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General Equilibrium Problems Click here for Strategy

Key Concept: For a structure to be in equilibrium the “net” force and “net” moment

acting on the structure must sum to zero. Click here for discussion of the strategy to solve

general equilibrium problems.

In a Nut Shell: Σ F = 0 and ΣM = 0

In scalar form for problems in a plane:

ΣF_x = 0 and ΣF_y = 0 and ΣM_z = 0

In scalar form for problems in space:

ΣF_x = 0, ΣF_y = 0 , ΣF_z = 0 and ΣM_x = 0, ΣM_y = 0 , ΣM_z = 0

To be able to sum forces and moments, one must first identify all the forces and

moments acting on a structure. So construction of a complete free body diagram

is the critical first step in the analysis. The net force and net moment must be

zero for equilibrium.

Example: Consider the truss ABCDE acted on by a vertical load of 1200 N

and a horizontal load of 800 N and supported by a pin and roller.

(Truss is a pin-connected structure with forces acting only at pin locations.)

In order to establish equilibrium, the first step is to identify all forces acting on the truss.

Start by constructing a FBD of truss ABCDE to determine the support reactions.