Showing papers in "Journal of Engineering Mechanics-asce in 1966"

Buckling of Shallow Arches

Abstract: The exact solution to the nonlinear problem of the buckling of a shallow, circular arch subjected to a uniform pressure or a concentrated load is given. In addition an explicit bifurcated equilibrium path is presented. The buckling loads, according to several criteria, are found and their range of validity is investigated in detail. It is shown that even if the smallest buckling load is associated with an asymmetric bifurcation this alone is not a sufficient condition for the asymmetric buckling criterion to govern the problem.

Earthquake Stress Analysis in Earth Dams

Abstract: The finite element method, which has been used extensively in the static analysis of elastic continua, is extended to the dynamic analysis of two-dimensional stress systems. The method involves calculation of vibration mode shapes and frequencies, making use of a stiffness matrix evaluated by the finite element method and a mass matrix formed by lumping the mass at the finite element nodal points. The dynamic response is then calculated by the mode-superposition method, the response of each mode being obtained by step-by-step integration. The method is demonstrated by the earthquake analysis of a triangular earth-dam cross section treated as an elastic plane-strain problem. Vertical and horizontal acceleration components of the 1940 El Centro earthquake are applied; results are presented in the form of plots showing the time history of stresses at selected points in the cross section and also plots of stress contours at selected instants of time.

Stability of Plates Using the Finite Element Method

Abstract: The finite element method of structural analysis is extended to the problem of stability of plates. Stability coefficient matrices are derived for rectangular plates for constant and variable direct stresses and shear stresses. These, in conjunction with the stiffness matrix, allow an easy modification of the conventional plate stiffness matrix to include the effects of in-plane stresses, thus giving a simple and rapid formulation of stability problems for plates. The method is applicable to a wide variety of problems. This includes plates with variable moment of inertia, anisotropic plates, plates with any type of edge or body loadings, plates subjected to thermal stresses and plates coupled with other elements such as beams, ribs, etc., with all types of boundary conditions.

Solution of Anisotropic Seepage by Finite Elements

Abstract: A new method of numerical solution of equations governing seepage flow, in non-homogeneous and anisotropic media is presented. The formulation is developed in some detail for two dimensional situations. In this, the region is divided into finite elements of triangular shape but of an arbitrary size. To each element different values of the two permeability coefficients and inclination of strata can be assigned at will in the computer program written. The solution is tested against a simple case of anisotropi seepage for which exact values are known and the accuracy obtained is excellent. The method is applied to obtain a solution to a hypothetical problem of some complexity in which the strata inclination varies from point to point together with the various values permeabilities. The method has obviously a general applicability to related problems such as torsion of anisotropic sections, etc. The basic flow theory in anisotropic materials is reviewed.

Analysis of Laminated Shells of Revolution

Abstract: A finite-element method is presented for the static stress analysis of laminated orthotropic shells of revolution under arbitrary loads. The shell is approximated by a system of short conical frusta, and the stiffness for each element is derived by means of variational principles. Various problems were solved and comparison of these results with known analytical solutions shows extremely good correlation.

Water Pressure on Dams Subjected to Earthquakes

Abstract: A method is proposed to estimate the maximum hydrodynamic pressure in a two-dimensional reservoir subjected to horizontal earthquake motions. The method parallels the modal analysis ordinarily used for buildings. The hydrodynamic spectrum concept introduced herein results in curves that almost match the response spectra for sine, cosine, and El Centro 1940 ground motions, this suggests that ordinary damped spectra can be used for computing hydrodynamic water pressure.

Response of Liquid in a Rectangular Container

Abstract: Ideal incompressible liquid motion in rectangular container due to rectangular double and sinusoidal pulse excitation

Plane-Framework Methods for Plates in Extension

Abstract: Plane-framework procedures are presented for the analysis of plates in extension. Two different types of rectangular framework models are used to represent a rectangular element of uniform thickness in the plate. The cross-sectional properties of the beams in each model are derived by equating the deformations of the model to those of the plate element when both are subjected to identical loads. One model consists of side and diagonal beams and is directly applicable for any value of Poisson's ratio, while the other consists of orthogonally connected beams only and the effect of a non-zero value of Poisson's ratio is incorporated by successive approximations.

Method for Minimal Design of Axisymmetric Plates

Abstract: A method of minimum volume design for axisymmetric plates, exclusively based on statical considerations, is developed. The method uses a novel technique of stress variation by which a given stress of the plate is transformed into another stress. The volume variation resulting from this transformation is assessed for plates of sandwich construction obeying Tresca’s criterion. A reduction in volume indicates that the given stress does not lead to the minimum volume design, which is eventually determined by a short elimination process. The minimum volume designs of a class of sandwich axisymmetric plates not studied before are determined and some unknown aspects of the problem in cases previously studied are revealed.

Effect of Boundary Conditions on Shell Buckling

Abstract: The results of an experimental study on the influence of boundary conditions on the elastic buckling behavior of spherical shells are presented. Eighty-seven uniform pressure tests on small-scale polyvinyl chloride shells include as variable parameters the shell thickness, base radius, edge restraint condition, and edge force disturbance.

Behavior of Elastic-Plastic Trusses with Unstable Bars

Abstract: Sufficient conditions for uniqueness of incremental response and overall stability are established and discussed for elastic plastic trusses containing unstable members. These criteria consist of the positive definiteness of matrices built up with the elastic influence coefficients of bar-forces for dislocations and with the plastic compliances of the members at the yield point. All conditions are proven to be weaker than the usual demand of local stability, for all redundant structures. Normality of the incremental plastic displacement vector in load-space is shown to hold, irrespective of instability, non-linearity in the elastic range and changes of the elastic behavior due to plastic strains. Convexity of the loading surfaces is also briefly discussed, with special reference to the case of non-linear elastic response of some members.

Elastic Stress Field in a Plate with a Skew Hole

Abstract: A general method is considered for the analysis of the stresses in a homogeneous, isotropic, elastic thin flat plate containing a skew hole. The method develops the solution for the problem of the skew hole from the plane stress solution for the equivalent right hole. As an application of the method of analysis, the stress concentration factor for a skew elliptic hole is determined, the solution being presented in such a manner that its components, taken singly and in combination, successively correspond to the ordinary and exact plane stress solutions for the right hole and an approximate correction for the effect of skewness.

Comparison of Static and Dynamic Hysteresis Curves

Abstract: Hysteretic force-deflection curves of a single-story laboratory structure made of mild structural steel were obtained experimentally for both static and dynamic loading conditions. The dynamic loading consisted of a sinusoidal force at about 3 cps applied to the roof of the structure. Maximum fiber strains up to 9 times the yield strain were realized. A strain softening type of modification of the steel was observed during the experiments with subsequent strain ageing occurring between experiments. Differences between static and dynamic hysteretic force-deflection curves were found to be smaller than changes in the static curves caused by the material modifications during repeated loading.

Effect of Foreign Inclusions on Properties of Solids

Abstract: Approximate expressions are given for the elastic properties of heterogeneous solids made of inclusions imbedded in a matrix with dissimilar properties and for the upper and lower limits of elastic properties for a case of rigid inclusions. Experimental results are presented on properties of epoxy-alumina composites. The results of the approximate theory are compared to theoretical results based on rigorous mathematical approaches, to existing experimental data, and to experimental results obtained by the author. In all cases, a good agreement is found to exist. A comparison between experimental and theoretical results on Young's modulus is given for heterogeneous solids with inclusion-to-matrix moduli ratios of 3.4, 7, 17, 25, 32, 69, and 100. To allow for tailor making of new composites, the inter-dependence between properties of composites and their constituents has been generalized through a selection of convenient parameters and is presented graphically. The approximate results are shown to be simple, relatively accurate, and quite suitable for engineering computations of the elastic properties of heterogeneous solids.

Vibration of a Viscoelastic Timoshenko Beam

Abstract: Coupled equations for vibrations of a linear viscoelastic Timoshenko beam of an incompressible material are obtained by replacing the elastic moduli by viscoelastic operators. Time-variables in these equations are separated out by means of a dual eigenfunction expansion in terms of the corresponding elastic modes. Specific problems on free and forced vibration for a beam of either Kelvin or Maxwell material are treated in detail. The problem of moving load and the problem of a time-dependent boundary condition are also included in the treatment. It is shown that the foregoing solutions obtained for different specific problems retain their forms if the viscoelastic material is changed from an incompressible one to one of identical behavior in bulk and in shear.

Flexural-Torsional Buckling of Planar Frames

Abstract: A method of analyzing flexural-torsional buckling frame failure is presented. The differential equations and equations of equilibrium and continuity at interior joints are derived by minimizing a total potential energy function for the structure. Although the paper is concerned with rectangular rigid frames, the equations are also applicable to single-span beams, continuous beams, and gabled frames. The differential equations are solved by numerical integration and the solution is used to set up a "buckling determinant," which is evaluated for increasing estimates of the critical load until a value is found that makes the determinant zero. This value is the critical load for the structure. The effect of lateral bracing at the knees of a rigid frame on the flexural-torsional buckling load of the frame is investigated for three loading conditions: Lateral load at the top of the left column, transverse loads at third points of the beam section of the frame, and axial loads at the tops of the columns. The results are presented in graphical form.

Vibration Tests of a Nine-Story Steel Frame Building

Abstract: A nine-story steel frame building has been subjected to an extensive ser of forced resonance tests. Seven translational and three torsional modes were investigated in detail. A mode in which the floor slabs vibrated horizontally as free-free beams was excited as well. Stiffness and damping matrices were calculated from the experimentally determined modal properties. Damping values were found to be considerably lower than those usually mentioned in the literature. The lowest translational modes in the two principal directions of the building had damping values of approximately 0.5%. The second lowest translational modes had damping values of approximately 1.0%. Damping was found to increase linearly with resonant frequencies. Consistent, but small increases in damping values were found as the amplitude was increased. The damping mechanism is well represented by relative dashpots.

Strain-Gradient Effects in Microlayers

Abstract: : An analytic solution is obtained for two composite-body problems employing the strain-gradient theory of elasticity as developed by Mindlin. The investigation is concerned with the effects produced by strain-gradients, especially bonding stresses in the vicinity of an interface separating two dissimilar materials when higher order contact conditions prevail at the common boundary. The composite body under consideration consists of an infinite elastic strip ('microlayer') embedded in two semi-infinite elastic regions. The first problem concerns the case of uniform tension at infinity applied in a direction perpendicular to the microlayer. The second considers simple shear applied at infinity parallel to the microlayer. It is shown that the stresses that develop in the vicinity of an interface may be at large variance with the classical results. The magnitude of these stresses may be many times greater than the classical values, thus emphasizing the uncertainty of the classical approach in this instance. This variance is very significant when one material is much more rigid than the other, as encountered in the practical case of composite materials.

Dynamic Deformations of Circular Membranes

Abstract: Equations of motion that govern the inelastic, large deformations of circular membranes subjected to blast loadings are derived and solved numerically. Good correlation with experimental results and with results of a related analytical study were obtained. Investigations were made into the effects of the applied pressure distribution and edge restraint on the final mechanical state of the deformed membrane.

Inelastic Response of Beams to Moving Loads

Abstract: The dynamic response of elasto-inelastic beams to moving loads is studied analytically based on a discrete beam model consisting of massless rigid panels connected by flexible joints with point masses. In determining the response, both the elastic and inelastic properties (including strain hardening) are taken into account. The moving load may be an unsprung mass or a sprung mass, or both, moving at a uniform speed. A feature in the analysis is the consideration of the discontinuities in vertical velocities and accelerations as an unsprung mass crosses a joint of the model beam. The emphas of the numerical results, obtained for simply supported bilinear beams, is on unsprung loads. Results indicate that for an elastic perfectly-plastic beam, loads smaller than the static yield load can cause permanent deformations. However, loads considerably heavier than the static yield load can still cross the beam. In addition to the load mass, the major factors influencing the inelastic deformations of the beam are the load speed and the inelastic stiffness of the beam. Even a small amount of positive inelastic stiffness reduces the permanent beam displacements significantly.

Edge Load Solutions for Conical Shells

Abstract: Solutions of the governing equations for truncated conical shells are developed for stress couples and transverse shear resultants at each end of the shell. Because of the rapid dissipation of the ...

Dynamic of Separable Multistory Buildings

Abstract: The wide multistory building having a set of identical parallel transverse frames and a set of identical floors is an example of a separable structure. Certain problems of such structures can be solved by combining solutions for a typical frame and a typical floor. Thus, the eigenvalues and two-dimensional eigenvectors for a separable building with mass concentrated at the joints can be found by calculating the eigenvalues and eigenvectors of a typical frame and a typical floor. A procedure for computing all of the frequencies of transverse vibration and all of the associated modes for such a building is presented along with the mathematical theory on which it is based.

Flow Direction Measurement by Hot-Wire Anemometry

Abstract: The theory of forced convection caused by the normal and the longitudinal components off the flow around a hot-wire is reviewed. The effect of wire length and the corresponding corrections are taken into account. The directional sensitivities of single wires and of electrically paired crossed wires are obtained. Single and crossed wires were tested in a variable speed air jet. The experimental results are presented in terms of the Nusselt number as a function of the Reynolds number. The directional sensitivity experiments show that single and crossed wires may be used to measure flow direction with an accuracy on the order of 0.05○. The method was used for the measurement of secondary flow in a trapezoidal duct.

Unsteady Flow of Solid-Liquid Suspensions

Abstract: Basic energy and momentum relationships are used to obtain analytical expressions for pressure and flow variations in suspended solid-liquid flow. The suspended flow occurs in a pressurized conduit system and transients are introduced into the system by rapidly closing a terminal valve. Pressure wave magnitudes and wave stapes generated by this action are investigated. Expressions are obtained describing the momentum exchange resulting from viscous action between the phases that occurs behind the wave front. Experimental results are obtained for several solid-liquid suspensions. The suspending liquid utilized is water and solid rubber, plastic, and sand particles with widely varied properties are used for the solid phase. Pressure wave magnitudes and wave shapes resulting from rapid closure of a terminal valve are recorded. Good agreement between the theoretical and experimental results is obtained.

Waves in a Smoothly Jointed Plate and Half-Space

Abstract: Propagating dilatational and distortional disturbances in a half-space, generate wave motion in a plate that covers the half space. The motion of the plate is described by the Bernoulli-Euler-Kirchhoff theory. The half-space (subgrade) is homogeneous, isotropic and linearly elastic. Plate and subgrade are in smooth contact and thus only normal disturbances are transmitted at the plate subgrade interface. The response of the plate to plane dilatational and distortional waves is examined. Explicit expressions are derived for the plate deflection, the bending moment, and the reflection coefficients. Several special cases such as normal incidence, grazing incidence, and wave incidence—for which the plate effect vanishes—are examined. Diagrams show the deflection and the bending moment as functions of the angle of emergence, the frequency, and the plate-subgrade parameters. The modifications of the equations, if a perfect bond between plate and half-space is assumed, are examined briefly.

Generalized Kelvin-Voigt Used in Soil Dynamics Study

Abstract: The interpretation of dynamic test results is complex relative to the static case, because the mass, shape, and stiffness of the dynamic testing apparatus as well as the properties of the specimen must be considered. This interpretation is facilitated by representing the response of the material by a simplified model and by modeling the apparatus so that an analytical solution may be obtained for the specimen-apparatus system. The general steady state solution for the forced vibration of a cylindrical shaft of material represented by the generalized Kelvin-Voigt model is presented. This general solution can be used, together with the boundary conditions and properties of the various types of apparatus (i.e., apparatus involving the vibration of cylindrical specimens), to obtain the analytical solutions for these specimen-apparatus systems. An example of this procedure is given for a boundary value problem that is typical of some of the specimen-apparatus systems used in the past. The measured response for a cylindrical specimen of sand obtained with such an apparatus is compared with the computed results obtained from the analytical solution.

General Theory for Thick Shell Analysis

Abstract: Applications of shell structures to many engineering fields have introduced the problem of analyzing thick elastic shells. A useful tool for describing shells is tensor analysis. By using such a tool, a formulation based on power series expansions for displacements is developed. The resulting equations may be considered as a recurrence group, permitting the obtaining of the series coefficients in terms of six principal variables. These principal variables are the three middle surface displacements, and the three rotations about the base vectors. The equations for the thick shell theory are developed for the geometrical nonlinear case. The engineering solution of such equations can be obtained by using a cartesian reference frame.

Resonance of Beams Due to Cyclic Moving Loads

Abstract: An analysis is presented for determining the conditions of resonance and the dynamic response of a simply supported beam subjected to a moving point load of variable magnitude \IP\N cos ωt oscillating longitudinally along the beam about a fixed point. In addition to ordinary resonance as produced by a variable magnitude load applied at a fixed point on an elastic body, it is shown that other interesting resonance conditions occur because of the oscillation of the force along the surface of the elastic body. The time rate of increase of the vibrational amplitude of the beam is determined numerically for two sets of initial conditions corresponding to: (1) a load initially at rest on the beam and (2) an oscillating load dropped from zero height on an initially undeformed beam. It is shown that the time rate of buildup of vibrational amplitude increases rapidly as the amplitude of longitudinal oscillation is increased for the typical examples presented.

Elastic, Large Deflections of Annular Membranes

Abstract: In studying various problems arising in the analysis of radially symmetric membranes, existing theories are investigated under the boundary conditions (1) simple continuous circular membrane, uniformly loaded and (2) pressure loaded membrane additionally loaded by an opposing force centrally applied through a smaller disc rigidly cemented to the membrane. Equilibrium equations of a higher degree of non-linearity than those usually encountered in the Foppl-von Karman theory are studied; these reduce to the latter as a special case. Using the method of power series, exact solutions are given to both systems of equations for the case of a uniformly loaded clamped membrane and curves of displacement versus pressure are included for comparison. These are compared with previously derived empirical relationships and experimental data. Two of the principal difficulties associated with the power series approach are avoided by using an iterative technique suitable for a digital computer. For the annular membrane, a numerical approach is developed whereby the two point boundary value problem is replaced by an initial value problem and a Runge Kutta numerical integration process operating directly on the simplified equations of equilibrium. The results of this theory area are compared with those of Iberall.

On the Bending of Spherical Shells

Abstract: The bending behavior of spherical shells is reduced to the solution of a second-order differential equation with complex coefficients. Influence coefficients and functions of truncated spherical shells are evaluated and presented in curve form for the analysis of structures composed of spherical segments. These coefficients are determined by an exact and an asymptotic solution of the governing equation. The asymptotic solution is valid over the entire range of the independent variable when the ratio of shell radius to thickness is greater than 100. An uncoupling criterion is given by which it is possible to establish whether the effect of loads applied at one edge of the shell is transmitted to the other edge. This criterion is determined by the cross-product terms in the influence coefficient matrix.