Browsing by Author "Thibodeaux, Murphy H."
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Item A comparison of analytical procedures for grid structures(1964) Sun, Tseng-Chen; Thibodeaux, Murphy H.In this paper three methods which take into account the torsional effect in analysis of rectangular two-way grid structures arc introduced and compared. The first method in the "Plate-Analogy Method" which treats the grid as an unisotropic plate. The solution of the basic equation of the equivalent unisotropic plate, by analogy, is the solution for the grid. In this study, the finite difference technique was used to naive the plate equation. Special treatment for the case of the fixed edge grid was introduced* The second method is the " Slope-Deflection Method" which adopts three unknowns at each intersection joint of the grid: the deflection, and two orthrogonal elopes at that joint. The moments torques, and shear at the joint can be expressed in terms of the slopes and deflections of the surrounding joints. Prom equilibrium relationships, three equations can be written at each joint. Solution of the resulting sets of simultaneous equations yields as results the unknown slopes and deflections. Then the moments, torquers, and shears can be calculated. The third method considered is the " Deflection Method" proposed by the writer. The basic idea is to treat the grid as composed of discrete rigid bars connected by elastic two-way joints. The moments, torques and shears can be expressed by the deflections of the surrounding joints. From equilibrium relationships one equation can be written at each joint. Solution of resulting simultaneous equations gives the unknown deflections. Then the moments, torquers, and cheers can be calculated An a 8 X 8 square grid, uniformly loaded, with edges either simply supported, fixed,or supported at four corners was studied. The Slope-Deflection Method yields the exact answer, Whereas the Plate-Analogy Method and Deflection Method are approximate methods. The study shows that both the Plate-Analogy Method and Deflection Method give results which are acceptable for most engineering applications. The Deflection Method is much easier to apply than the other two methods. The effect of torsional stiffness of the member should not be ignored in some grid analysis. This study shows that if a grid is made of pipes, the resulting error in deflection and stresses will be 100 %; whereas, for the case of open rolled sections the error will be less than 10 % for the case studied. By assigning a special member section with the property the " Slope-Deflection Method" can be adapted as the " Grid-Analogy Method" to solve plate problems. Molecular equations for various boundary conditions for each method are developed fully in this work. These equations are developed in a very general manner, so that they could be applied to a grid with member sizes and spacings not necessarily the same in two orthogonal directions.Item A procedure for synthesizing unit hydrographs for urban watersheds(1965) Davis, Edward Julien; Thibodeaux, Murphy H.The purpose of this study is to introduce a modification of the Taylor and Schwarz method of synthesizing unit hydrographs whereby the Taylor and Schwarz equations may be used for urban watersheds. Brief reviews and discussions of the rational method, the Snyder method, and the Taylor and Schwarz method are presented. An investigation and discussion of the effect on the unit hydrograph of variations in Manning's coefficient of roughness, n, and the hydraulic radius, r, as caused by channel rectification is presented. The proposed method consists of determining the lag time of a hypothetical instantaneous unit hydrograph and computing a synthetic slope factor for the watershed. These parameters are substituted into the Taylor and Schwarz equations, and the unit hydrograph is computed. An example problem is included to demonstrate the procedure.Item A study of continuous elastic beams on discrete non-linear elastic supports(1963) Kim, Sun Yong, 1968-; Thibodeaux, Murphy H.This study discusses an iterative approach to the problem of a continuous beam on discrete non-linear elastic supports and its application. The literature studied revealed that practically no work has been done on engineering approaches to this problem. The basic equations are developed from flexural theory and are solved by iteration utilizing Newton' s linear approximation method. The solutions obtained were checked by energy methods. Numerical results are presented for a marine fendering system, a typical example of a beam on non-linear elastic supports. For various loading conditions, a comparison is made between an approximate linear solution and the solution obtained using the non-linear approach developed in this study.Item An analytical study of a space frame(1960) Leach, Richard Peter Parton; Thibodeaux, Murphy H.; Pfeiffer, Paul E.; Holt, E. C.Item An experimental investigation of water wave inertial forces on large diameter piles(1966) Russell, Larry Rayner; Thibodeaux, Murphy H.An experimental investigation-was carried out in the Rice University wavetank facility with the object of determining the magnitude and variation in time of inertial forces due to wave action on large diameter pilings of circular cross-section. Mass coefficients were computed for various wave periods and wave heights using two different wave theories and comparisons are made between the results. The measured wave force and predicted wave force for a second order Stokes wave approximation are both plotted versus time. All of the Waves studied were "deep-water" waves . A discussion of the deviations of the experimental results from theory is included. A detailed description is provided of the equipment in the Rice University wavetank facility, including the "L"-shaped wavetank. The equipment performance is discussed.Item Analytical study of a rigid jointed space frame on elastic supports(1961) Desai, Ardeshir R; Thibodeaux, Murphy H.; Wilhort, J. C., Jr.; Holt, E. C.Item Numerical analysis of normally loaded articulated beams on elastic supports(1965) Krog, Joel Thomas; Thibodeaux, Murphy H.A numerical method for the analysis of normally loaded articulated beams on elastic supports is presented. The method is an iteration procedure using numerical integration to solve the differential equations governing the action of the beams. The procedure is applied to beams made up of straight line segments. Cross sections are allowed to vary. Two alternate methods are discussed. One uses the numerical integration technique to calculate deflections in terms of an assumed moment, shear, slope, twist or deflection. The true deflection can be determined by considering boundary conditions of the beam. The second alternate method uses the numerical integration technique to find influence coefficients, which are used in a general method solution. The alternate methods are not iteration procedures. Examples which apply these methods to various support conditions are given. Advantages of each method are given. Convergence of the iteration procedure is discussed.Item Photoelastic study of stresses in frames with deep members(1961) Tsai, Stephen Likuan; Thibodeaux, Murphy H.The photoelastic technique was employed to investigate the normal stress variation in elastic pinned-end portal rigid frames with deep members. Length to depth ratios were varied for both beams and columns.. Plastic models were loaded symmetrically by two equal concentrated loadm,. Photographs of stress pattern in the frame were used to evaluate the stresses. Also an analytical solution was obtained by using virtual work with the distance between center lines as the effective spalu EXperimental results and the results of the analytical solutions were compared and it was concluded that commonly used design methods are valid if the span-to-depth ratio is not smaller than 4 (center line span) or 3 (clear span). If the span-to-depth ratio is smaller than the above values, either experimental results or the ablutions based on elastic theory should be adopted as abatis for design.