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Über dieses Buch

This book is concerned with the static and dynamic analysis of structures. Specifi­ cally, it uses the stiffness formulated matrix methods for use on computers to tackle some of the fundamental problems facing engineers in structural mechanics. This is done by covering the Mechanics of Structures, its rephrasing in terms of the Matrix Methods, and then their Computational implementation, all within a cohesivesetting. Although this book is designed primarily as a text for use at the upper-undergraduate and beginning graduate level, many practicing structural engineers will find it useful as a reference and self-study guide. Several dozen books on structural mechanics and as many on matrix methods are currently available. A natural question to ask is why another text? An odd devel­ opment has occurred in engineering in recent years that can serve as a backdrop to why this book was written. With the widespread availability and use of comput­ ers, today's engineers have on their desk tops an analysis capability undreamt of by previous generations. However, the ever increasing quality and range of capabilities of commercially available software packages has divided the engineering profession into two groups: a small group of specialist program writers that know the ins and outs of the coding, algorithms, and solution strategies; and a much larger group of practicing engineers who use the programs. It is possible for this latter group to use this enormous power without really knowing anything of its source.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Background and Scope

Abstract
Structural mechanics is concerned with the behavior of solid objects (or assemblies of them) under the action of applied loads. The behavior is usually described by idealized models from which the internal forces and displacements are found. We present, in the following chapters, the stiffness formulated matrix methods as models to tackle some of the fundamental problems facing engineers in structural mechanics.
James F. Doyle

Chapter 2. Rod Structures

Abstract
A rod is a slender member that supports only axial loads. It is one of the simplest components and therefore a very suitable vehicle for introducing the basic concepts of the matrix analysis of structures. In this chapter, we consider only structures composed of rods arranged longitudinally; the more general arrangement is left to the chapter dealing with frames and trusses. We first review the basics of rod theory and derive the governing differential equations. These are then used to obtain the stiffness of a single rod element. The scheme for forming the structural stiffness matrix is established by using equilibrium and compatibility conditions at each node. Finally, the effects of boundary conditions are incorporated by simple row and column reduction of the matrices.
James F. Doyle

Chapter 3. Beam Structures

Abstract
A beam is a slender structural member designed to carry transverse loads and applied couples. In response to these loads, it develops internal bending moments and shear forces. We shall refer to a beam structure as a collection of beams arranged in a collinear manner. These are sometimes referred to as continuous beams. Additional aspects of the mechanics of beams can be found in strength of materials books such as Reference [13].
James F. Doyle

Chapter 4. Truss and Frame Analysis

Abstract
A truss is a structure composed of rod members arranged to form one or more triangles. The joints are pinned (do not transmit moments) so that the members must be triangulated. A frame, on the other hand, is a structure that consists of arbitrarily oriented beam members which are connected rigidly or by pins at joints. The members support bending as well as axial loads.
James F. Doyle

Chapter 5. Structural Stability

Abstract
In the previous chapters we investigated the equilibrium of various structural systems. Now we wish to consider a very important property of systems in equilibrium, namely stability. Basically, we are interested in what happens to the structure when it is disturbed slightly from its equilibrium position: does it tend to return to its equilibrium position, or does it tend to depart even further? We term the former case stable equilibrium and the latter unstable equilibrium. A load carrying structure in a state of unstable equilibrium is unreliable and hazardous — a small disturbance can cause catastrophic changes. Reference [20] gives a good background setting for the study of structural stability while Reference [41] is an excellent compendium of examples and solutions. Mention should also be made of Reference [51] which places stability in a much broader context.
James F. Doyle

Chapter 6. General Structural Principles I

Abstract
The previous chapters developed the analysis of particular structural systems by the consistent use of the twin concepts of compatibility and equilibrium. In each case, we derived a set of governing differential equations, integrated them, and then determined the constants of integration by satisfying the appropriate boundary and compatibility conditions. This approach will work in every case, but as a practical tool it suffers from a number of drawbacks. Primary among these is that the solution can become very cumbersome when more than one integration region is involved. It may also happen that the governing differential equations cannot be integrated in a closed form. When approximations are used the differential equations are not in a suitable form for direct manipulation. For example, we obtained the approximate geometric matrix in Chapter 5 by first obtaining its exact form, and then using a Taylor series expansion to obtain the linearized version. But if the cross-sectional area varies, for example, this approach is not feasible at all; it would be much more convenient if we could go directly to the approximate solution.
James F. Doyle

Chapter 7. Computer Methods I

Abstract
The use of the computer is essential for modern structural analysis; therefore, it is important that the engineer have some understanding of how the computer is actually used to accomplish this analysis. This chapter introduces some of the basic computer methods and algorithms used in structural analysis; these include schemes for solving simultaneous equations, solving eigenvalue problems, and for efficient data storage. In addition, it attempts to describe the computer environment in which the analysis takes place. References [4, 32, 45] consider many of the general aspects of using computers for structural analysis.
James F. Doyle

Chapter 8. Dynamics of Elastic Systems

Abstract
This chapter gives an introduction to the dynamics of elastic systems. We restrict the emphasis to those concepts that will be used directly in later chapters. The response of a simple spring-mass system will be used to motivate these concepts. References [25, 40, 44] are good sources for additional details on the material covered.
James F. Doyle

Chapter 9. Vibration of Rod Structures

Abstract
This chapter deals with our first application of the matrix methods to the motion of continuous systems. These systems can exhibit quite complicated behavior because the responses are functions of both space and time. We show, however, that spectral analysis can be used to reduce these problems to a series of pseudo-static problems and thus make them amenable to the solution procedures already established. As a special case, we establish the free vibration problem as an eigenvalue problem.
James F. Doyle

Chapter 10. Vibration of Beam Structures

Abstract
We treat the dynamics of beams in a manner similar to that for rods. The sequence of analysis followed is: derive the governing differential equations, use spectral analysis to obtain general solutions, obtain an exact matrix formulation, obtain an approximate matrix formulation.
James F. Doyle

Chapter 11. Modal Analysis of Frames

Abstract
In the previous two chapters, we obtained an exact formulation for the dynamics of continuous systems. For vibration problems, the natural frequencies and mode shapes are determined by solving a transcendental eigenvalue problem. Consequently, we found the approximate formulations easier to use because they lead to an algebraic eigenvalue problem. In this chapter, we take the approximate formulation one step further by utilizing properties of algebraic eigensystems to introduce the concept of the modal model. This model involves a transformation of the description of dynamic systems in terms of stiffness and mass to a new set of equivalent variables in terms of the structural modes of vibration. This provides a scheme for analyzing the dynamics of complicated structures in terms of more useful quantities. References [17, 50] give very readable introductions to modal analysis.
James F. Doyle

Chapter 12. General Structural Principles II

Abstract
In this chapter, we will develop alternative descriptions of the equations of motion. We are motivated to do this because in complex structures involving distributed mass and elasticity, the direct vectorial method of the last few chapters may be difficult to apply.
James F. Doyle

Chapter 13. Computer Methods II

Abstract
Determining the dynamic response of a structure is one of the most demanding challenges for implementing matrix methods on a computer. This divides into two distinct but highly related problems: direct integration in time of the dynamic equilibrium equations, and performing a modal analysis. Reference [5] is an excellent source of additional material.
James F. Doyle

Backmatter

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