Engineering Statics

D-2


Determine the components of the reactions at D and E if the frame is loaded by a clockwise couple of magnitude 150N-m applied (a) at point a, (b) at point B.

A FBD can be made of the entire structure.  Note that no 
attention is paid to members of the structure.  Since D and 
E are pinned connection, x and y components exist at both 
points but no moments exist there.
If the moment equation is written about point D, the 
vertical reaction at E is easily found.
The force equilibrium equation in the y direction yield 
the vertical value at D.
The force equation in the x direction yields a relationship 
between the x components of the forces at D and E.  Note 
that in the FBD both D<sub>x</sub> and E<sub>x</sub> are 
drawn to the right, hence the minus sign when the equation 
is solved.
A FBD is drawn of member ACD. The pinned connections at 
C and D have two vector components each.  For member 
BCE only CE needs to be drawn since no loads or moments 
exist to the left of C.
If the force equation in the x-direction is wirtten for 
member ACD, a relationship between the x-components of 
C and and E is found.
If the force equation in the y-direction is wirtten for 
member ACD, a relationship between the y-components of 
C and and E is found.
Since CE is a two force member a relationship between 
the x and y components of C and the magnitude CE can 
be expressed.
If the moment equation about C for member ACD is written 
a relationship between the x and y components of D is obtained.
Since D<sub>y</sub> has already been found, D<sub>x</sub> 
is gotten.
Since D<sub>x</sub> has already been found, E<sub>x</sub> 
is gotten.
Since D<sub>x</sub> has already been found, E<sub>x</sub> 
is gotten.