Journal of Engineering Mechanics

Parametric studies based on previously reported orthotropic sheet theory have been carried out on a number of realistic and multilayered helical‐strand constructions with widely different strand (and wire) diameters and lay angles. Based on the results, a series of easy to use routines have been recommended which provide a simple means of obtaining estimates of various strand axial and free‐bending characteristics such as stiffness and hysteresis of axially preloaded strands experiencing axial or free‐bending load perturbations. Due to the presence of interwire friction, axial or free‐bending stiffnesses are found to be functions of the external load perturbations: Using the present routines, it is possible to obtain the upper (no‐slip) and lower (full‐slip) bounds to the stiffnesses and maximum possible specific loss under continued uniform cyclic loading. Simple formulations are also presented for estimating various wire kinematical parameters such as wire axial strains, interwire movements and strand overall effective Poisson's ratio. Practical limitations of the formulations have been discussed elsewhere, in the light of recent experimental findings. The proposed formulations are amenable to hand calculations and should prove useful for design office purposes.

Associative, elastic‐plastic constitutive laws with linear kinematic hardening or softening are attributed to the discrete structures or structural models considered herein for their dynamic analysis in the range of small deformations. Discretizations are carried out in space by finite element consistent modeling and in time by various finite difference, implicit time‐integration schemes. In this context sufficient conditions are established for: (1) Uniqueness (nonbifurcation) of the time‐step solution; (2) a kinematic extremum property of this solution; and (3) convergence on it of modified Newton‐Raphson iterative procedure. The sufficient criteria proposed materialize in correlated upper bounds on a measure of the constitutive softening and on the time‐step amplitude. The stabilizing effects of inertia are expressed in these bounds through the maximum eigenfrequency of the structural model supposed linear elastic. Time‐integration techniques differ significantly in implications of softening: e.g., the average acceleration method permits larger steps for convergence than the backward‐difference method.

Recently, the writers and others considered the optimization of continuously linear segmented structures. This geometrical constraint has practical advantages in actual design problems from the viewpoints of fabrication and prevention of stress concentrations that occur in optimal solutions with sudden changes in the cross‐sectional area. So far in the studies, the segmental lengths of the structure are prescribed. The current work considers the segmented lengths to be unknown a priori and seeks to optimize them as well. A numerical method based on optimal control theory is proposed for the optimization exercise, and a simple beam problem is used to illustrate the validity and accuracy of the method.

This paper discusses the problem of flexural‐torsional stability of columns with open thin‐walled cross sections. It introduces an analytical solution technique applicable to the differential equation system describing the current problem. The approach derived is more comprehensive than those presented traditionally in the literature and is applicable in determining the value of critical load due to combined buckling modes. The system considered consists of three separate differential equations that are coupled in a general case. Various symmetries of the cross section release these couplings. This presentation is limited, for simplicity, only to columns having singly symmetric cross sections, or at least cross sections of point symmetry. Thus, there are couplings between two of the governing equations, The elastic restraints having varying stiffnesses with respect to translation, rotation, torsion and warping, separately, have been studied as boundary conditions through numerical examples. The stiffnesses of the restraints applied are chosen to cover the range from zero to infinity.

The behavior of the response of long‐span bridges under turbulent wind in the region of stable motion is investigated theoretically. Utilizing a single‐degree‐of‐freedom structural model the basic concept of the method of analysis is introduced. Based on the assumption that both the structural behavior and the fluid‐structure interaction can adequately be accounted for by linear models the bridge response is described by differential equations with time‐varying coefficients. Assuming the turbulent components of the oncoming wind to be weakly stationary wideband random processes, which is considered to be justified when carried by high mean wind velocities, a modified stochastic averaging procedure is employed to obtain the probability density function for the response quantities. Furthermore expressions for the expected rate of threshold crossings from below and for the exceedance probability are evaluated. The influence of the parametric excitation (motion‐induced loads) on the response behavior is clearly shown in the numerical example. A subsequent paper extends the concept to more realistic MDOF models.

The buffeting response of long‐span bridges in turbulent wind is dealt with in the present investigation. Herein the analysis is based on linear models describing the structural behavior and the fluid‐structure interaction. Accounting for both parametric excitation (motion‐induced loads) and buffeting (flow‐induced) loads the bridge response is described by differential equations in the time domain. The basic concept of the method of analysis presented in the first paper is now extended to multidegree‐of‐freedom systems. First, a critical mode, which is significantly affected by parametric excitation, is isolated. Utilizing Markov process theory a statistical description of this critical mode in terms of probability density functions is given. Classical spectral analysis constitutes the basis for the analysis of the remaining (noncritical) modes. Employing the so‐called Nataf model statistical information is obtained for the response quantities including exceedance rates of torsional and vertical bending displacements. Thus a most valuable basis for engineering decisions is provided by the present investigation. The suggested approach is then exemplified in the numerical examples showing among others the role of parametric excitation for the bridge response behavior in the region of stable motion.

An analysis and implementation of the thin‐layer element of Desai et al. for interfaces and joints shows that the planar approximation of the element treated as a solid element can provide satisfactory simulation of the finite‐sized interface zone, and in the limit, its results approach those from the zero‐thickness element. Advantages and limitations of the thin‐layer element are identified, and it is implemented in a nonlinear finite element procedure with the hierarchical single surface plasticity model. The computed results are compared with those from laboratory tests on joints in concrete with different asperity angles. The nonassociative version provides highly satisfactory correlation with laboratory observations.

An optimal frequency‐domain approach to active control of wind‐excited buildings is proposed in which the $H_2$ norm of the transfer function from the external disturbance to the regulated output is minimized. A wind‐excitation model established by factorizing the cross‐spectral density matrix of the wind fluctuation is included in the control design. The control of a 60‐story building under an along‐wind excitation by one mass damper, two mass dampers, and active tendon mechanisms is presented in the numerical examples. As an improvement over previous results in civil‐engineering structural control studies, measurement and minimization of building accelerations is achieved. The effects of using constant and frequency‐dependent weighting functions in the control design are also shown. In this case, the frequency‐dependent weighting functions are designed based on the frequency domain response characteristics of the building. The frequency‐domain‐based‐design approach is shown to be both flexible and powerful.

The parameter estimation algorithms for the autoregressive moving average (ARMA) simulation of multivariate random processes is considered. The recursive procedure for estimating the parameters of multivariate AR models is extended to the parameter estimation of multivariate ARMA models of same order for both the AR and MA components, which are usually used in the ARMA simulation of stationary multivariate random processes. The recursive parameter estimation procedure for ARMA models relies on the knowledge of the input-output cross correlation of the model, which is obtained with a procedure from the two-stage least-squares method, in that an AR model of high order is used to estimate the cross correlation. A numerical example shows that the recursive procedure for multivariate ARMA models leads to good ARMA representation of random processes, which is characterized by a specified target spectrum.

Long, unstiffened plates are thin plates stiffened at only one edge parallel to the direction of stress. These occur in various shapes, including a T-shaped section. For modeling purposes, the plates can be assumed to be simply supported along the stiffened edge parallel to the applied stress and along the transverse edges at the ends of the plates. The plates can be subjected to a range of linear stress gradients. For plates subjected to linear stress gradients with maximum compression at the simply supported edge and maximum tension at the free edge, elastic buckling coefficients are determined. A finite difference approach is taken, since an assumption of a simple geometric buckled shape (for use in a method such as the Galerkin method) cannot be made. The results from the finite difference solution and an equation that approximates the solution are presented, along with available elastic buckling coefficients for other linear stress gradients.