determinacy and stability of structures
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/1.jpg)
Determinacy and Stability of Structures
Theory of Structure - I
SWEDISH COLLEGE OF ENGG & TECH ,WAH CANTT
![Page 2: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/2.jpg)
2
Lecture Outlines
Introduction
Equations of Equilibrium
Types of Supports and Restraints
Stability and Determinacy
Idealized Structure
![Page 3: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/3.jpg)
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.
![Page 4: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/4.jpg)
4
FREE BODY DIAGRAM
![Page 5: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/5.jpg)
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).
![Page 6: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/6.jpg)
6
The above requirements may be stated mathematically as:
1. SFx = 02. SFy = 03. SMz = 0
Positive
Positive
Positive
Sign Conventions
![Page 7: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/7.jpg)
7
Types of Supports and Restraints
Roller Support Fixed Support
Hinge Support
![Page 8: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/8.jpg)
8
![Page 9: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/9.jpg)
9
Hinge Support
Roller Support
![Page 10: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/10.jpg)
10
![Page 11: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/11.jpg)
11
![Page 12: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/12.jpg)
12
![Page 13: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/13.jpg)
13
![Page 14: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/14.jpg)
14
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.
![Page 15: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/15.jpg)
15
Determinate Structure
![Page 16: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/16.jpg)
16
Indeterminate Structure The structure possesses more unknown reactions
than equations of equilibrium, is referred to as an indeterminate structure.
![Page 17: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/17.jpg)
17
Indeterminate Structure
![Page 18: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/18.jpg)
18
Unstable Structure A structure in which there are an insufficient
number of reactions to prevent motion from taking place, is called an unstable structure.
![Page 19: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/19.jpg)
19
Unstable Structure
![Page 20: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/20.jpg)
20
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.
![Page 21: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/21.jpg)
21
![Page 22: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/22.jpg)
22
![Page 23: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/23.jpg)
23
![Page 24: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/24.jpg)
24
![Page 25: Determinacy and Stability of Structures](https://reader033.vdocument.in/reader033/viewer/2022061316/56816582550346895dd821b1/html5/thumbnails/25.jpg)
25