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Title: Bending and torsion of thin-walled open section beams
Author: Black, Martin M.
Awarding Body: University of Glasgow
Current Institution: University of Glasgow
Date of Award: 1966
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The subject matter of this thesis concerns the flexural-torsional behaviour of thin-walled beams under conditions of small and large displacements. The relevant aspects are examined both theoretically and experimentally and consideration is also given to the nonlinear unstable behaviour of such beams. The published literature covering theoretical and experimental work is reviewed in Chapter 1 with special reference to beams of open section such as channels and angles. The review has been orientated to survey in particular, the analytical concepts introduced by previous investigators which are relevant to a solution for the problem of large elastic deformations of thin-walled open sections. In the theoretical analysis presented in Chapter II, the governing differential equations based on small displacement approximations, are first considered. Solutions of these equations for selected cases are obtained in closed form. It is further shown that by neglecting the St. Venant torsional rigidity term, the solutions can be appreciably simplified. The limitations implicit in this approximation are discussed. The general problem considering finite displacements is then examined and the corresponding nonlinear governing differential equations established. In developing these equations, additional effects such as initial axial stress, axial displacement and longitudinal stress due to the 'shortening effect' are included. Solutions of these equations using the Galerkin approach are presented. The results obtained give torque/angle of twist equilibrium paths under both stable and unstable conditions and are shown to be applicable to the determination of critical bending moment values causing flexural-torsional instability. The approximations used in obtaining the solutions are indicated and their limitations discussed. The experimental programme, apparatus and techniques are described in Chapter III. In this, the various experimental test rigs, including a controlled angle of twist loading arrangement used to examine both stable and unstable behaviour, and the arrangement for tests to failure, are described. The experimental results obtained and their comparison with corresponding theoretical values are presented in Chapter IV. In this it is shown that, in general, good agreement is obtained between theoretically predicted and experimentally, determined values in respect of both deformations and stresses. The application of the experimentally substantiated small displacement theory to practical structural design is presented in Chapter V. In this, specific cases of practical significance are analysed and discussed. The principal findings of the investigation are summarised in Chapter VI and the thesis concludes with a Bibliography, Author Index and Appendices. The latter give full details of the theoretical solutions, the material and section properties of the specimens tested and also includes a suggested safe load table for thin-walled channel sections.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available