# Equations of Static Equilibrium

I would like to clarify if the equations that I got from this figure are correct.

$$-T_{CD}sin(30) + T_{DE}cos(0) = F_x = 0$$

$$T_{CD}cos(30) - \frac{W}{2} = F_y = 0$$

and

$$-T_{ED}cos(0) + T_{EG}sin(10) = F_x = 0$$

$$T_{EG}cos(10) - \frac{W}{2} = F_y = 0$$

if

• the points D and E are pivot joints, or equivalently if all the connecting elements are wires/cables,
• GE does not change in length

then you've written the right type of equations.

Some minor notes:

• The equilibrium is $$\sum F_x$$ not $$F_x$$ (and $$\sum F_y$$) so for example:

$$-T_{CD}sin(30) + T_{DE}cos(0) = F_x = 0$$

is properly written:

$$-T_{CD}sin(30) + T_{DE}cos(0) = \mathbf{\sum F_x} = 0$$

• Usually the symbol $$T$$ in this context is used to denote the tension on a wire in that case, regarding the tension of the cables in GE, I would have preferred to write:

$$-T_{ED}cos(0) + \mathbf{\color{red}2\cdot}T_{EG}sin(10) = \sum F_x = 0$$

$$\mathbf{\color{red}2\cdot}T_{EG}cos(10) - \frac{W}{2} = \sum F_y = 0$$

The reason for $$\mathbf{\color{red}2}$$ is that you have two cables between GE and therefore the tension on each cable will be $$T_{EG}$$.