Showing papers in "Journal of Engineering Mechanics-asce in 1984"
TL;DR: In this article, the authors studied the structural size effect of fracture in concrete and rock structures, using dimensional analysis and illustrative examples, and showed that the energy release caused by fracture depends on both the length and the area of the crack band.
Abstract: The fracture front in concrete, as well as rock, is blunted by a zone of microcracking, and in ductile metals by a zone of yielding. This blunting causes deviations from the structural size effect known from linear elastic fracture mechanics (LEFM). The size effect is studied first for concrete or rock structures, using dimensional analysis and illustrative examples. Fracture is considered to be caused by propagation of a crack band that has a fixed width at its front relative to the aggregate size. The analysis rests on the hypothesis that the energy release caused by fracture depends on both the length and the area of the crack band. The size effect is shown to consist in a smooth transition from the strength criterion for small sizes to LEFM for large sizes, and the nominal stress σN at failure is found to decline as (1+λ/λ0)-1/2 in which λ0=constant and λ=relative structure size. This function is verified by Walsh's test data. If reinforcement is present at the fracture front and behaves elastically, ...
1,474 citations
TL;DR: In this paper, the problem of deriving approximations for multinormal integrals is examined using results of asymptotic analysis, where the boundary of the integration domain given by g(x¯) is simplified by replacing by its Taylor expansion at the points on the boundary with minimal distance to the origin.
Abstract: The problem of deriving approximations for multinormal integrals is examined using results of asymptotic analysis. The boundary of the integration domain given by g(x¯)=0 is simplified by replacing g(x¯) by its Taylor expansion at the points on the boundary with minimal distance to the origin. Two approximations which are obtained by using a linear or quadratic Taylor expansion are compared. It is shown that, applying a quadratic Taylor expansion, an asymptotic approximation for multinormal integrals can be obtained, whereas using linear approximations large relative errors may occur.
829 citations
TL;DR: In this article, it is shown that failure occurs by progressive distributed damage during which the material exhibits strain-softening, i.e., a gradual decline of stress at increasing strain.
Abstract: In heterogeneous materials such as concretes or rocks, failure occurs by progressive distributed damage during which the material exhibits strain‐softening, i.e., a gradual decline of stress at increasing strain. It is shown that strain‐softening which is stable within finite‐size regions and leads to a nonzero energy dissipation by failure can be achieved by a new type of nonlocal continuum called the imbricate continuum. Its theory is based on the hypothesis that the stress depends on the change of distance between two points lying a finite distance apart. This continuum is a limit of a discrete system of imbricated (regularly overlapping) elements which have a fixed length, l, and a cross‐section area that tends to zero as the discretization is refined. The principal difference from the existing nonlocal continuum theory is that the equation of motion involves not only the averaging of strains but also the averaging of stress gradients. This assures that the finite element stiffness matrices are symmet...
599 citations
TL;DR: In this article, a weighted global iteration procedure with an objective function is proposed for stable estimation, being incorporated into the extended Kalman filter algorithm, which is applied to system identification problems of seismic structural systems.
Abstract: The extended Kalman filter is applied to system identification problems of seismic structural systems. In order to obtain the stable and convergent solutions, a weighted global iteration procedure with an objective function is proposed for stable estimation, being incorporated into the extended Kalman filter algorithm. For the effectiveness of this present proposal, the identification problems are investigated for multiple degree-of-freedom linear systems, bilinear hysteretic systems, and equivalent linearization of bilinear hysteretic systems. As numerically shown examples, the weighted global iteration procedure may be useful to identification problems.
521 citations
TL;DR: An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented in this paper, which accounts for transverse shear strains and rotation about the normal to the shell midsurface.
Abstract: An extension of the Sanders shell theory for doubly curved shells to a shear deformation theory of laminated shells is presented. The theory accounts for transverse shear strains and rotation about the normal to the shell midsurface. Exact solutions of the equations are presented for simply supported, doubly curved, cross‐ply laminated shells under sinusoidal, uniformly distributed, and concentrated point load at the center. Fundamental frequencies of cross‐ply laminated shells are also presented. The exact solutions presented herein for laminated composite shells should serve as bench mark solutions for future comparisons.
495 citations
TL;DR: It is shown that translation processes can have any marginal distribution and autocorrelation function and that approximations proposed previously for the mean upcrossing rate of non‐Gaussian processes can be unsatisfactory.
Abstract: Mean upcrossing rates are determined for translation processes obtained from normal processes by univariate, nonlinear transformations. Monotonic and more general transformations are studied. It is shown that translation processes can have any marginal distribution and autocorrelation function and that approximations proposed previously for the mean upcrossing rate of non‐Gaussian processes can be unsatisfactory. These approximations assume that the process and its time‐derivative, considered to follow a Gaussian distribution, are independent. Theoretical findings are applied to determine crossing characteristics of wind speeds, river flows, and other non‐Guassian processes.
322 citations
TL;DR: In this article, the dynamic behavior of rigid-block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined, and several possible modes of steady-state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses.
Abstract: The dynamic behavior of rigid-block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no-toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady-state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid-block structure under a given amplitude-frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.
225 citations
TL;DR: In this article, a simple model was developed to obtain radiation damping coefficients of soil-foundation systems, for both plane-strain and axisymmetric loading conditions, and the results were in very good accord with available rigorous solutions for strip footings, circular footings and piles, resting on or embedded in a homogeneous space and subjected to vertical and horizontal vibration.
Abstract: A simple model is developed to obtain radiation damping coefficients of soil‐foundation systems, for both plane‐strain and axisymmetric loading conditions. Despite the simplifying assumptions made, the obtained closed‐form results are in very good accord with available rigorous solutions for strip footings, circular footings and piles, resting on or embedded in a homogeneous space and subjected to vertical and horizontal vibration. The models are readily extended to a class of realistic inhomogeneous media, for which no exact solutions are presently available. Considerable insight is provided on the nature of radiation damping and its dependence on frequency, and an analogy is drawn with the propagation of sound from a loudspeaker.
164 citations
TL;DR: In this paper, the one-dimensional imbricate nonlocal continuum is extended to two or three dimensions and a proper variational method is developed to derive the equations of motion from the principle of virtual work.
Abstract: The one-dimensional imbricate nonlocal continuum, which was developed in another paper in order to model strain-softening within zones of finite size, is extended here to two or three dimensions. The continuum represents a limit of a system of imbricated (overlapping) elements that have a fixed size and a diminishing cross section as the mesh is refined. The proper variational method for the imbricate continuum is developed, and the continuum equations of motion are derived from the principle of virtual work. They are of difference-differential type and involve not only strain averaging but also stress gradient averaging for the so-called broad-range stresses characterizing the forces within the characteristic volume of heterogeneous material. The gradient averaging may be defined by a difference operator, or an averaging integral, or by least-square fitting of a homogeneous strain field. A differential approximation with higher order displacement derivatives is also shown. The theory implies a boundary layer which requires special treatment. The blunt crack band model, previously used in finite element analysis of progressive fracturing, is extended by the present theory into the range of mesh sizes much smaller than the characteristic width of the crack band front. Thus, the crack band model is made part of a convergent discretization scheme. The nonlocal continuum aspects are captured by an imbricated arrangement of finite elements, which are of the usual type.
117 citations
TL;DR: In this article, the rectilinear motion and the conditions of reattachment and separation of a rigid body, in friction contact with another body are considered, and analytical expressions for the velocities and displacements are derived.
Abstract: The rectilinear motion and the conditions of reattachment and separation of a rigid body, in friction contact with another body are considered. A graphical representation of the motion is indicated, and analytical expressions for the velocities and displacements are derived. The existence of limiting values of velocity and displacement is shown for a special class of periodic ground motions which include harmonic motions. Also, the equations of motion and the conditions of reattachment and separation of a two degrees of freedom model of a sliding structure and foundation are derived. The numerical integration of the response of this system is carried out, as well as a parametric study showing the effect of different values of the mass ratio, coefficient of friction and amplitude of the ground acceleration. Use of results of the parametric study, concerning amount of slippage, resonance frequency ratios, minimum allowable frequency for sticked mode, etc. in the design for structural base isolation is indic...
89 citations
TL;DR: In this paper, a general procedure based on polynomial expansion of yield function in terms of invariants of the stress tensor is proposed in the context of associated plasticity for isotropic materials undergoing isotropically hardening.
Abstract: A general procedure based on polynomial expansion of yield function in terms of invariants of the stress tensor is proposed in the context of associated plasticity for isotropic materials undergoing isotropic hardening. The procedure can be used to evolve one or more models for a material by using appropriate laboratory test results. One of the functions showing invariance at ultimate and a single function to describe continuous yield and ultimate yield behavior is investigated in detail. Based on comprehensive series of bests on cubical specimens for different (geological) materials, a hardening or growth function is defined in terms of the trajectory of plastic strain and the ratio of deviatoric to total plastic strain. The predictions of the proposed model are verified with respect to the observed results from tests with different stress paths. The model provides highly satisfactory predictions for both stress‐strain and volumetric strain responses from various stress paths. The proposed model shows po...
Journal Article•
TL;DR: The boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is applied to the analysis of simply supported plates of any shape, resting on an elastic foundation as mentioned in this paper.
Abstract: In this investigation the boundary integral equation (BIE) method with numerical evaluation of the boundary integral equations is applied to the analysis of simply supported plates of any shape, resting on an elastic foundation. The numerical results are compared with those available from analytical solutions. Moreover, the efficiency of the BIE method is demonstrated and examined.
TL;DR: In this article, it is shown that the choice of the weighting function is not entirely empirical but must satisfy two stability conditions for the elastic case: (1) No eigenstate of nonzero strain at zero stress, called unresisted deformation, may exist; and (2) the wave propagation speed must be real and positive if the material is elastic.
Abstract: Nonlocal continuum, in which the (macroscopic smoothed‐out) stress at a point is a function of a weighted average of (macroscopic smoothed‐out) strains in the vicinity of the point, are of interest for modeling of heterogeneous materials, especially in finite element analysis. However, the choice of the weighting function is not entirely empirical but must satisfy two stability conditions for the elastic case: (1) No eigenstates of nonzero strain at zero stress, called unresisted deformation, may exist; and (2) the wave propagation speed must be real and positive if the material is elastic. It is shown that some weighting functions, including one used in the past, do not meet these conditions, and modifications to meet them are shown. Similar restrictions are deduced for discrete weighting functions for finite element analysis. For some cases, they are found to differ substantially from the restriction for the case of a continuum if the averaging extends only over a few finite elements.
TL;DR: In this paper, a numerical method to simulate discharging processes in mass flow silos is presented, which provides transient velocity and stress fields within the bulk material for a first period of discharging.
Abstract: A numerical method to simulate discharging processes in mass‐flow silos is presented. The essential point is to formulate the appropriate constitutive law for a granular bulk material, which covers solid‐like as well as fluid‐like behavior during discharging. An elastic‐plastic law is chosen for the former one, which is completed with a simple first approach for fluid‐like behavior. As large and fast deformations occur, geometric nonlinearities and mass properties of the bulk material are considered with respect to an Eulerian frame of reference. The complete set of field equations is numerically solved by the finite element method spatially and by the finite difference method in time. Due to the nature of the finite element method a broad variety of boundary conditions can be studied. The method provides transient velocity and stress fields within the bulk material for a first period of discharging. Remarkable stress redistributions with strong increases of wall pressures are computed.
TL;DR: In this paper, a theory is developed to predict the static response of a wire rope with complex cross sections and the solutions of the nonlinear equations of equilibrium are linearized, and the results are applied to a 6 × 19 Seale rope with an independent wire rope core.
Abstract: A theory is developed to predict the static response of a wire rope with complex cross sections. The solutions of the nonlinear equations of equilibrium are linearized, and the results are applied to a 6 × 19 Seale rope with an independent wire rope core. The linearization permits a considerable simplification in the theory so that the results can readily by applied to other types of cross sections. Expressions are presented for the stresses in the rope, and the maximum tensile stress is also determined. A load-deformation curve of a Seale rope is obtained experimentally, and the results are compared with the theory.
TL;DR: The Sydney Tower, the tallest building in Australia, is one of the first buildings with the installation of a large scale tuned mass damper (TMD) as discussed by the authors, which reduces wind-induced motions by 8 shock-absorbers installed tangentially to the tank and anchored to the floor of the turret.
Abstract: The Sydney Tower, the tallest building in Australia, is 820ft (250m) high and with the base of the structure anchored on the roof of a 15 storey building, it stands 1000ft (305m) above street level The tower is one of the first buildings with the installation of a large scale tuned mass damper (TMD) The doughnut-shaped water tank near the top of the turret, which normally serves as the tower’s water and fire protection supply, was incorporated into the design of the TMD to reduce wind-induced motions Energy associated with relative movements between the tower and the water tank is dissipated by 8 shock-absorbers installed tangentially to the tank and anchored to the floor of the turret A secondary TMD of similar design was later installed on the intermediate anchorage ring to further increase the damping level, particularly in the second mode Full scale measurements were taken to determine the natural frequencies of vibration and damping Dampings of the tower were determined for different damper configurations The natural frequencies of vibration were found to be 010 Hz and 050 Hz for the first mode and second mode respectively Significant increases in damping levels, particularly in second mode, are produced by the water tank tuned mass damper and the secondary damper
TL;DR: In this paper, a continuous damage theory is presented for the quasi-static and dynamic behavior of brittle materials, and a free energy function dependent on coupled invariants of strain and damage is derived consistently subject to thermodynamic restrictions.
Abstract: A continuous damage theory is presented for the quasi‐static and dynamic behavior of brittle materials. The fact that the strain‐rate effects observed can be mainly attributed to the rate‐sensitivity of the microcracking process makes the damage concept particularly attractive. Considering flat micro‐cracks a vectorial representation is adopted for the damage variable. A free energy function dependent on the coupled invariants of strain and damage is postulated, and the constitutive equations and the damage evolution equations are derived consistently subject to thermodynamic restrictions. The stress‐strain curves for uniaxial tension and compression resulting from the theory are compared with available experimental results for concrete. A decrease in the non‐linearity of the stress‐strain curves is observed as the strain‐rate is increased. A higher strain‐rate sensitivity in tension, as compared to compression, is also predicted. Further results on uniaxial tension illustrate how pre‐existing damage infl...
TL;DR: In this article, a finite strip method in conjunction with the theory of mode interaction is developed to study the interaction of local and overall buckling in thin-walled columns, and the effect of dynamic loads in the form of suddenly applied end compression is also investigated.
Abstract: The interaction of local and overall buckling in thin‐walled columns is considered. A finite strip method in conjunction with the theory of mode interaction is developed to study the problem. The method is applicable to doubly symmetric cross sections carrying uniform stress or monosymmetric cross sections subjected to uniform end compression. Imperfection‐sensitivity surfaces are presented for stiffened panels and I‐section columns. A brief parametric study on I‐section columns is presented to illustrate the effect of flange slenderness and the ratio of local to Euler critical load on the maximum load carried. The effect of dynamic loads in the form of suddenly applied end compression is also investigated. It is found that in the presence of overall imperfections likely to occur in practice, the suddenness of load application can cause a reduction of about 10% of the maximum static load carrying capacity. A test program on I‐section columns carried out in Cornell University is cited for an evaluation of ...
TL;DR: In this article, the first passage time problem for the response amplitude of a linear lightly damped single-degree-of-freedom oscillator under evolutionary random excitation is considered, and a Markovian approximation of the amplitude allows the use of a Fokker-Planck equation for the formulation of the problem.
Abstract: The first‐passage time problem for the response amplitude of a linear lightly damped single‐degree‐of‐freedom oscillator under evolutionary random excitation is considered. A Markovian approximation of the amplitude allows the use of a Fokker‐Planck equation for the formulation of the problem. This equation is solved exactly for the special case of a step function‐modulated stationary excitation. These results are used in determining a solution for the general excitation case via a Galerkin technique. Pertinent digital simulation data demonstrate the reliability and extreme efficiency of the developed solution method.
TL;DR: In this paper, the authors developed probabilistic descriptors for Morison-type wave forces based on the actual distribution of these forces and on the hypothesis that wave forces follow Gaussian distributions.
Abstract: Probabilistic descriptors are developed for Morison‐type wave forces. They are based on the actual distribution of these forces and on the hypothesis that wave forces follow Gaussian distributions. The Gaussian hypothesis is characteristic of analyses based on statistical linearization. Results show that this hypothesis provides unsatisfactory estimates for the peak of wave forces during design storms. Both the mean and the variance of the peak wave force can be underestimated significantly when the Gaussian hypothesis is applied. It is assumed in the analysis that the wave particle velocity process follows a Gaussian distribution.
TL;DR: In this paper, a differential equation model for hysteretic systems is analyzed under nonzero mean random excitation, and a closed form linearization of the equations of motion is possible.
Abstract: A differential equation model for hysteretic systems is analyzed under nonzero mean random excitation. Under certain conditions, a closed form linearization of the equations of motion is possible. Resulting mean and zero time lag covariance responses agree well with Monte Carlo response simulations. Generalization to degrading systems is straightforward. Skewness coefficients computed from simulation results indicate significantly asymmetric response. Stationary response statistics are found to relate closely to the zero mean case.
TL;DR: In this paper, the lower bound theorem of plasticity theory is applied to construct lower bounds that are optimized in a certain sense, which is useful for defining a strategy of search for the most important collapse mechanisms of certain general types of models of plastic frame and truss structures.
Abstract: Reliability analysis of highly redundant ideal‐plastic structures is difficult due to the existence of a very large number of possible failure modes. If only some of the failure modes are identified and included in the reliability calculation, the result will be an overestimation of the reliability. However, the lower bound theorem of plasticity theory allows for a calculation that underestimates the reliability. This theorem is applied to construct lower bounds that are optimized in a certain sense. Only a suboptimization is practicable. Therefore the resulting lower bounds are not particularly close to the exact reliability. However, some theorems originating from the lower bound optimization analysis turn out to be useful for defining a strategy of search for the most important collapse mechanisms of certain general types of models of plastic frame and truss structures. The total reliability can only be calculated up to upper and lower bounds, but examples show that the upper bound defined by the ident...
TL;DR: In this article, the crack tip locations of the macro-crack and the fracture process zone were determined experimentally and used as input conditions for these generation analyses, and the crack opening resistance along the process zone was then adjusted to achieve consistency in the computed CTOD.
Abstract: Finite element models of crack-line wedge-loaded, double cantilever beam (CLWL-DCB) fracture specimens were used in their generation mode to evaluate the crack tip opening displacements (CTOD) associated with a fracture process zone preceding the macro-crack tip in such specimens. The crack tip locations of the macro-crack and the fracture process zone were determined experimentally and used as input conditions for these generation analyses. The crack opening resistance along the process zone was then adjusted to achieve consistency in the computed CTOD. This modified finite element model was then used with reasonable success in the propagation analysis of stable crack growth in concrete CLWL-DCB fracture specimens.
TL;DR: In this paper, the dynamic response of a pipeline buried in a semi-infinite elastic medium is investigated, where the incident disturbances are assumed to be plane waves moving perpendicular to the axis of the pipeline.
Abstract: Dynamic response of a pipeline buried in a semi‐infinite elastic medium is investigated. The pipeline is modeled as a circular cylindrical shell of small thickness. The incident disturbances are assumed to be plane waves moving perpendicular to the axis of the pipeline. Thus, the problem is either one of plane strain, which will be examined herein, or antiplane strain. Two problems are considered: (1) The pipe is surrounded by a homogeneous soft soil; and (2) the pipe lies in a cylinder of soft soil, which is surrounded by a rock‐like material. It is shown by comparison that the stresses and displacements are significantly modified in the latter case. The response is also found to be considerably influenced by the frequency of the incident wave and depth of the embedment.
TL;DR: In this article, the fracture energy and tensile strength of a crack band front is considered as a fixed material property and can be taken as roughly five times the grain size of rock.
Abstract: The fracture of rock is assumed to arise from propagation of a blunt crack band with continuously distributed (smeared) microcracks or continuous cracks. This approach, justified by material heterogeneity, is convenient for finite element analysis, and allows analyzing fracture on the basis of triaxial stress‐strain relations which cover the strain‐softening behavior. A simple compliance formulation is derived for this purpose. The practical form of the theory involves two independent material parameters, the fracture energy and the tensile strength. The width of the crack band front is considered as a fixed material property and can be taken as roughly five‐times the grain size of rock. The theory is shown to be capable of satisfactorily representing the test data available in the literature. In particular, good fits are demonstrated for the measured maximum loads, as well as for the measured resistance curves (R‐curves). Statistical analysis of the deviations from the test data is also presented.
TL;DR: In this paper, a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points; then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk.
Abstract: When design factors are considered as random variables and the failure condition cannot be expressed by a closed form algebraic inequality, computations of risk (or probability of failure) may become extremely difficult or very inefficient. This study suggests using a simple and easily constructed second degree polynomial to approximate the complicated limit state in the neighborhood of the design point; a computer analysis relates the design variables at selected points. Then a fast probability integration technique (i.e., the Rackwitz-Fiessler algorithm) can be used to estimate risk. The capability of the proposed method is demonstrated in an example of a low cycle fatigue problem for which a computer analysis is required to perform local strain analysis to relate the design variables. A comparison of the performance of this method is made with a far more costly Monte Carlo solution. Agreement of the proposed method with Monte Carlo is considered to be good.
TL;DR: In this article, a new 6th order technical theory for the bending of beams is presented, which includes the influence of transverse normal strain, and appropriate boundary conditions are delineated.
Abstract: A new sixth order technical theory for the bending of beams is presented, which includes the influence of transverse normal strain. Appropriate boundary conditions are delineated. Application to the bending of a simple beam verifies improvement over shear deformation solution.
TL;DR: In this article, a method to evaluate the effect of parameter uncertainties on the dynamic response of a soil-structure system is described and illustrated, based on the response surface methodology and is fully compatible with current numerical modeling codes (computer programs) used to analyze dynamic soilstructure interaction.
Abstract: Uncertanties in dynamic soil-structure interaction are divided into two groups: Model and parameter uncertainties. Modeling uncertainties are associated with the differences between the real world phenomenon and the model, and parameter uncertainties are uncertainties in the parameters which appear in the model definition. A method to evaluate the effect of parameter uncertainties on the dynamic response of a soil-structure system is described and illustrated. The method is based on the response surface methodology and is fully compatible with current numerical modeling codes (computer programs) used to analyze dynamic soil-structure interaction. It consists of the development of a graduating function which approximates the true response, based on a limited number of code evaluations. The graduating function, called the response surface, is then used to evaluate the effects of uncertainties in place of the soil-structure interaction code. The method embodies the traditional parametric or sensitivity analysis techniques and can be considered an extension of the partial derivative method or first-order, second-moment method to the numerical realm.
TL;DR: In this paper, the dynamics of structures with their foundation mat supported only through gravity and thus permitted to uplift from the supporting system were investigated, and it was shown that foundation mat uplift has the effect of reducing the base shear for short-period structures, with these reductions being especially significant for the more slender structures.
Abstract: Investigated in this paper is the dynamics of structures with their foundation mat supported only through gravity and thus permitted to uplift from the supporting system. In its fixed base condition the structure is idealized as a single‐degree‐of‐freedom system attached to a rigid foundation mat, which is supported at each edge by a spring‐damper element. Analytical expressions are presented for the free vibration response of the system and the effects of foundation uplift are examined. An effective numerical procedure, based on expressions of the Rayleigh‐Ritz concept, to evaluate the structural response to earthquakes is presented. Based on the response spectra presented it is shown that foundation mat uplift has the effect of reducing the base shear for shortperiod structures, with these reductions being especially significant for the more slender structures.