1. Tech Studies - Mechanisms How to calculate moments Mr Leiper Aberdeen Grammar School V2.0 March 2006

2. How to calculate moments Sometimes a structural or civil engineer wants to know what forces are acting on say, the ends of a bridge. (A force is simply, the amount of ‘push’ that a weight exerts)

3. Example: A bus and a car are crossing a bridge. The weight of the bus is 12000N, the weight of the car is 5000N. Question: What are the reaction forces at the edges of the bridge? Also, take moments about the left hand side of the bridge. 5m 9m 10m

4. Step 1: Turn your picture into a ‘free body diagram’. (This is a diagram showing only the weights of the bus, the car, and the two reaction forces, R1 and R2, and distances) R1R2 F (bus) F (car) 5m 9m 10m

5. Think! There is a third weight that we are ignoring in this example. The bridge itself would have a weight – but we will ignore this at Standard Grade! What is it?

6. Step 2 - We need to say the first line: (and this is because the bridge is staying still) Our answer is in Newtons (ie N) ∑ clockwise moments = ∑ anticlockwise moments (5000 x 9) + (12000 x 5) = (R 2 x 10) 45,000 + 60,000 = 10 R 2 105,000 = 10 R 2 10R 2 = 105,000 R 2 = 105,000 R 2 = 10,500 N 10

7. Step 3 - Now we also know: ∑ upwards forces = ∑ downwards forces (In plain English, this means that all the forces pushing down, are equal to all the forces pushing up)

8. (This will help us find the 2 nd force that the bridge is pushing back with.) ∑ upwards forces = ∑ downwards forces R 1 + R 2 = F(car) + F(bus) R1 + 10,500 N = 5,000 N + 12,000 N R1 + 10,500 N = 17,000 N R1 = 17,000 N – 10,500 N R1 = 6,500 N This means the left hand side of the bridge has a force of 6500 N pushing down on it (and therefore the reaction force is pushing up with the same amount)