Thesis (M.S.)--University of Wisconsin--Madison, 1961. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 88-90).

Thesis (M.S.)--University of Wisconsin--Madison, 1963. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

The geographical distribution of the sense of the first motion of P waves (and to a very limited extent, S waves) has been studied by seismologists to provide information on the focal mechanism of earthquakes. In this thesis we investigate the inverse problem; knowing the type and form of displacement at the focus at the focal instant, we study the azimuthal distribution of the sense of first P and S motion, using model seismic technique. The source of elastic energy is a thermally induced tensile fracture in a glass plate. Two types of fractures have been studied: Initial (Bilaterally propagating) Fractures and Extended (Unilaterally propagating) Fractures. The azimuthal distribution of the P and S wave amplitudes is indicated. The experiments reported in this thesis constitute a partial test of a recent theory by Knopoff and Gilbert (1960) on first motions from seismic sources. The type of fracture studied corresponds to Case 3 of Knopoff and Gilbert. Our results show significant discrepancies with the theory. The sense of the measured first S motion is opposite to that predicted by the theory, for both Initial and Extended Fractures. The ratios Pө /P₉₀ and Sө/Pө differ in magnitude from the theory in many azimuths. It is suggested that the discrepancies are possibly due to the neglect in the theory of non-linear elastic effects near the tip of the fracture. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

A theoretical as well as a laboratory investigation into the effects of plane strain on pore pressure parameters is presented. Other observations relative to stress-strain relationships, intermediate principal stress values and shear strength parameters (c´ø´) in terms of effective stresses are also reported. Experimental work consisted of the following three types of Undrained Triaxial tests with pore pressure measurements: (1) Standard triaxial tests on cylindrical specimens. (2) Triaxial tests on rectangular specimens. (3) Confined tests on rectangular specimens, in which lateral expansion was prevented in one direction, to achieve plane strain condition. A strain-controlled triaxial machine equipped with a non-flow null indicating type pore pressure measuring device was used for all shear tests. The observed data show that for the soil tested the values of pore pressure ,parameter A[subscript]f and shear strength parameter (c´ø´) under plane strain condition are higher than those obtained in corresponding triaxial tests. Failure is observed to occur, in the case of plane strain tests, at strains much smaller than those for the corresponding triaxial tests. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

This is a report on tests of welded beam-to-column connections carried out in the Materials Testing Laboratory, Department of Civil Engineering, University of British Columbia. The test series included four basic types of connection commonly used in practice, and for each type, a set of stress distribution curves has been given for each part of the connection. Realizing also, that for a connection to be of any practical use, it must have adequate rotation capacity, moment-rotation curves have also been given. From the various stress curves given, an attempt has been made to tabulate magnification factors, which are described in the text, and in this way correlate the peak stress values obtained with the theoretical linear stresses assumed. In order to do this for the column of each connection, a linear stress distribution was assumed, using information obtained from the tests carried out. Finally, the calculated values for each connection are compared in the concluding section. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The analysis and design is presented for a shell composed of flat triangular plates approximating a smooth spherical shell. The geometry is based on the subdivision of the icosahedron and dodecahedron into many plane triangles. All corners of these triangles lie on a circumscribing sphere so that as the triangles become more numerous, the shell more nearly approximates a true sphere. The geometry is tabulated for a few of the possible subdivisions but may have to be carried further if a particularly large shell composed of relating small triangles is required. While some of the geometry is similar to geodesic domes already constructed, the structural analysis is entirely different. Previous geodesic domes are space trusses where the applied loads are supported predominantly by axial force in the truss bars. The structures considered here are frameless and the loads are therefore supported by shell action. The exact analysis to such a shell was not obtained since the solution is not composed of tabulated functions. However, an approximate analysis is presented which, in part, is a modification of smooth shell theory. Since the shell is composed of flat plates, the bending and buckling of individual triangles are additional design problems considered that are not present in more conventional shell design. In order to verify parts of the theoretical analysis, experimental studies were conducted with a plexiglas model. The experimental results verify the application of smooth shell theory to geodesic shells and determine the distribution of membrane stress. Finally the various design aspects are brought together and illustrated by the inclusion of the design notes for a typical shell. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A three dimensional bar cell in the form of a rectangular parallelopiped capable of imitating the action of elastic bodies of any value of Poisson's ratio is devised for three dimensional stress analysis by the finite element method and the stiffness matrix of the cell is derived. Furthermore a rectangular no-bar cell is also formed by extending the idea of linear displacement functions from two dimensional to three dimensional cases and the stiffness matrices of this cell are derived both by the method of virtual work and by statics. Both these types of cells are used to solve three dimensional problems and the results in the form of displacements and stresses are compared with the exact elasticity solutions using different mesh sizes and different values of Poisson's ratio. The stresses found by the Finite element method are calculated in two ways: by the Joint displacement method (using two different procedures) and by the Nodal force method and the quality of solution obtained by these methods is compared. Finally the same examples are also analysed by using the framework models proposed by "Yettram and Robbins". ⁽⁶⁾* The results obtained by these several methods were good, with the ones corresponding to the proposed bar model being consistently the best of the three. The stresses found by both the Joint displacement and the nodal force methods were found comparable in quality. * Numbers signify the references, listed in Bibliography. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

An experimental investigation into the effect of secondary compression on an undisturbed sensitive clay is presented. The test series consisted of ten consolidated undrained triaxial compression tests which were carried out at constant strain rate on undisturbed saturated samples of sensitive Haney clay. Each sample was normally and isotropically consolidated for a different length of time. Before each sample was subjected to shearing, the pore pressure build-up due to secondary compression was measured. The effect of this amount of pore pressure build-up on the shear strength characteristics is discussed. The results of the investigation indicated that the secondary compression has an appreciable influence on the pore pressure set up for samples consolidated a shorter period of time. For samples consolidated for longer than one day, the effect of secondary compression on pore pressure can be neglected. The sensitivity of the clay, has a primary importance in determining the behavior of soil under load. The "reverse thixotropy" effect due to high sensitivity is briefly mentioned. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

Framework cells and no-bar cells are used for solving plane stress problems by the Finite Element Method of Analysis and the results obtained by using the two types of cells are compared with the elasticity solution in two specific examples. The precision of the Finite Element Method is tested at different values of the Poisson's ratio of the material. The stresses found by the Finite Element Method are calculated in two ways: from the corner forces and the corner displacements, and the quality of the results employing the methods is compared. The precision of the results obtained with the bar cells has been found consistently better than with the no-bar cells. Comparable precision has been observed in the stresses found from the corner forces and the corner displacements. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

The stiffness properties of a finite sized square model element of an isotropic plate under plane stress are presented. The model is a piece of the material itself and not a configuration of bars that replace the material. It is shown that the use of an extra kinematic condition instead of an arbitrary displacement function usually produces better results. An example shows that this extra condition greatly increases the accuracy of the model and so reduces the number of degrees of freedom required to approximate the continuous system. A system of bounding the solution is shown by assigning values to free parameters. Thus the maximum error is known and can be reduced without going to a fine grid. The derivation of the isotropic square is then expanded to obtain the stiffness matrix of an elemental orthotropic rectangle. The limits of stability for both the isotropic and orthotropic models are investigated. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate