A three span continuous pedestrian bridge has one straight span and two equal curved spans $($making a quarter$-$circle$)$ as

shown in plan below.

The fixed and guided bearings are shown as black dots on the plan, with their coordinates in metres. The left abutment

has a fixed bearing, pier $1,$ pier $2$ and the right abutment have guided bearings. At the right abutment the bridge is

required to move in the $Y$ direction when it expands or contracts.

The bridge is concrete with a coefficient of thermal expansion of $12{10}^{-6}$ per $C.$

Calculate the angle of orientation of the three guided bearings with respect to the $x$ axis.

Draw the bridge plan and show the orientation of each guided bearing on your plan of the bridge.

Calculate the movement of each guided bearing for a bridge temperature rise of $40C.$