Journal of Engineering Mechanics

For biaxial states of stress in mass concrete structures, safety can be assessed in terms of the Mohr failure criterion. Safety is generally evaluated by a deterministic factor of safety. When loads vary and material properties are not known with certainty, reliability analysis evaluates safety probabilistically. In this paper, deterministic and probabilistic safety evaluations are compared in terms of levels of uncertainty associated with load and resistance parameters and the extent is indicated to which the probabilistic approach is more informative than the deterministic approach. The effect on this comparison of several characteristics of concrete material is investigated. Three widely recognized design criteria are likewise compared.

The effect of strain rate on the inelastic behavior of structural steel under cyclic loading condition is formulated by using the endochronic theory of plasticity. Analytical results are compared with limited experimental data. Very good agreement is observed.

A finite element formulation for a class of nonlinear viscoelastic continua subjected to stochastic excitation is developed by means of a stochastic equivalent linearization technique. The nonlinear viscoelastic properties of the continua are modeled in terms of the constitutive equation which linearly involves the hysteretic tensor and in terms of the auxiliary equation which describes a nonlinear relationship among the strain and hysteretic tensors and their time derivatives. This auxiliary equation is linearized with the aid of a stochastic linearization technique which minimizes the expected value of the square of the difference between the nonlinear and linearized auxiliary equations. The linearized boundary value problem then involves a set of two linearization coefficients which are functions of space and time. With the aid of the weighted residuals method, the boundary value problem developed for the continuum is transformed into that in the finite element formulation. In integrating the equation of motion representing the discrete model, an iterative upgrading of the values of these linearization coefficients is performed simultaneously for all the finite elements in the first time interval until a convergence criterion is satisfied. The iterative process is then repeated in the time intervals that follow, until the entire time interval for which the dynamic analysis is performed is covered. The proposed finite element analysis produces a covariance function and hence a variance function of the nodal displacement and velocity, and of the element strain and stress components, among other response quantities. The variance function developed on the basis of the present analysis and those constructed by means of the Monte Carlo technique show a reasonable agreement.

A simulation method of the behavior of fresh concrete is proposed in the present paper. To estimate the flow and deformation of fresh concrete, a method of viscoplastic finite element analysis is applied, in which fresh concrete is treated as a kind of Bingham model. In the analysis, slipping resistance between boundary surface and fresh concrete can be considered, and the dynamic behavior can be analyzed by calculation of the retardation of velocity change. In this paper, some analytical results for the slump test and the flow test are shown and discussed. The relationship between rheological constants and the values measured by the slump test and the flow test are clarified analytically, and the method for estimating rheological constants from the slump value and the flow value is proposed. Then, the adequacy of the analytical method proposed is examined by comparison with experimental results.

The airn in this paper is to present an explicit solution for the Green's functions associated with static and dynamic loads and dislocations acting on, or within, elastic cross‐anisotropic halfspaces and full spaces. The methodology employed represents a generalization of a procedure described by Kausel and Peek in 1982 for dynamic loads acting within isotropic strata of finite depth. In essence, the method consists of a discretization of the medium in the direction of layering and an idealization of the underlying halfspace, in the case of dynamic loads, in terms of paraaxial approximations. For static loads, on the other hand, the halfspace can be modeled exactly. The Green's functions are obtained, as before, with an integral transform evaluated in closed form. As a result, no numerical integrations are necessary, which constitutes a significant advantage over other numerical procedures currently available for this problem. Since the resulting equations for displacements are expressed in the spatial domain, they can be used directly as kernels in integral representations of problems in elastodynamics, such as seismic sources, soil‐structure interaction, and scattering of waves.

Analytical models that describe the strength of jointed rock under a wide variety of multiaxial states of stress with one or two components being tensile are presented. The intact rock is. isotropic and its strength is described by a Hoek and Brown criterion. The joints have zero tensile strength and a shear strength defined by a Coulomb criterion. The strength of jointed rock is represented by superposition of the intact rock and joint failure surfaces and the joint nonnegative normal stress condition in a coordinate system having two stress ratios as a measure of distance along the coordinate axes. The symmetry of the intact rock failure surface in this coordinate system is lost because of the directional nature of joint strength. The anisotropic strength reduction associated with the joints and the influence of the intermediate stress on the strength of regularly jointed rock are analyzed. The effect of water pressure on jointed rock strength is also addressed.

In this study, a dynamic model that determines exact vibration mqdes and frequencies for trusses is formulated. This model, based on the exact representation of element inertia forces, represents the rod vibration problem quasistatically through use of equivalent loads. Thereby, the need to iteratively form and decompose the stiffhess matrix in solving the vibration eigenproblem is eliminated without introducing discretization error. The effectiveness of this formulation is illustrated in numerical examples and tested against the current models available for vibration analysis of trusses. Exact solutions of the first and second modes of a plane truss are assessed with respect to computational efficiency for a given solution accuracy. The study leads to the conclusion that exact eigendata pairs can be evaluated using simpler representations and requiring less computer resources than with the conventional finite element or exact displacement model formulations.

An unbounded homogeneous transversely isotropic body of revolution containing two twin spheroidal cavities is subjected to an axisymmetric loading. The axis of loading symmetry coincides with the axis of elastic symmetry of the material and the axis of revolution of the body. The elasticity solution is obtained in series form utilizing the displacement potential representation for the equilibrium of transversely isotropic solids, and numerical results are presented for the cases of two spherical cavities perturbing uniaxial and hydrostatic tension fields in certain hexagonal crystals and in isotropic materials. Of primary interest is the influence of cavity spacing and material type on the degree of stress interference between the two perturbations.

The paper describes the application of a series of different concrete models to the analysis of a number of reinforced concrete panels tested by Vecchio and Collins. The different models involve both fixed and “swinging” (rotating) cracks with and without allowance for the tensile strength of the concrete. A simple plasticity model is also applied. Because the numerical solutions are obtained via the arc‐length analysis procedure, the complete (including post‐maximum) load‐deflection responses are traced, and consequently it is possible to clearly identify not only the computed collapse load but also the collapse modes. Differences between the various models as well as differences with the experimental behavior can thereby be investigated.

A new boundary integral equation for the scalar wave equation is developed and applied to obtain the hydrodynamic pressure distributions on dams when the dam‐reservoir system is subjected to ground motions. The effect of water compressibility is included in the formulation. The differentiation of the hydrodynamic pressure with respect to time is approximated by functions that satisfy the free surface boundary condition. The wave equations are solved by using the concept of the complementary function and the particular integral, in conjunction with the boundary element method. With this procedure, it is unnecessary to use the fundamental solutions, which are functions of frequency, but only as functions of geometry. As a consequence, the boundary integral equation can be reduced to a classical form that can be solved by using the well‐established method. Further‐more, substantial reduction in computing time is achieved. Numerical results based on the proposed procedure are obtained and compared with available analytical and numerical solutions.

The theory of the dynamic‐balance wind‐tunnel test is reviewed to identify sources of error that arise when the mode shapes of a structure are nonideal. A systematic process of applying corrections is developed, which results in two adjustment factors—one applicable to displacements and accelerations, and a second applicable to equivalent static loads. The factors are separated into unknown random effects arising from the external wind load distribution and a deterministic effect arising from the structure's mode shape and mass distribution. A simplified assumption on the former is made to evaluate the sensitivity of the correction factors to mode shape and external distribution and to compare them with previous results in the literature. Certain of those results are seen to be misleading in implying that torsional loads should be reduced by a significant, but inappropriate, factor. A simple means of distributing static‐equivalent loads over the height of the structure, while accounting for resonant and background response contributions, is also given.

Wave forces on fixed offshore structures due to short‐crested seas are investigated using the directional spectra and an alternative model accounting for spatial correlation of water particle motions in terms of coherence functions. The theoretical formulation of the latter approach is presented. The resultant wave forces acting on structural elements and on segments of structures are evaluated using both techniques. The characteristics of the wave forces are investigated and the advantages and limitations of both techniques are assessed.

The cylindrical buckling load of a composite laminated column is derived from plate theory. The effect of lamina orientation is taken into account by treating the stiffness parameter as a matrix product rather than as a single value drawn from the definition of the elastic coefficients. This refined stiffness parameter leads to significant improvement of the buckling load, depending on the stacking combination and orientation.

A new numerical method is presented for evaluating the buckling loads of columns with varying cross sections. By this method, the traditional eigenvalue problem is transformed into a special initial value problem, and the buckling loads of the columns can be evaluated by an iteration procedure, which is to satisfy the boundary conditions specified in each case using numerical integrations.. Two numerical examples, a built-up column and a two-component column, are provided for discussion. It is found that the proposed method can meet the precision requirements very well and is a convenient tool for structural designers.