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Determinacy and Stability of Structures

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

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Determinacy and Stability of Structures

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  1. Determinacy and Stability of Structures Theory of Structure - I SWEDISH COLLEGE OF ENGG & TECH ,WAH CANTT

  2. Lecture Outlines • Introduction • Equations of Equilibrium • Types of Supports and Restraints • Stability and Determinacy • Idealized Structure

  3. 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.

  4. FREE BODY DIAGRAM

  5. 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).

  6. The above requirements may be stated mathematically as: 1. SFx = 0 2. SFy = 0 3. SMz = 0 Positive Positive Sign Conventions Positive

  7. Types of Supports and Restraints Roller Support Fixed Support Hinge Support

  8. Hinge Support Roller Support

  9. 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.

  10. Determinate Structure

  11. Indeterminate Structure • The structure possesses more unknown reactions than equations of equilibrium, is referred to as an indeterminate structure.

  12. Indeterminate Structure

  13. Unstable Structure • A structure in which there are an insufficient number of reactions to prevent motion from taking place, is called an unstable structure.

  14. Unstable Structure

  15. 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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