Analytical and experimental investigations of the collapse load characteristics of thin walled structural forms under compressive load actions

Qureshi, I. H (1961) Analytical and experimental investigations of the collapse load characteristics of thin walled structural forms under compressive load actions. PhD thesis, University of Glasgow.

Abstract

The advent of thin walled structural compression members high-lighted the reservoir of strength which exists beyond the initiation of a state of elastic instability in thin flat rectangular plates loaded in lengthwise compression. The evaluation of this post-critical strength generally called "maximum" strength has been attempted on a variety of semi-empirical bases and in a few cases on purely theoretical grounds. The thesis presents a theoretical treatment for the maximum strength of flat plates, developed by the author, using the concepts of the classical large deflection theory of plates and the deformation theory of plasticity. A variety of unloaded edge conditions ranging from free through elastically fixed to built-in conditions and their symmetrical and unsymmetrical combinations are considered. This theory, developed for single plates is then applied by the introduction of appropriate assumptions to the assessment of the maximum strength of structural sections regarded as an assembly of such plates. Computations connected with the theory were programmed and carried out by the author on a "DEUGE" digital computer. To check the results of the theory an extensive experimental programme covering the measurements of strains and deformations corresponding to the initiation of instability and progress to collapse was carried out. In connection with the experimental programme an original application of the Moire fringe technique was developed by the author for the determination of deflection variations, following an introductory review of the relevant published literature, the subject matter of the thesis is divided into six Sections. Section l presents the derivation of the basic large deflection equations by minimization of the energy integral effected by the use of Euler's equations, and a procedure for the approximate solution of the large deflection equation by Galerkin's method. This energy approach to the problem considered, and the generalization of Euler's equations for two variables with higher derivatives put forward in this thesis is, to the author's knowledge, original. In Section2 the approximate solutions of the large deflection equations and the results of elastic critical loads obtained thereby for two general cases of plates are presented. These are then compared with other available published results obtained by classical methods. The comparisons show excellent agreement. Section 3 presents an analytical method for the maximum load carried by compressed plates, based on the application of the deformation theory of plasticity to the plates analysed by means of the large deflection concept. The application of this method of analysis to the evaluation of the maximum load for plates with free/and/or elastically supported unloaded edges is to the author's knowledge presented here for the first time. In Section 4 the results obtained for single plates have been applied to evaluate the local instability and maximum stresses for box sections, lipped channels and plain channels. The experimental work performed is presented in Section 5. This covers tests in uniform compression of plain and lipped channel, square tube and equal angle sections. In addition to the results of the actual tests, the various auxiliary techniques such as an original application of the Moire fringe method are fully described. The mechanical properties inclusive of tensile and compressive yield, Young's Modulus E at zero and varying mean stress, have been evaluated for all the specimens used and are presented in full. Section 6 contains the comparison of the theoretical and experimental results with a relevant critical discussion. The main test concludes with a Summary indicating that generally good agreement has been obtained between the theory and the experiments, establishing the former as a rational and reliable analysis for the maximum strength in compression of single-plates and structural sections. This is followed by 7 Appendices and an extensive Bibliography. The Appendices contain those details of the theoretical and experimental investigations which have been considered too bulky for inclusion in the main test.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: A ST Thomson
• Keywords: Civil engineering
• Date of Award: 1961
• Depositing User: Enlighten Team
• Unique ID: glathesis:1961-73492
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 14 Jun 2019 08:56
• Last Modified: 14 Jun 2019 08:56
• URI: https://theses.gla.ac.uk/id/eprint/73492