Determinacy and Stability of Structures

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 = 02. SFy = 03. SMz = 0

Positive

Positive

Positive

Sign Conventions

7

Types of Supports and Restraints

Roller Support Fixed Support

Hinge Support

8

9

Hinge Support

Roller Support

10

11

12

13

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.

15

Determinate Structure

16

Indeterminate Structure The structure possesses more unknown reactions

than equations of equilibrium, is referred to as an indeterminate structure.

17

Indeterminate Structure

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.

19

Unstable Structure

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.

21

22

23

24

25