Journal of Engineering Mechanics

This paper presents a detailed treatment of the formulation for buckling and dynamic instability analysis of tapered thin‐walled beams of generic open section. The theory developed is limited to small strains, moderate deflections, and small rotations. Shear straining of the midsurface of the member wall is neglected. Rigorous expressions for strains based on membrane theory of shells is obtained through which the effect of nonlinear tapering is considered. Computer solutions for classical buckling and vibration analysis by the finite‐element method is discussed. Numerical integration by using Gaussian quadrature over the cross section for the computation of section properties and stress resultants and over the length for the computation of flexural, geometric, and mass matrices is suggested. Critical buckling loads and the natural frequencies and the corresponding buckled and mode shapes are obtained by using Jacobi iteration procedure.

Buckling loads and natural frequencies and the corresponding modal shapes and forms for thin‐walled tapered beams of open sections are examined using the finite‐element method. A tapered thin‐walled bar finite element with seven degrees of freedom at each node is adopted. In the virtual work formulation, the updated Lagrangian approach is adopted in which the effect of geometric nonlinearity is considered. A rigorous expression for strains based on membrane theory of shells is considered. The flexural stiffness matrix, geometric stiffness matrix, and consistent mass matrices are derived in a companion paper. The convergence and accuracy of the method is tested based on other numerical results. Using the present theory, one is able to investigate various torsional and flexural static and dynamic instability problems. Examples are presented and comparisons are made with the existing solutions.

As is known, when a shear core presents rows of regular openings along the height, the stiffness properties of the connecting beams can be smeared over the height by making use of concepts of statics or energy equivalence. Hence, by virtue of the constraining action of the floor slabs, the shear core can be seen as a nonhomogeneous thin‐walled beam, with open or closed (possibly multicell) cross section, constituted by an assemblage of interconnected prismatic curtains having different elastic properties. This paper presents a one‐dimensional model for the flexural‐torsional analysis of such “nonhomogeneous” thin‐walled beam with any given cross section, allowing for shear deformations due to nonuniform bending and torsion. The axial displacement field is represented by separating the cross‐sectional and axial variables, and the governing equations for the coupled flexural‐torsional behavior are given. Some examples are solved of beams with one or two planes of symmetry, showing excellent agreement with experimental and finite‐element method (FEM) results.

In this investigation a nonlinear dynamic‐stability analysis is performed on a two‐bar geometrically imperfect frame subjected to an axial displacement of its joint, either suddenly applied or time dependent. The dynamic response of the frame is governed by a coupled system of two one‐dimensional partial differential equations for the axial and lateral motion of each bar. One and two‐mode solutions are thoroughly discussed for various geometric configurations of the frame. Dynamic buckling occurs when the corresponding frame under static loading loses its stability through a limit point. This happens for initial bar curvatures above a certain critical value; below this value the frame is dynamically stable. Numerical results are obtained by using Galerkin's method in connection with the seventh‐order Runge‐Kutta‐Verner scheme with appropriate step size. The results of the one‐mode solution are found to be in excellent agreement with those of previous analyses.

This paper presents an investigation concerning a turbulent boundary layer over a flat plate with flexible surface. Experiments were carried out in a wind tunnel for a flat plate model with rigid as well as flexible surfaces. Detailed measurements of mean velocity profiles, pressure distribution, and drag force were taken. For numerical prediction of the turbulent boundary layer characteristics, thin shear layer equations were solved numerically by finite‐difference technique using a modified turbulence model. Results of this study indicate a number of important differences between the characteristics of flow over rigid and flexible surfaces. The mean velocity of flow in the case of flexible surfaces is smaller than the corresponding velocity of flow in the case of rigid surface for major part of the boundary layer. The boundary‐layer thicknesses are consistently higher on flexible surfaces than those on the corresponding rigid surface. Further, in the case of flexible surfaces, drag reduction has always been observed during the present study.

Embedded fiber‐optic sensors have the potential of providing valuable information about the condition of the host structure when these sensors are used within an integrated health‐monitoring network attached to the structure. Although such sensors have been developed during the past 15 years for initial specialized applications in aerospace, hydrospace, and biomedical systems, recent attention has been given to the transitioning of these methods to the evaluation of civil structures. This paper reviews the state of the art of the application of fiber‐optic sensors in the structural mechanics field and reports some of the results of an experimental study concerned with the use of embedded short‐gauge‐length optical‐fiber sensors for the quantitative measurement of strain in reinforced concrete structures. Assessment of the validity of the measurements was accomplished through direct comparison between the performance of these sensors and collocated foil strain gauges. Pairs of fiber sensor elements and reference foil strain gauges were attached to specific rebar elements within a three‐dimensional reinforcement cage in a reinforced concrete beam‐column assemblage. The fiber sensors were extrinsic Fabry‐Perot interferometric elements operating at 1,300 nm. The beam‐column joint was subjected to cyclic dynamic loads leading to significant strain levels. Quantitative measurements of those strains were obtained from both the fiber and foil strain gauges. Measured values of strains varied by about 5% between the two types of sensors. Results of this study indicate that properly installed fiber‐optic strain gauges not only can survive the harsh environment involved in the embedment process, but can also yield accurate quantitative strain information from reinforced concrete structures.

Simultaneous extraction of all the aeroelastic parameters of a flexible bridge deck from a single section‐model test has been a desirable goal not fully attained in the past. In the work reported herein, an experimental setup was designed for executing coupled vertical‐torsional motion of a section model. In the present instance, the section model was located in proximity to a fixed model representing a section of the adjacent deck of a twin‐deck configuration. A robust system‐identification method was developed and applied to the noise‐corrupted displacement time histories of the section model. The experimental setup, the method of extracting the aeroelastic parameters, and the implications of the results obtained are presented in this paper. The tests were performed under both smooth and turbulent flow conditions, and in both the presence and absence of the second deck. This technique proved to offer good performance, which is evident from the consistent aeroelastic parameters obtained.

In this and a companion paper, a methodology for implementation of modal predictive control of structures is described. Predictive control is formulated, within an independent modal space control (IMSC) approach, for the control of each individual mode. In this paper, the ability of the predictive control strategy to provide stable and efficient control actions for every individual mode is numerically assessed. Two kinds of analyses have been carried out. The first analysis is a “plain assessment” that assumes all the elements in the control loop operate under ideal conditions and that there are no discrepancies between the parameters of the control loop and their values considered in the control algorithm. The second analysis is a “robustness assessment” without such assumptions. As a conclusion, criteria are given to choose the values of the parameters of the predictive control algorithm according to the modal characteristics of the structure and other parameters involved in the control loop. The results are used in the companion paper for implementation on multi‐degrees‐of‐freedom systems.

This paper is continuation of a companion paper in which a numerical assessment about the efficiency and the robustness of predictive control of structures was performed on single‐degree‐of‐freedom systems. In this paper a formulation for predictive control of multi‐degrees‐of‐freedom systems using a reduced number of sensors and actuators is presented. Control law is formulated, into an independent modal space control approach, for controlling individually some modes and the values of the parameters defining the control algorithm are chosen according to the recommendations derived in the companion paper. The efficiency and the stability of the control action are numerically assessed on a full‐size six‐story experimental building placed in Tokyo and subject to horizontal unidimensional seismic excitation. Three control cases have been considered using one, two, and three sensors and actuators, respectively. Presented results allow one to conclude that the proposed strategy seems to be able to generate stable and efficient control actions for active aseismic protection of building structures.

A recently developed technique for the digital simulation of spatially incoherent seismic ground motions is extended to include two or three spatial coordinates. This extended approach allows for four situations: (1) Simulation in the far field; (2) simulation in the near field of a small source; (3) simulation in the near field of an extended source; and (4) simulation in the near field of a limited source. In each situation, both direction‐dependent (isotropic) and direction‐dependent (anisotropic) coherency structures are accounted for. The developments proposed may facilitate the seismic analysis of structures involving foundation coupling in two or three dimensions accounting for ground motion spatial incoherence, response nonstationarity, and system nonlinearities. They can also be useful in evaluating the response of structures to other spatially variable random fields such as those of wave forces and turbulent winds.

Nonlinear dynamics of a heavy elastic suspended cable were investigated for application to a stack/wire system. Small oscillations of the cable at the support attached to the stack, the result of bending motion of the stack due to vortex shedding, lead to parametric and external excitation. Numerical analysis was used to predict the parametric and external resonances of the elastic suspended cable, which contained cubic nonlinearities due to cable stretching and quadratic nonlinearities due to equilibrium cable curvature in a tilted configuration. Numerical results agree well with the original stack/wire response. Additional parametric analyses were pursued to distinguish between parametric and external resonances and their couplings. It was found that excitation amplitudes and tilted angles play very important roles in parametric and external resonances.

Several analytical and experimental studies have been recently conducted on the behavior of cross‐bracing systems subjected to out‐of‐plane buckling. Semirigid connections, however, were not considered or modeled. This paper derives and solves for the exact expressions for evaluating the effective length factors of semirigidly connected cross bracings. Moreover, the expressions are derived for tapered systems where the bracings are connected at off‐midspan locations. Parametric solutions for the end flexibility coefficient versus the buckling parameter are graphically displayed to clarify distinct behavior, and solutions for typical cases are provided. In the example cases, a double‐wave mode versus a single‐wave mode is exhibited for the compression and tension members respectively when the tensile and compressive forces are equal, and when the tensile force is zero, both members show a single‐wave mode.

In this technical note, the effect of large deformation on the contact of an axisymmetric circular plate that rests unilaterally on an elastic foundation is investigated. Von Karman's equations for large deformation of a thin plate are modified to include the effect of the unilateral elastic foundation. The coupled equations in terms of the plate vertical displacement and the stress function are discretized using the finite‐difference method, and then solved using an incremental‐iterative algorithm. Results for a circular plate with a central point load are reported for different cases. Unlike the behavior observed in small‐deformation analysis, in which the contact area remains constant, the large‐deformation analysis shows that as the load increases, the contact area tends to expand until full contact is reached. The effects of the foundation modulus and the level of loading on the size of the contact zone and the plate displacement are also investigated.