Structural Analysis

INTRODUCTION

The structural analysis is a mathematical algorithm process by which the response of a structure to specified loads and actions is determined. This response is measured by determining the internal forces or stress resultants and displacements or deformations throughout the structure.

The structural analysis is based on engineering mechanics, mechanics of solids, laboratory research, model and prototype testing, experience and engineering judgment. The basic methods of structural analysis are flexibility and stiffness methods. The flexibility method is also called force method and compatibility method. The stiffness method is also called displacement method and equilibrium method. These methods are applicable to all type of structures; however, here only skeletal systems or framed structures will be discussed. The examples of such structures are beams, arches, cables, plane trusses, space trusses, plane frames, plane grids and space frames.

The skeletal structure is one whose members can be represented by lines possessing certain rigidity properties. These one dimensional members are also called bar members because their cross sectional dimensions are small in comparison to their lengths. The skeletal structures may be determinate or indeterminate.

CLASSIFICATIONS OF SKELETAL OR FRAMED STRUCTURES

Direct force structures such as pin jointed plane frames and ball jointed space frames which are loaded and supported at the nodes. Only one internal force or stress resultant that is axial force may arise. Loads can be applied directly on the members also but they are replaced by equivalent nodal loads. In the loaded members additional internal forces such as bending moments, axial forces and shears are produced.

The plane truss is formed by taking basic triangle comprising of three members and three pin joints and then adding two members and a pin node as shown in Figure 2.1 below.

Convention for internal axial force is also shown. In Fig.2.2, a plane triangulated truss with joint and member loading is shown. The replacement of member loading by joint loading is shown in Fig.2.3. Internal forces developed in members are also shown. The space truss is formed by taking basic prism comprising of six members and four ball joints and then adding three members and a node as shown in Fig.2.4.

Plane frames in which all the members and applied forces lie in same plane as shown in Fig.2.5. The joints between members are generally rigid. The stress resultants are axial force, bending moment and corresponding shear force as shown in Fig.2.6.

Plane frames in which all the members lay in the same plane and all the applied loads act normal to the plane of frame as shown in Fig.2.7. The internal stress resultants at a point of the structure are bending moment, corresponding shear force and torsion moment as shown in Fig.2.8.

Space frames where no limitations are imposed on the geometry or loading in which maximum of six stress resultants may occur at any point of structure namely three mutually perpendicular moments of which two are bending moments and one torsion moment and three mutually perpendicular forces of which two are shear forces and one axial force as shown in figures 2.9 and 2.10.

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