In this thesis, a computer program for graphically displaying finite element beam stresses is discussed. Beam elements are represented as thick lines with colored stress contours along the length. Stress gradients through the beam thickness are not displayed. Many program options are available to aid in creating a clear view of stress distributions in complex models. The front, right, top, and isometric views are preprogrammed views, or a rotated view of the model can be specified. Also, specific portions of the model can be magnified. A region may be defined for showing cut sections of the model. Contour options are available to help enhance stress representation. Node locations may be marked, and beam line widths modified. Finally, any view that has been developed can be saved in a file to be redisplayed at a later time. The program also has the capability of displaying resultant beam forces and moments. Beam stress displays for two train car models are used to demonstrate the usefulness of the program as both a presentation and modeling diagnostic tool. Stress gradients and high-stress regions are easily seen. With these displays some model discrepancies were uncovered and some highly stressed locations were observed that had not been discovered in the prior research. / Master of Science

Linear elastic theory of torsion and flexure of thin-walled beams as developed by Vlasov and Timoshenko respectively are well known and commonly used in everyday engineering practice. However there are noticeable differences between calculations and experimental results. The difference is partly due to one of the basic assumption of classical theory, namely that the secondary shear strains due to warping are negligible. In the present work a new three noded, with CO continuity, isoparametric beam finite element is developed based on a torsion theory by Benscoter. In the classical theory warping is assumed to be proportional to the rate of twist, whereas in Benscoter's theory it is assumed to be proportional to an independent quantity called the "warping function". The exact form of this function can be evaluated from equilibrium equations. This assumption of Benscoter's allows the formulation of a Co element based on the assumed displacement method. The other advantage of Benscoter's theory is that it takes into account the effects of secondary shear strains. These effects are quite significant for closed sections. The element is validated for several cases of a cantilevered beam of rectangular cross section and in every case the results are in good agreement with the exact solution. It is also shown that the element gives a very good representation of curved beams, for which there is torsional-flexural coupling. A number of cases of a curved I-beam under various loading and boundary conditions are analysed, and in every case the results agree closely with the analytical solution. In order to represent the torsional response the element uses seven degrees of freedom per node. This seventh degree of freedom is the "warping function" mentioned earlier. To make the element compatible with standard finite-element programs which have six degrees of freedom per node, static condensation is used. / Master of Science

M.S.

In intelligent structures, structural deformation is generally controlled by either embedding or surface bonding the induced strain actuator to the structure. With bonded or embedded actuators used for inducing flexure, the developed in-plane force contributes indirectly through a locally-generated moment. Control authority in this configuration is thus limited by actuator offset distance. The focus of this research was to investigate a new concept in which the actuator, as opposed to being bonded, is attached to the structure at discrete points. This configuration is fundamentally different from the bonded/embedded configuration in that the actuator and the structure between the two discrete points can deform independently; and the in-plane force of the actuator, which contributes only indirectly in the case of bonded actuator, can directly influence out-of-plane displacements of the structure. Additionally, the actuator offset distance can be optimized with respect to actuator force/strain saturation for increased authority. Two implementations of this concept as applied to beam structures were investigated. In the first, the actuator (e.g., shape memory alloy actuator wire) does not possess any flexural stiffness; and therefore, remains straight between the two attachment points. In the second implementation, the actuator (PZT's and electrostrictive) possesses flexural stiffness, and bends with the structure. The formulation and experimental results for both implementations are presented. Enhanced authority is demonstrated by comparing the static response of the discretely attached actuator beam systems with their bonded counterpart systems. / Ph. D.

Modal analysis is the experimental characterization of the dynanlical behavior of a structure. Recent advances in laser velocimetery have made available to the experimentalist a rich, new source of vibration data. Data can now be obtained from many different spatial locations on a structure. A method is presented to use this new data for the analysis of beams. Two approaches are investigated: minimum residual methods and boundary condition methods. The minimum residual approaches include autoregressive methods and non-linear least squares techniques. Significant contributions to sample rate considerations for parametric sinusoidal estimation resulted from this research. The minimum residual methods provide a good connection between the measured data and the fitted model. However, they do not yield a true modal decomposition of the spatial data. The boundary condition approach provides a complete modal model that is based on the spatial data and is completely compatible with classical beam theory. All theoretical constraints are included in the procedure. Monte Carlo investigations describe the statistical characteristics of the methods. Experiments using beams validate the methods presented. Advantages and limitations of each approach are discussed. / Ph. D.

The current end web crippling design equations are based on a collapse mechanism developed for interior web crippling of short-span plate girders. Yield-line theory and the mechanism solution were used to derive an expression for the web crippling capacity of a plate girder subjected to an interior patch load. The general form of this equation was then calibrated using available data to obtain an equation for end web crippling as well. This study examines the origin of the equation and identifies inconsistencies, which result from using the same assumptions for both types of web crippling. A new collapse mechanism, based on modified assumptions, is used to derive a new equation that applies specifically to end web crippling of hot-rolled sections. In addition, three full-scale tests were conducted on steel-concrete composite beams to verify the accuracy of the proposed equation. Finally, the current web crippling equations and the proposed equation are compared for all available end web crippling data, and conclusions and recommendations are made concerning the validity of the proposed end web crippling equation. / Master of Science

The purpose of this study is to model the beam/decking connectors (nails) of a glulam dome cap by beam/connector elements, and to analyze various dome cap models in order to investigate the potential of the beam/connector model to simulate the decking. Two- and three-dimensional beam/connector elements are formulated, tested, and evaluated. The dome cap is modeled with I-DEAS, and the modeling procedures are briefly discussed. Four series of beam/connector dome cap models are created and analyzed: (1) models with the nailed joints at bracing points (rigid link h=0), (2) models with the nailed joints at bracing points (h>0), (3) models with 16 nailed joints per beam element (h=0), and (4) models with 16 nailed joints per beam element (h>0). Their results are compared with the dome cap models with the truss bracings. Finally, conclusions and recommendations for future research are presented. / Master of Science

Studies of numerical methods to decouple structure and fluid interaction have reported the need for more precise approximations of higher structure eigenvalues and eigenvectors than are currently available from standard finite elements. The purpose of this study is to investigate hybrid finite element models composed of standard finite elements and exact-elements for the prediction of higher structure eigenvalues and eigenvectors. An exact beam-element dynamic-stiffness formulation is presented for a plane Timoshenko beam with rotatory inertia. This formulation is based on a converted continuum transfer matrix and is incorporated into a typical finite element program for eigenvalue/vector problems. Hybrid models using the exact-beam element generate transcendental, nonlinear eigenvalue problems. An eigenvalue extraction technique for this problem is also implemented. Also presented is a post-processing capability to reconstruct the mode shape each of exact element at as many discrete locations along the element as desired. The resulting code has advantages over both the standard transfer matrix method and the standard finite element method. The advantage over the transfer matrix method is that complicated structures may be modeled with the converted continuum transfer matrix without having to use branching techniques. The advantage over the finite element method is that fewer degrees of freedom are necessary to obtain good approximations for the higher eigenvalues. The reduction is achieved because the incorporation of an exact-beam-element is tantamount to the dynamic condensation of an infinity of degrees of freedom. Numerical examples are used to illustrate the advantages of this method. First, the eigenvalues of a fixed-fixed beam are found with purely finite element models, purely exact-element models, and a closed-form solution. Comparisons show that purely exact-element models give, for all practical purposes, the same eigenvalues as a closed-form solution. Next, a Portal Arch and a Verdeel Truss structure are modeled with hybrid models, purely finite element, and purely exact-element models. The hybrid models do provide precise higher eigenvalues with fewer degrees of freedom than the purely finite element models. The purely exact-element models were the most economical for obtaining higher structure eigenvalues. The hybrid models were more costly than the purely exact-element models, but not as costly as the purely finite element models. / Ph. D.

This report details the design and construction of an AASHTO Type IV prestressed girder and a PCI BT-56 prestressed girder. It also details the shear testing and shear performance of the BT-56 girder. The results are compared with results from previous research dating back to 1986. Finally, all research was compared with the AASHTO Standard (2002), AASHTO LRFD (1998) and AASHTO LRFD (2004) Specifications to examine thier overall accuracy in predicting shear strengths.

A number of older bridges built before the 1970’s were constructed with floor systems consisting of a non-composite concrete slab over steel girders. Many of these bridges do not satisfy current load requirements and may require replacement or strengthening. A potentially economical means of strengthening these floor systems is to connect the existing concrete slab and steel girders to permit the development of composite action. This dissertation describes a research program investigating methods to develop composite action in existing non-composite floor systems by the use of postinstalled shear connectors. Three types of post-installed shear connection methods were investigated. These methods are referred to as the double-nut bolt, the high tension friction grip bolt, and the adhesive anchor. These post-installed shear connectors were tested under static and fatigue loading, and design equations for ultimate strength and fatigue strength were developed. These post-installed shear connectors showed significantly higher fatigue strength than conventional welded shear studs widely used for new construction. The superior fatigue strength of these post-installed shear connectors enables strengthening of existing bridge girders using partial composite design, thereby requiring significantly fewer shear connectors than possible with conventional welded shear studs. Five full-scale non-composite beams were constructed and four of these were retrofitted with post-installed shear connectors and tested under static load. The retrofitted composite beams were designed as partially composite with a 30-percent shear connection ratio. A non-composite beam was also tested as a baseline specimen. Test results of the full-scale composite beams showed that the strength and stiffness of existing non-composite bridge girders can be increased significantly. Further, excellent ductility of the strengthened partially composite girders was achieved by placing the postinstalled shear connectors near zero moment regions to reduce slip at the steel-concrete interface. Parametric studies using the finite element program ABAQUS were also conducted to investigate the effects of beam depth, span length, and shear connection ratio on the system behavior of strengthened partially composite beams. The studies showed that current simplified design approaches commonly used for partially composite beams in buildings provide good predictions of the strength and stiffness of partially composite bridge girders constructed using post-installed shear connectors. / text