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Unreinforced masonry walls subjected to out-of-plane horizontal bending can fail by two alternate modes: stepped failure along the brick-mortar bond, or line failure cutting directly through the bricks. Because of random variations in material properties throughout a panel and the tendency for failure to occur across the weaker elements, vertical cracks will generally exhibit a combination of the two modes. This paper develops a pair of analytical methodologies that treat this phenomenon using a stochastic approach. The first part deals with calculating the ultimate moment capacity by allowing for the weakening effect associated with the mixed (stepped and line) mode of failure. This effect is quantified in terms of strength-reduction factors for mean and characteristic (0.05 quantile) values of strength, which may be applied toward generic ultimate strength design. The second part deals with estimating the relative probability of each failure mode and the probability distribution for the relative proportions of each failure mode along a crack. This is of particular relevance to seismic performance because the two failure modes lead to significantly different postcracking behavior. [ABSTRACT FROM AUTHOR]

Loss of support as a result of voids underneath concrete slabs can initiate and propagate slab cracking in jointed plain concrete pavements. This paper investigates the hypothesis that foundation voiding occurs because of localized plastic deformation of the depressurized foundation as a result of slab curling and repeated application of traffic loads. Plane strain and three-dimensional (3D) nonlinear finite-element models of the subgrade foundation are presented. The analysis shows that voids underneath concrete slabs usually occur along the edge of slabs adjacent to the shoulder. The sizes of voids are primarily determined by foundation properties (cohesion stress and internal friction angle), slab properties, axle loads, and temperature gradients. Voids along the edge of slabs adjacent to the shoulder lead to high transverse tensile stresses on the top surface, which may result in top-down longitudinal cracking close to the outer wheel path. These same voids increase the longitudinal tensile stresses on the bottom surface at the edge of the slabs, which can increase the potential for bottom-up transverse cracking at the middle of the slabs. [ABSTRACT FROM AUTHOR]

This study examined the vibrations of a hinged-free nonlinear beam placed on a nonlinear elastic foundation. The authors found that specific combinations of an elastic modulus in the elastic foundation resulted in 1:3 internal resonances in the first and second modes of the beam. This prompted adding a dynamic vibration absorber (DVA) on the elastic beam in order to prevent internal resonance and suppress vibrations. When the DVAwas placed at the free end of the beam, the boundaries were time dependent. Thus, a shifting polynomial function was used to convert the nonhomogeneous boundary conditions into homogeneous boundary conditions. The authors analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed-point plots were also used to facilitate the observation of internal resonance. This made it possible to study the influence of nonlinear geometry and nonlinear inertia associated with the vibration of the elastic beam. The authors also examined the combination of optimal mass ratio and elastic modulus for the DVA in order to prevent internal resonance and achieve optimal damping effects. In the nonlinear beam investigated in this study, the placement of a DVA between 0.25l and 0.5l from the hinged end of the beam proved the most effective for damping; locations between 0.7l and 0.8l on the beam were ineffective. Finally, numerical methods and simple experiments were studied to compare the results from MOMS and demonstrate the effects of the DVA of this model. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid numerical method for the evaluation of dynamic impedance of rigid foundation embedded in anisotropic multilayered soil. The proposed approach includes two main parts: (a) the solution of wave propagation in anisotropic multilayered soil in the frequency wave-number domain; (b) the evaluation of Green's functions for a buried source lying in the anisotropic multilayered soil in the frequency spatial domain. The derivation of part (a) is based on the precise integration method (PIM) and the mixed variable formulation (MVF) of wave motion equations, which ensure accuracy of the solution and make it convenient to deal with the assembly of layers for multilayered soil. Part (b) can be preceded by applying the inverse Fourier transformation directly. Finally, the flexible volume method is used to obtain the impedance of foundation embedded in anisotropic multilayered soil. A comparison of the numerical results with those available in the literature validates the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

An analytical solution for the dynamic response of an infinite beam resting on a viscoelastic foundation and subjected to arbitrary dynamic loads is developed in this paper. Fourier and Laplace transforms are utilized to simplify the governing equation of the beam to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The validation of the proposed solution is verified by considering the solutions of several special dynamic loads and comparing the degraded solution to the known results. Further complicated dynamic loads, such as impulsive loads and time-lag loads, are also discussed and analytical solutions are presented. These relationships can be an effective tool for practitioners. [ABSTRACT FROM AUTHOR]

In this paper, we examine the use of boundary springs as approximate external boundary conditions for the typical soil islands encountered in finite-element (FE) models of soil-foundation interaction problems. We present a set of simple uniformly distributed boundary springs and a set of variable boundary springs that account for the lateral distribution of contact forces between the foundation and the soil. We evaluate the accuracy of the approach for shallow foundations resting on soil islands of different dimensions. It is shown that significantly smaller errors can be achieved with these boundary springs than those obtained when fixed-fixed or fixed-free external boundary conditions are used. We present an iterative approach to determine the boundary springs for cases in which extremely small soil islands are required. Although the approach suggested to determine the boundary springs is best suited to shallow foundations, good results are also obtained for pile foundations. The approach presented applies to a uniform elastic half-space, but extensions to layered media are possible. [ABSTRACT FROM AUTHOR]

In this paper, we study the deformation and stability of a pinned buckled beam under a point force. The buckled beam is constrained by a tensionless elastic foundation, which is flat before deformation. From static analysis, we found a total of five different deformation patterns: (1) noncontact, (2) full contact, (3) one-sided contact, (4) isolated contact in the middle, and (5) two-sided contact. For a specified set of parameters, there may coexist multiple equilibria. To predict the response of the buckled beam foundation system as the point force moves from one end to the other, we have to determine the stability of these equilibrium configurations. To achieve this, a vibration method is adopted to calculate the natural frequencies of the system, taking into account the slight variation of the contact range between the buckled beam and the tensionless foundation during vibration. It is concluded that among all five deformation patterns, Deformations 1, 2, 3, and 4 may become stable for certain loading parameters. In the extreme case in which the foundation is rigid, on the other hand, only Deformations 1 and 3 are stable. [ABSTRACT FROM AUTHOR]

The principal objective of this study is the development and calibration of a macroelement model for soil-pile interaction under simultaneously applied lateral and vertical loads. Herein, we focus on cast-in-drilled-hole single piles that are partially or fully embedded in soil, which are frequently used as support structures in highway construction. The model is calibrated and verified using primarily three-dimensional finite-element simulations and, whenever possible, with experimental data obtained from open literature. These data indicate that lateral loads significantly affect the vertical response of single piles, whereas the converse coupling is negligible. The proposed macroelement model is capable of mimicking this phenomenon. As such, it is a computationally efficient alternative to finite-element analyses, and is feasible to be utilized in practical applications. [ABSTRACT FROM AUTHOR]

This note summarizes a theoretical and experimental study undertaken to provide a deeper understanding of the effect of different parameters on the coupled modal characteristics of circular cylindrical tanks. First, the most common case of clamped-free tanks resting on rigid foundations is investigated by using finite-element (FE) modeling and holographic experiments. A good agreement between experimental and numerical results is a basis to draw a number of conclusions. For both tank geometries investigated, the frequencies for modes of circumferential parameter n=1 (the “beam” modes) are found to be reduced most significantly by the presence of liquid. Very significant dependence of the radial shell mode shapes on the filling ratio is confirmed both by the FE and experimental results. In addition, nonclassical vibration patterns for radial shell modes were extracted numerically and recorded experimentally. Special attention is paid to the pairs of shell modes. Second, the effects of a flexible foundation and axial compression are investigated using holographic interferometry. The modal responses of this shell–liquid system are found to be different from those of the existing theoretical models. [ABSTRACT FROM AUTHOR]

A new full two-dimensional semianalytical method is developed to rigorously and efficiently solve the problem of a rigid cylinder rolling with any given constant speed over a viscoelastic foundation of finite thickness. In this new method, the solution is expanded into a set of Fourier series, the master curves of G′ and G″ characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special boundary element based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. A verification example is given to validate the methodology. Several numerical examples are given to study the influences of various factors on rolling resistance. The method as well as the conclusions drawn from the examples may be of interest to roller and belt-conveyor designers. This approach can be easily generalized to solve the general rolling contact problems of two viscoelastic bodies. [ABSTRACT FROM AUTHOR]

The emphasis of this note is placed on finding out whether dynamic snap-through will occur when a shallow arch resting on an elastic foundation with elastic constant β is stretched or compressed with constant speed. It is found that for β>8/7 no dynamic snap-through will occur when the arch is stretched. However, as long as β<4, dynamic snap-through is still possible when the arch is compressed. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train. [ABSTRACT FROM AUTHOR]

Some fundamental dynamic characteristics of a railway subjected to a harmonic or constant moving load are established and presented in this paper. The railway is modeled as an infinite or finite Timoshenko beam on viscoelastic foundation. The dynamic-stiffness matrices characterized by the complex wave numbers are employed to deal with this problem. The relationship between the forced frequency and the resonant velocity of the moving load, and the resonant frequency of the railway are especially emphasized and intensively discussed. The fundamental dynamic characteristics of a railway modeled as a Bernoulli-Euler Beam on viscoelastic foundation are also included for comparison. [ABSTRACT FROM AUTHOR]

In this paper, some biparametric models for an elastic foundation are proposed. It is assumed that the foundation has the shape of the wedge. The modeling procedure starts from the linear elasticity equations into which we introduce some simplifying assumptions based on the conceptions of decay functions. The simplified models are described by the ordinary differential equations. Stationary and nonstationary Green's functions for the foundation considered are obtained by applying the Hankel and Laplace transform methods. An example of the interaction between the rigid plate and the elastic wedge foundation is studied. [ABSTRACT FROM AUTHOR]

Presents a study which computed the stress and displacement fields that develop in response to moisture and temperature variations in concrete slab used as a plate on an elastic foundation. Equations on stretching and bending; Conclusions.

Part I. Determines a simple estimate of the stresses resulting from a circular foundation subjected to concentric or eccentric loading. Potential function formulation for transverse isotropy; Potential functions for normal and shear loading; Hankel transforms and elliptic integrals for normal loading; Linear shear loading; Isotropy.

Describes a boundary element model for the computation of dynamic stiffness of strip foundations resting on or embedded in soils that are fluid-filled poroelastic and may also have single-phase visco-elastic zones. Representation of the behavior of the porous medium according to Biot's theory; Depth of the porous stratum.

Analyzes the dynamics of axisymmetric foundations on poroelastic media. Boundary element method; Time-harmonic excitation; Biot's poroelastic theory; Domain dicretization for piecewise homogenous media; Behavior of circular foundations.

This technical note presents an analytical method, accompanied by a numerical scheme, to evaluate the response of beams on nonuniform elastic foundations, namely, when the foundation modulus is k5k(x). The method employs a Green's function formulation, which results in a system of nonsingular integral equations for the distributed reaction q(x). These equations can be discretized in a straightforward manner to yield a system of linear algebraic equations that can be solved by elementary numerical techniques. [ABSTRACT FROM AUTHOR]