support force question

hey, i need help with a question

a uniform bridge span of weight 1200kN and of lenghth 17.0m rest on a support of width 1.0m at either end.

A stationary lorry of weight 60kN is the only object on the bridge.
its centre of mass is 3.0m from the centre of the bridge.

calculate the support force on the bridge at each end

ive kind of done through trial and error can some explain how to do it properly.

thanks

Reply 1

azhao

Take moments about each side of the bridge, factoring in the mass of the bridge/center of mass, mass of the lorry/position and reaction force/length of bridge.

Reply 2

devan5

i still dont understand

Reply 3

azhao

Does the 17m include the length of supports?

Take moments about 1 support, say this is the side the lorry is on. R=Reaction of the other support. So 16xR=8x1200k + 5x60k. So rearrange for R of the opposite support. For R of the support you take moments about the total downwards force = total reaction. Call this reaction A
=> A+R=60k+1200k