Determinacy and Stability of Structures Theory of Structure - I
Lecture Outlines Introduction Equations of Equilibrium Types of Supports and Restraints Stability and Determinacy Idealized Structure Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
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 Engineering University of Engineering and Technology, Taxila, Pakistan
FREE BODY DIAGRAM Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
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). Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
The above requirements may be stated mathematically as: 1. SFx = 0 2. SFy = 0 3. SMz = 0 Positive Positive Sign Conventions Positive Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Types of Supports and Restraints Roller Support Fixed Support Hinge Support Simple Support Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Hinge Support Roller Support Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
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. Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Determinate Structure Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Indeterminate Structure The structure possesses more unknown reactions than equations of equilibrium, is referred to as an indeterminate structure. Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Indeterminate Structure Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Unstable Structure A structure in which there are an insufficient number of reactions to prevent motion from taking place, is called an unstable structure. Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Unstable Structure Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
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 Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan
Thank You Department of Civil Engineering University of Engineering and Technology, Taxila, Pakistan