Browsing by Author "Austin, Walter J."
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Item A study of the propagation methods for the analysis of simply supported cylindrical shells(1964) Shah, Pravin M., 1932-; Austin, Walter J.The use of certain propagation methods for the analysis of simply supported cylindrical shells is described and the accuracy of these methods is studied with the help of two illustrative problems. It is shown that this method is convenient for more complex problems of shells with discontinuities along the generators, or for shells of arbitrary shape. With respect to the former, a transformation matrix is given which is useful for bridging over the line of discontinuity, while for the latter, the governing differential equations are derived.Item A study of three numerical methods for the analysis of circular plates symmetrically bent(1965) Lu, Li-Shun; Austin, Walter J.This dissertation contains a study of three numerical methods for the solution of radially symmetric plate bending problems. Two of the methods consist of numerical integration procedures applied to the well-known governing, differential equations. The first numerical integration technique proceeds one interval at a time and employs closed-type, consistent integration formulas based upon a linear variation of the highest derivatives in each interval. The second numerical technique proceeds two intervals at a time and employs closed-type, consistent integration formulas based upon a parabolic variation of the highest derivatives in the two intervals. In both methods recurrence formulas are used to avoid iteration. The third numerical method is an original finite element procedure which employs finite difference expressions to evaluate the bending moments. The accuracies of the three methods have been investigated by applying them to ten problems of wide diversity, including plates with and without a central hole, with uniform and with non-uniform thickness, and with abrupt steps in the thickness, and subjected to edge couples and shears, distributed loadings, ring line loads, and with concentrated load at the center. The outer edge is considered to be either fixed or hinged in all problems. The numerical solutions of the ten problems by the three methods are presented herein in complete form. In a number of the problems solutions have been obtained for several interval sizes. These solutions are compared with each other and with the exact solutions to give an indication of the accuracies of the methods.Item Accuracy of several finite difference methods for plate problems(1964) Doshi, Arvind D; Austin, Walter J.The accuracy of several finite difference methods for the analysis of the flexure of plates with fixed edges is studied in this dissertation. The investigation has been confined to a study of a square fixed edge plate subjected to uniform loading. Three different approaches are taken. First, the accuracy of the solutions obtained by the conventional finite difference procedure on a uniform square network was investigated by solving the test problem with seven different sizes of networks. Then the improvement of the accuracy of these solutions by the Richardson's extrapolation technique was studied. The second approach involved the use of graded networks with finer divisions near the fixed edge. Two different network patterns were used. The improvement of accuracy with the increase in fineness of the net was determined. The Richardson's extrapolation procedure was also studied to examine if it is useful for graded networks. Finally, in the third approach the use of higher order differences was investigated for uniform networks. A comparison is made of the accuracy of the various methods discussed above.Item Analysis and design of slender arches(1975) Volz, Robert Dennis; Austin, Walter J.A numerical procedure is presented for the elastic stress analysis of symmetric arches. Both linear and nonlinear methods of analysis are considered as well as a linear stability analysis. The procedure is very general and is applicable for either prismatic or nonprismatic arch ribs of different geometries, shapes, loading conditions, and slenderness ratios. The method of analysis employs a combination of a numerical integration technique and a successive approximations procedure. Both axial and bending deformations are considered. A computer program has been developed from the procedure to find the magnitude of a given load distribution which will produce first yielding in the arch. A study has been conducted to determine the location of a distributed live load which minimizes the magnitude of the load necessary to produce yielding. Comparisons are made with the results of linear and nonlinear analyses to determine situations for which a linear analysis is adequate.Item Analysis of plates with variable thickness(1966) Huang, Qiuyuan, 1913-1979; Austin, Walter J.In this thesis is studied the effect of variable thickness upon the moments, reactions, and deflections of tapered rectangular plates with three edges fixed and one edge free, subjected to uniform loading. The plates are tapered in one direction with the least thickness at the free edge and the greatest thickness at the opposite fixed edge. The solutions may be uaeful for the design of reinforced concrete retaining walls, tanks, and other structures. Solutions are given for a wide range of parameters. Poisson's ratio is taken as zero for all collations. The results are presented in detail in tables and charts in a form convenient for design uae. A Kantorovich-Galerkin method of solution was employed, using a series involving Duncan symmetric functions between the fixed edges. The resulting coupled ordinary differential equations were then solved by the finite differenceItem Analysis of thin shells by modifications of thin wall beam theory(1966) Childers, Jim Bob; Austin, Walter J.The use of thin wall beam theory for the analysis of simply supported shells is described and the necessary modifications to the thin wall beam theory are shown which will make the solution as theoretically correct as the basic classical theories used in the analysis of simply supported shells. A simply supported circular cylindrical shell is analyzed by this method and the results compared with a solution by the classical theory for the same shell which is given in the American Society of Civil Engineers Manual No. 31. The results show close agreement. The analysis is similar to the method of analysis of H. Lundgren. Either a successive corrections methods as used by Lundgren, or a successive approximations procedure, developed in this thesis, may be used. Slow convergence, or even divergence, is obtained in many problems. However, very rapid convergence may be obtained by the use of extrapolation formulas based upon the assumption that in successive cycles the differences between the true solution and the trial solution decrease, or increase, in a geometric ratio. The basic purpose for presenting the "mOdified thin wall beam theory" is not just to simplify the analysis of thin shells from the standpoint of the mathematics involved, but rather to provide an addi-tional method to use in the analysis of shells in cases where the goy- , erning differential equations cannot be solved exactly or even be de- fined in explicit mathematical terms.Item Approximate flexural-extensional relations for steel structural members(1975) Nazar, Serkis; Austin, Walter J.The object of this investigation is to propose approximate moment-curvature-axial load-mean strain relations for steel members loaded beyond the yield point by combined bending and axial load, accounting for initial residual stresses induced in the members during their formative hot-rolling or welding processes. Since no exact relations can be found, except for residual stress-free members, with rectangular cross sectional, numerical procedure has been developed for integrating stresses at certain points obtained by dividing the cross-section into small elements. A Newton-Raphson type iterative procedure has been developed for obtaining curvatures and mean strains, given moments and axial loads. Moment-curvature and axial load -mean strain relations, with axial load and moment, respectively held constant. A least-squares procedure has been developed to approximate the curves by simple mathematical functions A hyperbola was found to be the most valuable approximation.Item Buckling of tapered columns under combined axial load and end moment(1962) Wu, Julian Juh-ren; Austin, Walter J.; Sims, James R.; Jacobson, WarrenThis study is concerned with the elastic buckling strength of a simply—supported tapered I—column subjected to uniform axial compression and end moments which are proportional to the depth. The governing differential equation are derived and then these equations are solved numerically for a wide range of parameters. The results are presented in three sets of curves. A design procedure for such members is proposed.Item Dynamic response of simple systems to periodic forces(1983) Dotson, Kirk Wayne; Veletsos, Anestis S.; Lutes, Loren D.; Austin, Walter J.A study of the response of viscously damped single-degree-of-freedom systems to non-harmonic periodic excitations is presented. The objectives have been (1) to assess the effects of the various factors that affect the response of such systems; and (2) to present information and concepts with which the salient features of the response may be identified readily. The following aspects of the response are examined: (a) the steady-state response, which is the response obtained after the free vibrational component is damped and the resulting motion repeats itself; (b) the absolute maximum response, which is generally obtained prior to the attainment of the steady-state response; (c) the rate of "build-up" of the response; and (d) the effects of possible cessation of the excitation. The factors investigated include the characteristics of the structure and the excitation. Special attention is paid to the behavior of low-frequency systems. For a number of excitations, closed-form expressions are also presented for the steady-state response of undamped systems.Item Effect of a slab on the behavior of exterior beam to column connections(1985) Zerbe, Hikmat Edward; Durrani, Ahmad J.; Lutes, Loren D.; Austin, Walter J.In reinforced concrete frame buildings, slabs are usually cast monolithically with the floor beams. The currently used recommendations for the design of beam to column connections for seismic loading, however, completely ignore the presence of the slab. Even though, previous studies have shown slabs to have a significant effect on the performance of connections, it has been believed that the test data are not adequate to justify revisions of the design recommendations. In this experimental investigation, the interaction of a slab with exterior beam to column connections is studied. The experimental program consisted of tests under simulated earthquake type loading on seven large-scale exterior beam to column connections. Except for the slab width, which was varied in each specimen, the basic design and configuration of subassemblages remained the same and conformed to the current design criteria. Based on the test results, it is concluded that it may be nonconservative to ignore the slab in the design of connections. It is suggested that a certain width of the slab effectively acts as a part of the floor beam. It is also concluded that at larger levels of interstory drift, transverse beams may not be effective in confining the joint. Ignoring either of these effects can lead to nonconservative connection designs.Item Effect of loaded length on the buckling strength of slender arches(1978) Chang, Kou-Chuan (b. 1957); Austin, Walter J.The broad objective of this investigation was to gain an improved understanding of the in-plane, elastic buckling behavior of slender arches subjected to a static dead load that is uniform over the structure and to a static live load that is uniform on a horizontal projection. The live load starts at one end and extends over a variable length. The effect of the length of the live load on the buckling behavior of a prismatic arch and the loading which minimizes the buckling magnitude was first determined. Then the effects of different parameters on the minimum buckling loads were also studied for various rise/span ratios, end conditions, arch geometries and slenderness ratios. Thirdly, the effect of temperature strains on the buckling behavior was investigated for the optimum live load length. Finally, a study was made of the rib shortening effect caused by thrust on the buckling behavior. A numerical integration technique combined with a successive approximation procedure which is based on the method developed by Newmark for straight beams and columns and the adaptations made by Austin for arches was used for the analysis. The program developed is very general and is applicable to either prismatic or nonprismatic arch ribs of different geometries and shapes.Item Elastic behavior and design of arches(1979) Leung, Alen Wah Kwok; Austin, Walter J.; Holt, Edward C.; Merwin, John E.A detailed parametric study of the elastic behavior of symmetric arches with hinged and fixed ends is presented herein. The study is restricted to parabolic arches of moderate and low rise (<.25 span) with prismatic cross-section subjected to a uniform dead load and a uniform live load which extends from the left support over a variable length. Both the dead and live loads are of uniform intensity on the horizontal deck of the arch. The effects of load magnitude, slenderness ratio, rise/span ratio, live/dead load ratio and length of live loading on the internal forces, displacements and reactions are investigated. Approximate equations to predict stresses and deflections are derived. Special study has been made of the occurrence of first yielding. The live load length, load magnitude and location on the arch axis corresponding to first yielding have been found for a wide range of parameters. Approximate procedures are presented for estimation of the load at first yielding. The analytical study was made with the use of a computer program. The information presented herein is expected to be useful for the design of arch bridges.Item Free vibration of circular arches(1969) Pereira, Carlos Antonio Lopes; Austin, Walter J.The lower natural frequencies and the associated modes of vibration of uniform circular arches which are either fixed or simply supported at the ends are computed and studied in this thesis. A general theory which considers the effects of rotatory inertia and shearing deformations as Well as extensional and flexural deformations was used. When both rotatory inertia and shearing deformations are neglected the general theory reverts to a well -known classical theory which is based upon the same assumptions as Flugge's theory for the bending of cylindrical shells. The governing differential equations were solved numerically by a Holzer -type iterative procedure combined with an initial value integration method. A Runge- Kutta integration technique was used. The method was programmed for an IBM 7040 computer, and all results were obtained on this computer. A detailed study has been made of the lowest ten vibration frequencies and modes for fixed arches for a wide range of slenderness ratios and for angles of opening of 45° , 90° and 180°, using the classical theory. The effects of rotatory inertia and shearing deformations have been investigated only for arches with an angle of opening of 90°. Simple approximate expressions for estimating the natural frequencies of I fixed-ended arches (classical theory) are developed and their accuracy evaluated ii by comparing them with the results obtained by exact analysis. In addition, exact solutions of classical theory were made for hinged circular arches with angles of opening of 45° and 180° and the accuracy of approximate expressions for estimating the natural frequencies of hinged arches proposed by Austin, Veletsos and Wung were evaluated for these angles of opening.Item Large deflection bending and buckling analysis of arches(1974) Tawfik, Adel Said; Austin, Walter J.A numerical procedure is presented herein for the analysis of buckling of arches under the effect of general unsymmetrical loadings. The prebuckling deflections caused by the loadings are considered. The analysis is nonlinear and is limited to the elastic behavior. A numerical integration technique combined with a successive approximation procedure is used for the large deflection bending analysis and for a linear buckling analysis. The numerical integration technique is based on the method developed by Newmark for straight beams and the adaptations made by Austin. A computer program was developed to solve the problem and to provide valuable quantities for design studies. The program can handle general unsymmetrical distributed and concentrated loads for circular and parabolic arches. Effects of different parameters on the buckling loads were studied for various rise-span ratios, end conditions, and arch geometries. Rib shortening was also considered. The solutions were obtained to an accuracy of about .5 percent. A classical bending and buckling numerical analysis which does not consider prebuckling deflections was also developed to check the accuracy of the numerical integration and to provide values to start the iterations in the large deflection analysis.Item Lateral buckling of tapered, cantilever I-beam(1963) Begnaud, Eugene Enile; Austin, Walter J.It is the purpose of this study to examine theoretically the effect of flange and web taper on the lateral stability of a cantilever I-beam loaded with a point load at its end in the plane of maximum flexural rigidity. Both the flange and the web are tapered linearly. The load is allowed to move with the structure as it deflects, but its direction does not change, i.e., the load remains vertical. The governing differential equations are derived and the method of finite differences is used to solve the problems. Three cases are studied: load at the top flange, at the shear center, and at the bottom flange. In each case the initial direction of the load is through the shear center. Curves are plotted for a range of tapers from which may be obtained the critical buckling load. Three solutions are compared with experimental results obtained at Columbia University.Item Lateral buckling of uniformly loaded, tapered, cantilever I-beams(1965) Vanderzyl, Richard Lynn; Austin, Walter J.The purpose of this thesis is to report a theoretical investigation concerned with the effect of web and flange taper on the lateral stability of a uniformly loaded, cantilever I-beam. The I-beam is loaded along its entire length in the plane of maximum flexural rigidity. The web and flanges are tapered linearly from the free end to the fixed end. Results are obtained for three positions of load application: at the top flange, at the shear center or centroid, and at the bottom flange. In each case, the initial direction of the load is vertical through the shear center and the load is assumed to remain acting in a vertical direction, but is allowed to move as the beam deflects. The governing differential equations are derived and the method of finite differences is used to numerically solve these equations. Tables and representative plots of the results are provided from which the critical buckling load may be readily determined.Item Numerical analysis of plates of variable thickness(1966) Albafull, Jaime Sabater; Austin, Walter J.The accuracy of five finite difference methods when applied to the analysis of plates of variable thickness is 'studied in this thesis. The plates are rectangular with two opposite edges simply supported. The thickness varies only in the direction parallel to the simply supported edges. In this case, the governing partial differential equation can be reduced to a series of independent, linear, fourth order, complete, ordinary differential equations with variable coefficients. The numerical solution of this two-point boundary value problem is studied for the special case of exponential variation of thickness.Item Numerical large deflection bending and buckling analysis of arches(1973) Ross, Timothy Jack; Austin, Walter J.A numerical procedure for the analysis of slender arch buckling problems for general symmetric loadings is presented herein. Such loadings cause bending moments in the arch which result in significant prebuckling deflections and changes in the arch profile. The problem is nonlinear. The numerical procedure is limited to an inextensible analysis and to elastic behavior. Based on a numerical integration technique developed by Newmark for straight beams, a large deflection bending analysis is combined with small deflection buckling routines to formulate the numerical procedure. The numerical procedure is composed of a combination of the numerical integration and a successive approximations procedure. A computer program was developed from the numerical procedure to obtain useful design data. A study is made of the fundamental buckling loads for a wide range of rise/span ratios for varying combinations of arch geometries, support conditions, symmetric loadings, and antisymmetric and symmetric buckling modes. Results acquired in this study for circular arches are compared to existing exact values and then the numerical procedure is extended to obtain new data on parabolic arches. Comparisons are made between buckling loads computed with the inclusion of prebuckling deflections and buckling loads computed by neglecting all bending deflections.Item Plates on flexible supports (a theoretical investigation of the behavior of a plate on flexible beams using a numerical procedure)(1964) Khalil, Hatem Mohamed; Austin, Walter J.Solutions for displacements, moments and reactions in rectangular plates under transverse loading, supported at the corners, with or without supporting beams at the plate boundaries and with or without corners being free to lift, are presented in this paper. The problems are solved numerically using the method of finite-differences programed for a digital computer. Moment and reaction coefficients are evaluated at positions along the axes of symmetry and the boundaries for several values of the parameters of relative flexural rigidity and Poisson's ratio and covering three different panel side-ratios. The analyses of the plate-beam systems are based on the ordinary theories of flexure of plates and beams.Item Shear strength of prestressed concrete t-beams with welded wire fabric as shear reinforcement(1985) Robertson, Ian Nicol; Durrani, Ahmad J.; Austin, Walter J.; Lutes, Loren D.In thin webbed prestressed concrete T-beams, the placement of conventional stirrups is difficult and time consuming. Welded wire fabric appears to provide a relatively economical alternative. In this study, the shear strength of prestressed T-beams reinforced with welded wire fabric as shear reinforcement is investigated. Thirteen large-scale bonded and unbonded prestressed T-beams were tested. The test variables included the type, amount and anchorage conditions of the shear reinforcement. These beams were tested under static third-point loading over a span of eleven feet. In all beams, shear failures occured along shallow diagonal tension cracks at loads in excess of the code predicted values. Anchorage of the welded wire fabric by means of two horizontal wires at top and bottom of the vertical web wires as recommended in the code performed well. However, the quality of the welded wire fabric was found to be critical for satisfactory performance.