# The analysis of structures with particular reference to elastic instability of frames

thesis

posted on 2023-05-27, 14:46 authored by Van der Woude, FBroadly speaking, an engineer's constant aim is the creation of something which serves mankind. In order to achieve his aim the engineer has to tackle numerous problems arising between the time of conception and the final bringing into service of the product. To this end it is convenient to picture the process as divided into three stages. The first stage is to recognise the existence of the real problem, with its multitude of complexities and details, all at varying levels of importance. The real problem is always too difficult to handle directly, and as an aid to thinking, great simplifications are made. The simplified problem may be called the physical model, in which only the more important aspects of the real problem are defined. The setting up of a physical model requires skill, judgement and, in most cases, experience with similar situations. It follows that the first physical model may at times be subject to subsequent variations and revisions. Finally, a mathematical model is formulated this model attempts to describe, by means of mathematical equations, the behaviour of the physical model. For example, if the real problem is one of structural design, the unknowns in the final equations are usually design parameters such as stress, deflection, beam depth and so on. Thus the solution of the equations defines the behaviour of the physical model in terms of design parameters, but the degree to which these apply to the real problem depends on how well the physical model represents the real structure. Final design is achieved only after many cycles of appraisal, modifications to the physical model, refinements, re-evaluation, and so on. The above philosophy is generally applicable, indeed it is believed to be the only successful method of problem solving in any field, especially in engineering. This thesis is concerned with the problem of the behaviour of framed structures. Throughout the work, emphasis is placed on the geometry of the deformations of the frame. Although it is often not appreciated, the geometric approach has dominated throughout the history of structural engineering development. The reason for this is obvious, because once the deformations of a structure are known, other quantities like stresses, strains, bending moments and so on, are easily calculated. Another reason is that deformations, unlike forces (the alternative to a geometric approach is a force approach), can be pictured and drawn to scale or sketched. Such a picture is readily obtained from experiments and one is always pleasantly surprised at how much information can be drawn from but the simplest measurements of deformations. The author has experienced most success from simply constructed, light and flexible models which, apart from being inexpensive, are easily deformed by hand, and the deformed models are quickly sketched or traced. Frequently a wire or cardboard model may be used in order to gain a preliminary understanding of the deformations.

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