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Bearing reactions under sloping load

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!

Beam on two supports with sloping load
Beam on two supports with sloping load

Solution

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

Lagerreaktionen bestimmen - Technische Mechanik 1, Übung 14
Free body diagram of the beam
Free body diagram of the beam

The equilibrium of forces in the x-direction is

Fx=0=Fsinα+FBx

FBx=Fsinα

The equilibrium of forces in the y-direction is

Fy=0=FAyFcosα+FBy

The equilibrium of moments around point A is

M(A)=0=Fcosαa+FBy(a+b)

FBy=Fcosαaa+b

From equation 3 follows

FAy=FcosαFBy

FAy=FcosαFcosαaa+b

FAy=Fcosα(1aa+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!