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

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.

Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan

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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.

Department of Civil EngineeringUniversity of Engineering and Technology, Taxila, Pakistan

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