Journal of Engineering Mechanics

This paper presents an analytical approach in the study of bifurcation and stability behavior for nonlinear galloping of iced transmission lines. Equations of motion are established to describe three-dimensional galloping behavior observed on iced transmission lines. Stability analysis of iced conductor galloping is carried out. The center manifold theory, together with the normal form theory, is used to derive the governing bifurcation equations. A new formula is also proposed to calculate the maximum dynamic tension of iced conductors. The technique developed in this paper is implemented using a symbolic analysis module for practical usage. A real transmission line with a span of 244 m, which was damaged by the galloping accidents, is presented to demonstrate the effectiveness and accuracy of the developed two-parameter bifurcation analysis technique for nonlinear galloping of iced conductors. The galloping amplitudes in three orthogonal directions are analytically obtained for a broad range of galloping wind speeds and attack angles. The analytical solutions of galloping amplitudes are also verified by the numerical time-stepping method.

Bond slip of RC structures occurs wherever primary cracks are present. These cracks usually appear at the beam-column and column-foundation joints, for example, when structures are subjected to seismic loadings. As a result, it is imperative to consider bond slip in performing an accurate evaluation of the response of RC structures. The distributions of stress and strain in an embedded rebar vary depending on the geometry, such as concrete cover and embedment length, which are referred to here as configuration effects. Because bond stress and bond slip can be defined as functions of stress and strain of the embedded rebar, respectively, the relationships of bond stress and bond slip also differ. This, in turn, leads to different crack patterns: splitting cracks, shearing-off failures, or no cracks in the concrete. These differing crack patterns also cause distinct governing failure modes involving splitting failure, shearing-off failure, and bar fracture, respectively. Consequently, the relationships of bond stress and bond slip should be defined considering configuration effects, and a method should be developed to predict the governing failure mode for given geometric conditions. Furthermore, because cracks are the main sources of size effects, bond stress and bond slip should be evaluated carefully given that splitting cracks and shearing-off failures are tied to bond stress and bond slip. To investigate size effects of an embedded rebar and configuration effects of concrete cover and embedment length, a series of pullout tests was performed. In each test, a pullout force was applied to the rebar, which was embedded in a concrete cylinder. To examine size effects, three different sizes of rebar and associated concrete cylinder specimens were selected, whereas to address configuration effects, four different geometric settings for the concrete cylinders were considered. Based on the experimental program, an analytical stacked hollow cones (SHC) model was developed to evaluate the relationships of bond stress and bond slip at the failure states by assuming that imaginary concrete cones, which represent the transferring paths of forces generated by ribs of a rebar to the surrounding concrete, are supported by imaginary tension annuli formed at the cracked section. A method to predict the governing failure modes for given geometric conditions is proposed using critical energy release rates when cracks occur in the concrete. Meanwhile, a bond capacity model is proposed for prediction in the case of bar fracture for which no cracks develop in the concrete. Depending on the rebar-cylinder geometry, these size effects can vary. The bond stresses follow the general size effect law, with the strength of structures decreasing as size increases. For bond slip, however, the short-embedment cases follow the general size effect law, whereas the long-embedment cases do not. Scaling dimensionality factors, which depend on the geometric configuration, are established to capture the size effects. The proposed analytical model, along with the appropriate scaling dimensionality factors, then is able to predict the bond stress–bond slip relationship at failure states considering size effects and the governing failure modes for given geometric configurations. Experimental data obtained from the literature also are used to verify further the proposed analytical model. Although all this provides encouraging results that emphasize the importance of configuration and size effects on bond stress and bond slip, a more comprehensive experimental program is recommended as future work to refine the proposed models and to establish model parameters with increased confidence.

Biobased composites have been widely proposed in the literature as suitable replacements for a variety of engineered materials, with applications ranging from biomedical devices to automotive components to construction materials. Previous research has primarily focused on engineering biobased alternatives with mechanical and physical properties that either duplicate or exceed those of their synthetic counterparts. Although several elastic biobased composite design techniques have been proposed, modeling the complete material constitutive response, including the significant anisotropy and nonlinearity exhibited by many biobased composites, has not yet been explored. In this research, a transversely isotropic nonlinear constitutive model is modified and implemented in a finite-element framework to predict the mechanical response of natural woven fabric biopolymeric composites. A novel method for indirect calibration of constitutive model parameters from simple tension and flexure tests is proposed using a fiber section analysis and nonlinear optimization. Numerical predictions of anisotropic elastic and nonlinear hardening behavior are demonstrated in a comparison between experimental and finite-element analysis results for oriented hemp fabric–reinforced poly(3-hydroxybutyrate)-co-poly(3-hydroxyvalerate) (PHBV) polymer composites tested in flexure. Model results for 0, 45, and 90° and ${\left[\pm 30/\pm 60/0\right]}_s$ oriented laminates tested in uniaxial tension and three-point bending closely matched the results of experiments. This modeling technique is proposed within the context of developing effective design tools that facilitate the adoption of engineered biobased composites into practice.

To quantitatively estimate the contributions of component failure modes to system output, failure-mode importance measures have been proposed in this paper. This issue is discussed in two schemes: in Scheme 1, failure-mode importance is measured by the change in the characteristics of the system output after removal of the interested failure mode; and in Scheme 2, failure-mode importance is measured by the expected change in the characteristics of the system output after fixing the failure mode of interest at nominal values. Properties and the computational strategies of the failure-mode importance measures also are presented. Discussions with numerical and engineering examples demonstrate that the importance measures are of great significance for the purpose of system improvement.

Nonviscous damping models in which the damping forces depend on the history of velocities via convolution integrals over some kernel functions have risen in many different subjects. The aim of this paper is to extend the Newmark method from viscously damped structure systems to nonviscously damped structure systems. The proposed analysis method for nonviscously damped structure systems is derived based on Newmark’s assumption of acceleration. The convolution integral term is calculated directly using the trapezoidal rule. The computational procedure of the proposed direct time integration method for nonviscously damped structure systems is given in detail. Finally, the dynamic responses of two nonviscously damped structure systems are computed using the proposed method. The accuracy and efficiency of the proposed method are discussed through comparison with another developed method.

Conventional deformation measurement techniques, such as utilizing a LVDT, a demountable mechanical strain gauge (demec gauge), and an electrical strain gauge, despite their vast usage in experimental studies, suffer several disadvantages, including high cost, time-consuming specimen preparation, and the inability to obtain the whole displacement or strain fields. The aforementioned drawbacks on one hand and the importance of deformation measurements in all civil engineering laboratory tests on the other hand have led researchers to develop other measurement techniques, especially image-based techniques, capable of evaluating whole deformation fields. Among all of these recently developed methods, particle image velocimetry (PIV) has attracted much interest in all branches of civil engineering experimental investigations; PIV is a powerful image-based technique for evaluating both displacement and strain fields by analyzing successive digital images of a field undergoing deformation. Despite its great potential, however, few studies have been reported that use PIV for obtaining deformations for structural tests, especially for evaluating displacement and strain fields in a conventional bending test. Consequently, the intention of the current paper is to show the performance of the PIV technique for displacement and strain field measurement in bending tests of steel and RC beams subjected to four-point flexural loading. Based on different validation experiments of the current study, the PIV technique can be widely used as an alternative to conventional displacement and strain measurement techniques in bending tests. Moreover, the PIV technique demonstrated a great potential for investigating the fracture process in RC beams during the test process.

The critical state line of Tacheng rockfill material (TRM) was described by a pressure-power function. A simple bounding-surface plasticity model, combining the dilatancy stress ratio and peak-failure stress ratio pertaining to the state pressure index, was developed for TRM within the framework of critical-state soil mechanics and the bounding surface plasticity. Detailed investigations of influences of design parameters on the model predictions were carried out. The developed model, using a set of model constants, captured well behaviors such as strain hardening and volumetric contraction for TRM in a loose state (e.g., at a large initial void ratio or a high initial confining pressure) and strain softening and volumetric expansion in a dense state (e.g., at a small initial void ratio or a low initial confining pressure).

Solving the Fokker-Planck-Kolmogorov (FPK) equation is one of the most important and challenging problems in high-dimensional nonlinear stochastic dynamics, which is widely encountered in various science and engineering disciplines. To date, no method available is capable of dealing with systems of dimensions higher than eight. The present paper aims at tackling this problem in a different way, i.e., reducing the dimension of the FPK equation by constructing an equivalent probability flux. In the paper, two different treatments for multidimensional stochastic dynamical systems, the FPK equation and the probability density evolution method (PDEM), are outlined. Particularly, the FPK equation is revisited in a completely new way by constructing the probability fluxes based on the embedded dynamics mechanism and then invoking the principle of preservation of probability. The FPK equation is then marginalized to reduce the dimension, resulting in a flux-form equation involving unknown probability flux caused by the drift effect. On the basis of the equivalence of the two treatments, this unknown probability flux could be replaced by an equivalent probability flux, which is available using the PDEM. An algorithm is proposed to adopt the data from the solution of the generalized density evolution equation in PDEM to construct the numerical equivalent flux. Consequently, a one-dimensional parabolic partial differential equation, i.e., the flux-equivalent probability density evolution equation, could then be solved to yield the probability density function of the response of concern. By doing so, a high-dimensional FPK equation is reduced to a one-dimensional partial differential equation, for which the numerical solution is quite easy. Several numerical examples are studied to verify and validate the proposed method. Problems to be further studied are discussed.

High interfacial stresses near the edges of bonded joints are responsible for their debonding failure. This paper reports a new semianalytic stress-function variational approach to the interfacial stresses of a bonded joint, which is made of a straight tension bar covered with a reinforcing patch and subjected to mechanical loads and/or uniform change of temperature. The process introduces two interfacial shear and normal stress functions, which are correlated via the approximately same radius of curvature of the slender adherends. All the stress components in the joint are expressed in terms of the interfacial stress functions based on the classic Euler-Bernoulli beam theory and equilibrium equations of elasticity. Deformation compatibility of the joint is satisfied by minimizing the complementary strain energy, which leads to a fourth-order ordinary differential equation (ODE) of the interfacial shear stress function. The interfacial shear and normal stresses are determined explicitly and compared with those given by the elementary beam theory and FEM, respectively. The results gained in this study are applicable to scaling analysis of joint strength and optimization of structural design of joints. The present formalism can be extended conveniently to the mechanical stress and thermal stress analysis of various bonded structures, including adhesively bonded joints, composite joints, and recently developed flexible electronics.

A methodology for computing thermal loads in arch dams is proposed. The methodology considers the nonuniform distribution of solar insolation over dam faces because of shading, curvature of dam faces, orientation, and slopes. Because, in most cases, the mean daily global solar radiation is the only type available, a methodology for estimating hourly solar energy reaching dam faces is described. The methodology is applied to a case study where observations from 21 thermometers embedded in the concrete and data of climatic variables are available. The concrete temperature field is successfully computed, with good agreement between observations and predictions. The proposed methodology is compared with other approaches, and the consequences on the stress calculations are analyzed.