A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that extensional effects are included. Other departures from the previous theory are that the strain - displacement relations are derived and that the expressions for the stress resultants are developed from the strain - displacement relations instead of assuming that the resultants are proportional to changes in the curvatures. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. Using a vector approach the exact expressions for the curvature components of a deformed space beam are developed. Because inextension of the beam is not assumed an additional term appears in each of the linearized curvature expressions. These expressions are utilized in the derivation of the strain - displacement relations. The normal and shearing physical components of the strain tensor are given. These relations are not restricted to beams whose cross-sectional dimensions are very small compared to the radius of curvature. Next, a development of the stress resultants is presented. Effects arising from the initial twist of the beam are obtained which are not reflected in the classical theory. Finally, the six equilibrium equations are derived using a vector approach. The governing equations are given in the form of twelve first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented. / Ph. D.

Purpose The purpose of this study was to investigate the relative effectiveness of an individualized laboratory approach upon the mathematics achievement of underachieving third-grade students performing below grade level. In the study, achievement of students receiving mathematics instruction in an individualized laboratory was compared with achievement of students receiving traditional mathematics instruction in the classroom. A similar comparison of the mathematics achievement of male and female subjects was also included in the investigation. Procedures Mathematics laboratories were established in two elementary schools designated as ESEA, Title I schools in terms of socio-economic deprivation. From these two schools, an experimental group was selected consisting of 62 third-grade students achieving in the lower three stanines as measured by pretest scores on the Metropolitan Achievement Test. A control group was formed by selecting 62 subjects from three other Title I schools to match the experimental group in terms of sex, race, and achievement in mathematics. The treatment period for the experimental group consisted of 45 minute daily sessions in the laboratory for a period of seven weeks. The laboratory program consisted of a systematic method of diagnosis, prescription, evaluation, and recording of individual progress with utilization of a wide variety of materials and equipment to match the learning styles and rates of laboratory participants. The control group received traditional mathematics instruction daily in the classroom for the same treatment period. The mathematics section of the Metropolitan Achievement Test, including subtests on computation skills and concept development and problem-solving skills, and the Criterion Referenced Tests were administered as pretest and posttest measures to both groups. A three-factor analysis of variance procedure with repeated measures on one factor was used to analyze data obtained. F tests were used, whenever appropriate, to determine the significance of the pretest-posttest differences for both treatment and sex. A significance level of .05 was selected as the basis for acceptance or rejection of the hypotheses in the study. Findings Findings of this study indicated that students receiving instruction in an individualized mathematics laboratory demonstrated significant gains (α= .01) in: (1) total mathematics achievement and concept development and problem-solving skills as measured by the mathematics section of the Metropolitan Achievement Test, and (2) mastery of specific skills as measured by the Criterion Referenced Tests. No significant difference was found between the two groups in regard to scores on the computation skills subtest of the Metropolitan Achievement Test. In addition, no significant differences in achievement were found for males as compared to females on either of the tests. Conclusions With the exception of improvement in computation skills, findings of this study indicated that the individualized laboratory approach significantly improved the mathematics achievement of underachieving third-grade students. However, the individualized laboratory approach did not significantly affect achievement of males as compared to females. Implications Further research is recommended; (1) utilizing a broader sample and longer treatment period, and (2) involving different grade levels and socio-economic groups. / Ed. D.

The purpose of this study was to obtain information about the continuous progress education programs in reading in the pilot and non-pilot elementary schools in Kanawha County, West Virginia, using selected fourth-grade students as the population sample, in order to provide a basis for making judgments about the programs. The difference between the programs was that locally-developed learning packages were made available to the teachers in the pilot schools but not to the other teachers. The assumption of the Kanawha County school officials was that the"achievement of children in classrooms where these learning packages are used will be significantly greater than the educational attainment of children in … classrooms" in which the learning packages are not utilized. A crossbreak of twelve cells was established in which the three major variables were treatment (pilot and non-pilot), school SES level (higher and lower), and reading achievement levels (high, middle, and low local stanine groups from scores on the EDS Reading pre-test). The sample was comprised of 221 students selected randomly from the available population. Achievement data were obtained by administering pre-tests and post-tests using two instruments, one a standardized norm-referenced-type test (the STS Educational Development Series' Reading test) and · the other a locally-developed criterion-referenced-type test (the diagnostic placement test). Data was also obtained regarding the instructional situation. Based on the various benefits and characteristics of continuous progress education identified in the literature, a questionnaire for teachers was prepared which was designed to assess the extent to which these benefits and characteristics occurred and were evident. The questionnaire was administered to the teachers of the students in the sample, permitting a comparison of the teacher responses with the achievements of each teacher's students. On the basis of the data obtained and the subsequent analyses (including MANOVA and factor analysis), it was concluded that students in the pilot schools did not, generally speaking, achieve better in reading than the students in the non-pilot schools at a level that was statistically significant. The exceptions occurred in one of six comparisons made of comparable pilot and non-pilot cells in the crossbreak model as measured by the criterion-referenced-type test and in two of the six similar comparisons made as measured by the norm-referenced-type test. The first exception reflected the very superior performance of the low stanine, lower school SES students in the pilot schools as compared with their counterparts in the non-pilot schools. The second two exceptions reflected the superior performance of the pilot school students in both high stanine group level cells (both the lower and higher school SES levels). In no instance of comparison did students in non-pilot school cells achieve better than their counterparts at a level that was statistically significant. No significant relationship was found between student achievement and teacher attitudes regarding continuous progress education or to operational characteristics of the program except in one instance, classroom grouping arrangement, favoring heterogeneous grouping. / Ed. D.

The characteristic properties of boundary layer and separation in unsteady flow, play a very important role in fluid and structural mechanics because of their drastic effect on control forces generated by aerodynamic surfaces and loads carried by aerodynamic structures. Prandtl's criterion for separation has been proven experimentally and analytically to be invalid for other than two-dimensional steady flows over fixed walls. Sears and Telionis have proposed a theoretical model for separation for unsteady flow based on the concept of Goldstein's singularity. According to this model a thin layer of reversed flow, embedded within the boundary layer and upstream of separation, may develop in unsteady flows. In the present study a method is developed to solve numerically the unsteady, two-dimensional, incompressible, boundary-layer equations with arbitrary pressure gradients, capable of integrating through the point of zero skin friction into partially reversed flow and the properties of the boundary layer flow and separation in unsteady flows are studied in detail. In particular the singular behavior of quantities like ∂²u*/∂s*∂n*, v*, etc. with u*, v* the velocity components and s*, n* the coordinates parallel and perpendicular to the surface of the body, respectively, is investigated and compared with predictions of Goldstein, Moore, Sears and Telionis. The path of zero skin friction and separation singularity with respect to time is also determined. Comparison of the numerical results with existing analytical, numerical and experimental results is made whenever possible. It is believed that the results prove that the point of zero skin friction should not be a downstream limit of the boundary layer calculation in unsteady flow. Further, most of the features of separation predicted by the Sears-Telionis model of unsteady separation are found to be present. Certain characteristic properties of unsteady viscous flow, like vorticity diffusion, steady streaming, etc., are also studied in detail. / Ph. D.

Study of prolonged diffusion in Cu-Au and Cu-Pd systems has revealed that the diffusion generated misorientations tend to mend themselves because of reduced concentration gradients. Previous studies of the Cu-Ni system in which a 8.0 micron nickel plated single crystal copper was diffused up to 5 hours at 900°C, did not reveal such features. It was desirable to obtain more information on the structure oriented diffusion of this system at prolonged diffusion times. For this purpose a 3.0 micron nickel plated copper single crystal was subjected to diffusion anneals at 900°C for times as long as 7 hours. The diffusion and structure data were obtained by the nondestructive X-ray method with supporting measurements using a Scanning Electron Microscope and computer simulations. It has been found that the diffusion behavior is dynamic and is influenced by structure. At lower times a unified grain boundary-volume diffusion model is able to account for the diffusion behavior whereas at intermediate and higher times a volume diffusion model with anomalously varying range of pseudo diffusion coefficients is required to match the experimental intensity patterns. Scanning Electron Microscope studies made at the end of the six different anneals show extensive flow patterns and porosities indicative of structural modifications. Rocking curve measurements obtained at chosen compositions over the treatments indicate no tendency of reorientation of the structure; the variance and halfwidth analysis demonstrate this feature. In fact, strong indications of the structure, having undergone a recrystallization are revealed at the end of the last diffusion anneal. / Master of Science

Water treatment plant sludge disposal has become a timely problem to consider. While many methods of sludge treatment and disposal have been suggested, coagulant recovery may prove to be the most economical. This investigation was concerned with recovery of iron coagulant by chemical addition. Sulfuric acid, hydrochloric acid, and sodium hydroxide were added to a water treatment plant sludge containing precipitated iron. The acidic method of recovery proved to be technically feasible. Iron dissolved upon addition of acid to the sludge. The concentration of soluble iron increased substantially when the pH was lowered to a level of 2.0 and then diminished at pH values below 1.0. Iron recovery appeared to generally follow the stoichiometry predicted. Acid addition to the sludge resulted in an improvement in sludge dewatering properties. Settling rates increased consistently with greater amounts of acid added, causing substantial reductions in sludge volume. The filterability of the sludge was also improved. Specific resistance decreased as the pH was lowered, reaching a minimum value at a pH level of about 3.0, and then increased due to compaction. Sludge volume reduction and iron recovery did not occur simultaneously at a given pH. It appeared that the acid acted to either solubilize the iron or to destabilize the colloidal particles, depending on the system pH. The recovered iron proved to be superior to fresh iron for coagulation of low turbidity waters. The suspended solids in the recovered iron solutions appeared to aid in nucleation. While coagulation with fresh iron resulted in a lower raw water residual turbidity, the critical coagulation concentration was less when recovered coagulant was used. / Master of Science

The growing concern for energy conservation is placing many new demands on materials, especially oxide thin films. A few of these new applications include solar collectors, solar reflectors, and thermal transparent insulation. The engineer must fully understand how oxide thin films optically behave and what mechanisms govern this behavior before utilizing them for these new applications. Only when oxide thin films are fully understood, will they be used to their potential. This thesis probes into the basic mechanisms governing the optical properties of oxide thin films. Thin films are complex and their behaviors do not always correspond to those of bulk oxides. Absorption in the oxide films studied is due to electronic excitations and it is also found to be dependent upon crystallinity; the more crystalline films being more absorbing. It was determined that absorbance is related to the semiconducting behavior of the oxides. Absorbance increases when conditions are reducing for n-type oxides and when conditions are oxidizing for p-type oxides. A maximum solar reflectance of 35% was obtained with a Co₃O₄ film that was annealed in 95%N₂-5%H₂. Metals such as gold, exhibit higher solar reflectances than both the pure oxides and mixtures of Co₃O₄, Fe₂O₃, SnO₂, TiO₂, and VO_xH_y. However, configurational designs utilizing the oxide film properties to their greatest advantage could selectively screen solar and thermal energy effectively. / Master of Science

The purpose of this research was to compare the relationships between body concept and clothing attitudes of blind and visually handicapped adolescents. The instruments used in this research were three subscales (Special Attention, Management, and Social Approval) of the Importance of Clothing Questionnaire developed by Dr. Anna M. Creekmore, et al., and the Body Concept Questionnaire developed by the researcher. Data were collected from 29 blind and visually handicapped adolescents, ranging from 14 to 19 years of age, at the Virginia School for the Deaf and Blind in Staunton, Virginia. A factor analysis was used to determine the two underlying constructs of the Body Concept Questionnaire. These two constructs, self-consciousness and body satisfaction, were then correlated with the summed scores of the three subscales and then with the 33 individual items of the Importance of Clothing Questionnaire, by Pearson product moment correlations. Two of the six null hypotheses were rejected: relationships were found between self-consciousness and attitudes toward clothing management, and between self-consciousness and the social approval provided by clothing of blind and visually handicapped adolescents. A positive intercorrelation was indicated between the two subscales, Management and Social Approval. Significant correlation coefficients were found between the five items of the Body Concept Questionnaire and the 33 items of the Importance of Clothing Questionnaire. Relationships were shown between body concept and selected clothing attitudes of the blind and visually handicapped adolescents who took part in this study. / Master of Science

The excretion of Ca, Cu, Fe, Mg, Mn, Na, K and Zn in the sweat of 7-10 year old girls living in southwest Virginia was investigated. Sweat samples were collected in an arm bag which covered the hand and forearm of the subject. The samples were wet ashed and assayed on an Atomic Absorption spectrophotometer. No significant correlation was found between mineral intake and excretion in the forearm sweat. There was no apparent relationship between the environmental temperature and the excretion of minerals in the sweat. There were great variations in mineral excretion among subjects. Calcium excretion ranged from 3.39-35.32 mcg/hr. Copper and magnesium excretion in the forearm sweat ranged from 0.04-0.66 mcg/hr and 0.00-7.98 mcg/hr, respectively. The range of excretion for the other minerals studied was: 0.005-0.074 mcg/hr of Mn; 9.78-62.51 mcg/hr of K; 9.95-57.9 mcg/hr of Na; 0.014-0.529 mcg/hr of Fe; and 0.10-3.71 mcg/hr of Zn. Reasons for discrepancies between these results and those reported in the literature are discussed. Suggestions for further research on the cutaneous mineral excretion of the preadolescent age group are recommended. / Master of Science

An application of relaxation techniques to the solution of transonic flow in a converging - diverging nozzle is presented. The assumptions of steady, isentropic flow of a perfect gas were made. Successive line relaxation, similar to that of Garabedian and Korn, was employed in a transformed computational plane. The potential function at interior points was obtained column by column through repeated application of the Thomas algorithm. Once the interior-point calculations were complete the values of the potential function on the boundaries were obtained by extrapolation using the wall-tangency and centerline-symmetry conditions where appropriate. A final solution was considered obtained when negligible changes were observed in the Mach number at all flow-field points from one iteration to the next. To determine the accuracy of the method, the flow through a hyperbolic converging - diverging nozzle was calculated and the results were compared with an existing solution obtained by a series expansion method. The calculated lines of constant Mach number were in excellent agreement with the series expansion solution. The time required for this solution was faster than time-dependent and error-minimization-type solutions by more than a factor of four even though no attempt was made to optimize the computational efficiency of the program logic. / Master of Science