An approach to structural analysis

The purpose of this thesis is to present to the engineering profession a method of structural analysis which is peculiarly suited to the way engineers think. The range and the power of structural analysis are extended by careful study of the actual deformations of structures, leading to the formulation of simple mathematical models. The theme throughout this thesis is the deliberate effort to look for, and to describe characteristic shapes which define the deformed structure; general statements are obtained similar to the historically valuable models which used \plane sections remain plane\" or \"radial lines remain radial\". Once an appreciation of the deformations of the structure is gained the forces to sustain these deformations are then found easily. This is one of the oldest approaches of engineering analysis and the most powerful methods of analysis of structures have been along these lines Men like Galileo Parent Navier Bernoulli and Ooidoimb developed an appreciation of structural behaviour by looking for simple geometric characteristics which would describe the deformed shape of the structure. (We may note also that Kepler's purely geometric study of the motions of the planets paved the way for Newton's formulation of his laws). And todayp when one tries to visualize and calculate the deformations of a bent beam it is difficult to improve upon the first overall approximation that plane sections remain plane. The key to obtaining a simple mathematical model of a real problem is to start with a simple physical or laboratory model. Simple geometric approximations are then obtained by fitting an analytic function to the form of the deformations of the simple structure. The functional form is chosen so that the strains the stresses and hence the overall statical equilibrium of the structure can be evaluated. With this basis on which thoughts can be focussed the laboratory and mathematical models can be improved to be a closer representation of the real problem. This approach reduces the need to test full size structures as the geometric functional form acts as the geometric scaling factor. When full size testing is carried out model tests are still a valuable means of providing a quick overall picture. This picture can then be used to determine which important geometric deformations should be measured. At present full size testing although expensive is still necessary as the relationships between the strength and the size of the material remain unanswered. Nevertheless improvements in this field can be made; for example R.E. Rowe (Ref. 1) has shown that concrete mixtures can be scaled to produce the same geometric crack pattern as would be expected in the full size structure. An engineer is frequently using approximate overall characteristics of a simple model as a basis for obtaining further thoughts on the real problem. However the inability to measure quickly the overall geometric deformations of a simple model has led to specialized full size structural tests not by engineers but by research workers. The aim of this thesis if to show how to use simple experimental studies to obtain simple mathematical models and thus fulfil the sentiment expressed by Sir Alfred Pugsley (Ref. 2) that \"Drawing and design office staffs can and like to play a part in the extension of their methods and if they could do so directly not only by theoretical but by simple experiment would welcome the opportunity\". The design of a through plate girder bridge is taken as the main problem throughout this thesis in order to co-ordinate the whole. Existing mathematical models and methods of design are based on the ideas developed after the buckling failure of several through bridges made with heavy floor beams. Bridges nowadays are being made with lighter floor beams and model studies are used in the investigations for this thesis to indicate characteristic deformations of these lighter through bridges. An understanding of the problem is obtained from these model studies and is used to develop a new mathematical model. The predictions of this new model are then compared with measurements taken on a full size bridge with strain gauge spirit level and rule and reasonable agreement is obtained. This new mathematical model is then used as the basis for recommendations concerning the design of through bridges made with light floors."