Vertical Concentrated Load Research Articles

Dynamic response of elastic layer on stiff foundation under time harmonic surface vertical concentrated load

In this paper, the line-load integral equation method proposed in reference [1] is first used for solving the elastodynamic problems. A set of one-dimensional regular integral equation is derived for calculating the dynamic response of elastic layer on stiff foundation under time harmonic surface vertical concentrated load. And the numerical solution of the integral equation is obtained.

Spherical membranes subjected to vertical concentrated loads: an experimental study

The behaviour of spherical inflatable membranes subjected to vertical concentrated forces is investigated experimentally. Vertical and lateral instabilities were observed for spherical membrane models of various profiles subjected to symmetric and asymmetric vertical concentrated loads. Special attention is paid to the lateral instability phenomenon and, in particular, to the post-buckling behaviour of these membranes. Three types of wrinkling patterns associated with lateral instability of these structures are identified and documented. The experimental results confirm, in general, the theoretical predictions derived elsewhere for magnitudes of critical concentrated loads applied to such membranes.

Deformation and strength of an underground pipe (Technical data)

In this repot, we obtained the useful results of the stress and deformation of an underground pipe fixed at both ends and subjected to the soil pressure due to a vertical concentrated load acting on the surface of the ground by the method proposed in the previous paper. Numerical computations were carried out for the more various cases and the results were shown graphically to be practical use.

円形開口のある壁の鉛直荷重時応力について

In this study, stresses of wall with round opening are analyzed for the case of vertical loads acting on the straight boundary of a semi-infinite plane. For this solution, Bariansky and Ohkawa have given to apply Jeffery's approach which gave the general solution of the plane oroblem using bipolar coordinates, to the problem of the distortion introduced in the so-called plane Boussinesq field by the presence of a circular hole. But, the method is solved with the great complexity of expression by decomposing the Boussinesq stress function into Fourier series. Therefore, in this paper, a new stress function χ_0 is assumed in terms of bipolar coordinates, and the distribution of vertical loading along the straight upper edge is directly expanded to Fourier series. In treating the stress function in the coordinates, the distributions of arbitrary loads along the straight boundary are easily expressed to Fourier series. The solution of the case acting a concentrated vertical load at the center on the straight boundary agrees with that of Boussinesq problem. For the each case under (1) a concentrated load, (2) concentrated loads acting at two points placed distance γ apart, and (3) uniform loading on the distance at the center of the straight boundary, the stress distributions of the analytical and the experimental results are shown in Figs.7, 9 and 11, respectively. The distributions of the case (1) are analogous to the case (3). The maximum tensile stress produces on the top of a circular hole. In Fig. 13, the tensile stress of the case (1) is about 2.5 times of (3) in the type λ=0.80 and so the case is notable. On the other hands, the case (2) is effective for diminishing the tensile stress, as increasing values ofλ. The analytical and the expimental results accord with each other.

APPLICATION OF A TRANSFER MATRIX METHOD TO VIBRATION PROBLEM OF AN ELASTIC MULTI-LAYERED HALF-SPACE DUE TO BURIED SOURCES

This paper is concerned with the computational procedure of displacements and stresses of an elastic multi-layered half-space due to harmonic loads acting in the interior of the half-space. In calculating the fundamental solutions of displacements and stresses, the authors propose a transfer matrix method taking advantage of a vectormatrix form which expresses the general solutions of displacements and stresses being used in the derivation of dispersion function of an elastic multi-layered half-space. The results shown in this paper can be used as the fundamental solutions in the Boundary Element Method. As numerical examples, the stresses of an elastic half-space due to vertical and horizontal concentrated loads are calculated for the various non-dimensional frequency ωH1/Vs1.

Deformation and Strength of an Underground Pipe : 3rd Report, Arbitrary Loading

In this paper, the deformation and strength of an underground pipe subjected to the soil pressure due to a vertical concentrated load applied at an arbitrary position on the soil surface, are investigated by an exact method using a differential equation of a thin cylindrical shell introduced by one of the authors, K.Mizoguchi. Considering the ground as a semi-infinite elastic solid, the soil pressures on a buried pipe are evaluated by using Boussinesq formulas and by introducing the coefficient of subgrade reaction. In the case of two or four traveling concentrated loads maintaining constant discussed. We carried out numerical computation and the results are shown for various combinations of the positions and distances of the points of application of loads.

The effect of various parameters on the nonlinear sway-buckling of a three-bar frame

In this investigation the postbuckling response of an unbraced rectangular three-bar frame subjected to a vertical concentrated load at its joint is discussed on the basis of an energy (variational) approach and nonlinear kinematic relations. It is found that the sway-buckling mode of the perfect frame is associated with a symmetric unstable bifurcation point which degenerates into a limit point when small initial imperfections are present. The effects of loading eccentricity, slenderness ratio, moment of inertia and length ratios on the carrying load capacity of the frame are fully assessed.

A tensionless contact without friction between an elastic layer and an elastic foundation

The plane contact problem for an infinite elastic layer lying on an elastic half space is considered. The layer is acted upon by a uniform clamping pressure po, a uniform vertical body force ρ1g due to the effect of gravity in the layer and a concentrated vertical line load P. It is assumed that the contact between the layer and the half space is frictionless and that only compressive normal tractions can be transmitted through the interface. The contact along the interface will be continuous if the value of P is less than a critical value Pcr However, for P >Pcr interface separation takes place along a certain finite region. First, the problem of continuous contact is solved and the value Pcr is determined. Then the discontinuous contact problem is formulated in terms of a singular integral equation. Two loading conditions are considered assuming that the concentrated line load P is either a tensile load or a compressive load. Numerical results for Pcr contact stress distributions, and separation regions are given for various material combinations.

Vibrations of the elastic half‐space due to vertical surface loads

AbstractThe displacements of the surface of the homogeneous elastic half‐space subjected to a vertical concentrated load acting at the surface are calculated. The solution is shown to approach Lamb's simple formula for the far‐field. The solution for the concentrated load can be used to calculate displacements due to distributed loads with high accuracy and economically. The results are applied to define the regions ‘near‐field’ and ‘far‐field’. Some near‐field phenomena are described.

Postbuckling Analysis of Continuous, Elastic Systems Under Multiple Loads—Part 2: Applications

In Part 1, a theoretical stability analysis of continuous, elastic systems subjected to multiple independent loads was developed. Postbuckling behavior and imperfection-sensitivity were investigated. Three examples are presented here to illustrate the procedures and results of that study. The first example consists of a cantilever subjected to a pair of concentrated axial loads, one applied at the tip and the other at midspan. In the second example, involving nonconservative loading, an axial load and a follower load are applied at the tip of a cantilever. Finally, a shallow arch under three concentrated vertical loads is considered, in order to demonstrate a case with prebuckling deformations.

Concrete bearing strength under combined lateral and vertical concentrated loads

Existing information on concrete bearing strength is based predominantly on unidirectionally applied forces. There appears little or no published test data concerning the bearing strength under multidirectional concentrated forces. This paper gives the results of an experimental investigation into the bearing strength of cement-sand mortar specimens under combined mutually perpendicular strip and rectangular patch loading. The principal variables were the relative distance of the strip load, the magnitude and bearing area of the rectangular patch load. The results will prove useful for determining the bearing values of post-tensioned elements at the anchorage and support regions.

Elastic Buckling of Arches under Symmetrical Loading

Critical loads and the corresponding reactions, maximum moments, and crown deflections of two-hinged and fixed, parabolic and circular arches of constant cross section subjected either to a vertical concentrated load at the crown or a vertical load uniformly distributed along the arch axis are tabulated for a wide range of rise/span ratios. It is shown that the critical loads and the corresponding horizontal reactions for antisymmetrical (sidesway) modes are rather insensitive to the prebuckling displacements while the opposite is true for the symmetrical models. The antisymmetrical mode corresponds to a bifurcation type instability while the symmetrical mode corresponds to a snap-through type of buckling. The data are analyzed and simplified methods for estimating the critical loads and the critical horizontal reactions, or both, are suggested for antisymmetrical buckling. In addition to the solutions described previously, accurate values of the critical loads and horizontal reactions are reported for antisymmetrical buckling of two-hinged and fixed, parabolic and catenary arches subjected to loadings which cause pure axial compression and no prebuckling displacements.

The suspended elastic cable under the action of concentrated vertical loads

This investigation treats the static response of a single elastic cable which is suspended between two points that are not necessarily at the same level. The cable is loaded by its self-weight and any number of concentrated vertical loads which may be arbitrarily placed along its length. The analysis presented uses a Lagrangian approach. For the strained cable profile, the tension and displacements are given as functions of a single Lagrangian co-ordinate. A specific application of the general analysis is made and compared with a simple experiment.

The Frictionless Contact Problem for an Elastic Layer Under Gravity

The paper presents a technique for solving the plane frictionless contact problems in the presence of gravity and/or uniform clamping pressure. The technique is described by applying it to a simple problem of lifting of an elastic layer lying on a horizontal, rigid, frictionless subspace by means of a concentrated vertical load. First, the problem of continuous contact is considered and the critical value of the load corresponding to the initiation of interface separation is determined. Then the mixed boundary-value problem of discontinuous contact is formulated in terms of a singular integral equation by closely following a technique developed for crack problems. The numerical results include the contact stress distribution and the length of separation region. One of the main conclusions of the study is that neither the separation length nor the contact stresses are dependent on the elastic constants of the layer.

Settlement of Rectangular Foundation on Soil Layer

The settlement of the surface of a finite layer of soil due to a concentrated vertical load has been determined by Taylor as mentioned by Poulos. This technical note presents the results of a numerical integration that has given the average settlement over the whole rectangular area instead of the corner of a uniformly loaded rectangular area. The results apply with a good approximation to rigid rectangular foundations.

Behavior of a Steep Prestressed Arch Made From a Buckled Strut

The buckling and snap-through behavior of a steep prestressed arch (or shell) obtained by first buckling a thin elastic strut (or plate) into a deformed shape and then attaching it to its supports is studied by solving a set of nonlinear boundary-value problems on a digital computer. Finite displacements of the arch as produced by vertical concentrated load and uniform load are determined for several cases, including both symmetric and unsymmetric modes of buckling. Bifurcation points that give the snap-through load are located in each case. Comparisons are made with the behavior of conventional steep arches and between the theoretical results and experimental data obtained from model tests.

Model Studies of Beams Resting on a Silt Subgrade

Models of beams of different stiffnesses resting on a subgrade of compacted micaceous silt were equipped with strain gages and loaded by various combinations of concentrated vertical loads. Investigations indicate that the pressure distribution, bending moments, and deflections are similar to those occurring under beams resting on an elastic solid. The investigation also confirms that the elementary approach using the concept of mudulus of subgrade reaction is plausible if the beams are sufficiently long. In addition, it was confirmed that the modulus of subgrade reaction depends on the relative flexibility of the beam. Only small changes were observed in pressure distribution as the loads were increased to and over the ultimate values; and little difference was found between bearing capacities of soil beneath beams of differing stiffnesses so long as conditions existed for failure in the soil occurring while beam stresses were still in the elastic range.