L3_Structural analysis (1) Analysis of SD structures-green background 2.ppt
- 1. Copyright September, 2010 Copyright September, 2010 1 1 Analysis of Statically Analysis of Statically Determinate Structures Determinate Structures Prof. Basuony El-Garhy Civil Engineering Department Faculty of Engineering
- 2. 2 2 Analysis of SD Structures Analysis of SD Structures The most common type of structure an engineer will analyze lies in a plane subject to a force system in the same plane. In general, it is not possible to perform an exact analyze of a structure. Approximations for structure geometry, material parameters, and loading type and magnitude must be made.
- 3. 3 3 Types of Supports Types of Supports Hinge or pin support prevents horizontal and vertical displacements; allows rotation. However, in reality, a pin connection has some resistance against rotation due to friction A fixed connection prevents vertical and horizontal displacements and rotation The most common types of supports are hinge or pin support, roller support and fixed support. Roller support prevents vertical displacements and allows horizontal displacement and rotation
- 4. Support Idealization Support Idealization Hinge or pin support 4 4 Fixed support Roller support
- 7. 7 7 Typical hinge (pin) support Typical hinge (pin) support
- 8. Typical fixed support Typical fixed support 8 8
- 9. Typical roller support Typical roller support 9 9
- 10. Typical fixed support Typical fixed support 10 10
- 11. Actual beams pin connected Actual beams pin connected to column to column 11 11
- 14. 14 14 Typical pin support Typical pin support
- 15. Typical fixed support Typical fixed support 15 15
- 16. Idealized structure Idealized structure 16 16 A structure may be idealized as a line drawing where orientation of members and type of connections are assumed. The elements of a structure, like the beams and girders of this building frame, are connected together in a manner where the analysis can be considered statically determinate.
- 28. Principle of Superposition 28 28 Basics for the theory of linear elastic structural analysis: The total displacement or stresses at a point in a structure subjected to several loadings can be determined by adding together the displacements or stresses caused by each load acting separately. There are two exceptions to these rule: 1. If the material behaves in a nonlinear 2. If the geometry of the structure changes significantly under loading (example: a column subjected to a bucking load)
- 29. Principle of Superposition 29 29 = + w w P P
- 30. Equations of Equilibrium 30 30 From statics the equations of equilibrium in plane are: Requires that a free body diagram be constructed of the structure or its members. All forces and couple moments must be shown that act on the member Method of sections will be used to determine the internal loadings at a specific point with a cut perpendicular to the axis of the member at that point.
- 31. The Ideal Cut Section The Ideal Cut Section Internal Loadings Internal Loadings M M V V N N V = Shear Force (kN or tons) M = Bending Moment (kN-m or t-m) N = Normal Force (kN or tons) 31 31
- 32. Determinacy and Stability Determinacy and Stability 32 32 Determinacy: provide both necessary and sufficient conditions for equilibrium. When all the forces in structure can be determined from the equations of equilibrium then the structure is considered statically determinate If there are more unknowns than equations of equilibrium, the structure is statically indeterminate.
- 33. Determinacy Determinacy 33 33 For plane structures, there are three equations of equilibrium for each Free Body Diagram (FBD), so that for n members and r reactions: r = 3n statically determinate structure r > 3n statically indeterminate structure Degree of determinacy = 3n - r r = number of reactions n = number of members Where:
- 35. Example 1 (Continued) Example 1 (Continued) 35 35
- 38. Stability Stability Stability: Structures must be properly held or constrained by their supports. 38 38 Cases in which the structures is considered unstable 2. When all the reactions are parallel 1. If r < 3n Unstable structure 3. When all the reactions are concurrent at a point
- 40. Example 4 (Continued) Example 4 (Continued) 40 40
- 41. Example 4 (Continued) Example 4 (Continued) 41 41