This exercise shows how to calculate the bearing reactions under sloping load.
Task
A bridge on a floating bearing and a fixed bearing is loaded by a braking car as shown. Determine the bearing reactions in A and B!

Solution
The following video is in german language. Please scroll down for the written solution.

The equilibrium of forces in the x-direction is
∑Fx=0=F⋅sinα+FBx
FBx=−F⋅sinα
The equilibrium of forces in the y-direction is
∑Fy=0=FAy−F⋅cosα+FBy
The equilibrium of moments around point A is
∑M(A)=0=−F⋅cosα⋅a+FBy⋅(a+b)
FBy=F⋅cosα⋅aa+b
From equation 3 follows
FAy=F⋅cosα−FBy
FAy=F⋅cosα−F⋅cosα⋅aa+b
FAy=F⋅cosα⋅(1−aa+b)
This was the basic exercise "bearing reactions under sloping load", used to show the appliance of fixed and floating bearings. Don't miss the other interesting exercises!