INTRODUCTION OF ADVANCED METHOD OF STRUCTUAL METHOD :
The subject and purposes of the Theory of Structures in the broad sense is the branch of applied engineering that deals with the methods of analysis of structures of different types and purpose subjected to arbitrary types of external exposures. Analysis of a structure implies its investigation from the viewpoint of its strength, stiffness, stability, and vibration.
The purpose of analysis of a structure from a viewpoint of its strength is determining internal forces, which arise in all members of a structure as a result of external exposures. These internal forces produce stresses; the strength of each member of a structure will be provided if their stresses are less than or equal to permissible ones.
The purpose of analysis of a structure from a viewpoint of its stiffness is determination of the displacements of specified points of a structure as a result of external exposures. The stiffness of a structure will be provided if its displacements are less than or equal to permissible ones.
The purpose of analysis of stability of a structure is to determine the loads on a structure, which leads to the appearance of new forms of equilibrium. These forms of equilibrium usually lead to collapse of a structure and corresponding loads are referred as critical ones. The stability of a structure will be provided if acting loads are less than the critical ones.
The purpose of analysis of a structure from a viewpoint of its vibration is to
determine the frequencies and corresponding shapes of the vibration. These data are necessary for analysis of the forced vibration caused by arbitrary loads.
The Theory of Structures is fundamental science and presents the rigorous treatment for each group of analysis. In special cases, all results may be obtained in the close analytical form. In other cases, the required results may be obtained only numerically. However, in all cases algorithms for analysis are well defined.
The part of the Theory of Structures which allows obtaining the analytical results is called the classical Structural Analysis. In the narrow sense, the purpose of the classical Structural Analysis is to establish relationships between external exposures and corresponding internal forces and displacements.