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 P₁ and P₂ with resultant R, act at a point, there must be a third force, P₃, 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 R₁ and R₂ at the piers must be such that R₁ + R₂ = - W for it to be in equilibrium. Similarly, we examine the members of the bridge to determine the stresses acting on each.