Olga Lebed

Advanced Methods of Structural Analysis

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Three-Hinged Arches

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Multispan Beams and Trusses

This chapter is devoted to the analysis of statically determinate three-hinged arches, subjected to fixed and moving loads. Analysis of an arch in the case of fixed loads implies determination of reactions of supports and construction of internal force diagrams. Analysis of an arch in the case of moving load implies construction of influence lines for reactions, thrust, and internal forces.

Plastic Behavior of Structures

This chapter is devoted to the analysis of statically determinate multispan beams and trusses, subjected to moving loads. Methods for the generation of beam and trusses, and the construction of influence lines are discussed. Different types of trusses are considered; among them are trusses with subdivided panels and some special types of trusses.

Influence Lines Method

This chapter is devoted to the analysis of a structure, taking into account the plastic properties of material. Such analysis allows the use of the reserves of strength of material, which remains unused considering the material of structure as elastic. Therefore, plastic analysis allows us to define the limit load on the structure and to design a more economical structure. Fundamental idea of the plastic analysis is discussed using the direct method. Kinematical and statical methods of calculation of the limit loads are considered. Detailed plastic analysis of the beams and frames are presented.

Deflections of Elastic Structures

This chapter is devoted to construction of influence lines for different statically indeterminate structures. Among them are continuous beams, frames, nonuniform arches, and trusses. Analytical methods based on the force and the displacement methods are applied. Also, kinematical method of construction of influence lines is discussed. This method allows tracing the models of influence lines.

Stability of Elastic Systems

This chapter describes some effective methods for computing deflections of deformable structures. The following structures are considered: beams, frames, arches, and trusses subjected to different actions, such as variety of external loads, change of temperature, settlements of supports, and errors of fabrication. Computation of different types of deflections is shown. They are linear, angular, as well as the mutual linear and angular deflections. Advantages and disadvantages of each method and field of their effective application are discussed. Much attention is given to a graph multiplication method which is a most effective method for bending structures. Fundamental properties of deformable structures are described by reciprocal theorems; they will be widely used for analysis of statically indeterminate structures.

The Force Method

Theory of structural stability is a special branch of structural analysis. This theory explores the very important phenomenon that is observed in the behavior of the structures subjected to compressed loads. This phenomenon lies in the abrupt change of initial form of equilibrium. Such phenomenon is called loss of stability. As a rule, the loss of stability of a structure leads to it collapse. Engineering practice knows a lot of examples when ignoring this feature of a structure led to its failure.

The Displacement Method

The force method presents a powerful method for analyzing linear elastic statically indeterminate structures; this method also has a wide application in problems of stability and dynamics of structures. The method is very attractive because it has clear physical meaning, which is based on a convenient and well-ordered procedure of calculation of displacements of deformable structures, and presently, this method has been brought to elegant simplicity and perfection. In this chapter, the reader find the numerous examples of application of this method for analysis of different structures subjected to external loads, temperature change, settlements of supports, and errors of fabrication.

Dynamics of Elastic Systems

The displacement method is a powerful method for analysis of statically indeterminate frames subjected to different external exposures.