The response characteristics of beams and plates made from composite laminates are strongly affected by the shear deformations of their layers. However, incorporation of the shear deformation further complicates the equations of motion and their analysis. As a result the vibration analysis of such structures have been limited to simple free vibration studies such as determination of their frequencies. The forced vibration problems of these structures have been solved by exact methods for only some very simple cases. In this study, a generalized modal approach is presented to solve more general vibration problems of composite beams and plates. The coupled systems of partial differential equations, representing the equations of motion, are uncoupled into modal equations by utilizing the eigenfunctions of the system and its adjoint. A method is presented to obtain these eigenfunctions for beams with arbitrary boundary conditions and for plates with Levy-type boundary conditions. The forced vibration solutions obtained by this method are then used to calculate the random response characteristics of beams and plates subjected to spatially and temporally correlated random loads. In the analysis of beams, both symmetric cross-ply and angle-ply configurations have been considered. In the symmetric cross-ply configuration with no torsional loads, of course, the warping effects are absent. The angle-ply case, however, includes torsion-warping effects and coupled bending-torsion motions. A simple displacement field is introduced to reflect warping in the third-order shear deformation theory. In the analysis of plates also two configurations of the laminates have been considered: symmetric cross-ply and antisymmetric angle-ply. At this time, these are the only two configurations which can be solved by the closed-form modal analysis approach for the Levy-type boundary conditions. In both cases of the beams and plates, the numerical results with and without shear deformations are obtained and compared. The results for no shear deformation are obtained with the classical lamination theory. The results have also been obtained for the first-order shear deformation theory with a somewhat simpler displacement field which has been commonly used in the past by several investigators. The numerical results are obtained for the global response quantities such as frequencies, displacements and crossing rates as well as for the local response quantities such as normal and shear stresses across a cross section. The numerical results obtained with various deformation theories for the frequencies as well as response quantities are compared to evaluate the effect of the shear deformations. For thicker and rigid beams and plates, one observes large differences in the frequencies and responses obtained with (the first- and third-order shear deformation theories) and without consideration of shear deformations (classical theory). For the frequencies and global responses both the first- and third-order theories give about the same results. But for the local response quantities, the results obtained with the two shear deformation theories can also be quite different in some cases. In any case, the results clearly point out the importance of including the shear deformations in thick and rigidly constrained composite beams and plates. Although, in this study only uniform cross section or uniform thickness beams and plates have been considered, it is felt that the eigenfunctions developed herein can also be conveniently utilized with advantage as comparison functions in approximate Rayleigh-Ritz type of approaches to analyze non uniform structures. / Ph. D.

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Advancements in design technology and construction materials have allowed composite floor systems to become longer and shallower. As a result, serviceability considerations rather than strength considerations have started to control designs. Partial continuity in composite floor systems has been suggested as a means by which the serviceability aspects could be improved. A new beam-to-girder connection referred to as a composite semi-rigid beam-to-girder connection is investigated as a possible method to provide partial continuity in floor systems. Four of these connections are evaluated experimentally and analytically to determine their behavior and the feasibility of their use in typical composite floor systems. The results indicate that these connections would improve serviceability aspects of the floor system and would improve the general efficiency of the floor design. / Master of Science

The strength of materials solution for a new bonded cantilever beam test specimen to determine adhesive shear properties is reviewed and discussed. A parametric analysis for the adhesive shear stress and for the end deflection reveals the specimen dimensions required for reliable bonded adhesive shear properties determination. Recommendations are provided for conducting reproducible tests. A pure and quasi-uniform shear test for stiff adhesives is proposed. Analytical solutions are compared with Finite Element solutions from VISTA and NOVA for the stresses in the adhesive. It appears that the assumption of pure shear is nearly valid even for very stiff and/or very thick adhesives. In order to increase the end point deformations for stiff adhesives, a modified specimen is proposed. Three-dimensional effects through the thickness of the adhesive layer are studied with the program ABAQUS. Experiments were performed using the two methods derived from theory and good correlation between theory and experiment were obtained with some restrictions. For both methods, experimental results underlined the need for defining proper specimen geometry prior to testing. Simple numerical codes are proposed to facilitate this purpose. / Master of Science

The large deformation response of composite beams subjected to a dynamic axial load was studied. The beams were loaded with a moderate amount of eccentricity to promote bending. The study was primarily experimental but some finite element results were obtained. Both the deformation and the failure of the beams were of interest. The static response of the beams was also studied in order to determine the difference between the static and dynamic failure. Twelve different laminate types were tested. The beams tested were 23 in. by 2 in. and generally 30 plies thick. The beams were loaded dynamically with a gravity-driven impactor traveling at 19.6 ft./sec. and quasi-static tests were done on identical beams in a displacement controlled manner. For laminates of practical interest, the failure modes under static and dynamic loadings were identical. Failure in most of the laminate types occurred in a single event involving 40% to 50% of the plies. However, failure in laminates with 30° or 15° off axis plies occurred in several events. All laminates exhibited bimodular properties. The compressive flexural moduli in some laminates was measured to be 1/2 the tensile flexural modulus. No simple relationship could be found among the measured ultimate failure strains of the different laminate types. Using empirically determined flexural properties, a finite element analysis was reasonably accurate in predicting the static and dynamic deformation response. / Master of Science

A mathematically one-dimensional model was developed to predict the static response of composite sandwich beams subjected to loads induced by piezoelectric (PZT) actuators. The model was derived using Reddy's (1984) displacement field for a laminated plate which consists of cubic variation of the in-plane displacement through the thickness. In this model, beam deformations include extension, bending, transverse shear, St. Venant torsion, and torsion due to warping of the cross section out of its plane. The PZT actuators can be configurated to induce a bimoment, resulting in twist cf the beam through the warping of the cross section. Hence directionally attached PZT (DAP) actuator elements, which cause twist by inducing tensile and compressive strains at 45° to the longitudinal axis of the beams, are not necessary to actuate twist. For an aluminum beam example, it is shown that the PZT bimomet control produced about 2.7 times more twist than the conventional DAP control. / Master of Science

periments and predictions was found to be excellent around the net-section region. Although predictions for other strains were not as good, they were within the range of experimental data. Distribution of contact stresses between the pins and the hole edges was also studied. Numerical analysis suggests that the prevalent assumption of radial cosine distribution of contact stress between the pin and hole edge is in substantial error. It can also be concluded that the strength of the joint is for the most part, independent of its width, though for narrower specimens, the holes were quite highly loaded. / Master of Science

This study investigates the effects of typical construction details on the strength of steel deck reinforced concrete composite slabs. Past research on composite slabs has been centered primarily around single span, single panel width slabs with unrestrained ends. The test specimens in this study are more representative of actual slab construction. The effects of multiple spans, multiple panels, end restraint from pour stops, and deck anchorage from shear studs and welds are investigated. The results of this experimental study are analyzed using methods given in the Steel Deck Institute Composite Deck Design Handbook. The models were found to conservatively predict the strength of the composite slabs. Recommended modifications to the calculation methods are given. / Master of Science

The results of sixty-five double-sided pushout tests utilizing the Elco grade 8, 5/16 in. diameter, standoff screw functioning as a mechanical shear connector are presented. In all tests, the base material, through which the screw was fastened, was fabricated out of back to back angle to simulate the top chord of an open web steel joist. Varied test parameters include: steel deck profile, base angle thickness, screw embedment depth, slab thickness, and slab width. The objectives of the testing were (1) to provide an understanding of the strength of the standoff screw in various test geometries and (2) to provide an understanding of the slip characteristics, or ductility, of the connector. A review of literature presents several applicable existing welded stud strength models based on post-test observations of failure mechanisms. Modeled failure mechanisms include: concrete splitting, concrete pullout, rib shear, and stud shear. After applying the existing models to the pushout test data, the following conclusions are drawn: (1) the concrete splitting model developed by Oehlers (1989) can be used to predict the strength of the standoff screw in flat slab geometries and (2) no existing model adequately predicts the strength of the standoff screw in geometries utilizing profiled steel deck. An equation, based on a rederivation of a wedged shaped shear-cone pullout model (Lloyd & Wright 1990), is presented which predicts the strength of the standoff screw in geometries with steel deck with acceptable accuracy. / Master of Science

This paper discusses an investigation into thermal buckling and post-buckling of symmetrically laminated composite plates. In this study, thermal buckling is investigated for laminates under two different simple support conditions, fixed and sliding. These laminates are subjected to the conditions of a uniform temperature change and a linearly varying temperature change along the length of the plate. Postbuckling in the presence of a uniform temperature change and nonlinear response to imperfections in the form of a thermal gradient through the thickness of the plate and a lack of initial flatness are also studied. The buckling response is studied using variational methods, specifically the Trefftz criterion. Postbuckling and responses to imperfections are studied using nonlinear equilibrium conditions. A Rayleigh-Ritz formulation is used to obtain numerical results from the formulations for the prebuckling response, the buckling response, and the post-buckling and imperfection responses. The analyses are applied to graphite-reinforced materials with (± 45/0₂)_s and (± 45/0/90)_s lamination sequences. Numerical results are obtained for these laminates and also for the case of these laminates being rotated 30° inplane. For the first laminate, for example, such a rotation results in a (+75/ — 15/30₂)_s. stacking sequence. Such skewing of the principal material directions may be encountered when using fiber-reinforced materials in a structurally tailored design. In addition, the influence on thermal buckling of a lack of ideal boundary conditions in the form of boundary compliance and thermal expansion, which would occur in any real set-up, are investigated. / Master of Science