Determinacy and Stability of Structures
Theory of Structure - I
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Lecture Outlines
Introduction
Equations of Equilibrium
Types of Supports and Restraints
Stability and Determinacy
Idealized Structure
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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.
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FREE BODY DIAGRAM
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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).
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The above requirements may be stated mathematically as:
1. Fx = 0
2. Fy = 0
3. z = 0
Positive
Positive
Positive
Sign Conventions
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Types of Supports and Restraints
Roller Support Fixed Support
Hinge Support Simple Support
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Hinge Support
Roller Support
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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.
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Determinate Structure
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Indeterminate Structure The structure possesses more unknown reactions
than equations of equilibrium, is referred to as an indeterminate structure.
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Indeterminate Structure
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Unstable Structure A structure in which there are an insufficient
number of reactions to prevent motion from taking place, is called an unstable structure.
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Unstable Structure
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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.
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