# Principles of statics

Principles of statics consists of the study of structures that are at rest under static equilibrium conditions.  To ensure equilibrium,

• the forces acting on a structure must balance,
• net torque acting on the structure should be zero.

The static analysis methods provide the means to analyze and determine both internal and external forces acting on a structure.  For structures in a plane, three equations of equilibrium are used for the determination of external and

internal forces. A statically determinate structure is one in which all the unknown member forces and external reactions may be determined by applying the equations of equilibrium. An indeterminate or redundant structure is one that possesses more unknown member forces or reactions than the available equations of equilibrium.

These additional forces or reactions are termed redundants. To determine the redundants, additional equations must be obtained from conditions of geometrical compatibility. The redundants may be removed from the structure, and a stable, determinate structure remains, which is known as the cut-back structure. External redundants are redundants that exist among the external reactions. Internal redundants are redundants that exist among the member forces.

## Conditions of equilibrium

In order to apply the principles of statics to a structural system, the structure must be at rest. This is achieved when the sum of the applied loads and support reactions is zero and there is no resultant couple at any point in the structure. For this situation, all component parts of the structural system are also in equilibrium.

A structure is in equilibrium with a system of applied loads when the resultant force in any direction and the resultant moment about any point are zero. For a system of coplanar forces this may be expressed by the three equations of static equilibrium:

ΣH = 0
ΣV = 0
ΣM = 0

where H and V are the resolved components in the horizontal and vertical directions of a force and M is the moment of a force about any point.