Journal of Engineering Mechanics

How do boundary conditions influence strain localization in concrete loaded in compression? To answer this question, compressive tests were performed on prismatic specimens of mortar. The blocking or nonblocking of rotation of the top platen of the press and the use or absence of an antifriction system have led us to consider four different boundary conditions. The onset of strain localization and its development in the course of loading are determined by the stereophotogrammetric method. The results obtained show that rotation (when it is free) always starts after the peak load. The postpeak portion of the load‐displacement curve depends to a very large extent on the boundary conditions: the use of an antifriction system increases the mean slope of this part. But, on the other hand, the onset of strain localization occurs at the peak, whatever the boundary conditions.

An alternative integral‐form solution of the Lamb's problem is developed for the transient response inside of the medium as well as at the surface, when subjected to impulsive/sudden application of surface strip loads. A distributed‐source solution that yields a Green's function for the boundary‐integral equation for half‐space problems has more advantages for the effective use for actual boundary‐value problems when compared to the Lamb's classical point/line source solution of 1904. The present procedure applies the Fourier‐Laplace integral transform to the governing equation so that after getting the Fourier (wavenumber) Laplace domain solution, it performs the inverse Fourier transform analytically and the inverse Laplace transform by contour integration. Such obtained expressions are amenable to numerical computation with excellent accuracy. The interior and surface responses of the medium under the uniform surface loading are the focus of the illustrative computations. The results are verified by comparing the surface response at the extreme loading state with the existing closed‐form solution for line source. The interior response features are stated.

A three‐degree‐of‐freedom model is developed to comprehensively describe and predict different galloping behavior observed on a single iced, electrical transmission line. Interactions are accommodated between a line's plunge, twist, and swing in the along‐wind direction. Eccentricity of the cross section is also considered and the longitudinal static stiffnesses of adjacent spans are included. The initiating conditions for galloping are derived in closed form. For the parameters causing galloping, perturbation techniques are employed to derive the governing bifurcation equations under the assumption of a weak nonlinearity. A total of 10 (one nonresonant and nine internal resonant) plausible cases are considered. Two different time averaging approaches are used for different cases to simplify the algebra in deriving the explicit solutions. Aerodynamic effects are incorporated in the structural stiffness matrix to improve accuracy and to extend the range of application of the perturbation. A robust criterion is developed to assess the reliability of the solutions. Explicit periodic and quasiperiodic states and their stability conditions are computed in a companion paper.

Internal nonresonant and resonant galloping of an iced electrical transmission line is studied by employing a three‐degree‐of‐freedom (3DOF) model formulated in part I where the conditions for the initiation of galloping and the governing bifurcation equations were derived for dynamic motions. Perturbation techniques are employed so that the governing equations can be manipulated algebraically to obtain explicit expressions for the periodic and quasiperiodic solutions as well as their stability conditions. For the nonresonant case, sequent bifurcation solutions and stability boundaries show that secondary and tertiary bifurcations exist. It is also demonstrated that phase differences between different component movements do not affect the stability conditions for the nonresonant case even though they are significant for the resonant cases. Practical examples are presented to demonstrate the applicability of the theory. Results at different wind speeds indicate that a previously defined “smallness” parameter is appropriate for assessing the reliability of the solutions. Furthermore, a comparison of the results from simple models having various degrees of freedom suggests that it is advisable to employ at least 3DOF.

A random‐vibration‐based force‐response spectrum of a simple oscillating frame is proposed as a simplified measure of the effect of spatial seismic excitations on structures. Such a response spectrum reflects the effect of incoherent support motions on quasi‐static and dynamic response of structures. The response spectrum is formulated as a dynamic coefficient in terms of point spectral density and unlagged coherency of excitations as well as frequency‐response function of the oscillator. A concise analysis is performed in order to study joint effect of dynamic and quasi‐static excitations. The effect of two principal parameters (separation distance and apparent wave velocity) is analyzed in detail. It appears that for some values of natural frequency, separation distance, and apparent wave velocity the force spectrum is reduced and that for the others it is amplified. After some calibration, the derived response spectrum may find application in engineering practice as a partial coefficient.

A theoretical formulation is developed for large‐strain analysis of reinforced, multilayer membranes that contain nonlinear, viscoelastic materials and are subjected to unidirectional, in‐plane loading. Regularity conditions, satisfied by the displacement fields of interest, allow the problem to be formulated in terms of a single, in‐plane component of the displacement field, even when strains are large. The theory is implemented in a finite‐element software package called REMA (reinforced membrane analysis), designed to run on a personal computer. An explicit stiffness matrix is used. The software is designed to investigate a wide range of membrane behaviors and to model the sequential stages of reinforcement and matrix subcomponent failure. Here, it is used to predict the load‐deflection behavior and sequence of subcomponent failures produced by typical in situ loading of a reinforced roofing membrane. The predictions are compared with corresponding laboratory tests.

A numerical method is developed for analysis of elastoplastic frames. Yielding is represented by concentrated displacement discontinuities with extension and rotation components. The possible yield points are located at the ends of the beam elements. The corresponding plastic degrees of freedom are added to the system as they arise, increasing the size of the global system of equations but avoiding refactorization. The yield deformations follow a hardening plastic rule. By using a piecewise linearized (polyhedral) yield surface and linear hardening a formulation is developed in which the gradual development of yielding of the frame is computed as a sequence of linear problems, each leading to the formation of a new yield hinge or change of an existing yield hinge. The method has been implemented in the C programming language with fully dynamic memory allocation but can be used to extend existing linear frame analysis programs.

Methods are studied that permit larger time intervals to be used in structural dynamics calculations than are possible by the usual techniques. The size of time interval is often restricted by the rapidity of variation in excitation or by yielding and unloading in the structural members. In earthquake engineering, the input is proportional to ground acceleration, a rapidly varying function of time. In many structural dynamics problems when nonlinearity is present, rapid or even sudden changes of stiffness occur. Either the times of such rapid stiffness changes must be determined or else very small time intervals must be used nearby. Any factor that limits the size of time interval can result in a large volume of computation. A set of methods is developed to handle these limitations, finally permitting the use of fairly large time intervals while preserving high accuracy. Integrated displacements are used as the new variables in integrated equations of motion; a more accurate numerical integration method is employed; and an interpolation procedure eliminates the difficulties at yield and unloading.

A crude analysis of a dynamic system involves very few degrees of freedom. When a more refined model is desired, more degrees of freedom must be introduced. This will increase the number of modes present and result in modes with very high frequencies in the model. The presence of these modes causes severe restriction in the size of time interval that can be used for step‐by‐step dynamic analysis in nonlinear problems. This restriction is removed by a new type of perturbation procedure that generalizes the method of static condensation and can treat relaxation of constraints in addition to variables associated with small masses. The additional degrees of freedom are treated algebraically rather than as true dynamic variables. The method is applied to structures with significant material nonlinearity. The lower‐frequency motions are corrected as a result of the presence of the additional degrees of freedom, but the very high frequency motions are not introduced. Thus, the time interval is selected corresponding to the highest frequency involving only the dynamic variables rather than to the much higher freqencies that would ordinarily be present.