Engineering Statics

C-15


Two slots have been cut into plate DEF, and the plate has been placed so that the slot fit two fixed, frictionless pins, A and B. Knowing that P is 15 lb., determine the force each pin exerts on the plate and the reaction at point F.

Since the reaction at F is through a roller, only a vertical 
force can be transmitted.  The slots are frictionless, hence 
the forces there are perpendicular to the slots.  (If there 
were a horizontal force at F, the roller would roll.  Similarly 
if there were a force component along the slot the pins would slide.
The slanted slot is the only location where an unknown 
force has a component in the x-direction.  Chosing the 
force equilibrium equation in the x-direction first, 
allows us to solve for one unknown.
The moment equation about point A again allows us to write 
one equation with one unknown.
Solving for F gives us a downward force.
Now the force equation in y direction only has one 
unknown left.
Solving, gives us an upward force at A.