Principle of Statics in Structural Analysis | Conditions of Static Equilibrium |Sign Convention

"Statics is the study of structures that are under equilibrium conditions. Equilibrium of the structure means - all the forces acting on the structure must balance and the net torque must be equal to zero".

The principle of statics can be used to:
  • Analyze the Structures
  • Determine Internal acting on structures
  • Determine the External Forces acting on the structures
A statically determinate structure is a structure whose internal and external forces can be determined by the equations of equilibrium. Those structures that cannot be analyzed by the equilibrium equations are called as statically indeterminate structures. 

More about statical determinacy can be read in the article

Representation of Forces in Structural Analysis

The force is represented by a vector quantity that has a magnitude, sense, location, and direction that is based on respective force. An arrowhead will show the direction of the force.

When considering the action of forces on structures, the point of application of the force will affect the internal forces. Consider the portal frame in figure-2(a).


                                          (a)                                                                                    (b)
Fig.2.Action of Forces on a Portal Frame and simply supported beam

The change in point of application will bring change in the final resultant internal forces. Now the forces that are acting along the same line of action is called as Collinear Forces.
The forces that are acting on a single plane are called as Coplanar Forces. If all the forces have a common point of intersection it forms a concurrent force system.

Conditions of Equilibrium

Principles of a statics can be applied to a structure only if the structure is at rest. This condition is obtained when the sum of the applied loads, the support reaction is equal to zero and there is no resultant couple at any point in the structure. All the structural system must also be in equilibrium.

Then for the body to stay in static equilibrium the condition to be satisfied is:

ƩFx = 0   ;  ƩFy = 0   ; ƩFz = 0

The above equations are called as equations of static equilibrium of a planar structure that is subjected to a system of forces.

Sign Convention in Static Structural Analysis

The forces that are acting along the right are positive and the vertical forces acting upward forms positive.
The forces that are acting downwards and leftwards are considered negative. The moment acting in counter clock direction is positive and along the anti-clockwise direction forms negative.

Fig.3.Sign Convention of Forces in Structures

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