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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 - PowerPoint PPT Presentation
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Determinacy and Stability of Structures
Theory of Structure - I
SWEDISH COLLEGE OF ENGG & TECH ,WAH CANTT
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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. SFx = 02. SFy = 03. SMz = 0
Positive
Positive
Positive
Sign Conventions
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Types of Supports and Restraints
Roller Support Fixed Support
Hinge 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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