The Rayleigh-Ritz method is a convenient tool for the analysis of deflections in structures subjected to external forces. Bending moment relations can be developed and reliable values obtained for bending moments. In this thesis the Rayleigh-Ritz method is used for the analysis of a single-span, pin-connected circular arch subjected to uniform load along the arch. The method is explained, equations for deflections and moments are developed and the results of an illustrated problem are tabulated. The illustrated problem is also solved by a conventional method using the dummy load and virtual work techniques. Results are compared and found to be good. In both methods, account is taken of bending and axial forces; shear distortion is neglected. For the Rayleigh-Ritz method where undetermined coefficients are evaluated, a tabulation of the rate of convergence is presented. Computer programs for both methods are included. / Master of Science

Climatic variables have been used to calculate evapotranspiration loss by many researchers. Evapotranspiration formulas have been developed for local use in predicting soil moisture in many parts of the United States. The objective of this study was to develop a method to estimate soil moisture in Virginia using data collected by the Agricultural Engineering Department, Virginia Polytechnic Institute, Blacksburg, Virginia. The first step in the study was to determine the relationship between soil moisture and loss pan evaporation. This relationship was found on a seasonal cumulated basis. For shorter periods, the results were poor. No workable relation could be found that would satisfactorily estimate soil moisture from any of these procedures. A soil moisture accounting system based on the soil moisture balance principle was then devised in which daily evapotranspiration loss was calculated by Van Bavel’s nomogram method. Daily soil moisture and measure soil moisture were compared by the student t-test for paired observations. The results of the statistical analysis indicated it could be used to estimate soil moisture in local conditions. Finally, the correlation between daily evapotranspiration and pan evaporation was determined. A high correlation was found. The problem encountered in analyzing the data available for this study indicated the need for a detailed statistically controlled experiment. Hence an experimental design has been formulated that, hopefully, will allow an systematic investigation and evaluation of the problem. / Master of Science

Ballistic measurements were made of the critical magnetic fields of superconducting. cylinders of cerium-doped lead. Within the accuracy of our measurements, the introduction of the paramagnetic impurity, cerium, in lead has no effect other than a slight broadening of the transition. The samples, containing 0.00, 0.10, 1.0, and 1.5 atomic percent cerium in lead had been vacuum cast in pyrex tubes. The relative fractions of the cerium in these samples and their final purities were tested by the techniques of neutron activation analysis. / Master of Science

The purpose of this work was to determine the enthalpies and specific heats of polymethyl methacrylate, polydimethylaminoethyl methacrylate, polycyclohexyl methacrylate, polyallyl methacrylate, and polyethyl acrylate from 120 to 300°C, and to determine a method for estimating their specific heats. Enthalpies of the selected polymers were determined by using a drop calorimeter constructed by the Chemical Engineering Department of Virginia Polytechnic Institute. Specific heats were obtained by measuring the slopes of the enthalpy-temperature curves. Good agreement with existing data for polymethyl methacrylate was obtained. An existing semi-theoretical quantum mechanical method was modified to provide specific heat estimations for linear methacrylic polymers accurate within six percent. An empirical correlation yielding estimations within twenty percent was proposed. / Master of Science

Small oscillations of a beam-column with finite electrical conductivity in a transverse magnetic field are examined under the assumption that the vibration of the bar causes only a weak perturbation in the electromagnetic-field. The frequency equation is derived for a column and reduced to that for free vibration of a beam by equating the end load to zero. The roots of this equation are obtained approximately and the effect of the magnetic field on the frequencies is noted. In addition, the elastic stability of a conducting column and beam-column are investigated. The effect of the magnetic field on the buckling load is determined. Numerical results are presented which indicate that the effect of the dynamic electromagnetic forces is negligible except at extremely high frequencies of vibration. / M.S.

The problem of the deflection of spur gear teeth has been previously investigated analytically by several authors. Two of the papers dealing with this topic were written by Timoshenko and Baud (18)t and Marin and Shenk (11). Both papers employ the cantilever beam approach in which the spur gear tooth is represented as a rigidly supported, cantilever beam of uniform thickness tapered in the plane of load application. Deflection is considered to be caused by bending moment, shearing force, and Hertzian pressure at the point of load application. Two additional papers were written by Weber (25) and Attia (3) in which the actual involute gear tooth was considered to be an elastically supported cantilever beam rather than rigidly clamped at the root of the tooth. Likewise, circumferential deformation of the gear body was considered. However, the derived equations for the total deflection due to these effects are exceedingly complicated and require the use of numerical methods for their solution since some of the equations are in integral form. / Master of Science

The object of this thesis is the synthetic generation of possible future flows in the James River at Buchanan, Virginia, through the utilization of existing records of monthly precipitation and runoff. Twelve separate monthly regression models were chosen on the basis of the degree of correlation as indicated by the correlation coefficient. Random monthly precipitation totals were generated from the twelve separate distributions of historical monthly precipitation totals. The synthetic precipitations were used in the twelve monthly models to generate 5000years of artificial record. The 5000-year synthetic record was divided into fifty separate 100-year records for the purpose of analysis. The dependable flows were found for each of the fifty records for each of eight reservoir sizes. The ninety percent confidence interval and the dependable flow for each of eight reservoir sizes was found. The model had a negative bias of approximately thirteen percent. This bias appeared to be alleviated when the dependable flow was expressed as a percent of the average flow for the period in question. It appears that there is great variability in the estimated value of the dependable flow in the James River. / Master of Science

Results are presented of an experimental and analytical study of the longitudinal vibrational response of a modified Agena-B vehicle. The empty, unpressurized vehicle was excited with sinusoidal loads and the response was measured through a frequency range including the first two classical longitudinal. modes of the structure. Non-axisymmetric shell response (shell vibration modes) was noted extensively during the experimental tests. Comparison of the analytical and results indicates that a one-dimensional analytical model gave good results in comparison with experimental results. / Master of Science

The object of this was to investigation the effect of continuous mechanical mixing on the disinfection of settled domestic of settled domestic sewage with iodine. The variable investigated was the power input to the system which was a function of mixing intensity. Five experiments were run usfrtt a six-bladed turbine agitator in a fully baffled tank. The mixing intestines of the first three experiments were 0.292, 0.00748, and 0.0641 foot pounds per second per 1,000 gallons, respectively. The mixing was contInuous throughout the experiment. The last two experiments employed a mixing intensity of 0.000876 foot pounds per second per 1,000 gallons. Most Probably Number determinations of Escherichia coli were made at time intervals of 0, 0.5, 1.5, 2, 3, 4, 6, 8, and 10 minutes respectively, for each experiment. All ten minute Iodine residuals were in the range of 1.70 to 1.80 parts per million. Alt experiments were conducted at 20 degrees centigrade. Similar rates of disinfection were obtained at mixing intestines of 0.292, 0.0641, and 0.00748 foot pounds per second per 1,000 gallons. The disinfection rate at 0.000876 foot pounds per 1,000 gallons was inferior to that of the previously mentioned rates. The following conclusions were made after comparing these results with a previous investigation. 1. Similar continuous mixing disinfection occurred in the range of power to volume ratio of 0.00748 to 148 foot pounds per second per 1,000 gallons. 2. Inferior continuous mixing disinfection·occurred at the power to volume ratio of 0.000876 foot pound per second per 1,000 gallons and under the condition of no mixing. 3. A system operating at the power to volume ratio of 0.00748 foot pounds per second per 1,000 gallons for one minute·appears to provide for complete blending of iodine with the sewage under the conditions of the present Investigation. The suggested power requirement is equivalent to 9.46 x 10⁻⁶ horsepower per million gallons per day. / Master of Science

Although many studies have been made on the operating characteristics of instrument bearings, most were conducted at two rpm or less and with thrust load only. A study by H.H. Mable tested the running torques of radially loaded bearings from 1,000 to 40,000 rpm. The purpose of this investigation was to study the running torques of R-3 size instrument ball bearings at speeds up to 40,000 rpm while under combined radial and axial load. Much of this investigation was devoted to the construction of an accurate torque sensing device. The method employed relied on the amplification of strain gage signals by a strain gage indicator and an x-y plotter. The strain gages were used to detect the strain at the base of a small beam that prevented rotation of the outer race.of a test bearing while the inner race was driven at test speed by an air turbine. The accumulated data was the result or 30 test series, with each series being constituted of a test sample of six ball bearings. From the study, it was consluded that the strain gage method of torque sensing accurately measured the running torque of R-3 size ball bearings at ambient temperatures. It was also concluded that the effect of axial loading or an R-3 ball bearing loaded with 47 grams radially is negligible until the axial: load equals o.r exceeds the radial loading. By comparing lubricants, it was concluded that grease lubricated ball bearings demonstrate running torques approximately twice as great as bearings lubricated with a similar weight of oil. / Master of Science