Journal of Engineering Mechanics

This paper presents the result of a study on the effect of pounding at expansion joints on concrete bridge response to earthquake ground motions. An engineering approach, rather than continuum mechanics approach, is emphasized. First, the dynamic behavior of a damped multidegree-of-freedom bridge system separated by an expansion joint involving an impact is examined by means of the finite element method. Second, the sensitivity analysis of the stiffness in gap elements is performed. Third, usefulness of the analysis method for simulation of pounding phenomena is demonstrated and the effect of pounding on the ductility demands measured in terms of the rotation of column ends is investigated. Two-dimensional finite element analysis using a bilinear hysterestic model for bridge substructure joints and a nonlinear gap element for the expansion joint is performed on a realistic bridge with an expansion joint. The effects of the primary factors on the ductility demand such as gap sizes and characteristics of earthquake ground motion are investigated through a parametric study. The major conclusions are (1) the effect of impact most directly depends on the size of momentum (or pounding magnitude); and (2) the pounding effect is generally found to be negligible on the ductility demand for wide practical ranges of gap size and peak ground acceleration, but is potentially significant at the locations of impact.

A triangular element based on Reissner–Mindlin plate theory is developed and it is applied to free vibration analysis of plates in different situations. The element has three corner nodes, three mid-side nodes and an internal node at the element centroid where each node contains three usual degrees of freedom (transverse displacement and bending rotations). To make the element free from the shear locking problem, the formulation is done in an efficient manner taking transverse displacement and transverse shear rotations as the field variables. The degrees of freedom of the internal node are condensed out to improve the computational elegance. As the condensation cannot be done with a consistent mass matrix, a lumped mass matrix having no mass contribution at the internal node is used. In this context two mass lumping schemes are proposed where the effect of rotary inertia is considered in one of these schemes. All these features have made the element quite elegant, which is tested with numerical examples to show its performance.

The present investigation deals with the dynamic stability behavior of laminated composite curved panels with cutouts subjected to in-plane static and periodic compressive loads, analyzed using the finite element method. A generalized shear deformable Sanders’ theory with tracers is used in this study. Numerical results obtained for vibration and buckling of composite panels with cutouts compare well with literature. The principal dynamic instability region of composite perforated panels is obtained using Bolotin’s approach. The study reveals that curved panels with cutouts depict higher stiffness with the addition of curvatures. The laminated hyperbolic paraboloid panel shows the highest stiffness with the onset of instability at higher excitation frequencies. The effect of curvature in laminated composite curved panels is reduced with an increase in size of the cutout. The principal instability regions are influenced by the lamination parameters. Thus, the laminate construction, coupled with cutout geometry, can be used to the advantages of tailoring during design of composite structures for practical applications.

The elastic stability and second-order analysis of three-dimensional (3D) multicolumn systems including the effects of cross-section orientation of each column are presented in a condensed manner using the classical Timoshenko’s stability functions. This formulation is an extension of an algorithm recently presented by the writer in 2002 by which the effective length K-factor for each column, the total critical load, and second-order analysis of a 3D multicolumn system can be determined directly. Extended characteristic transcendental equations corresponding to multicolumn systems with sidesway and twist uninhibited, partially inhibited, and totally inhibited with semirigid connections are derived and discussed. The proposed method is limited to 3D multicolumn systems made up with doubly symmetrical vertical columns with the principal axes of each column cross section oriented in any direction with respect to the floor global axes and with every column sharing the same interstory sidesways (i.e., two horizontal translations and a rotation about the vertical axis). Shear and axial deformations in all members are omitted. Three comprehensive examples are presented and the calculated results compared with those obtained using SAP2000 (Version 6.1, 1997) showing: (1) the effectiveness and simplicity of the proposed approach; (2) its validity to carry out stability and second-order analyses of 3D multicolumn systems; and (3) the importance of the orientation of the cross section of the columns on the lateral response of 3D multicolumn systems. Analytical results indicate that a frame reaches its maximum overall lateral stiffness and a dominant sidesway buckling (without overall frame torsional rotation or twist about its vertical axis) when all columns are oriented with their minor axis tangent to the circumscribed circle such that the multicolumn system acts as a tube offering its maximum twist stiffness.

A control algorithm based on the instantaneous optimal control method, is presented for on-line control of the civil engineering structures subjected to earthquake excitations. This algorithm employs the unconditionally stable Wilson-θ method to discretize the continuous second-order form of the dynamical equation of motion, and uses a new performance index having an acceleration term as well as velocity and displacement terms. This method is named the instantaneous optimal Wilson-θ method. An eight-story shear-type building frame using one active mass damper/driver mechanism installed on the roof is used to demonstrate the efficiency of the proposed control algorithm in comparison to the other optimal control methods. Behavior of different combinations of weighting matrices related to displacement, velocity, and acceleration response vectors of the entire building are examined, and compared with the complete feedback control of the response vectors.

It has been known that inherent material anisotropy influences the mechanics of geoengineering applications. Aiming at the experimental studies associated with geoengineering applications in anisotropic materials, this paper proposes a poromechanics analysis of a fully saturated transversely isotropic hollow cylinder. Closed-form analytical solutions for the pore pressure and stress fields were derived. These solutions are obtained under various loading conditions that are encountered in laboratory testing procedures. Numerical analyses were carried out to demonstrate the material anisotropy effect on stress, displacement, and pore pressure distributions in the cylinder. It is also shown that uncertainties in the estimation or measurements of the poromechanical parameters have proven effects on the time-dependent responses of the hollow cylinder geometry during laboratory testing.

Extreme value analyses of any environmental phenomenon are fraught with difficulties, but the additional difficulty of collecting reliable data during hurricane events makes their analysis even more complicated. A widely accepted procedure is to use calibrated hurricane models to simulate hurricane events. The simulated data can then be subjected to standard extreme value procedures. The estimation uncertainties which arise from such analyses depend upon (1) the extent to which the hurricane models are physically realistic, (2) the length of the simulated series, which consists of about 1,000 or even 10,000 simulated events, and therefore introduces negligible errors, and (3) the length of the historical record on which the simulations are based, which usually consists of about 50 events. In this paper, we propose the use of resampling schemes in an attempt to obtain some reasonable measure of uncertainties due to the relatively short length of the historical record. An intuitive, “naive” procedure is first described, which leads to an alternative approach that has connections with the statistical procedure of bootstrapping. Standard application of these procedures for extremes induces bias, and we propose a simple, though nonstandard method for reducing this effect. The results are illustrated in detail for a dataset of simulated hurricane wind speeds corresponding to a location in Florida and are also summarized for a sequence of 55 locations along the U.S. Gulf and Atlantic coasts.

In recent years, the method of x-ray computer tomography imaging has been used to characterize the microstructure of asphalt concrete, cement concrete, soil, and rock. This paper focuses on developing an algorithm that links the particle identity at different load steps and thus provides sequential movements of particles. The measured data from a specimen under triaxial load is analyzed to study the nonuniform strain field and to identify shear band formation. Packing structure change and the evolution of fabric tensors due to external load are discussed. The validity of a commonly used kinematic hypothesis in granular mechanics is also evaluated.

An analytical model is developed to study the time-dependent behavior of concrete-filled fiber reinforced polymer (FRP) tubes (CFFT) and fiber-wrapped concrete columns (FWCC) under sustained axial loads. The model utilizes the double power law creep function for concrete in the framework of rate of flow method, and the linear viscoelastic creep model for FRP. It follows geometric compatibility and static equilibrium, and considers the effects of sealed concrete, multiaxial state of stresses, creep Poisson’s ratio, stress redistribution, variable creep stress history, and creep rupture. The model is verified against previous creep tests by the writers on FWCC and CFFT columns. It is then used to study the practical design parameters that may affect creep of FRP-confined concrete under service loads, or lead to creep rupture at high levels of sustained load. Creep of FWCC is shown to be close to that of sealed concrete of the same mix, as the effect of confinement on creep of concrete is not very significant. CFFT columns, on the other hand, creep much less than FWCC, mainly due to axial stress redistribution. As the stiffness of the tube increases relative to the concrete core, larger stress redistributions take place further reducing the creep. However, there is a threshold, beyond which, stiffer tubes would not significantly lower the creep of concrete. Creep rupture life expectancy of CFFT columns is shown to be quite acceptable.

The present study is a comparison of two- and three-dimensional models of flow past a square cylinder at a Reynolds number of 250. The models are computational in nature. The governing equations have been solved by the Marker and Cell (MAC) method with higher order spatial and temporal discretization. Essential differences have been observed in the predictions of the two models. Results reveal that the rms values of the aerodynamic forces in the two-dimensional simulation are higher. These are related to higher stochastic fluctuations near the cylinder surface and a shorter spread of the fluctuating fields. The three-dimensional model shows a longer shear layer and the fluctuations are smaller. An interesting observation of the present study is that the fluctuations are the highest at the points of inflexion in the time-averaged velocity profile. The findings of the present study have been discussed with the help of physical reasoning along with the transport equations of velocity fluctuations.

This paper considers the vertical vibrations of an elastic circular plate in a multilayered poroelastic half space. The plate is subjected to axisymmetric time–harmonic vertical loading and its response is governed by the classical thin-plate theory. The contact surface between the plate and the multilayered half space is assumed to be smooth and either fully permeable or impermeable. The half space under consideration consists of a number of layers with different thicknesses and material properties and is governed by Biot’s poroelastodynamic theory. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Contact stress and pore pressure jump are established in terms of generalized coordinates through the solution of flexibility equations based on the influence functions corresponding to vertical and pore pressure loading. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results are presented to portray the influence of various parameters on dynamic interaction between an elastic plate and a multilayered poroelastic half space.

An exact solution technique for the response of a bilinear hysteretic multi-degree-of-freedom system subjected to arbitrary dynamic loadings is proposed. Each function in the loading vector is represented by a piecewise interpolation polynomial. By using the modal superposition method and the Duhamel integral procedure on each branch of the force-displacement relationship and matching transitional conditions, one can obtain a closed-form solution. When the system is subjected to such piecewise polynomial loadings as an earthquake acceleration, which usually can be represented by a series of straight line segments, an exact result can be obtained. Thus the proposed method can provide much higher accuracy, and requires less computational effort than the traditional step-by-step integration solution technique. The reason for these advantages is discussed and the related formulas are provided.

Finite element and Rayleigh-Ritz methods have been effectively used to evaluate the thermal postbuckling behavior of columns with immovable ends in the axial direction. However, these methods do suffer from problems like large computational effort or complex algebra because of the nonlinear nature of the problem. A simple, intuitive method is proposed herein to predict the postbuckling load carrying capacity of uniform columns on elastic foundation. The present method requires the knowledge of only the linear thermal buckling load parameter and the tension developed in the column. The present method, when applied to simply supported and clamped columns gives exactly the same results as those obtained by the Rayleigh-Ritz method.

An analytical approach is proposed for determining vibratory characteristics of cracked Timoshenko beams. Based on the rotational spring model for describing the local flexibility induced by a crack and the developed fundamental solutions, the frequency equation for a Timoshenko beam with any kind of two end supports and an arbitrary number of cracks can be established from a second-order determinant. The decrease in the determinant order can lead to significant savings in the computational time.