Journal of Engineering Mechanics

This paper presents a general weighted residual formulation (both collocation and Galerkin) for the problem of the lateral buckling of nonprismatic cantilevers. The approach is first validated against exact solutions to the linear elastic, prismatic case, and then against the available data for the elastic stability of beams with a linear taper. Complete results are given for both rectangular and inverted T sections with linear and parabolic web tapers subjected to either a distributed load or an end point load, for a number of span to depth ratios; the effect of applying the load through the top fiber, rather than the centroid, is also studied. For the limiting cases where results have been cited by others, the values obtained are shown to compare well. Finally, the technique is used to study buckling of inverted T sections when material nonlinearity is included. This is achieved by providing functional forms for the degradation of flexural and torsional stiffness with load, the aim being purely to assess the relevance of buckling as an ultimate limit state.

Wind conditions around high‐rise buildings in cities may create serious environmental problems at the pedestrian level. In spite of the progress of computational techniques in wind engineering, wind‐tunnel experiments are still considered to be the most reliable approach for the evaluation of pedestrian‐level winds. A number of techniques have been developed for assessing the mean and turbulent characteristics of the wind regime around buildings near the ground. These techniques can be grouped into two categories: point methods and area methods. This paper reviews the experimental methods and discusses their advantages and limitations with respect to the requirements of pedestrian‐level wind studies. In addition to conventional techniques such as thermal anemometry, pressure sensor, flow visualization and erosion, some newly developed methodologies such as laser‐Doppler anemometry, particle‐image velocimetry, and infrared thermography are described. The selection of the most appropriate experimental methodology for the best assessment of pedestrian‐level wind conditions is discussed in terms of spatial coverage and accuracy.

In this paper the behavior of plate and stiffener assemblies in uniaxial compression is investigated. As the geometric properties of the stiffeners dictate the in‐ and out‐of‐plane boundary conditions of the attached plate, a set of restraining parameters is defined that quantify the rotational, in‐plane bending and translation restraints the stiffeners offer to the plate. The plate is modeled as partially restrained against rotation and in‐plane translation. Extensive results are obtained showing the transition from the rotationally free boundary condition, i.e., the attached stiffener possesses zero rotational stiffness, to the rotationally clamped boundary condition, i.e., the stiffeners have infinite rotational stiffness. A similar treatment is given for the in‐plane boundary condition, from free expansion of the unloaded edges to fixed, immovable boundaries developing quasi‐biaxial compression. The sensitivity of the buckling mode to these restraints is also examined. The investigation highlights the equal importance of defining the in‐plane and the outof‐plane boundary conditions to characterize critical and postcritical behavior of the uniaxially loaded plate.

The postbuckling behavior of plate‐stiffener assemblies in uniform axial compression is investigated in which the energy method is used to model various in and out‐of‐plane boundary conditions. The loaded edges are treated as simply supported and remain straight. The unloaded edges can be simply supported or elastically restrained against rotation. Beside these out‐of‐plane boundary conditions, the in‐plane boundary condition for the unloaded edges may be any of the following: free translation, fully restrained against translation, straight, free to bend, and partially restrained against in‐plane bending. Analytical expressions for the membrane strain energy for each of these boundary conditions for any plate aspect ratio are derived and the geometric properties of the stiffeners that dictate these boundary conditions are defined in the paper. Typical numerical results are obtained for square plates and the influence of these boundary conditions on the load‐deflection and load‐end shortening behavior is illustrated.

A four‐noded quadrilateral pure shell element based on the thin‐shell theory of Koiter (1966) has been developed. The element, having a variable number of nodal degrees of freedom with a maximum of 12, is formulated on the plane reference domain by a mapping of the curved shell middle surface from the three‐dimensional space. Any arbitrary global coordinate system can be used due to the implementation of tensorial coordinate transformation. Excellent behavior of the element is observed when tested against a set of severe benchmark tests. The benchmark tests demonstrate that the element is able to handle rigid‐body motion without straining, inextensional modes of deformation, complex membrane strain states, and skewed meshes. The two‐dimensional interpolation functions are formed from the tensor product of Lagrange and Hermitian one‐dimensional interpolation functions, and the order of interpolation can be varied.

An optimal‐control algorithm with acceleration, velocity, and displacement feedback is proposed. The algorithm, which is derived by minimizing a quadratic time‐dependent performance index, includes constant control gains that need to be calculated once in the beginning of the control process. Numerical results indicate that for base‐isolated structures, the utilization of acceleration feedback in the control scheme performs as well as the previously proposed algorithm that includes only velocity‐displacement feedback. In the case of non‐base‐isolated structures, the new scheme demonstrates a better performance. Due to difficulties present in measuring the displacement of a system, inclusion of the acceleration feedback in the control algorithm increases its practical value for possible implementations.

Transient creep, an important deformation mechanism for polycrystalline ice at quasi‐static strain rates, is characterized by rate and temperature sensitivity, by isotropic and kinematic strain hardening, as well as by fabric and deformation‐induced anisotropy. A physically based constitutive model, using internal state variables, has been developed by Shyam Sunder and Wu (1989a, b) to describe the multiaxial behavior of ice undergoing transient creep. To solve boundary value problems using this constitutive theory requires the numerical time integration of a coupled set of stiff and highly nonlinear first‐order differential equations. A closed‐form Newton‐Raphson (tangent) formulation, in conjunction with the α‐method of integration, is developed to solve the constitutive equations. The fully consistent constitutive Jacobian matrix that is used to assemble the finite element tangent stiffness matrix is also established in closed form. This algorithm is implemented as a subroutine in the finite element program ABAQUS and its predictions are verified against experimental data and known solutions. The importance of transient creep is demonstrated by performing simulations of: (1) Arrested subsurface penetration; and (2) in‐plane indentation of a floating ice sheet.

The paper presents a method of analysis for the short‐term and time‐dependent response of slender, reinforced concrete columns using the age‐adjusted effective modulus method. For the long‐term case, a recommended general numerical procedure used in a computer program is described in detail. The distributions of strain and stress on cross sections and the prediction of lateral deflection are given under both short‐term and long‐term (one‐time‐step and multiple‐time‐step case) situations. The formula for calculating column shortening is derived based on the principle of virtual forces. The method is applied to determine the axial and bending shortening of a pin‐ended, isolated column. Shortening‐time‐relation curves show the effects of axial and bending shortening on the total shortening respectively. The influence of eccentricity and column length on shortening are also studied. The results from the computer program are in good agreement with experimental and theoretical results reported by other investigators.

The response of fluid‐saturated porous media to moving surface load is important in many fields of engineering and physics. The approach outlined in this paper represents an attempt at expanding the state‐of‐the‐art in the estimation of the dynamic response of a layered nonlinear soil deposit subjected to a moving load. A more computationally efficient semianalytical method based on Biot's formulations for porous medium is proposed for loads under plane‐strain conditions. It is a continuum‐based approach that uses a Fourier transform technique in which the soil deposit can be saturated, unsaturated, or a combination of both. The approach can handle complex surface loading, such as multiple loads, non‐uniform pressures, and other types of time‐varying loads. This paper (Part I) presents the formulation, and a companion paper (Part II) presents the application of this approach in which the predictive capability of the model and the associated computer code are verified using laboratory model tests and classical solutions.

A semianalytical approach based on Biot's formulation for porous medium to evaluate the layered nonlinear response of a soil subjected to a moving load is presented in Part I of this paper. Part II describes the verification study undertaken to validate the predictive capability of the preceding approach and the ensuing computer program. The validation study includes: (1) Laboratory verification, in which the moving load response of two three‐layer foam‐rubber models are compared with those predicted by the approach; and (2) verification using results from a number of classical solutions. The comparisons between the predictions and the laboratory test results and the classical solutions are very good. The application of the approach is also illustrated by undertaking a parametric study in which the response of a medium dense sand subjected to a moving strip load is evaluated. The study reveals that the properties of the soil deposit and porefluid and the moving velocity of the load are important factors that affect the displacement response of the deposit.

This paper introduces a new base isolation system—a friction‐controllable sliding system—for seismic response control of buildings. To overcome the limitations of conventional passive sliding isolation systems, a hybrid sliding system has been developed using friction‐controllable bearings. This innovative system uses a variable friction force produced by changing the pressure in its fluid chamber with computer control. In this study, the applicability of this system to buildings is examined through computer‐simulation analysis. A control algorithm is developed for this purpose, which considers various problems associated with the application of this system to buildings. It is shown that this hybrid system is more effective for earthquakes with a broad range of intensity, compared to its conventional passive counterparts. The proposed hybrid system is in the process of being installed in a four‐story office building in Tokyo to replace the existing passive isolation system.

A structural stability modeling technique based on representing the in‐plane forces as discretized or lumped parameters is developed and applied to various structural members. Elastic critical loads on structures such as frames, curved beams, circular plates, and shells of revolution are calculated and compared with solutions obtained using other methods. This modeling procedure leads to a diagonal geometric stiffness matrix that provides the same advantages as lumped‐mass modeling in a dynamic analysis (including simplicity of formulation, relative accuracy, efficiency in computer time), and it usually yields eigenvalues that are less than the exact values. As in vibration problems, this modeling procedure can be easily adopted to provide a guaranteed lower bound for the critical buckling load of the system using Dunkerley's method.

For the dynamic stiffness of a sagging cable subject to harmonic boundary displacements, frequency‐dependent closed‐form analytic functions can be derived from the corresponding continuum equations. When considering such functions in stiffness matrices of composed structures, however, these matrices become frequency dependent, too—a troublesome fact, especially in regards to the eigenvalue problem, which becomes nonlinear. In this paper, a method for avoiding such difficulties is described whereby an analytic dynamic stiffness function is reduced to a linear matrix polynomial; the matrices of this polynomial are of any desired order. The reduction corresponds to a mathematically performed transition from a continuum to a discrete‐coordinate vibrating system. In structural dynamic applications (dynamic cable stiffness), the two resultant matrices correspond to a static stiffness matrix and a mass matrix. Beyond the particular problem focused on, the method may be applied to all kinds of analytic impedance functions. In every case, the resultant matrices can easily be considered within the scope of a linear matrix‐eigenvalue problem.