Journal of Engineering Mechanics

A theoretical formulation has been proposed for obtaining upper bounds to single‐layer helical strand damping under cyclic bending to a constant radius of curvature. The model employs an alternative interwire/interlayer friction formulation to the traditional rigid‐plastic Coulomb model: this, then, enables one to follow the no‐slip‐to‐full‐slip friction transition over the individual contact patches. Results are presented for cables in which the helical outer wires only touch the core and also for spiral strands with no core whose outer wires just touch each other in line contact. Parametric studies show that the traditional Coulomb friction model tends to grossly overestimate cable damping for large radii of curvature such as those found in connection with vortex shedding dynamic instabilities of, for example, overhead transmission lines and underwater cables where the maximum amplitude of vibration is of the order of one cable diameter. For small enough radii of curvature, however, the present model's predictions approach those based on the Coulomb rigid‐plastic model. It is found that cable damping may be increased by increasing the number of wires and/or decreasing the helix angle. However, for sufficiently large levels of radii of curvature and cable axial strain, the present theory suggests that for certain ranges of helix angle, increasing helix angle leads to increases in cable damping that can only be predicted with the newly proposed model, which takes no‐slip‐to‐full‐slip interwire friction interaction into account.

An incremental model is proposed for the nonlinear relationship between the normal action effects N, $M_y\text{,}$ and $M_z$ and the corresponding cross‐sectional deformations, ${\epsilon }_o\text{,}$ ${\varphi }_y\text{,}$ and ${\varphi }_z\text{,}$ of rectangular reinforced concrete cross sections. The incremental relationship is of the bounding‐surface plasticity type: The bounding surface of the cross section, which corresponds to ultimate strength, is constructed in the stress space of $N‐M_y‐M_z\text{,}$ and the plastic moduli of the incremental flexibility or rigidity relation are functions of the distance of the current stress point from the bounding surface, along the current direction of incremental loading. The functional dependence of the bounding surface and of the plastic moduli on the amount and distribution of longitudinal and transverse steel is given, as well as the coupling terms between axial deformation and curvatures in the incremental flexibility relation. The simple hysteresis rules, which make the model applicable for arbitrary load paths in the $N‐M_y‐M_z$ space, including reversals, are also given.

A distributed inelasticity cyclic model of reinforced concrete (RC) columns is developed, using as a building block the tangent flexibility matrix of a section, which relates the three nondimensional normal stress resultants to the three corresponding section deformations. It is given in a companion paper in terms of the amount and distribution of the column longitudinal and transverse reinforcement. The tangent flexibility matrix of the cross section is integrated numerically along the element length to give the tangent flexibility (and stiffness, by inversion) matrix of slender reinforced concrete columns, in which flexure dominates the cyclic inelastic behavior. The model is implemented into a finite element program for the nonlinear static or dynamic analysis of structures in three dimensions. The program is applied to predict the results of cyclic uniaxial or biaxial tests, as well as the dynamic response of an actual reinforced concrete building to the three components of the Kalamata 1986 earthquake. The model predictions are in good agreement with the test results and with the damage inflicted to the building by the earthquake.

This paper offers a set of partial differential equations designed to enable static analysis of incomplete composite plates with regard to the thickness of a steel plate. The paper also analyzes the relationship of lateral deflections among complete composite plates, incomplete composite plates, and individual plates that do not interact with regard to simply supported rectangular composite plates; $\beta =0$ signifies complete composite plates, $0<\beta <1$ signifies incomplete composite plates, and $\beta =1$ signifies individual plates that do not interact. The paper also submits a diagram that represents the essential features of the lateral deflection characteristics of simply supported rectangular incomplete composite plates that will be found suitable for most design purposes. Lateral deflections can be derived by the use of the diagram without too much difficulty. The present method can also be applied to the finding of lateral deflections undergone by continuous incomplete composite plates and other types of load.

A procedure for progressive nonholonomic analysis of elastoplastic plane frames neglecting axial force effects is developed. Within the framework of simple plastic theory the governing condition is expressed in terms of total values of loads, bending moments, and hinge rotations. The path‐dependent load‐deformation behavior is traced incrementally through linear phases, imposing the yield criterion and flow rule as auxiliary conditions. The method is intended for implementation as an interactive system for analysis and design. Computations are organized as a series of four modules such that a loading data modification can be responded to with little effort and the next fastest response is for changes in member sections, nodal coordinates, and structural connectivity, in that order. Deflection components are computed only as and when queried by the user. A special feature of the approach is that the complete solution can be provided whenever lack of uniqueness of kinematic solution arises. A detailed example is included.

The dynamic behavior of an extensible sagging cable is investigated. A dynamic stiffness matrix is presented whose coefficients are functions of the frequency of motion, and that is suitable for dynamic direct‐stiffness analysis of composed systems such as cable‐stayed bridges and guyed masts. The study is restricted to small displacements (linear theory) and considers motion within the vertical cable plane only. Viscous damping due to external fluid is taken into account. Trigonometrical solution functions with complex arguments are utilized, which implies a substantial simplification in the analysis of damped vibrations. By means of example calculations, stiffness functions are discussed and compared to the results of other authors. For tightly stretched inclined cables, utilization of the more accurate theory presented in this paper is indispensable.

Practicing engineers continue to use the Winkler model for the analysis of beams and plates resting on elastic foundations in spite of the disclosure of inconsistencies in the use of the Winkler model by past researchers. In this paper, using variational principles, the model developed by Vlasov and Leont'ev is refined, and a numerical model using the finite difference method is introduced to solve a rectangular plate resting on a layered soil medium. Instead of the coefficient of subgrade reaction of the soil, the material properties of the soil are used in the analysis. The basic parameters required for the analysis are computed from the geometry and material properties of the soil and the structure. Some of the basic inconsistencies in the classical Winkler model are brought out in this paper. Results of some examples are presented.

This paper investigates the stability of externally pressurized tubes subjected to bending. A rigorous analytical technique based on the finite element method and accounting for geometric and material nonlinearities is described. Its advantages over existing analytical tools include the capability of simulating tubes of arbitrary thickness and the introduction of a “pressure node, “which facilitates the transition over limit pressure points. The formulation is applicable to pipe analysis in two as well as three dimensions. Results, presented in the form of pressure‐curvature interaction diagrams, indicate good agreement with the available experimental data. In agreement with earlier work, it is shown that ultimate tube strength is sensitive to loading path. A simple stability criterion is employed and leads to proper characterization of instability for all histories of pressure and curvature. Finally, the three‐dimensional simulation of the common experimental procedure, in which end rotations are applied to the specimen by means of welded plates, shows that curvature may not be nearly constant lengthwise, and, therefore, care must be exercised in extracting a characteristic value that is independent of end conditions. Suggestions, based on findings from several three‐dimensional analyses, are made concerning this matter.

A three‐dimensional elasticity solution of a three‐pile cap is presented. The solution of the governing equations of the theory of elasticity is expressed in terms of the Galerkin vector. The components of the Galerkin vector are expressed as double‐Fourier series. The method consists of superposition of three‐dimensional elasticity solutions for a rectangular block subjected to four different patch loadings. By this approach the boundary conditions for a three‐pile cap can be satisfied exactly. Contours of tensile stresses at the bottom face reveal the regions of maximum stresses. No attempt seems to have been made so far for the rigorous analysis of three‐pile caps in the literature.

A linear theory for wire rope that considers individual wire geometry and equilibrium is extended to include the effect of contact deformations between wire layers. Contact compliance between wire layers is determined using Hertz contact theory and results from contact mechanics for a point and line contact case. Analysis is presented for simple as well as multilayered strands that may incorporate compliant layers. Numerical procedures are presented for efficiently solving the resulting nonlinear simultaneous equations, and numerical results are presented for several typical multilayered metallic strand and instrumentation cable geometries.

In the second‐order reliability method the principal curvatures of the limit‐state surface at the design point are used to construct a paraboloid approximation of the surface, which is then used to compute a second‐order estimate of the failure probability. The principal curvatures are the eigenvalues of the Hessian of the surface. In this paper an efficient algorithm is developed to determine the principal curvatures without computing the Hessian. The curvatures are computed in an iterative manner using the gradient of the limit‐state function, and are obtained in the decreasing order of their absolute magnitudes, which is also the order of their importance in reliability analysis. The computation can be terminated when the last curvature obtained is sufficiently small. The method is efficient for problems with large numbers of random variables, especially when an efficient algorithm for computing the gradient is available. Several numerical examples, including a finite‐element application involving 99 random variables, demonstrate the accuracy and efficiency of the method.

A general criterion to qualify ARMA representations of ocean spectra is presented. An objective criterion to qualify simulators becomes the key element to justify the selection or rejection of ARMA representations for practical applications. A technique to calculate robust AR representations appears to be the natural engineering solution to overpass the instability and poor results provided by classical methods. An addition of modicum white noise (0.0025 $m_0$) to the theoretical JONSWAP-type spectra is proved to be sufficient to generate robust AR representations free of instabilities and showing an excellent qualification according to the general criterion justified for most ocean engineering applications.

A theoretical investigation has been carried out to determine the effective properties of fiber-reinforced concrete with randomly oriented fibers. Two analytical approaches have been considered: one with continuous cylindrical fibers based on the composite cylinders model and the other with prolate spheroid fibers based on the Mori-Tanaka averaging scheme. In both cases, initial analysis has been carried out for a transversely isotropic medium (aligned fibers in concrete) and then a geometric averaging procedure has been performed to convert these properties to the effective properties of the isotropic composite (concrete with randomly oriented fibers). An asymptotic prediction has also been made for the effective properties, valid for very low concentration of fibers.