Question

A 10000 N vehicle is stalled 1/4 of the way across a bridge. The bridge is 20m in length, from support to support. The bridges weight of 50,000N is uniformly distributed.
<-------20m----->
Fa---(Car)--------Fb
<--5m-->
a) find the support force of Fb

b) find the support force of Fa

Answer 1

a:
supposing this is no space bridge or something on high altitude we can analyse the forces equation by taking a point on the bridge (I choose point a (where Fa is placed)).
and I calculate the momenta around that point of the forces. The sum of the moments should be zero as the construction is in statical balance, and point a does not take up any moments, only translational forces.
The car makes a moment clockwise (clockwise is +) of 10000N*5m = 50000Nm
The point b of the bridge should therefore make the same moment of -50000Nm
The force Fcb is therefore -50000Nm/20m = 2500 Newton
Than I add half off the bridges weight : 25000N
Fb = 27500N
b:
to get the
now I take the the point b for my balance equation
in point b we have following moments:
Mb = 0 = Fca*20m - 10000N*15m
Solve for Fca = 150000N/20 = 7500N
I add half of the bridges weight and get
Fa = 57500N

Answer 2

ok a bit fuzzy, but the priciple is that one can calculate first the forces on the points a and b from one weight (ex the car), just like there are no other forces, then the forces of the other weight (the bridge), and add them.(superposition of forces)