The theory underlying the design of minimum volume space frameworks is reviewed. Fundamental theorems and relations proposed and developed by Maxwell, Michell, Cox, Chan, Hemp, Johnson and Barnett are discussed and examined from a practical viewpoint. Two dimensional frames, which are close geometric approximations to the theoretical concepts of Michell, are defined and formulas established for their design and complete solution. Computer programmes are established for the analysis of pin jointed trusses having a wide range of parameters. The effect of changing parameters on the structural properties is discussed. Rigid frames are analyzed by the use of STRUDL, [STRUctural Design Language], a multi-purpose computer programme for the calculation of forces and displacements in rigid structures. The effects of biaxial stress in the joints and other deviations from the theoretical concept are examined. Comparison is made with other structural designs to establish the superiority and economy of the Michell design. Birefringent models are made, using a numerically controlled milling machine, and tested under load in a polariscope, to confirm the predicted stress levels in the members and stress concentrations in the joints. Examples are given of practical application of Michell space frames. The design of a high tension transmission tower and of a lightweight astronomical mirror support are considered. Alternative solutions to both problems are suggested to provide a basis for more detailed design. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Reusing RAP in the base layer became a common practice in the last decade. However, some crucial issues must be resolved to succeed in using RAP satisfying the standard specifications as a base layer. The most important unknown factor is the mechanistic behavior of RAP. This question may be satisfied by understanding the role of RAP in terms of whether it just behaves as a black rock or has a stabilizing effect with traditional aggregates used for base layer. The first stage of this study is modeling the structural behavior of RAP via prediction MR. This stage then comprises comparing the predicted results to actual measured data under several field conditions. The second stage focuses on the modeling behavior of PD. This stage takes in consideration two sets of data, the first is for the measured PD data calculated from MR test. While another traditional set of measured data for PD from repeated tri-axial loading (RTL) test either single or multi-stage is collected for the same RAP sources used in the first stage. The third stage concerns on MR-PD relationship. It indicates the typical relationship for the MR-PD behavior that can be understood for the RAP in base layer. The fourth and last stage is essential to investigate the Poisson’s ratio of RAP blends and its effectiveness on both parameters MR and PD. This ratio is measured during un-confined compression test. Two main testing conditions: various water and RAP contents are taken in consideration during this measurement for different RAP/Aggregate sources. This study proves that both prediction models used in the MEPDG for prediction of both parameters MR and PD are totally significant for RAP/Aggregate blends used for pavement base layer. The prediction is at the highest accuracy at water content levels close to OMC%, MDD and with 50% to 75% RAP content. In addition, it is proved that Poisson’s ratio is an effective parameter on both MR and PD parameters especially with variation of water content. This conclusion recommends to take in consideration Poisson’s ratio as an effective parameter in MR and PD prediction models used in MEPDG software. / National Science Foundation (NSF)

published_or_final_version / Civil Engineering / Master / Master of Philosophy

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The semi-analytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this research. The research shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Local and global indices are developed to test the accuracy of the semi-analytical method. The local indices provide insight into the problem of large errors for the semi-analytical method. Local error magnification indices are developed for beam and plane truss structures, and several examples showing the severity of the problem are presented. The global index provides us with a general method for checking the accuracy of the semi-analytical method for any type of model. It characterizes the difference in errors between a general finite-difference method and the semi-analytical method. Moreover, a method improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented showing the use of the global index. / Ph. D.

The method of dimensional analysis has been used for almost a century with experimental methods to obtain, among other things, prediction equations in the physical sciences and engineering. Only recently has the method been considered in the statistical sense. A thorough literature research is presented, including history, method and theory, problems, and disadvantages of dimensional analysis. The dimensional analysis preliminary model is transformed into a multiple linear regression model and is compared to a quadratic regression model with respect to prediction of a single variable in some practical examples. Whereas dimensions are the main consideration in the dimensional analysis model, they are ignored in the quadratic regression model. Two sets of experimental data were used, each set on both models, and the respective residual sum of squares and multiple correlation coefficients compared. The results were similar in both cases. The correlation coefficients of the quadratic model were higher than those of the dimensional analysis model and the residual sum of squares were lower for the quadratic than for the dimensional analysis model. / M.S.

With a great amount of research currently being aimed towards dynamic analysis and control of very large, flexible structures, the need for accurate knowledge of the properties of a structure in terms of the mass, damping, and stiffness matrices is of extreme importance. Typical problems associated with existing structural model identification methods are: (i) non-unique solutions may be obtained when utilizing only free-response measurements (unless some parameters are fixed at their nominal values), (ii) convergence may be difficult to achieve if the initial estimate of the parameters is not "close" to the truth, (iii) physically unrealistic coupling in the system matrices may occur as a consequence of the identification process, (iv) large, highly redundant parameter sets may be required to characterize the system, and (v) large measurement sets may be required. To overcome these problems, a novel identification technique is developed in this dissertation to determine the mass, damping, and stiffness matrices of an undamped, lightly damped, or significantly damped structure from a small set of measurements of both free-response data (natural frequencies, damping factors) and forced-response data (frequency response functions). The identification method is first developed for undamped structures. Through use of the spectral decomposition of the frequency response matrix and the orthogonality properties of the mode shapes, a unique identification of the mass and stiffness matrices is obtained. The method is also shown to be easily incorporated into a substructure synthesis package for identifying high-order systems. The method is then extended to include viscous damped structures. A matrix perturbation approach is developed for lightly damped structures, in which the mass and stiffness matrices are identified using the imaginary components of the measured eigenvalues and, as a post-processor, the damping matrix is obtained from the real components of the measured eigenvalues. For significantly damped structures, the mass, dauping, and stiffness matrices are identified simultaneously. A simple, practical method is also developed for identification of the time-varying relaxation modulus associated with a viscoelastic structure. By assuming time-localized elastic behavior, the relaxation modulus is determined from a series of identification tests performed at various times throughout the response history. Many interesting examples are presented throughout the dissertation to illustrate the applicability and potential of the identification method. It is observed from the numerical results that the uniquely identified structure agrees with simulated measurements of both free and forced·response records. / Ph. D.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Civil Engineering. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / M.S.