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Thesis (Ph. D.)--Virginia Polytechnic Institute, 1965. / Vita. Abstract. Includes bibliographical references (leaves 78-79). Also available via the Internet.

The bifurcation phenomenon occurring in twisted square plates with free edges subject to contrary self-equilibrating corner loading was examined. In order to eliminate lateral deflection of the test plates due to their own weight, a special loading apparatus was constructed which held the plates in a vertical plane. The complete strain field occurring at the plate centre was measured using two strain gauge rosettes mounted on opposing sides of the plate at the centre. Principal curvatures were calculated and related to corner load for several plates with differing edge length/thickness ratios. A Southwell plot was used relating mean curvature to the ratio mean curvature/Gaussian curvature, from which the Gaussian curvature occurring at bifurcation was determined. The critical dimensionless twist ka was then calculated for each plate size. It was found that there is a linear relation between the critical dimensionless twist ka occurring at bifurcation, and the thickness to edge length ratio h/a ratio, specifically: ka = 10.8h/a. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

An experimental and finite element investigation of the behavior of single-span, simply-supported folded plate structures containing rectangular openings is summarized. A seven-plate aluminum model was tested under a uniform load of 40.26 psf. on the horizontal surfaces. Six different cases are analyzed by changing the number, size, and location of the holes. The results of only the two extreme cases, no-hole and 12-hole analyses, are presented. Good agreement is shown between experimental and theoretical solutions, thus the validity of the finite element analysis is established in dealing with cutouts in folded plate structures. A comparison of experimental results and analytical results, obtained by the finite element method of analysis, is made and the effects of the holes on the behavior of the structure are discussed. Recommendations for future research are indicated. / Master of Science

Call number: LD2668 .T4 1985 A35 / Master of Science

An experimental study is presented on the non-linear twisting of plates with free edges, through the application of self-equilibrating corner loads. A simple apparatus was designed and various sizes of plates were twisted while measuring the surface strains on both sides at the centre. Initial difficulty was encountered due to unwanted deflection of the plate under its own weight. The Rayleigh-Ritz method is used to determine an analytical relationship between midsurface strains and curvatures in the pre- and post-bifurcation regions of twisting. In both the experimental and analytical results, the midsurface strains are found to vary linearly with the Gaussian curvature. Non-dimensional groups are identified which collapse the experimental load-strain, load-curvature and midsurface strain-Gaussian curvature relationships. These non-dimensional groups collapse the results in both the linear and non-linear regions. The curvature at the point of bifurcation is identified as a function of plate dimensional parameters. Also shown are the expressions for critical surface strain and corner load at which bifurcation occurs. The experimental load-curvature relationship and point of bifurcation are compared with analytical results found in the literature. A large discrepancy in the literature is resolved for the theoretical point of bifurcation. The present results form a basis for verification of future analytical results, and are important in the measurement of constitutive relationships using the twisted plate test. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Ph. D.

A general method of analysis is developed for the solution of single or continuous span folded plate surfaces, with general end conditions, for any load. By considering the folded plate surface as a single, longitudinal unit throughout the analysis, the continuity of the surface is maintained over transverse supports, Within the limitations of the assumptions, this method yields an "exact" solution of the structural action based upon a difference technique in which the surface is divided into : segments: combatibility of the surface is insured at the center of each finite segment along the span and over the supports. A computer program for the analysis of simply supported, © single-span and continuous-span folded plate surfaces, with and without overhangs at each end, under three load conditions is described. A comparison is made between this general method of analysis and presently accepted techniques; and a final solution for a continuous folded plate surface is presented. The results of an experimental investigation to study the behavior of four different folded plate structures and to verify the general method of analysis are discussed. / Ph. D.

Concrete folded plate structures have gained increasing use and popularity in the United States during the past fifteen years. They have proved to be especially economical in the construction of longspan roof systems. The folded plate shape has come into wide use because of its low coat of construction for long spans, high load carrying capacity, and rigidity. Moreover, the folded plate structure hu the structural advantage of thin shelled, curved surface structures, and is much easier and less expensive to construct than the latter. With reference to folded plate structures continuous over a support, the problem arises of relating the geometry of the folded plates to a number of points along the entire length of the plate edges, in an attempt to find the true condition of stress at these points, and to find the contribution of each stress condition to the overall effect. The investigation of this thesis consists of analyzing a reinforced folded plate concrete roof, continuous with overhang. The method of analysis used is that of successive iteration, i.e. balancing angle changes against internal moments and/or stresses. This method is similar to one presented by Howard Simpson - “Design of Folded Plate Roofs” - in the ASCE Proceedings, Vol. 84, January, 1958, but extended to apply to the cantilevered folded plates. / Master of Science

The performance of thin-plate structural systems is known to be greatly influenced by the effect of buckling and post-buckling behaviour. The main factors, which affect the buckling, and post-bucking characteristics and consequently the ultimate performance of thin plate structural components, are noted to be structural geometry, material properties, loading and boundary conditions and geometric imperfections. Present day knowledge and understanding of the buckling and post-buckling behaviour of thin plate structures is at a fairly sophisticated level due to the intensive research that has been carried out over the years in this field of study. This is particularly true for the case of compressive loading whereby the collapse and unloading failure mechanics of thin plate structures has been well documented for this case. The same is not true for the case of shear loading and although much work has been carried out there is a lack of knowledge and in-depth understanding of shear post-ultimate conditions which essentially defines the initiation and progressive development of the plastic failure mechanisms of thin plate structural system. This thesis makes a contribution to the area of study by taking advantage of the developments in recent years of computational technology and computing power to develop finite element modelling strategies and solution procedures using the commercially available FE package PATRAN/NASTRAN to describe in detail the post-buckled shear failure of thin plate structural systems. The work of this thesis provides an in-depth understanding of the complex post-buckled failure mechanics associated with thin-plate structures subjected to in-plane shear displacement and combined shear and compression loading. Simply supported in-plane normal stress free and straight edge boundaries are employed to examine the shear performance as well as the failure mechanisms of thin and stocky web plates. Finite element modelling strategies are developed, which are able to describe the complete loading history from the onset of initial buckling through the nonlinear elastic post-buckling to initial material yielding and its further propagation throughout the structure leading to the development of an appropriate failure mechanism that causes final plastic collapse and subsequent load drop-off. The post-buckled failure response of the thin plate structures is determined with due consideration being given to the effects of geometric and material nonlinearities. The effect of stiffeners on structural performance is detailed for single and multiple asymmetrical and symmetrically attached stiffeners. The degrading influence on the structural performance of cut-outs as well as the considerable redeeming effect due to reinforcements attached at the cut-out boundaries is highlighted in this thesis. The work of the thesis covers the in-plane shear displacement loading of thin web plates, thin web plates with transverse stiffeners, web plates with cut-outs, web plates with stiffened cut-outs and the interactive shear and compressive loading of transversely stiffened web structures. The in-plane shear displacement loading of these structures using the multipoint constraint loading strategy in the finite element modelling procedures has shown to be highly successful in being able to provide an in-depth understanding of the failure mechanics of these structures to a level not to be found in the existing literature.