Engineering Statics

C-13


Neglecting friction, determine the tension in cable ABD and the reaction at C.

The FBD indicates two unknowns at C, the x and y components of the 
reaction (these are independent variables) and the tension T at 
both point A and point D.  Since there is no friction, the tension 
at both points is equal.
The moment equation about point C eliminates the two unknowns at C 
and allows us to solve for the tension, T.
Combination of terms simplifies the equation.
Notice that tension must always be positive!
The force equilibrium equation in the x direction allows to solve for the 
x component of the force at C.
Arithmetic yields the answer for the horizontal force component.
The equilibrium equation in the y direction allows us to solve for the 
y component of the reaction at C.
The y component at C is up.
The force at C is the vector sum of the two components of the force.