Several researchers engaged in family housing have recently become concerned about the vibrational behavior of residential floors. This concern resulted in a need for methods of sensing floor vibrations. Some investigators have sensed floor vibrations with electric resistance strain gauges bonded to the underside of the floor joists. These experiments using strain gages as vibration sensing devices resulted in a need to be able to determine the vibration amplitude (or deflection) from strain vibration data. The objectives of this project were to theoretically and experimentally determine the relationship between midspan flexural strain and midspan deflection of freely vibrating wood beams with various end conditions. Theoretical strain-deflection relationships of freely vibrating wood beams with pinned-end and fixed-end conditions were derived from vibration theory. Free vibration tests on three wood beams with pinned-ends and fixed-ends gave results which were in agreement with theory. The theoretical relationship between the end rigidity and natural frequency of beams with semi-rigid end connections was derived. Vibration tests performed on wood beams with semi-rigid end connections produced frequency-rigidity results which agreed with theory within five percent. The semi-rigid end connections were achieved by using a torsion bar on each end designed so that the beam would have a static behavior midway between pinned-end conditions and fixed-end conditions. However, it was found both theoretically and experimentally that these torsion bars resulted in a dynamic behavior (strain-deflection ratio and frequency) much closer to pinned-end conditions than to fixed-end conditions. It was established that the strain-deflection relationship of freely vibrating wood beams can be predicted from vibration theory if the rigidity of the end connections is known. / Master of Science

Corrosion of reinforcing steel is a major cause of damage to bridges in the United States. A possible solution to the corrosion issue is carbon fiber reinforced polymer (CFRP) material. CFRP material has been implemented as flexural reinforcement in many cases, but not as transverse reinforcing. The CFRP material studied in this thesis was NEFMAC grid, which consists of vertical and horizontal CFRP tows that form an 8 in. by 10 in. grid. The use of NEFMAC grid as transverse reinforcing has not been previously investigated. First, the development length of NEFMAC grid was determined. Next, an 18 ft long 19 in. deep beam, modeled after prestressed Bulb-T beams, was created with NEFMAC grid reinforcement. The beam was loaded with a single point load near the support to induce shear failure. Beams were fitted with instrumentation to capture shear cracking data. Shear capacity calculations following four methods were compared to test results. Lastly, a parametric study with strut-and-tie modeling was performed on Precast Bulb-T (PCBT) girders to determine the amount of CFRP grid needed for reinforcement in the anchorage zone. This thesis concludes that NEFMAC grid is a viable shear design option and presents the initial recommendations for design methods. These methods provide a basis for the design of NEFMAC grid shear reinforcing that could be used as a starting point for future testing of full scale specimens. When designing with NEFMAC grid, the full manufacturer's guaranteed strength should be used as it is the average reduced by three standard deviations. AASHTO modified compression field theory provides the best prediction of shear capacity. For anchorage zone design, working stress limits for CFRP grids need to be increased to allow more of the strength to be implemented in design. / Master of Science

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

Three models are presented which predict frequencies and mode shapes of transverse vibration for a continuous prismatic Bernoulli-Euler beam on elastic supports, subjected to a compressive axial load. The first model, which approximates support stiffnesses by an equivalent elastic foundation, is found to be inaccurate for wave lengths close to the support spacing. A discrete mass model is formulated which accounts for axial load by stability functions which modify the element stiffness matrices. A continuous model is formulated which yields an exact solution for Bernoulli-Euler beam theory. The frequencies predicted by the discrete mass model and continuous model are in excellent agreement. A method of predicting axial compressive load and support stiffness based on measured frequency and phase data is presented which can be used for either the discrete mass model or the continuous model. A frequency reduction factor is derived which accounts for the effects of shear deformation and rotatory inertia. Tests are performed on an eight span beam with compressive axial load. Test results show that the models accurately predict frequencies and mode shapes of vibration. Results indicate that the method formulated can be used to determine compressive axial load and support stiffness. / 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

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

This thesis presents an investigation and derivation of the expression: fer bending moment, torsional moment, and shear at the ends and at any intermediate point along a circularly curved beam. The investigation includes both cantilever beams and fixed ends beams, loaded with a uniformly distributed load, concentrated loads or a combination of the two. The solutions of the equations have been presented in a graphical form for the case of the uniformly distributed load, and a tabulated form representing the ordinate of the influence lines for the case of the concentrated loads. The graphs and tables cover a series of beams whose arcs are subtending central angles of 50, 45, 60, 75, 90, 120, 135, 150, 165 and 180 degrees and whose stiffness ratio: (K) are 1.33, 2, 4, and 10.67. Special emphasis has been given to reinforced concrete curved beam design as based on the theories and experiments presented in the literature by Timoshenko and Gowan. The investigation shows that many questions still remain to be answered in the design of reinforced concrete beams subjected to bending moment, torsional moment and shear; and there is a need for the ACI Code to give some criteria for such designs in the near future. / Master of Science

Corrosion of reinforcing steel causes shorter life spans in bridges throughout the United States. The use of carbon fiber reinforced polymer (CFRP) materials as the flexural reinforcement in bridge girders has been extensively studied. However, CFRP transverse reinforcement has not been as rigorously investigated, and many studies have focused on CFCC stirrups. The use of C-Grid as an option for transverse reinforcing has not been previously investigated. This thesis concludes that C-Grid is a viable shear design option and presents the initial recommendations for design methods. These methods provide a basis for the design of C-Grid shear reinforcing that could be used as a starting point for future testing of full scale specimens. This testing program first determined the mechanical properties of C-Grid and its development length. Four 18 ft long 19 in. deep beams, modeled after prestressed Bulb-T beams, were created to test the C-Grid, as well as steel and CFCC stirrups. The beams were loaded with a single point load closer to one end to create a larger shear load for a given flexural moment. Overall beam displacement was measured to determine when flexural reinforcement yielding was reached, and beams were fitted with rosettes and instrumentation to capture initiation of shear cracking. Shear capacity calculations following four methods were compared to test results. The design method should follow the AASHTO modified compression field theory with equations for β and θ. The manufacturer's guaranteed strength should be used for design as long as that strength is the average reduced by three standard deviations. Shear crack widths are controlled to a similar size as steel stirrups when using at least two layers of grid. / Master of Science

A theoretical technique is presented for computing the stress distribution, the torque-rotation relation, and the torsional capacity for prismatic beams with arbitrary cross-sections subjected to pure torsional loading. The technique may be applied to any beam with isotropic, homogeneous, linear or non-linear elastic properties and a known shearing stress–shearing strain relation. The theoretical analysis is substantiated with experimental data obtained from pure torsion tests on five unreinforced plaster model beams: three circular, one rectangular, and one T-shaped in cross-section. Results are also presented on a second series of twenty-nine qualitative tests made on plaster model T-beams reinforced with small gage wire to determine the crack pattern and failure mechanisms. / Ph. D.

The study presents the results of an experimental and analytical investigation aimed at examining the lateral stability of rectangular reinforced concrete slender beams. In the experimental part of the investigation, a total of eleven reinforced concrete beams having a depth to width ratio between 10.20 and 12.45 and a length to width ratio between 96 and 156 were tested. Beam thickness, depth and unbraced length were 1.5 to 3.0 in., 18 to 44 in., and 12 to 39.75 ft, respectively. Each beam was subjected to a single concentrated load applied at midspan by means of a gravity load simulator that allowed the load to always remain vertical when the section displaces out of plane. The loading mechanism minimized the lateral translational and rotational restraints at the load application point to simulate the nature of gravity load. Each beam was simply-supported in and out of plane at the ends. The supports allowed warping deformations, yet prevented twisting rotations at the beam ends. In the analytical part of the study, a formula was developed for determining the critical loads of lateral torsional buckling of rectangular reinforced concrete beams free from initial geometric imperfections. The influences of shrinkage cracking and inelastic stress-strain properties of concrete and the contribution of longitudinal reinforcement to the lateral stability are accounted for in the critical load formula. The experiments showed that the limit load of a concrete beam with initial geometric imperfections can be significantly lower than the critical load corresponding to its geometrically perfect configuration. Accordingly, a second formula was developed for the estimation of limit loads of reinforced concrete beams with initial lateral imperfections, by introducing the destabilizing effect of sweep to the critical load formula. The experimental results were compared to the proposed analytical solution and to various lateral torsional buckling solutions in the literature. The formulation proposed in the present study was found to agree well with the experimental results. The incorporation of the geometric and material nonlinearities into the formula makes the proposed solution superior to the previous lateral torsional buckling solutions for rectangular reinforced concrete beams.