# statics

Statics is the branch of mechanics that deals with forces acting on bodies that are motionless.
We can combine forces much as we do velocities.
If forces **P**_{1} and **P**_{2} with resultant **R**, act at a point, there must be a third
force, **P**_{3}, equal and opposite to **R**,
for equilibrium. We can combine forces similarly over more complex structures.
For a bridge whose weight (*w*) acts as a downward force **W** at the center, the upward reactions **R**_{1} and **R**_{2} at the piers must be such that **R**_{1} + **R**_{2} = - **W** for it to be in equilibrium.
Similarly, we examine the members of the bridge to determine the stresses
acting on each.