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In this dissertation, the response of a slender, elastic, cantilevered beam to a simple harmonic excitation is investigated. The effects of nonlinear curvature, nonlinear inertia, viscous damping and static load are included. The nonlinear equations governing the motion of the beam are derived by the Lagrangian approach. The deflections are expressed as expansions in terms of the linear free-vibration modes. Galerkin’s method is used to eliminate the spatial functions from the governing equations. Three modes are used in this procedure. Approximate solutions of the temporal equations are determined by the method of multiple scales. Four first-order ordinary differential equations govern the amplitudes and phases, and predict a whirling motion under certain situations. The solutions of the modulation equations can be fixed points, limit cycles or chaotic motions. Previous studies considered whirling produced by a primary resonance. In this dissertation, secondary resonances are considered in addition to primary resonance. Previous derivations of equations of motion contain only the linear and cubic terms without consideration of the static displacement produced by the weight of the beam. As a result of this static deflection, there are quadratic terms in the governing equations which introduce the possibility of a superharmonic resonance of order two and a subharmonic resonance of order two. It is shown that out-of-plane motion is possible in every resonance when the principal moments of inertia of the beam cross-section are approximately equal. The longer the beam is, the more prominent the whirling motion becomes. If the excitation frequency is increased or decreased through a resonance, for most cases, the non-stationary response from the method of multiple scales shows good agreement with that from the original differential equations. / Ph. D.

In this study equations are developed for the direct determination of stiffness factor and carry-over factor for parabolic haunched beams. the conventional methods require long and tedious calculations, so the development of these equations, which require only the direct substitution of the variables, is useful. A digital computer was used to generate the data required to develop these general equations. A mathematical model was chosen for the general equation; then, by the statistical "Method of Least Squares," the coefficients in the general equation were determined. The equations were then checked against the generated data to determine average errors in calculated values. Illustrative examples are given to explain the use of the equations. / Master of Science

published_or_final_version / abstract / toc / Civil Engineering / Master / Master of Philosophy

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No description available.

No description available.

Results are presented on tests of reinforced concrete T-beams with a flange 20 inches wide by two inches thick setting on a stem five inches deep and four inches wide. These beams were loaded at the quarter points of an eight-foot span and also at the end of cantilever sections of two feet. The beams were loaded until they collapsed. The reinforcing steel was varied at the support section, but remained constant at the center. Moment-curvature information is developed from the experimental results, and conclusions are drawn concerning present theory for deriving analytical moment-curvature relationships for reinforced concrete sections. Ultimate concrete strain in confined sections is reviewed in light of the experimental results. Discussed also are current theories for calculating ultimate loads for indeterminate reinforced concrete beams. / M.S.

The problem of determining the deflection and stress in a plate under transverse loading can be approached by first considering the plate to be a portion of an infinite plate, ignoring the prescribed boundary conditions. The known loads are then applied to the infinite plate and their effects are calculated at those points which correspond to the boundary of the original plate. A system of suitably chosen loads and moments is then applied on the infinite plate at points beyond the boundary of the original plate such that the prescribed boundary conditions are satisfied. For an exact solution, the number of external loads and moments would have to be infinite. However, in order to deal with the problem numerically, only a finite number of each are considered. Thus, solutions are obtained by satisfying the boundary conditions at only a finite number of points. The method is illustrated for beams and then extended to plates. Several problems with known solutions are solved and the results compared with the exact values. Also, plots of the deflection and moment along the centerline of a cantilevered triangular plate are presented. Discussions of the problem of plates with holes and the effect on the solution of various placements balancing loads are also presented. An IBM 1620 digital computer is used to facilitate calculations / Ph. D.