Determinacy and Stability of Structures Theory of Structure - I SWEDISH COLLEGE OF ENGG & TECH ,WAH CANTT

Lecture Outlines Introduction Equations of Equilibrium Types of Supports and Restraints Stability and Determinacy Idealized Structure

Introduction Free Body Diagram Simplified picture of the structure, isolated from its supports, on which are shown all the external forces that act on the structure. These forces include the applied loads and the reactions that the supports exert on structure.

FREE BODY DIAGRAM

Equations of Equilibrium For complete static equilibrium in 2D, three requirements must be met: 1. External Horizontal forces balance (translation). 2. External Vertical forces balance (translation). 3. External Moments balance about any point (rotational).

The above requirements may be stated mathematically as: 1. SFx = 0 2. SFy = 0 3. SMz = 0 Positive Positive Sign Conventions Positive

Types of Supports and Restraints Roller Support Fixed Support Hinge Support

Hinge Support Roller Support

Stability and Determinacy Determinate Structure A structure for which all the unknown reactions can be determined using the equations of equilibrium is referred to as a determinate structure.

Determinate Structure

Indeterminate Structure The structure possesses more unknown reactions than equations of equilibrium, is referred to as an indeterminate structure.

Indeterminate Structure

Unstable Structure A structure in which there are an insufficient number of reactions to prevent motion from taking place, is called an unstable structure.

Unstable Structure

Idealized Structure The structure is made in a line form and the supports are replaced with the reactions. This new line shape of a structure along with the symbolic reactions and applied loadings (similar to free body diagram), is called the IDEALIZED STRUCTURE.