for safety.