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This paper investigates the effect of the horizon size on failure due to strain and damage localization in the case where peridynamics is a nonlocal theory by its own, which corresponds to most bond-based peridynamics models. Two constitutive relationships are discussed: the microelastic brittle model and a progressive damage model. The usual practice with the microelastic brittle model is to fit the microelastic constant for a given horizon size so that elasticity is recovered. At the same time, the fracture energy provides the critical bond stretch. This methodology yields an indirect determination of the tensile strength of the material, that goes to infinity as the horizon size trends to zero. With the damage model, the stretch at the inception of damage can be obtained from the tensile strength. Then, a simple one-dimensional case of wave propagation and interactions in a bar is considered. For fixed values of the horizon, convergence with a refinement of the discretization is checked. The energy dissipated upon fracture is found to be a linear function of the horizon. It is also a function of the softening response. The horizon cannot be chosen arbitrarily, unless the softening parameter is adjusted to fit the fracture energy, like in the crack band model. Surprisingly, such a methodology is very seldom mentioned in the current literature dealing with fracture modeled by peridynamics. [ABSTRACT FROM AUTHOR]

In this paper, a meshless method for analyzing the elastodynamic behavior of two-dimensional problems is introduced. The nonsingular method of fundamental solutions (NMFS) is combined with the method of particular solutions. To overcome singularities arising from point-shaped sources, a technique known as the boundary distributed source (BDS) method is used, which involves distributing sources across disks centered on the boundary. The NMFS is regarded as a mesh-free boundary method due to source point independence to the neighboring source details. The dual reciprocity method (DRM) with a suitable approximation is used to obtain the particular solution corresponding to the nonhomogeneous inertial term; moreover, added benefits of eliminating domain integration and readiness for computer algorithms anchor desirability. Cautious investigation of solutions to various numerical examples using DRM reinforces reliability and accuracy. Finally, the study comprehensively examines factors such as the number of collocation points, internal points, the radius of the circular disk, and the time-step size to assess their impact on achieving convergence. [ABSTRACT FROM AUTHOR]

The free vibration of two-dimensional (2D) functionally graded annular sector plates is analyzed based on the three-dimensional (3D) theory of elasticity, using the 2D differential quadrature method. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. This paper presents a novel 2D power-law distribution for ceramic volume fraction of 2D functionally graded material that gives designers a powerful tool for flexible designing of structures under multifunctional requirements. Various material profiles along the thickness and radial direction are illustrated using the 2D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. A semianalytical approach composed of the differential quadrature method and series solution is adopted to solve the equations of motion. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. [ABSTRACT FROM AUTHOR]

Ground behavior during surface and subsurface coal mining activity is primarily governed by the geomechanical and elastic properties of the encountered rocks. A quick estimation of these parameters would provide an advantage to various mine design operations. However, a direct method to determine these parameters is, in general, expensive, laborious, time-consuming, and requires precision and experienced labor. In this paper, a quick, easy, indirect, and nondestructive method is proposed to determine the geomechanical and dynamic elastic properties of Lower Gondwana coal measure rocks from eight different coal mines in three coalfield regions of the Damodar and Mahanadi coal basins in India. The uniaxial compressive strength (UCS), Brazilian tensile strength (BTS), density (ρ), and dynamic elastic properties including the dynamic Young's modulus (ED), dynamic shear modulus (GD), dynamic bulk modulus (KD), and dynamic Poisson's ratio (μD) were determined and correlated with the P-wave velocity for sandstone and shale rocks to yield empirical correlation equations. Finally, a comparative regression analysis was performed to characterize the Lower Gondwana sandstone and shale and the regressions were statistically tested using the Student's t-test. [ABSTRACT FROM AUTHOR]

The assessment of the behavior of the ground is highly critical for any geotechnical and geological projects. Uniaxial compressive strength (UCS) is an essential mechanical parameter for any rock mass characterization, whereas the elastic properties of rocks help us understand the deformational behavior of the rocks. However, the determination of these parameters is challenging, time-consuming, destructive, and expensive and requires a skilled workforce. In contrast, the dynamic elastic properties require P-wave velocity (VP), S-wave velocity (VS), and density (ρ) for calculation, which are easy, quick, nondestructive, and cost-effective to determine. Therefore, in this paper, to understand the behavior of different rocks, UCS has been correlated with the dynamic elastic properties, including dynamic bulk modulus (KD), dynamic shear modulus (GD), dynamic Young's modulus (ED), and dynamic Poisson's ratio (µD) for carbonate, serpentinite, shale, sandstone, volcanite, and ignimbrite rocks incorporated from the databases of eight previous studies. Based on the lithology, different correlation equations have been proposed to predict the UCS from dynamic elastic properties using simple regression (SR) analysis. From SR analysis, it was observed that the coefficient of correlation (R) values depended on the type of rock. The R-values for the overall rocks, including all six rock types, for different correlations, were observed to be inferior to the R-values obtained on the basis of lithology. The principal component analysis (PCA) reduced the dimension of the data sets, and the trendline obtained for each rock type was observed to be dependent on the lithology. Moreover, descriptive statistics were also used to validate the lithological control for six different rock types. [ABSTRACT FROM AUTHOR]

High-density polyethylene (HDPE) is one of the most commonly used materials for manufacturing pipelines. In this paper, the deformation behavior of HDPE materials under uniaxial tensile stress was investigated by employing uniaxial tensile tests and macroscale/mesoscale morphology analysis. The experimental results indicated that the stress–strain relationship of HDPE is nonlinear, and the ductile fracture characteristics of necking and local failure appear in the sample after the engineering strain reaches 35%. Therefore, for the first time, a hyperelastoplastic constitutive model that describes the elasticity by the Marlow model and combined the isotropic plasticity-ductility damage correction is established, and a corresponding numerical approach is proposed. The simulation scheme was implemented in finite-element software, and the mechanical responses of HDPE under uniaxial tensile and bending loads were predicted. Obtained calculations were relatively consistent with experimental observations. Hence, the proposed model and approach have a good simulation effect on the mechanical properties of HDPE and can be employed for the process prediction of such materials. This study is beneficial to the in-depth understanding of the hyperelastoplasticity and failure mechanism of HDPE and provides ideas for the deformation and failure study of other polymer materials. [ABSTRACT FROM AUTHOR]

A method for constructing an approximation of the critical excitation that drives an elastoplastic system from rest to a target threshold at a specified time instant, referred to as the “suboptimal excitation,” is presented in this paper. It is based on the observations gained from study of the critical excitations in the companion paper. Essentially, for the usual case of interest where the failure time is not small compared to the natural period, the duration of the positive and negative pulses of the critical excitation are roughly equal to half of the natural period. This consideration allows for a simple intuitive approximation of the critical excitation. The amplitudes of the positive and negative pulses are obtained in closed forms using energy balance. Numerical investigations show that the critical excitations are well approximated by the suboptimal excitations. [ABSTRACT FROM AUTHOR]

Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have any design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the biaxial bending behavior of restrained beams, a third has studied the lateral buckling of unrestrained beams, and a fourth the biaxial bending of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle beams under major axis bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper of the series and the lateral buckling proposals of the third paper to approximate the member capacities. This method is extended to steel unequal angle beams in a companion paper. [ABSTRACT FROM AUTHOR]

Existing Euler-Bernoulli beam theories in classical elastostatics suffer from the inconsistency that either the elasticity law or the equilibrium equations are not satisfied in local form. It has recently been shown that by assuming elastic anisotropy subject to internal constraints, it is possible to make the theory consistent. This has been proved to be true also for a simple gradient elasticity law. Usually, bending of beams is viewed as a one-dimensional problem. We consider in this paper two known one-dimensional formulations for Euler-Bernoulli beam and gradient elastic material behavior. The two formulations seem to be different, as the free energy functional of the one includes the cross-sectional area of the beam, whereas the other does not. The aim is, by using consistent Euler-Bernoulli beam theory, to derive the two one-dimensional formulations as special cases of a three-dimensional simple gradient elasticity model and to show that these are equivalent to each other. [ABSTRACT FROM AUTHOR]

Random regret minimization (RRM) interpretations of discrete choices are growing in popularity as a complementary modeling paradigm to random utility maximization (RUM). While behaviorally very appealing in the sense of accommodating the regret of not choosing the best alternative, studies to date suggest that the differences in willingness to pay estimates, choice elasticities, and choice probabilities compared to RUM are small. However, the evidence is largely based on a simple multinomial logit (MNL) form of the RRM model. This paper revisits this behavioral contrast and moves beyond the multinomial logit model to incorporate random parameters, revealing the presence of preference heterogeneity. The important contribution of this paper is to see if the extension of RRM-MNL to RRM-mixed logit in passenger mode choice widens the behavioral differences between RUM and RRM. The current paper has identified a statistically richer improvement in fit of mixed logit compared to multinomial logit under RRM (and RUM) but found small differences overall between the empirical outputs of RUM and RRM, with no basis of an improved model fit between these two nonnested model forms. The inclusion of both model forms should continue to inform the likely range of behavioral outputs during investigation of a broader range of process heuristics designed to capture real world behavioral response. [ABSTRACT FROM AUTHOR]

The induced traffic model is an essential component of travel demand analysis, which has been primarily researched with elasticity models in the United States and U.K. This paper aims tofind the most suitable elasticity model based on the set of panel data regarding annual observations of 30 cities and provinces across China (except Chongqing city) for the years 1990 to 2010. To derive the ideal elasticity model, several basic elasticity models are included; among them are the elasticity-based model, distributed lag model, growth model, and fixed-effect model. Advanced elasticity models, such as the three stages of least squares (3SLS) are also discussed. According to relative researches and data collection, any increase of passenger kilometers of transport (PKT) with the growth of lane kilometers is considered induced traffic and is routinely used as such in this paper. Lane kilometers in China are found to have a statistically significant relationship with PKT measurements of approximately 0.026-0.274 in the short term and 0.367-0.773 in the long term. Population and gross regional product (GRP) numbers are also considered in basic elasticity models. Based on the detailed analysis of empirical results, the 3SLS is judged as the best suitable model for China. It can reflect the time effect, consider endogenous variables (including congestion and vehicle stock), and eliminate the simultaneity bias. [ABSTRACT FROM AUTHOR]

Although steel single angle sections are commonly used as beams to support distributed loads which cause biaxial bending and torsion, their behavior may be extremely complicated, and the accurate prediction of their strengths very difficult. Further, many design codes do not have design rules for torsion, while some recommendations are unnecessarily conservative, or are of limited application, or fail to consider some effects which are thought to be important. This paper is one of a series on the behavior and design of single angle section steel beams. Two previous papers have studied the biaxial bending and torsion of restrained beams, a third has studied the lateral buckling of unrestrained beams, a fourth the biaxial bending of unrestrained beams, and a fifth and sixth the buckling and torsion of unrestrained beams. In each paper, simple design methods have been developed. In this present paper, an approximate method of predicting the second-order deflections and twist rotations of steel equal angle section beams under biaxial bending and torsion is developed. This method is then used to determine the approximate maximum biaxial bending moments in such beams, which are then used with the section moment capacity proposals of the first paper and the lateral buckling proposals of the third paper to approximate the member capacities. [ABSTRACT FROM AUTHOR]

While piezoelectric (PZT) actuators exhibit only mild nonlinear response at low voltage levels, it is well known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise induces sources of mechanical hysteresis (friction, backlash, etc.) that can couple with this material nonlinearity to yield a structural scale nonlinearity that is nonnegligible. These two sources of hysteresis, due to mechanism response and nonlinear material response, are not easily decoupled. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the results of previous papers for the derivation of closed loop control for active material actuated devices. The goal is to derive a control methodology that accounts for the overall, total hysteresis due to material nonlinearities and mechanism response. In this technique, a compensator derived from an offline identification of a Krasnoselskii-Pokrovskii hysteresis operator is cascaded with the plant. We show that the methodology is well posed for the class of problems under consideration; we describe relevant closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results. [ABSTRACT FROM AUTHOR]

The effective in-plane elastic moduli of different types of honeycomb cores with thick walls are studied using analytical and numerical approaches. Analytical equations derived in this paper take a proposed jointed rectangle into consideration. The analytical results under plane stress and plane strain conditions are also obtained. The effective in-plane elastic moduli are studied as a function of their own relative densities because of the different methods of describing the geometrical shapes of honeycomb cores. The results are quantitatively compared with the available experimental results in this paper. It indicates that the present model can better predict the elastic properties in x -direction but are less suitable in y -direction. The proposed jointed rectangle has significant effect at high relative density. Moreover, the effective in-plane modulus increases with the relative height of honeycomb cores because of the Poisson effect of the material, and the results under plane stress and plane strain conditions are the lower and upper bounds, respectively. [ABSTRACT FROM AUTHOR]

In this paper, four types of truss lattices are designed by combining octet truss (FCC) unit cells with other elementary unit cells, including Simple Cubic (SC), Body-centered Cubic (BCC), Body-centered Block (BCB), and Z-pinned (Z). The elastic properties (uniaxial, shear, and bulk moduli, Zener's anisotropy index, and Poisson's ratio), yield strength, deformation modes, and energy absorption under quasi-static loading, and impact resistance under dynamic loading of these lattices were investigated through finite elements. The initial peak stress and subsequent plateau stress are elevated under dynamic loading. The stress waves velocity of the lattices is calculated by the dynamic enhancement term. Results indicate that the mechanical properties of the designed lattices are better than the reported FCC and BCC lattices. FCCBCB (which is combined with FCC and BCB elementary unit cell) remains stable for uniaxial compression at a relative density of about 0.2 and exhibits the highest energy absorption capacity at the relative density considered; the Zener index of FCCSC (which is combined with FCC and SC elementary unit cell) does not vary greatly with the increase of relative density (1.18 to 1.11 at the relative density considered), and the Zener index approaches unity indicating elastic isotropy; and FCCZ (which is combined with FCC and Z elementary unit cell) features the highest yield strength and Young' modulus among all lattices considered. The computational results are confirmed through uniaxial compression experiments on three-dimensional (3D)-printed specimens. [ABSTRACT FROM AUTHOR]

There is a scarcity of natural river sand due to the ban on mining of sand from riverbeds, attributed to environmental and ecological issues. Therefore, there are attempts to use nonorganic solid wastes and industrial by-products as sand substitutes. The paper reports experimental studies on the suitability of processed granulated blast furnace slag (PGBS) as fine aggregate in the mortars used in masonry construction. The physical and chemical characteristics of the PGBS and the properties of mortars made with PGBS, such as workability, compressive strength, water retentivity, drying shrinkage, and elastic properties, were examined. The masonry properties such as compressive strength, flexure bond strength, and stress-strain characteristics were investigated using PGBS- and sand-based mortars. The investigations show that PGBS can be a potential substitute to river sand in the masonry application. The addition of PGBS was beneficial in terms of mortar and masonry characteristics. In the case of lean mortars, the addition of PGBS showed 30% to 45% spike in compressive strength. Thermogravimetry was used to quantify hydration products formed in PGBS-based and river sand–based mortars. The experimental outcomes indicate that (1) the physical and chemical properties of PGBS were similar to those of river sand except that the PGBS may show mild pozzolanic activity and higher water absorption; and (2) the masonry compressive strength increased by ∼22% , and the flexure bond strength nearly doubled when PGBS-based mortars were used. [ABSTRACT FROM AUTHOR]

This paper is concerned with the bending response of nonlocal elastic beams under transverse loads, where the nonlocal elastic model of Eringen, also called the stress gradient model, is used. This model is known to exhibit some paradoxical responses when applied to beams with certain types of boundary conditions. In particular, for clamped-free boundary condition, this nonlocal model is not able to predict scale effects in the presence of concentrated loads, or it leads to an apparent stiffening effect for distributed loads in contrast to other boundary conditions for which softening effect is observed. In the literature, these paradoxes have been resolved by changing the kernel of the nonlocal model or by modifying the standard boundary conditions. In this paper, the paradox is solved from the nonlocal differential model itself via some related discontinuous nonlocal kinematics. It is shown that the kinematics related to the nonlocal constitutive law lead to the use of moment or shear discontinuities. With such a nonlocal differential model coupled with the nonlocal discontinuity requirements, the beam effectively shows a softening response irrespective of the boundary conditions studied, including the clamped-free boundary conditions, and thereby resolves the paradox. The model is also compared to lattice-based solutions where an excellent agreement between the present nonlocal model and the lattice one is obtained. Finally, the stress gradient model is shown to be cast in a stress-based variational framework, which coincides with a Timoshenko-type model where the shear effect is shown to play the nonlocal role. [ABSTRACT FROM AUTHOR]

Although there are many methods for assessing vertical stiffness of footings on the ground, simplified solutions to evaluate lateral, rotational, and torsional static stiffness are much more limited, particularly for nonhomogeneous profiles of shear modulus with depth. This paper addresses the topic by introducing a novel "work-equivalent" framework to develop new simplified design methods for estimating the stiffnesses of footings under multiple degrees-of-freedom loading for general nonhomogeneous soils. Furthermore, this framework provides a unified basis to analyze two existing design methods that have diverging results. 3D finite element analyses were carried out to investigate the soil–footing interaction for a range of continuously varying and multilayered nonhomogeneous soils, and to validate the new design approach. [ABSTRACT FROM AUTHOR]

Structural weakening and addition of damping is an approach previously proposed for the reduction of seismic forces and drifts in the retrofit of structures. It is also used in the design of new buildings with damping systems. While this approach is efficient, it does not significantly reduce and may even amplify inelastic excursions and permanent deformations of the structural system during a seismic event. This paper describes a negative stiffness device (NSD) that can emulate weakening of the structural system without inelastic excursions and permanent deformations. The NSD simulates yielding by engaging at a prescribed displacement and by applying a force at its installation level that opposes the structural restoring force. The NSD consists of (a) a self-contained highly compressed spring in a double negative stiffness magnification mechanism; and (b) a gap spring assembly (GSA) mechanism which delays the engagement of negative stiffness until the structural system undergoes a prescribed displacement. The NSD employs double chevron braces that self-contain the large vertical forces needed for the development of the horizontal negative stiffness without transferring these forces to the structure. This paper reports the development and operation of the NSD and presents analytical and computational tools that describe the behavior of the device. The principles of global control of structures using the NSD are presented in a companion paper. Additional papers present the results of testing of the device, and the results of analytical and experimental studies on the application of the device in a three-story conventional structure and a three-story seismically isolated structure. [ABSTRACT FROM AUTHOR]

Owing to their importance to the structural analysis and evaluation of cement-based materials, it is essential to determine the mechanical properties of cement paste. This paper presents a simple three-step analytical scheme for predicting the elastic moduli of hardened cement paste. In this scheme, hardened cement paste is modeled as a multiphase composite material, composed of unhydrated cement, C-S-H, CH, and capillary pores and further represented by five two-phase composite spheres. The elastic moduli of hardened cement paste are obtained in terms of the volume fractions and elastic moduli of unhydrated cement, C-S-H, CH, and capillary pores by the three-step scheme. Finally, the validity of the three-step scheme is verified with three independent sets of experimental data. The paper concludes that, when the water-cement ratio is in the range of 0.4-0.6, the simple three-step analytical scheme presented in the paper can predict the elastic moduli of hardened cement paste with an average relative error smaller than 8%. [ABSTRACT FROM AUTHOR]

In this paper, a three-member tensegrity structure is used as a conceptual model for the dendritic actin network in living cells. The pre and postbuckling behavior of the tensegrity is analyzed basing on the energy method. Analytical simulations are carried out on the tensegrity by using the experimentally obtained scales and mechanic properties of actin-filaments for the structural members of the tensegrity. The model exhibits a stress stiffening regime followed by a stress softening regime in the load-stiffness relationship, which qualitatively tallies with the experimentally observed response of actin networks. Due to the simplicity of the model, there is only a single compressed member and the structure buckles abruptly, which results a softening regime much steeper than that observed in the actin network. To take the member length variety into account, we propose a conceptual large-scale tensegrity system with various member lengths, and its behavior is approximately estimated by the mean response of a large number of three-member tensegrity cells with their member length varying in the range of filament lengths. The obtained mean response exhibits a much better fitness to the response of actin networks than those exhibited by the single tensegrity model. The findings reported in this paper indicate that the dendritic actin network may work as a complex tensegrity system, when it is subjected to a stress. [ABSTRACT FROM AUTHOR]

The paper discusses finite element models for predicting the elastic settlement of a strip footing on a variable soil. The paper then goes on to compare results obtained in a probabilistic settlement analysis using a stochastic finite element method based on first order second moment approximations, with the random finite element method based on generation of random fields combined with Monte Carlo simulations. The paper highlights the deficiencies of probabilistic methods that are unable to properly account for spatial correlation. [ABSTRACT FROM AUTHOR]

To determine the stress state of a wire rope is tedious although analytical solution of a simple rope subjected to static load is available. While facing the problems involving complex ropes, it is usual practice to take approximations based upon the concepts of an average stress state for the constitutive ropes or for every wire. For a statically loaded cable superimposed with a tensile impulse, practically in sudden lifting of a heavy weight, the coupled axial-shearing strain waves in the cable has rarely been studied and explored through analytical approaches. Based on Costello’s force-deformation relationship and elastic wave propagation theory, analysis procedures and results are presented in this paper. Time-dependent coupled axial-torsional displacements and axial-shearing strain waves in a simple straight wire rope, due to a longitudinal impact at one end, are obtained. At the instance of the strike, a pair of coupled primary axial-torsional waves is created and begins to travel in the cable independently with different speed. Meanwhile, a coupling induced secondary torsional wave and an axial wave were observed to travel with the primary axial wave and the primary torsional wave, respectively. Phenomenon such as the traveling, reflections from ends, and intersections of the primary waves as well as the secondary wave are presented. Information provided in this paper would be useful in the study of unexpected overstress and/or fatigue problems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the elastic flexural buckling of doubly symmetric columns with oblique restraints under concentric loading. Oblique restraints cause coupling between the principal axis deflections and rotations, and the flexural buckling mode involves simultaneous bending about both principal axes. Oblique restraints may resist deflections as well as rotations, and may be rigid or elastic. They may be concentrated at points along a column, or distributed along portions of its length. This paper discusses the nature of oblique end restraints, summarizes their finite element analysis, presents examples of their effects on the elastic buckling of columns, and demonstrates the design of columns with oblique restraints. [ABSTRACT FROM AUTHOR]

This paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a central concentrated load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tension caused by large deformations. [ABSTRACT FROM AUTHOR]

The design of steel storage pallet racks is quite complex, despite the fact that these structures are built with economical components and manufactured from thin coils or sheets. The most advanced approaches for rack design recommend the use of simplified methods to estimate the key parameters governing both static and seismic design. In the first case, which is the core of this first part of a two-part paper, an evaluation of the elastic critical load multiplier for the sway buckling mode (αcr) is required to select the method of analysis and check member instability. The term αcr can be predicted through simplified approaches, which have been adequately calibrated for traditional steel structures constructed with members having a double-symmetric cross section. Rack uprights (columns) have, in general, an open cross section, with one axis of symmetry, and thus the overall frame response and member behavior is significantly influenced by Wagner's coefficients, warping torsion, and shear-center eccentricity. Currently, these effects are neglected in routine rack design, owing to the absence of clear indications in standard provisions and the limited availability and knowledge of appropriate software tools supporting this complex design approach. This paper addresses the applicability of simplified approaches for the static design of medium-rise unbraced pallet racks, whereas the second part companion paper considers seismic approaches. A numerical analysis of several racks composed of different geometries, components, and degrees of stiffness of both beam-to-column and base-plate joints has been completed by using an open source finite-element analysis program for academic use, which is characterized by a refined beam formulation accounting for warping effects. Furthermore, the application to model racks of a traditional beam formulation on the basis of the coincidence between the shear center and the cross section centroid allows a direct appraisal of the warping influence on the prediction methods. Finally, to improve the accuracy of the critical load multiplier prediction, a suitable safety factor has been proposed to be used when beam formulations, including warping, are not available for structural analysis. [ABSTRACT FROM AUTHOR]

This study examines the effect of weathering on bituminous composites containing polyphosphoric acid (PPA). PPA has been commonly used in bitumen to increase bitumen's stiffness and elastic properties. However, the effect of PPA on bitumen's properties is highly affected by the interplay between PPA and other bitumen modifiers such as liquid and solid additives. Wax-based additives generally reduce PPA's efficacy, and a mineral additive such as montmorillonite (MMT) clay increases PPA's efficacy. MMT has been typically used to enhance the resistance of a bituminous matrix to aging. This paper uses laboratory experiments to evaluate changes in the properties of bitumen containing PPA and MMT when exposed to water. Samples were conditioned in water at 60°C for up to 100 h, and their thermomechanical properties were evaluated at different intervals. The study results showed that the presence of PPA in bitumen alleviates the swelling of MMT when montmorillonite-doped bitumen is exposed to water. However, extended water exposure reduces the elastic properties of bitumen. This is attributed to PPA's losing its branches as water promotes the separation of PPA's branches from its backbone, leading to a reduction in binding energy between bitumen and PPA. The latter was reflected in a rapid loss of bitumen's elasticity, healing capacity, and shear thinning, as water conditioning continued. [ABSTRACT FROM AUTHOR]

A novel Hencky bar-grid model (eHBM) was developed to address plane stress elasticity problems. This model comprises rigid bars arranged in a grid which are joined by frictionless hinges, frictionless pulleys, elastic primary and secondary axial springs, and torsional springs. Based on the energy approach, the in-plane displacements at the joints were determined and the in-plane stress resultants were obtained from the stress resultant–displacement relations. This paper calibrated the elastic spring stiffnesses for the eHBM for the first time by matching them with the finite-difference governing equation for elasticity problems. Some rectangular plane elasticity problems were solved by using the newly developed eHBM. The solutions obtained from the eHBM converged to the exact solutions for the continuum plane body with respect to decreasing the eHBM segment size. It was shown that the eHBM readily can handle any boundary conditions, and furnishes accurate solutions for plane elasticity problems with any complex geometry, such as a rectangular plane body with cutouts. [ABSTRACT FROM AUTHOR]

This paper considers the practical application of analytical solutions for estimating ground movements caused by shallow tunneling in soft ground using closed-form expressions presented in a companion paper based on linearly elastic and average-dilation models of soil behavior. The analytical solutions express two-dimensional distributions of ground deformations as functions of three parameters: the uniform convergence and relative ovalization of a circular tunnel cavity, and either the Poisson's ratio or the average dilation angle for elastic and plastic behavior, respectively. This paper shows that the analytical predictions can achieve very good representations of the distribution of far field deformations through a series of case studies in clays and sands. In some cases, the input parameters can be interpreted from a simple calibration to three independent measurements of ground displacements comprising surface settlements above the tunnel centerline and at a reference offset, and the lateral displacement at the spring line elevation, recorded by an inclinometer at an offset of one tunnel diameter from the centerline. However, it is generally more reliable to use a least-squares fitting method to obtain the model input parameters, using all available extensometer and inclinometer data. [ABSTRACT FROM AUTHOR]

This paper presents simplified closed-form analytical solutions that can be used to interpret and predict ground movements caused by shallow tunneling in soft ground conditions. These solutions offer a more comprehensive framework for understanding the distribution of ground movements than widely used empirical functions. Analytical solutions for the displacement field within the ground mass are obtained for two basic modes of deformation corresponding to uniform convergence and ovalization at the wall of a circular tunnel cavity, based on the assumption of linear, elastic soil behavior. Deformation fields based on the superposition of fundamental, singularity solutions are shown to differ only slightly from analyses that consider the physical dimensions of the tunnel cavity, except in the case of very shallow tunnels. This work demonstrates a simplified method to account for soil plasticity in the analyses and illustrate closed-form solutions for a three-dimensional (3D) tunnel heading. A companion paper describes applications of these analyses to interpret field measurements of ground response to tunneling. [ABSTRACT FROM AUTHOR]

The objective of this paper is to propose relationships for the reduction in mechanical properties of cold-formed steels at elevated temperature. Predicting the degradation of strength and modulus of cold-formed steels with temperature is critical to enable fire design of cold-formed steel members. Here, the properties of elastic modulus, 0.2% proof stress, 2% stress, and ultimate stress are studied for grades up to and including 550 MPa. Data are collected from the literature as well as from recent tests conducted by the authors at Johns Hopkins University. Steady-state and transient test results in the range of 20°C–1,000°C are analyzed. Retention factors are then proposed for the mechanical properties adopting a standardized format developed through committee work with the American Iron and Steel Institute. [ABSTRACT FROM AUTHOR]

Poisson's ratio is an elastic property needed as input in a wide range of geotechnical engineering applications. Despite experimental evidence, there is currently no model in the literature to explicitly account for the effect of saturation on the Poisson's ratio. This paper presents the concept of Poisson's ratio characteristic curve (PRCC), which establishes a relationship between Poisson's ratio and degree of saturation (or matric suction). The PRCC concept is developed based upon the observation that variations of Poisson's ratio are mainly dominated by water retention mechanisms. A sigmoidal function is employed to describe the PRCC with two fitting parameters, funicular degree of saturation and pore fluid continuity, and both are related to the soil water retention curve (SWRC). The functional form is calibrated and validated against Poisson's ratios calculated from measured compressive and shear wave velocities from experimental data sets for 22 different soils from the literature. Further, a set of laboratory tests is performed to measure wave velocities using bender elements and determine the Poisson's ratio of Bonny silt at different suctions. The PRCC fitting parameters are shown to be linearly correlated with the SWRC fitting parameters. To illustrate the PRCC application, three sets of laboratory-measured data of at-rest earth pressure coefficient for different unsaturated soils are collected from the literature and compared against the predicted values using the PRCC model and those using constant Poisson's ratio values. The values using the PRCC model closely match the measured values, whereas using a constant Poisson's ratio can significantly underpredict or overpredict the at-rest earth pressure coefficient. The proposed model can readily be incorporated into analytical and numerical models, leading to more accurate assessments of unsaturated soil behavior. [ABSTRACT FROM AUTHOR]

An integral-type nonlocal elastoplasticity model is proposed and formulated in a one-dimensional scenario to address the strain-softening problem. This nonlocal model includes not only the nonlocal plasticity but also the nonlocal elasticity. The resulting elastic constitutive equation and the plastic consistency condition are ill-posed Fredholm integral equations of the first kind whose solutions are instable without appropriate regularization. In this paper, the Tikhonov-Phillips regularization method is used to reformulate the integral-differential consistency condition to obtain an approximate solution of the local internal variable, which is stable and smooth. A detailed parametric study is carried out to examine the influences of the regularization parameter, the internal length scale, the plastic modulus ratio, and the tolerance of the nonlocal yield condition on the regularized solutions. A numerical example shows that the solutions from the proposed model and the regularization method are mesh-independent. A comparison of the results from the proposed model with those from the nonlocal plasticity model and from the gradient-dependent plasticity model shows good agreement. [ABSTRACT FROM AUTHOR]

Corrosion resistant alloy steel (MMFX) reinforcing bar is increasingly utilized in structural engineering applications due to their high yield strength and corrosion resistance. This paper aims to characterize the thermomechanical response of MMFX rebar by examining their elastic and inelastic properties at a wide range of temperatures and strain rates. To achieve that, a series of quasi-static tensile tests at rates of 0.0015, 0.015, and 0.15 s−1 were conducted at a range of temperatures between room temperature and 650°C. In addition, dynamic tests were conducted at room temperature using a drop mass bench at strain rates of up to 500 s−1. Results showed that at room temperature, the flow stress of the MMFX steel alloy observed slight dependence on the quasi-static strain rate. However, the strain rate-sensitivity became more effective as the temperature increases with very active regions of dynamic strain aging encountered at different levels of strains, strain rates, and temperatures. Moreover, the reduction in the elastic properties was less than 18% at temperatures up to 450°C, then followed by a sharp decrease at 650°C. The stress–strain responses were utilized to identify the material constants for constitutive modeling. The Voyiadjis–Abed constitutive model was utilized to describe the material flow stress and was implemented into a finite-element (FE) model that was developed using ABAQUS version 2017. The FE model is capable of reproducing the experimental results and simulating the dynamic hammer-tests at room temperatures. [ABSTRACT FROM AUTHOR]

In recent years, the need for resilient structural systems has led to renewed interest in the use of rocking members instead of conventional ones for the design of earthquake-resistant structures. Due to the usually constrained nature of such members, in addition to the deformability along their height, the nonlinear stress distribution at their base resulting from the partial loading of the rocking interface needs to be taken into account for an accurate estimation of the rocking motion. In this paper, a new approach is proposed for the prediction of the response of elastic rocking bodies under static loading that is able to consider such effects. The nonlinear stress distribution near the contact area results in additional displacements compared to those of the technical theory of bending, and a method to estimate them is presented and incorporated into a macroelement formulation that can be used in the context of a finite-element program. Results for typical examples are presented and compared with those of corresponding commercial software models, showing excellent agreement, while the proposed macroelement requires extremely low runtimes compared to conventional finite-element codes. [ABSTRACT FROM AUTHOR]

Mobile equipment operators in surface and underground mines are protected against falling objects by a canopy over the operator's seat. Designing a structurally safe canopy poses challenges to the design engineer because of a number of assumptions that have to be made in establishing rational design criteria. This paper investigates the design and analysis of falling object protective structures (FOPSs) by proposing a method of energy balance between falling objects and a structure. Elastic and inelastic responses of the structure are considered. The structure is assumed to be supported on springs, simulating the elasticity of the equipment chassis and rubber tires. This realistic assumption results in significant reductions of the impact force on the canopy and supports. It is concluded that these canopies should be designed with column supports that incorporate springs. The design methodology is illustrated by solving a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, complex variable boundary element method (CVBEM) is used for the solution of de Saint-Venant's torsion problem in homogenous isotropic elastic beams with a generic cross section, considering a complex potential function related to the stress field. Generally, CVBEM, when used for torsion problems, leads to evaluation of the stress field divided by the twist rotation. The latter has been evaluated by performing a domain integral. In this paper, taking advantage of the aforementioned potential function, it is possible, by applying CVBEM, to evaluate the complete stress distribution and the twist rotation of the cross section and the torsional stiffness factor, performing line integrals only. Numerical results were compared with both analytical and numerical results proposed by other authors, thus assessing the validity of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the buckling behavior of generic higher-order shear beam models is investigated in a unified framework. This paper shows that most higher-order shear beam models developed in the literature (polynomial, sinusoidal, exponential shear strain distribution assumptions over the cross section) can be classified in a common gradient elasticity Timoshenko theory, whatever the shear strain distribution assumptions over the cross section. The governing equations of the bending/buckling problem are obtained from a variational approach, leading to a generic sixth-order differential equation. Buckling solutions are presented for usual archetypal boundary conditions such as pinned-pinned, clamped-free, clamped-hinge, and clamped-clamped boundary conditions. The results are then extended to general boundary conditions based on generalized linear elastic connection law including vertical and rotational stiffness boundary conditions. Engineering analytical solutions are derived in a dimensionless format. The model valid for macrostructures is generalized for micro- or nanostructures using the nonlocal integral Eringen's model. The nonlocal framework is also developed in a variational consistent framework. Buckling solutions are finally presented for the nonlocal higher-order beam/colum models. [ABSTRACT FROM AUTHOR]

Yielding can be emulated in a structural system by adding an adaptive negative stiffness device (NSD) and shifting the yielding away from the main structural system, leading to the new idea of apparent weakening that occurs, ensuring structural stability at all displacement amplitudes. This is achieved through an adaptive negative stiffness system (ANSS), a combination of NSD and a viscous damper. By engaging the NSD at an appropriate displacement (apparent yield displacement that is well below the actual yield displacement of the structural system) the composite structure-device assembly behaves like a yielding structure. The combined NSD-structure system presented in this study has a recentering mechanism that avoids permanent deformation in the composite structure-device assembly unless the main structure itself yields. Essentially, a yielding-structure is mimicked with no, or with minimal, permanent deformation or yielding in the main structure. As a result, the main structural system suffers less acceleration, less displacement, and less base shear, while the ANSS absorbs these effects. This paper presents comprehensive details on development and study of the ANSS/NSD. Through numerical simulations, the effectiveness and the superior performance of the ANSS/NSD as compared with a structural system with supplemental passive dampers is presented. A companion paper presents the NSD and its mechanics in detail. [ABSTRACT FROM AUTHOR]

This paper considers the problem of modeling railway track substructure. The most commonly used methodology for designing the railway substructure cross section does not considerably differ from that proposed in the 1980s. For the bearing capacity of the subgrade, the currently used design methodology implicitly meets one objective: the stresses transmitted to the subgrade must be compatible with its bearing capacity. The bearing capacity depends on the qualities and thicknesses of the soils that compose the subgrade, from the formation layer to the lower layers. In addition, railway administrations have included additional recommendations based on their experience. During the last decade, finite-element models (FEM) have been shown to be a very useful tool for designing cross sections. These models are often very complex and require a very high computational time to be solved. To reduce this complexity and computational time while remaining faithful to the reality to be modeled, this paper proposes some recommendations to develop a parameterized numerical model in three dimensions within the elastic nonlinear range under the static load of a given railway section. To adequately reproduce the real behavior of materials (elastoplastic) and the contact surfaces between very different materials adequately, artifices to use the model in the elastic range are propsed. In addition, the goodness of this design is analyzed using multilayer numerical models. This model may be a very useful tool for analyzing the behavior of different types of railway cross sections. [ABSTRACT FROM AUTHOR]

With the advent of climate change, it is thought that desiccation cracking of soil will lead to increases in damage to buried infrastructure. Desiccation cracking is a complex phenomenon that historically has been very difficult to model either numerically or analytically. Therefore, there is a need for knowledge on such models to be advanced rapidly. This paper discusses the introduction of cohesive cracks to model fracture attributable to desiccation. The cohesive crack method does not have the limitations of linear elastic fracture mechanics, namely, that an initial notch must be present and that the bulk material must behave in a linear elastic manner. This paper describes how the cohesive crack method has been successfully used to model laboratory desiccation tests of a clay soil. It is shown that, in addition to the tensile strength, the magnitude of fracture energy specified for the material has an impact on crack propagation. The cohesive crack method is proposed as a tool for the numerical modeling of desiccation cracking in many diverse fields. [ABSTRACT FROM AUTHOR]

This paper addresses the hydromechanical postclosure behavior of an underground long cylindrical deep tunnel drilled into a massif (host medium) and backfilled at the end of its service life. It is concerned with the development of quasi-analytical Laplace transform solutions based on a simplified life cycle of the tunnel, idealized in four stages: (1) excavation, (2) pore-pressure dissipation before lining installation, (3) lining installation and tunnel exploitation, and (4) postclosure. The solutions proposed in this paper therefore extend the previous work of the authors, in this case by explicitly taking into consideration the excavation, waiting for lining installation, and tunnel exploitation stages of the life cycle. Results from a parametric study are also presented to highlight the hydromechanical responses of the tunnel over periods of its life cycle. The accuracy and correctness of the solutions from a finite-element model have been verified with the quasi-analytical results. The present solutions will be used later for benchmarking finite-element-based solutions currently under development, taking into account more complex material behaviors. [ABSTRACT FROM AUTHOR]

The formulation of and solution to the problem of the free vibrations of a geometrically nonlinear column, supported at the loaded end by a spring with linear characteristics, are discussed in the paper. Transversal free vibrations around a rectilinear form of static equilibrium are considered in this work. The considered system was subjected to a generalized load with a force directed toward the positive pole. The boundary problem was formulated using Hamilton's principle and the straightforward expansion method. A series of numerical simulations were conducted using the mathematical model. The characteristic curve in the plane of load versus natural frequency was assigned to different parameters of the considered system. Experimental research was carried out to confirm the accuracy of the assumed mathematical model. The research relied on modal analysis and the determination of the natural frequency of the system for chosen values of an external load. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution methodology for a tubular structure subjected to a transient point loading in low-strain integrity testing. The three-dimensional effects on the pile head and the applicability of plane-section assumption are the main problems in low-strain integrity testing on a large-diameter tubular structure, such as a pipe pile. The propagation of stress waves in a tubular structure cannot be expressed by one-dimensional wave theory on the basis of plane-section assumption. This paper establishes the computational model of a large-diameter tubular structure with a variable wave impedance section, where the soil resistance is simulated by the Winkler model, and the exciting force is simulated with semisinusoidal impulse. The defects are classified into the change in the wall thickness and Young's modulus. Combining the boundary and initial conditions, a frequency-domain analytical solution of a three-dimensional wave equation is deduced from the Fourier transform method and the separation of variables methods. On the basis of the frequency-domain analytic solution, the time-domain response is obtained from the inverse Fourier transform method. The three-dimensional finite-element models are used to verify the validity of analytical solutions for both an intact and a defective pipe pile. The analytical solutions obtained from frequency domain are compared with the finite-element method (FEM) results on both pipe piles in this paper, including the velocity time history, peak value, incident time arrival, and reflected wave crests. A case study is shown and the characteristics of velocity response time history on the top of an intact and a defective pile are investigated. The comparisons show that the analytical solution derived in this paper is reliable for application in the integrity testing on a tubular structure. [ABSTRACT FROM AUTHOR]

Toroidal shells are widely used in structural engineering. The governing equations of toroidal shells are very complicated because of its variable coefficients with singularity. To find their analytical solution, traditionally, the complex form governing equations were proposed and some useful solutions were obtained. Unfortunately, no any closed-form solution has even been obtained for either general or slender toroidal shells. This paper focus on a special case of toroidal shells, i.e., slender symmetrical toroidal shells. For the first time, the closed-form solution of this kind of shell has been successfully obtained from displacement form governing equations. The closed-form solution is demonstrated for the example of thermal compensation devices. The correction of well-known Dahl formula for slender toroidal shell has been proposed based on the solution obtained in this paper. [ABSTRACT FROM AUTHOR]

Nested logit models calibrated on revealed preference (RP) and stated preference (SP) data have been used in this paper to study the potential market of a cybernetic transportation system for airport ground access. This innovative concept of transit mode could complement mass transit and nonmotorized transport modes, providing passenger service for any location at any time. Our analysis is based on a data set collected at Baltimore Washington Thurgood Marshall International (BWI) airport; the proposed cybercar service was designed to connect the Greenbelt metro station to the airport. The explanatory variables used in the utility functions of the RP/SP joint models are level of service attributes, characteristic specific to the new service offered, and socioeconomic variables. The estimated models are used to predict the market share of automobile, taxi, cybercar, and modified transit. In addition, elasticity tests are performed in order to study individuals’ sensitivity to the change of travel time and travel cost for automobile and cybercar. The estimation and application results in this paper can be used as a reference for the CityMobil program of the European Union to popularize this fast, convenient, and environmentally friendly cybercar. Meanwhile, the results provide useful behavioral data and models on the potential of advanced technological transportation system for airport ground planning in the United States. [ABSTRACT FROM AUTHOR]

Closed-form equations for the initial thermal postbuckling response of axially restrained elastic columns with six well-known sets of rotational and lateral end restraints are presented. These equations, which are consistent with the conventional beam-column (Euler–Bernoulli) theory, are based on the assumption that the column axial force remains constant at the buckling level in the postbuckling phase, i.e., the (additional) thermal axial extension because of the increased temperature above the buckling temperature is converted into the column's lateral deflection via the bowing effect. The equations consider the effects of partial axial restraints as well as the degradation of elastic material properties with rising temperatures. To evaluate their accuracy, the postbuckling response predicted by these approximate equations is compared to the exact (elastica) solutions available in the literature and to the finite-element solutions. The results of these validation studies indicate that these relatively simple closed-form equations can predict, with a high degree of accuracy, the initial thermal postbuckling response of axially restrained columns with the various rotational and lateral end restraints considered in this paper. [ABSTRACT FROM AUTHOR]

This paper gives a set of time-dependent displacement solutions for the case of a vertical concentrated force acting in the interior of fractional derivative viscoelastic soils. First, a three-dimensional fractional derivative viscoelastic model is introduced to describe the creep behavior of soils. Then based on the well-known Mindlin's elastic solutions and the correspondence principle from static elasticity to quasi-static viscoelasticity, the proposed precise solutions are systematically obtained in the Laplace transform domain. Subsequently, the proposed displacement solutions are validated against three previously published solutions, and all of the comparisons show a good agreement. Finally, parametric study and discussion are given, to analyze in detail the influence of parameters on the solutions. It is indicated that the displacements for fractional derivative viscoelastic models are smaller in the early stage and larger in the later stage than those for conventional viscoelastic models, and the proposed displacement solutions are more general. [ABSTRACT FROM AUTHOR]

This paper shows that for perfect plasticity, the closest point projection method (CPPM) and the cutting plane algorithm (CPA) for return mapping are exactly equivalent for piecewise linear yield criteria under both associated and nonassociated plastic flow. The paper demonstrates this by presenting closed-form expressions for returned stresses in terms of predicted stresses. A consequence of this exact approach is that the final stresses can be obtained in a single iteration. The equivalence of CPPM and CPA is further demonstrated numerically by comparing five previously published algorithms for return mapping to Mohr–Coulomb in a finite-element analysis of bearing capacity. The analyses also highlight issues relating to singularities that occur at the corners of the Mohr–Coulomb surface. It is shown that many of these problems can be avoided if the return mapping is performed in principal stress space as opposed to general stress space. [ABSTRACT FROM AUTHOR]

Large discrepancies exist among current classical theories for the in-plane buckling of arches that are subjected to a constant-directed radial load uniformly distributed around the arch axis. Discrepancies also exist between the classical solutions and nonlinear finite-element results. A new theory is developed in this paper for the nonlinear analysis of circular arches in which the nonlinear strain-displacement relationship is based on finite displacement theory. In the resulting variational equilibrium equation, the energy terms due to both nonlinear shear and transverse stresses are included. This paper also derives a set of linearized equations for the elastic in-plane buckling of arches, and presents a detailed analysis of the buckling of deep circular arches under constant-directed uniform radial loading including the effects of shear and transverse stresses, and of the prebuckling deformations. The solutions of the new theory agree very well with nonlinear finite-element results. Various assumptions often used by other researchers, in particular the assumption of inextensibility of the arch axis, are examined. The discrepancies among the current theories are clarified in the paper. [ABSTRACT FROM AUTHOR]