Lecture 1: STABILITY AND DETERMINACY OF STRUCTURES

Introduction: A stable structure is the one, which remains stable for any imaginable system of loads.A statically indeterminate structure is the one in which all the reactive components plus the internal forces cannot be calculated only from the equations of equilibrium available for a given force system. We know that there are three equations of equilibrium.

The determinacy of a structure is identified by the degree of indeterminacy (ID), is calculated as..

ID = | number of unknown - number of equilibrium condition|

The degree of indeterminacy for a given structure is, in fact , the excess of total number of reactive components over the equations of equilibrium available.

External Stability and Determinacy:  

Example 1: 

                 Here, 

                 Number of unknown = 3

                 Number of available equations = 3

                 ID = | number of unknown - number of equilibrium condition|

                      = 3-3 = 0

                 So, the structure is Stable and Determinate.

Example 2: 

                 Here, 

                 Number of unknown = 3

                 Number of available equations = 3

                 ID = | number of unknown - number of equilibrium condition|

                      = 3-3 = 0

                 So, the structure is Stable and Determinate.

Example 3: 

 Here, 

                 Number of unknown = 5

                 Number of available equations = 3

                 ID = | number of unknown - number of equilibrium condition|

                      = 5 -3 = 2

                 So, the structure is Stable and indeterminate 2nd degree

Important Links: Lecture 2: STABILITY AND DETERMINACY OF STRUCTURES

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