Engineering Statics

D-8


The shelf ABC is held horizontally by a self-locking brace which ocnsists of two parts, BDE and EDF, hinged at E and bearing against each other at D. Knowing that the shelf is 16 inches wide and weighs 39.5 lbs, determine the force P required to release the shelf. (Hint: To release the brace, the forces of contact at D must be zero.)

A FBD of member ABC is drawn.

The vertical components of force at B and C have been found.  B is up and 
C is down.
The geometry of BEF is established.
The FBD of BEF is drawn, paying special attention to the fact that P is 
not perpendicular to BE.  In addition the proportionality of the geometry 
and the components of B is established.
Since the y component of B was found from the FBD of ABC, the x component 
of B can now be found.
The moment equation about F will allow us to solve for P.