How do you choose the locations of forces when calculating moments? 
A uniform bridge of weight 1200kN and of length 17m rests on supports at each end which are 1m wide. A stationary lorry of weight 60kN has it’s centre of mass 3.0m from the centre of the bridge.
Calculate the support force on the bridge at each end.

I got the answer to be 642N and 618N. Whereas, the answer in the book says 640 and 620.
I took the distance between the two supports to be 15, should I take it as 17m, if so why?
 A: The book is correct - how many significant figures are you given the data to ?
I would probably use the middle of the supports (ie 16m) but that doesn't matter for working out the vertical forces. This question is also nothing to do with momentum, unless there is a part 2 where you work out the sideways force when the truck moves. 
A: To determine where the force acts, you need to understand the flow of stress in the supports--- the bridge is deforming the supports slightly due to its sag, and the contact is most significantly stressed at the point closest to the center of the bridge, and this is where you place the force. If the supports were metal springs instead of rigid blocks, you could calculate the deformation in each spring, and see that it is somewhat bigger nearer the center, but as the spring gets saggier, the force distributes more equally. In the limit of complete sagginess, the force is distributed over the whole meter length of the support, and in the limit of complete rigidity, it is right at the end closest to the center. Assuming complete rigidity is the closer approximation, your calculations are correct, and equal to the answer in the book to the given precision.
