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Determinacy and Stability of Structures
Theory of Structure - I
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Lecture Outlines
Introduction
Equations of Equilibrium
Types of Supports and Restraints
Stability and Determinacy
Idealized Structure
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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FREE BODY DIAGRAM
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Types of Supports and Restraints
Roller Support Fixed Support
Hinge Support Simple Support
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Hinge Support
Roller Support
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Determinate Structure
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Indeterminate Structure
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Unstable Structure
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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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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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan
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