01 - Introduction to Statically Indeterminate Structures.pptx

The support reactions and internal forces of statically determinate structures can be determined from the equations of equilibrium.
the equilibrium equations alone are not sufficient for determining the reactions and internal forces of such structures and must be supplemented by additional relationships based on the geometry of deformation of structures.
Compatibility conditions, ensure that the continuity of the displacements is maintained throughout the structure and that the structure’s various parts fit together.
Regardless of whether a structure is statically determinate or indeterminate, its complete analysis requires the use of three types of relationships:

Equilibrium Equations

Compatibility Conditions

Member force-deformation relations
In the analysis of indeterminate structures, it is necessary to solve the equilibrium equations in conjunction with the compatibility conditions of the structure to determine its response.
The resulting system of equations containing only one type of unknowns is then solved for the unknown forces or displacements, which are then substituted into the fundamental relationships to determine the remaining response of the structure
Force and displacement methods are exact because they satisfy the equilibrium and compatibility of the structure.

The preliminary designs of indeterminate structures are often based on the result of the approximate analysis.

Internal forces are estimated by making certain assumptions about the deformations or the distribution of forces
Statically indeterminate structures have more supports or members than required for static stability
The excess reactions and internal forces of indeterminate structure are referred as Redundants.
The number of redundants is termed as degree of indeterminacy.

The support reactions and internal forces of statically determinate structures can be determined from the equations of equilibrium.
the equilibrium equations alone are not sufficient for determining the reactions and internal forces of such structures and must be supplemented by additional relationships based on the geometry of deformation of structures.
Compatibility conditions, ensure that the continuity of the displacements is maintained throughout the structure and that the structure’s various parts fit together.
Regardless of whether a structure is statically determinate or indeterminate, its complete analysis requires the use of three types of relationships:

Equilibrium Equations

Compatibility Conditions

Member force-deformation relations
In the analysis of indeterminate structures, it is necessary to solve the equilibrium equations in conjunction with the compatibility conditions of the structure to determine its response.
The resulting system of equations containing only one type of unknowns is then solved for the unknown forces or displacements, which are then substituted into the fundamental relationships to determine the remaining response of the structure
Force and displace

1. Structural Theory 2 Introduction to Statically Indeterminate Structures Prep by: Engr. Buluran

2. Introduction

3. Advantages Smaller Stresses Greater Stiffness Redundancies

4. Disadvantages Stresses due to support settlements Stresses due to temperature changes and fabrication errors

5. Analysis of Indeterminate Structures Regardless of whether a structure is statically determinate or indeterminate, its complete analysis requires the use of three types of relationships: Equilibrium Equations Compatibility Conditions Member force-deformation relations

6. Sample Problem FBD At joint A

7. Indeterminate Structures

8. Sample Problem FB at joint A:

9. Methods of Analysis Since the mid-1800s, many methods have been developed for analyzing statically indeterminate structures. Force (flexibility) Methods Displacement (Stiffness) Methods

10. Approximate Analysis of Rectangular Building Frames Force and displacement methods are exact because they satisfy the equilibrium and compatibility of the structure. The preliminary designs of indeterminate structures are often based on the result of the approximate analysis. Internal forces are estimated by making certain assumptions about the deformations or the distribution of forces

11. Statical Determinacy

12. Degree of Statical Indeterminacy for Beams and Frames Where: n = Degree of Statical Indeterminacy s = Number of support reactions i = Number of internal forces at hinges m = Number of closed loops without hinge p = number of parts

13. Sample Problem Determine the Degree of Indeterminacy of the figure given below.

14. Degree of Statical Indeterminacy for Trusses Where: n = degree of statical indeterminacy s = number of support reactions m = number of truss members nn = number of nodes

15. Sample Problem Determine the Degree of Indeterminacy of the figure given below.

16. References