Clothing is an important factor in the life of the high school girl and with the changing times it seems to become increasingly more so. Living as adolescent girls do today, there is a greater tendency for them to be judged by the clothing they wear. / Master of Science

The search for a better method of analyzing skew arches and rigid frames has gone on for years. During that time many theories were presented, most of which were an improvement or a simplification of previous methods. However, no exact analytical solution, based on classical plate theory, for the analysis of skewed plates as found in rigid-frame bridges had been developed prior to this thesis. As previously mentioned, the complete solution is being presented in three separate theses. This thesis contains all the equations needed for the analysis that arise from considering the extensional forces acting in the skewed slab. All the equations have been given in the form of an infinite series. These equations, together with the ones for the other parts of this problem, must be expanded for a few terms, combined and solved. Due to the size and number of equations involved, the only practical solution would involve the use of a modern high-speed computer. Since Virginia Polytechnic Institute has a computer of this type, the entire analysis could he completed at the college. Once the results are obtained, a comparison can be made with the experimental analysis referred to in the thesis. / Master of Science

This study presents estimates of the marginal productivity of the different classes of resources on Extension T. V. A. test demonstration farms in Southwest Virginia. The data were taken from 106 farm records kept by Unit Test Demonstrators in Southwest Virginia during 1951. The records were divided into four type-of-farm groups. These groups were beef brood farm with and without tobacco, and general farms with and without tobacco. The data were aggregated into independent variables of land, labor, machinery and power, livestock and feed crops, and tobacco. Gross income was taken as the dependent variable and production functions of the Cobb-Douglas type were fitted to the different farm types, and marginal value productivities were derived from the coefficients, The marginal value product of each dollar invested in livestock and feed crops was high on each type farm studied. Marginal values were highest ($2.05) for beef brood farms with tobacco and lowest ($1.45) for general farms without tobacco, Furthermore, the coefficients related to livestock and feed crops were significant in all cases. The marginal value product of land was relatively high ($12.75 per acre) on beef brood farms with tobacco and ($16.36 per acre) on beef brood forms without tobacco. The marginal value product of machinery and power was $4.15 on general forms without tobacco and the coefficient was statistically significant in this case. However, estimates were extremely low for other type farms. The marginal productivity of labor on beef brood farms without tobacco seems reasonable, but it was not statistically significant. The same is true of tobacco on general farms. Generally the analysis indicated that: (1) The typical Southwest Virginia former could apparently not profitably expand acreage until present acres used are more fully developed and stocked. (2} The productivity of labor, and thus its earning power, can be increased on most Southwest Virginia forms by additional investments in high producing livestock and feed crops. (3) Investments in livestock and feed crops were paying high returns on most Southwest Virginia forms in 1951 and could be profitably increased. (4) Machinery and power were earning low returns on most Southwest Virginia forms in 1951. / Master of Science

M.S.

The temperature distributions encountered in thin solid wings subjected to aerodynamic heating induce thermal stresses that may effectively reduce the stiffness of the wing. The effects of this reduction in stiffness were investigated experimentally by rapidly heating the edges of a cantilever plate. The midplane thermal stresses imposed by the nonuniform temperature distribution caused the plate to buckle torsionally, increased the deformations of the plate under a constant applied torque, and reduced the frequency of the first bending and first torsion modes of vibration. By using small-deflection theory and employing energy methods, the effect of nonuniform heating on the plate stiffness was calculated. The theory predicts the general effects of the thermal stresses, but becomes inadequate as the edge-to-center temperature difference increases and plate deflections become large. / M.S.

By a study of the duality relationships of a large number of balanced and partially balanced incomplete block designs, certain ones have been found which lend themselves nicely to interblock analysis. Besides facilitating this analysis, these designs make possible the use of a new method for studying the relative variability of the inter and intra-block error. These "nice" designs, which are called twice balanced, have the property that their duals are also balanced or partially balanced. In the partially balanced designs, the investigation has been confined to those with two associate classes. Some methods are shown which may be used to prove that a dual is twice balanced. The twice balanced designs which have been found are catalogued, showing the plan numbers of the design and the dual,and the necessary identifying parameters or both. The proofs used in verifying the designs to be twice balanced are also indicated. Finally, there is an illustrative example making use of the methods and tables introduced in this paper. It includes a new computing method to be used for finding estimates of the treatment effects in a mixed model experiment. / Master of Science

Master of Science

The first purpose of the present paper is to provide an elastic theory from which problems involving coupling may be approached. Potential energy and equilibrium expressions will be derived for these are the components of the theory which are lacking. The potential energy expression may be used either in small- or large-deflection analysis. Equations of equilibrium are presented for both small- and large-deflection theory. The second purpose of the present paper is to determine the effect of coupling on deflections and buckling of a simple supported anisotropic plate in compression. A small deflection analysis of this problem is made using the theory presented herein. No large deflection analysis is attempted; however, an estimation of the large deflection effect of coupling is made. The electric theory presented herein forms a basis from which problems involving coupling may be treated. The significance of coupling is most apparent in problems which would involve stability considerations in the absence of coupling. The presence of deflections due to coupling prior to reaching the uncoupled buckling load forces the problem to be treated asa one of deflections rather than stability. Coupling has a general detrimental effect upon this type of problem in that it lowers the load at which deflections grow rapidly (that is, buckling in the uncoupled case). The effect of coupling on the buckling of plates of equal bending stiffnesses in their two orthogonal directions becomes negligible as the aspect ratio of the plate becomes large. Some lateral deflection prior to buckling will occur, however, even for large aspect ratios. The general anisotropic plate is considered in the small-deflections solution to the differential equation of equilibrium. Computations were made for cases in which the bending stiffness were equal. The equations and methods are applicable to cases in which the bending stiffness are not equal. / Master of Science

In an economy characteristics by keen competition among commodities for consumers' disposable income, the per capita demand for a product may shift over a period of time. With a decline in demand (a shift to the left of the demand curve) for a commodity, the total consumption may be less than in previous years even with an expanding population. In the past four decades the trend in per capita consumption of apples has been downward. This downward trend is evident when the per capita rates of apple consumption are compared for various time periods during these years. In fact, the trend in per capita consumption of apples has been steadily downward from 1909 to 1953 as shown by the averages for each five-year period beginning with 1909¹. The trend in total yearly consumption of apples in the United States has likewise been downward. However, this decline has been less pronounced than per capita consumption declines because of the counteracting influence of population increases in this country. Shifts in demand for a commodity create economic problems in both production and marketing. These problems are especially acute for products such as apples, which require large fixed investments of capital for production and handling. Apple production initially requires large outlays of capital for land, labor, and nursery stock. It is approximately eight years before an apple tree is brought into production and the orchardist begins to realize a return on his investment. During these formative years, and more especially in later years, the land planted in trees is not easily and readily shifted into production of other commodities. Likewise, the special equipment and storage facilities necessary for efficient marketing of apples represent a sizable investment of capital of a specialized nature that is not easily and readily adaptable for other uses. In order to make production and marketing decisions that are economically sound, people in the apple industry need adequate information on changes in consumer reactions to apples. To be adequate, this information must not only reflect the changes in the movement of apples moving into consumption, but must also provide information concerning the effectiveness of current merchandising practices on apple sales. The best source of this information is the market place where consumer preferences are registered. / Master of Science

The solutions to many problems in structural design and analysis are quite laborious and time-consuming. This fact has motivated the search for analogies that might lead to quicker, yet accurate solutions. Fortunately, the laws governing structural behavior find many parallels among the laws of electricity and, therefore, it is conceivable that electrical circuits may be devised which are equivalent to certain structural problems. It is the purpose of this thesis to set up several equivalent circuits and to present solutions using accepted methods of analysis. Only statistical loadings are considered. Information about necessary equipment for experimental work is given. Examples given show which analogs are best suited to certain structural problems. It is hoped that the foregoing will stimulate more investigation in the field of electrical analogies for structural problems. A discussion follows which will present the work which has previously been done in this field. This will help to acquaint the reader with the subject and show the need for further development. / Master of Science