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This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method. / Master of Science

Poisson's ratio for aluminum is estimated from velocity profile measurements of a free-free beam under dynamic loading conditions A weighted least-squares method is used to select a beam model which is subsequently used to determine the transverse and anticlastic radii of curvature. The model of the beam velocity profile is selected using forward regression with the possible regressor set formed by products of Legendre polynomials in x and y, the two-dimensional coordinates of the beam. The resulting model is manipulated to extract the transverse and anticlastic radii of curvature of the beam which are then used to find local and global estimates of Poisson's ratio. Estimates for Poisson's ratio are found for three different forcing frequencies and three force amplitudes at each frequency. The frequencies selected correspond to the frequencies of the operating shapes dominated by the first, second, and third bending modes. A statistical analysis is performed to assess the quality of the estimates of Poisson's ratio. Results show that the estimates of Poisson fs ratio are dependent on the forcing frequency and forcing amplitude. All estimates are below the accepted value of .33 for aluminum. Contributions of plate modes adversely affect the estimates. Estimates based on the first and third operating shapes exhibit a lower variance than the estimate based on the second operating shapes. / Master of Science

Composite diaphragm strength and behavior were studied using non-linear finite element analysis. A total of 57 three panel diaphragm models were analyzed to failure. Parameters studied included beam size and orientation, panel dimension, connector type and distance, slab opening, yield plateau, and beam connection flexibility. Shear connector, deck-to-concrete interface, and beam connection were the components modeled non-linearly. Orthotropic behavior was used for the deck elements. 2-D and 3-D contours of concrete slab, steel deck and deck-to-concrete interfacial stresses and connector forces are presented to clearly show the behavior of the diaphragm in relation with the component behavior. Complete and incomplete connector force redistributions were observed and an expression of yield plateau length required to develop a complete connector force redistribution was developed. Expressions for diaphragm strength based on beam, beam connection and connector strength for both the complete and incomplete connector force redistribution cases were presented. The diaphragm strength predicted by the expression compared favorably with the finite element results. / Master of Science

The main objective of this study is to develop an analytical model to explain the behavior of a hybrid structure under different loading conditions. The model developed for a simply supported beam on moment capacity, stiffness, and deflection can be generalized to deal with any type of material combination. The dependence of moment capacity of the hybrid beam on the thickness of the composite sheet was investigated. The inherent property of a high Young's modulus and strain-to-failure properties of the composite material increased the moment capacity of the RC beam dramatically. The moment model showed a percentage increase of 284% for KFRP while on the other hand the percentage increases for CFRP and GFRP were 191% and 174% respectively when using a FRP sheet of thickness 0.025 mm. KFRP showed the highest increase in moment capacity because of its high strain-to-failure. CFRP on the other hand has a high Young's modulus, but its strain to failure is low, causing it to lie in the middle range. The analytical model is that the ability of a beam to handle moment is strongly dependent on the strength characteristics and the thickness of the FRP sheet. / Master of Science

A numerical model was developed to analyze the effectiveness of active and passive secondary support systems on the stability of a retreating longwall tailgate opening. The range of loading conditions that any tailgate can be subjected to was identified to form the basis of numerical modeling. The tailgate entry was considered as a part of roof-pillar-floor system, whose behavior is controlled largely by the structural integrity of each member. Numerical modeling was then conducted on tailgate openings to determine roof, floor, and rib responses, including failure modes to a variety of loading conditions for wood cribs and roof trusses employed as active and passive means of secondary support. Trends were developed from numerical modeling to determine optimum load capacity and paints of application for reducing the potential for entry failure. / Master of Science

see document conclusions / Master of Science