Journal of Engineering Mechanics

In order to design a new power‐transmission tower built with a cantilevered and tapered thin‐walled steel member instead of the usual angle steel or pipe, the governing equations for a doubly symmetric and linearly tapered thin‐walled member are presented in a general way by means of Hamilton's principle. Closed‐form solutions are indicated for the static problems. Next, the exactness of the proposed elastic solutions is proven using numerical calculations for a cantilevered and linearly tapered thin‐walled member with a circular, octagonal, or rectangular transverse cross section. It is shown that the mechanical behavior of the cantilevered and linearly tapered thin‐walled members is remarkably different from that of the cantilevered thin‐walled member with uniform cross section and that the difference arises even for fairly small tapering angles. The effect of the transverse shear deformation for the current problem is shown to be negligible.

This paper presents a mechanistic approach to constitutive modeling of asphalt concrete under complicated repetitive loading conditions with rest periods. From an extensive literature review, two mechanisms are identified as important to understanding of inelastic stress‐strain behavior of asphalt concrete: vis‐coelastic relaxation and fatigue as a damage accumulation process. The nonlinear viscoelastic correspondence principle developed by Schapery is applied to separate the influences of these two mechanisms to the stress‐strain hysteresis behavior of asphalt concrete. The damage growth in asphalt concrete beam samples is modeled by a damage parameter that is based on a generalization of microcrack growth law. In the verification stage, a random sequence of multilevel loading with random durations of rest periods was applied. The resulting constitutive equation satisfactorily predicts the effect of the sequence of the load applications of varying magnitudes, as well as the beneficial effect of rest periods.

The results of triaxial tests on coarse‐grained soils are often strongly influenced by the effects of membrane penetration. Analytical attempts at description of and experimental attempts at elimination of membrane penetration have not been successful. An analytical expression for the variation of membrane penetration volume change with net membrane pressure is developed. The expression is obtained from an approximation to the deformed shape of a membrane stretched across a regular array of uniform spheres. Laboratory tests performed on regular arrays of spheres and on coarse‐grained soils verify the ability of the expression to represent membrane penetration behavior accurately.

A micromechanical analysis is carried out to introduce a tensor measure for the strain of granular media. This strain tensor, being different from that of the conventional definition, includes explicit descriptions for the spin of particles in granular media. A stress‐strain relationship is then derived based on the new definition of strain tensor. Due to the assumption of a linear displacement field, the stress‐strain model is intended for estimating mechanical properties of a packing under conditions of low shear stress levels. The Hertz‐Mindlin theory of nonlinear contact is used in the mathematical model to predict the mechanical behavior of rod assemblies with various packing structures. The theoretical predictions are compared with the measured results obtained from experimental tests. Results of this comparison are used to evaluate the applicability of the stress‐strain model. The laboratory device, test samples, and loading conditions are described and the comparisons between measured and theoretical results are discussed.

The pseudodynamic test method is a hybrid, computer‐controlled, experimental technique that adopts a step‐by‐step integration procedure to analyze the seismic behavior of structures. Since the response of the structural specimen in each step of a test is evaluated with the experimental data obtained in the previous step or steps, experimental errors introduced in each step are accumulated in the numerical procedure. The error‐propagation characteristics of several integration algorithms that are currently used for such tests are examined. Mathematical equations that characterize the cumulative growth of experimental errors are formulated, and used to evaluate the error‐amplification effects of the algorithms. It is shown that the magnitude of cumulative errors depends on the numerical properties of the algorithm, the frequency characteristics of the specimen, and the nature of experimental errors. Moreover, it is found that numerically computed displacements should be used instead of experimentally measured displacements in the step‐by‐step computations.

Wire rope is a structural element that is generally used to resist relatively large axial loads in comparison to bending and torsional loads. In many cases, rope is subjected to impact loads that send axial and torsional responses up and down the rope. A theory is presented that predicts the contact force between an outer strand and a core strand in a rope (or an outer wire and a core wire in a strand) subjected to an axial impact load. When the contact force remains positive, no separation occurs. If, however, the contact force becomes negative somewhere along the rope, the outer strands will separate from the core strand. When this separation strains the rope material beyond its elastic limit, instability or bird‐caging occurs in the form of a permanent deformation. This theory predicts an interesting situation in which bird‐caging can occur even when the rope remains under a positive axial strain. Hence, the rope does not have to go into compression for bird‐caging to occur.

A continuum theory is presented for representing the high‐temperature deformation behavior of metallic composite materials. The composite is considered pseudohomogeneous with its own properties that can be measured for the composite as a whole. A class of constitutive equations in which the inelastic strain rate and internal state are expressible as gradients of a dissipation potential function is extended for a composite. The potential is taken to depend on invariants that reflect local transverse isotropy. Applications illustrate the capability of the theory of representing the time‐dependent, hereditary, anisotropic behavior typical of these materials at elevated temperature.

Blind predictions for the response during forced vibration tests of a large‐scale containment model supported on soft soils and located in Lotung, Taiwan, are compared with recorded data. The predictions for two sets of models, including soil‐structure interaction effects, were obtained by use of a substructure approach. The first set of models (model set A) was based on basic geotechnical data, including unit weight, water content, void ratio, and standard penetration test results at several boreholes. The second set (model set B) was based on more complete geotechnical and geophysical information including S‐ and P‐wave velocities to a depth of 150 m. The differences between the vibration test data and the predictions decrease as the quality of the soil data increases. For model set B, the differences fall within the uncertainty of the recorded response and the input data. An after‐the‐fact model (model C), which minimizes the discrepancy between theory and experiments, is also presented.

In recent years, there have been many papers on dynamic properties of cooling towers. However, the bottoms of the tower shells were assumed as a fixed boundary, or discrete column systems of towers were considered as elastic boundary conditions. In the present paper, tower shells and discrete supports are treated as before. Furthermore, a dynamic model of an infinite soil is developed, and dynamic properties of the whole system of the cooling tower have been calculated. Model tests of free vibrations of cooling towers on different simulated soils are investigated. The numerical and experimental results are in agreement. The results show that the elasticity of the soil reduces the natural frequencies of the cooling tower and the reduced value depends on the stiffness of the soil. Some of the mode shapes of the cooling tower are changed much as compared to a built‐in tower.

A procedure is presented for determining the stress and deformation in prismatic members with general cross sections due to end restraints in torsion. The end restraint conditions are represented by superposition of a system of eigenvectors, each depicting a self‐equilibrated end effect. These eigendata, which may be called the Saint‐Venant end solutions, are extracted from an algebraic ei‐gensystem of a two‐dimensional finite element model of the cross section. The dominant (lowest nonzero) eigenvalue and corresponding eigenvector are associated with the behavior that persists the greatest distance into the interior from the end. Examples on elliptical and rectangular cross‐sectional members and on wide flange and angle beams are presented to illustrate the procedure. Comparison of the present results with those determined by approximate analysis and ad hoc methods leads to some understanding of the factors that influence the attenuation of the stresses and deformations in restrained torsion.

Simplified response of buildings with a soft first floor and excited by propagating wave motion at the base are studied, so that the physical phenomena associated with phased input excitation can be characterized. Analytical solutions are obtained for two‐dimensional continuous building models, neglecting the soil‐structure interaction, and for monochromatic antiplane excitation. It is shown that the wave energy does not always propagate from the ground into the building, depending on the value of the horizontal phase velocity of the ground motion. There is a possibility that it propagates only into the “soft” first floor, which then acts as an “isolation layer” for the upper floors. However, this is at the expense of very large deformations of the columns of the first floor, that are not considered in the conventional analysis of buildings. Also, the out‐of‐phase motion of the base may excite torsional vibrations with large amplitudes. It is concluded that the design for P‐delta effects in the soft first floor should not ignore those additional wave passage effects.

This paper presents an alternative definition of finite strains that can be considered as a new subset of Hill's general family of strain measures. The Lagrangian and Eulerian finite‐strain tensors are two extreme special cases of the proposed measure. One of the special cases $(\lambda =1/2)$ possessing linear characteristics is selected and examined in detail. In addition to providing a general and alternative definition, the proposed measure with the special case of $\lambda =1/2$ offers a simpler definition for finite strains compared with other conventional measures.

Based on fundamental equations of three‐dimensional elasticity and giving up any assumptions about displacement models and stress distribution, the state equations for the axisymmetric free vibrations of transversely isotropic circular plates are established. Because the four quantities appearing in the state equations happen to be the compatibility quantities of the interfaces, it is extremely convenient to develop the state equations of laminated circular plates with transversely isotropic layers. The exact solutions for such problems with simply supported and clamped edges are presented in this paper. Every fundamental equation of three‐dimensional elasticity can be exactly satisfied and all five elastic‐flexibility constants can also be taken into account by the present method. No matter how many layers are considered, the calculation always leads to solving a set of linear algebraic equations of the second order. Numerical results are obtained and compared with the results calculated using the Reissner and Mindlin theories, respectively.

The harmonic response of an infinitely long thick elastic tube is considered. Exact displacement and stress fields for steady‐state vibration are developed. Stiffness equations are derived, relating the internal and external boundary tractions and displacements. Assembly of these tube stiffness equations is used to evaluate the response of laminated tubular structures. The formulation is extended so that the behavior of viscoelastic tubes can also be determined. Comparisons are made with solutions based on thin‐shell theory, to assess how accurately shell theory models thick‐tube vibration. Distributions of displacement and normal stress through a laminated tubular structure are studied. The response of a tube with an elastic core and a viscoelastic tube also are investigated.

The dynamic steady‐state response of long elastic and viscoelastic tubes to patch loadings is considered. Tube response to an isolated load set is assembled from harmonic behavior using Fourier transforms, and response to periodic loads is assembled using a Fourier series. Solution techniques for both prescribed tractions and prescribed displacements are described. Example calculations for various elastic tube systems are provided. Response to bands and patches of uniform radial pressure is investigated for both plane and laminated tube structures. Viscoelastic material response is studied using the generalized Kelvin model.

Qualitative analysis of the antiplane vibrations of long structures shows that the dynamic response to excitation by ground waves can be described by the translation of the foundation only if η (ratio of the length of structure to the wavelength of incident waves) is less than $\sim 1/1\text{,}000\text{.}$ For $1/1\text{,}000<\eta <1/100-1/10$ antiplane response of structures can be approximated by translation and rotation of ground motion about the vertical axis (torsional excitation). For $\eta >1/100-1/10$ actual wave motion of the ground must be considered, not only for the correct representation of the dynamic response of structures, but also for proper analysis of the resulting deformation of the foundations.

Structural models are considered that are conveniently viewed as a composite of subsystems. Conditions are sought that assure the simultaneous existence of classical uncoupled modes of vibration for the composite system and for each of the subsystems. It is shown that the Rayleigh condition for the composite system is the only situation giving precisely the desired uncoupled modes. More general conditions give approximately uncoupled modes if the system is composed of a massive primary system and a light secondary system.

The snap-through instability of a uniform, shallow, elastic arch is considered. The arch has a sinusoidal shape and is subjected to a uniformly distributed load. As the load is increased, the flexural resistance of the supports is assumed to increase. In order to model this behavior, rotational springs act at the immovable arch ends, and their stiffnesses are assumed to be linear functions of the compressive thrust induced by the load. The effect of this support stiffening on the critical load is investigated. Both symmetric and asymmetric supports are treated. The critical load may be increased significantly due to support stiffening, especially if the initial flexural resistance is low.