1. **State the problem:** We have a simply supported beam with a concentrated load of 82 kN at 1.6 m from point A and a uniformly distributed load (UDL) of 45 kN/m extending 5 m from that point towards B. We need to find the distance from point A where the UDL can be replaced by a single concentrated load acting. 2. **Formula and concept:** The resultant force of a UDL is the total load, which is the intensity multiplied by the length: $$F = w \times L$$ where $w$ is the load per meter and $L$ is the length of the UDL. The point of action of this resultant force is at the centroid of the UDL, which for a uniform load is at the midpoint of the loaded length. 3. **Calculate the resultant force of the UDL:** $$F = 45 \times 5 = 225 \text{ kN}$$ 4. **Find the position of the resultant force from point A:** The UDL starts at 1.6 m from A and extends 5 m, so its midpoint is: $$1.6 + \frac{5}{2} = 1.6 + 2.5 = 4.1 \text{ m}$$ 5. **Final answer:** The UDL can be replaced by a concentrated load of 225 kN acting at 4.1 metres from point A. **Answer: 4.1 metres**