Worked example 10.4: Truck crossing a bridge
Question: A truck of mass
is crossing a uniform horizontal
bridge of mass
and length
. The bridge is
supported at its two end-points. What are the reactions at these supports when the
truck is one third of the way across the bridge?
Answer: Let
and
be the reactions at the bridge supports. Here,
is the
reaction at the support closest to the truck. Setting the net vertical force acting on
the bridge to zero, we obtain
Setting the torque acting on the bridge about the left-most support to zero, we get
Here, we have made use of the fact that centre of mass of the bridge lies at its midpoint. It follows from the above two equations that
and