Journal of Engineering Mechanics

Monitoring of distributed strains provides important information about the behavior of structural systems. However, detection and quantification of cracks while still at micro size levels will play a more-important role in structural-health monitoring. In addition to the early discovery of safety-related issues such as design flaws, detection of microcracks will allow for quick repairs, as opposed to later-stage infrastructure replacements and shut downs. This article focuses on the establishment of a theoretical approach for quantification of the crack-opening displacements from the measured dynamic distributed strains based on a Brillouin optical time-domain analysis (BOTDA) technique. The strain-averaging effect due to the spatial resolution, inherent in Brillouin systems, was also considered in the formulation of the method. The proposed approach takes into account the effect of cyclic loading and unloading on the accumulation of residual plastic strains in the optical-fiber coating. The experimental program involved employment of a BOTDA system in the dynamic mode for testing a 15-m length of a steel beam with two fabricated cracks. Experimental results indicated that it is possible to detect and quantify crack-opening displacements of 200 μm and larger.

Stress distribution on a membrane surface plays a key role in the structural safety and bearing capacity of an inflatable membrane structure, especially for the state under service condition. This paper presents an in situ method to determine the stress distribution of an inflatable membrane structure by using a force-finding method based on measured configuration. On the basis of the previous in situ measurement of geometrical shape and internal pressure, the target inflatable membrane structure is simplified to a membrane link structure with external forces on connection nodes. As a result, the stress distribution of the target structure can be determined based on the optimal solution of force equilibrium between the membrane internal force and internal pressure, as well as the thickness of the constructive membrane material. In order to validate the proposed method, the stress distribution of an experimental model of ETFE (ethylene–tetrafluoroethylene) cushion structure is evaluated following the suggested determining procedure. By carefully comparing the determining results with the numerical results for the forming process of the ETFE cushion model, acceptable agreement is obtained in terms of the stress distributions in the $x$-direction and maximum principle stress. Furthermore, the influence of mesh size on the stress distribution is also investigated by using four mesh sizes during the determining process. It is thus demonstrated that the proposed method is suitable for determining the stress distribution of an inflatable membrane under service conditions, which only requires the geometrical shape and inflated internal pressure of the final state, as well as the thickness of constructive material.

The coefficient of thermal expansion (CTE) of concrete depends on temperature, the internal structure of concrete, and the moisture content in concrete. An analytical model was developed to characterize the CTE of concrete under low temperatures. Three pore configurations are defined as pores with water and pores with ice. The effective strain of concrete is a combination of three processes during the cooling process, each containing a different configuration of pores. A general multiphase model for the effective expansion (and contraction) of concrete with a certain amount of ice was developed. The model can predict effective strain at different temperatures, which can reflect the influences of concrete pore size distribution and volume fractions of different phases. The predictions by the present model were compared with some available experimental data, and they agreed very well.

The mechanical behavior of the interface between gravelly soils and structures may play a significant role on the response of many soil-structure systems to loading. Under cyclic excursion of shear stress, the gravelly soil in contact with the structural material may undergo particle breakage which could lead to significant volumetric deformation of the interface zone. This paper proposes a new elastoplastic constitutive model for simulating gravelly soil-structure interface behavior, including particle breakage. The model is formulated in the frameworks of two-surface plasticity and critical state soil mechanics. Particle breakage under shear cycles is simulated by a hyperbolic function of total plastic work to capture stress degradation and cyclic densification. The model requires a total of 10 parameters to predict both monotonic and cyclic responses. The same set of model parameters is required to simulate interface behavior for gravelly soils of different densities, and for different normal stresses and stress paths up to a large number of cycles. The performance of the proposed model is evaluated using experimental observations under different normal stresses and boundary conditions.

The motion of a slender rigid block resting on an isolated base supported by rolling bearings is analyzed. This paper investigates what happens when the ground upon which the isolation system rests is subjected to a pulse-like acceleration, representative of floor motion in a building. The isolator–block system exhibits planar motion: the block may rotate about either of its bottom corners, and the isolated base may displace both horizontally and vertically. The rolling surfaces are concave and may have an arbitrary geometry, which imposes a kinematic constraint relating the base’s vertical and horizontal displacements. During an impact when the block rocks from one corner to the other, the preimpact and postimpact translational (isolator) and rotational (block) velocities are related through the principle of impulse and momentum. The response of the system is sensitive to the ground-motion parameters (amplitude and frequency), and regions of Safe (no overturning) and Unsafe (overturning) outcome are plotted in the excitation parameter plane. Boundaries between these regions are inherently sensitive to the displacement capacity of the isolation system but not to the mass ratio (block to base).

A new boundary integral method (BIM) is employed in this paper to study the two-dimensional (2D) and the three-dimensional (3D) nonlinear sloshing problems. Applying the subtracting and adding-back technique by regularized boundary integral method, the integrals of singularity and near-singularity in the boundary integral equation (BIE) can be removed and replaced appropriately by the alternative terms, respectively. In contrast to boundary element method (BEM), BIM is simpler and more straightforward. Therefore, BIM can not only provide an accurate prediction of the nonlinear free surface oscillation but also demonstrate the excellent efficiency of numerical calculation. Several small-scaled model tests on a shaking table, including harmonic and earthquake excitations, are carried out to verify the numerical methods. An artificial damping coefficient is introduced to simulate the energy dissipation of liquid motion. By comparison of the experimental and numerical results, BIM will be more reliable, efficient, and practical for nonlinear sloshing simulation.

An innovative method of using viscoelastic (VE) dampers as coupling members between reinforced concrete shear walls has been recently developed for enhancing the wind performance and seismic resilience of tall buildings. Although three-dimensional finite-element models are used for the final design of such systems, fundamental analytical models that can be used to gain broader insights into their dynamic response have not yet been developed. Therefore, in this paper a sixth-order partial differential equation governing the dynamic properties of tall shear walls coupled using VE dampers is derived by explicitly taking into account the stiffness of the connecting elements as well as that of the slab directly above the dampers. The governing equation is solved numerically using the Taylor series expansion method and the periods and added damping ratios in various modes of vibration are evaluated. It is found that for given frequency independent VE material properties, the added damping ratios of such systems are independent of the mass of the building. Analyses using a commercially available VE damper by taking into account the frequency dependency of the VE material revealed that progressively higher maximum damping ratios are achieved in higher modes of vibration. Based on the conclusions derived through the analytical formulation, recommendations are provided for enhancing the efficiency of VE dampers in tall buildings.

The increasing rate of deterioration of buried pipelines has necessitated the development of a robust assessment method for their structural integrity and service life prediction. Among various deterioration mechanisms, ductile iron pipes are most prone to pitting corrosion and subsequent leakages. This paper intends to develop a methodology to predict the perforation induced by pitting corrosion on buried ductile pipes. The methodology integrates the random fields, gamma process, and copulas into an interrelated simulation algorithm for reliability analysis of pipe perforation. It is found that the average value of a pit depth predicted by the developed method is in good agreement with the theoretical mean of the proposed gamma process for pitting corrosion. It is also found that selecting an appropriate copula which models the dependent behavior of corrosion pits on pipes is very important to accurately predict pipe perforation. The paper concludes that the developed methodology can accurately predict the perforation of ductile iron pipe induced by pitting corrosion. Proactive asset management of buried pipelines can lead to considerable savings of resources and prolonged service life.

The mechanical properties of asphalt mixture always exhibit large degrees of variability due to asphalt’s random internal structure. A stochastic constitutive model is proposed to describe the random mechanical response of an uniaxially compressed asphalt mixture. In this model, the simplified Schapery’s nonlinear viscoelastic model and the modified Swchartz’s viscoplastic model are combined to estimate the material average deformation, and a random parameter with lognormal probability distribution is introduced to reflect the specimen dispersion. Based on statistical methods, the model is calibrated by the multiple-stress repeated creep-recovery test and the 1-h creep test, and then validated by the irregular loading test and the uniform repeated creep-recovery test. It is shown that the model can predict not only the average mechanical behavior but also the scattering range of the material responses at a certain probability.

Previous studies have demonstrated that a sudden change in stiffness at the base of a building (e.g., due to nonlinear deformation in the base isolator including sudden sliding) during seismic excitations may result in an increase in the floor-level acceleration responses when compared with the results of the same building but modeled as a linear structure (i.e., without allowing any stiffness change). It has also been demonstrated that this phenomenon occurs due to high-frequency modes getting excited during the nonlinear phase of the motion as a result of energy transfer from the adequately excited fundamental mode. In this part, a systematic analytical study is carried out to understand this energy-transfer phenomenon by formulating the equations of motions for different stages of hysteresis. For simplicity, an initial velocity profile proportional to the fundamental mode of a multi-degree-of-freedom (MDOF) system is considered and the free-vibration response of the system is studied. A numerical investigation is then carried out in which the influence of different parameters on the energy transfer to higher modes of a system is studied. Further, using the results of the perturbation approach, simplified approximate expressions are also obtained to understand the contribution of different terms. It has been shown that the second mode receives the maximum amount of energy from the fundamental mode and the transfer of energy reduces with the increase in mode number. Further, it has been observed that the transfer of energy to the second mode increases for (1) higher initial energy content of the fundamental mode, (2) less spacing between the second and fundamental modes, and (3) lower postyield stiffness of the bilinear spring. To validate the energy-transfer phenomenon experimentally, shake table experiments with a scaled model were conducted alternatively with two different base conditions: (1) fixed base, and (2) structure isolated by sliding isolators. To better understand the energy-transfer phenomenon, a secondary component was also attached to the second floor of the structure with its frequency tuned to the second mode of the structure. A low-amplitude sinusoidal base excitation followed by a sudden jerk was considered. From the recorded floor accelerations and component acceleration responses, it is concluded that energy transfer from the adequately excited fundamental mode to higher modes occurs due to a sudden change in stiffness of the structure as a result of sudden sliding.

This paper presents an analysis of thermal-mechanical snap-through instabilities in structures using a hybrid load-controlled/displacement-controlled algorithm. The derivation uses the finite element method with a combination of modified Newton-Raphson and arc-length methods, aimed at providing a robust and efficient means for modeling the buckling response of structures that exhibit instability in the presence of nonuniform time-varying temperature fields and temperature-dependent material response. Load control is used to model the system’s response up to the point of instability, which is identified using the method of bisections. During the instability, the analysis switches to displacement control to capture the load-shedding behavior. Once a stable point is reached, the algorithm switches back to load control. The novelty lies in the ability of the hybrid algorithm to model instabilities that are caused by material degradation under nonuniform transient temperature fields, which is particularly important in the study of structural response under fire hazards. Numerical analyses are carried out using a two-dimensional (2D) fiber-based corotational beam element. Verifications at room temperature and at elevated temperature demonstrate that the proposed approach exhibits a high level of accuracy. A brief study of toggle frames subjected to various types of heating and loading conditions is presented to illustrate the kinds of behaviors that can be captured with the proposed modeling approach.

Damping plays an important role in structural dynamics by absorbing energy and reducing structural responses. The inherent damping in a building ranges from approximately 2 to 10% critical damping in the first mode; even greater levels of damping are achieved when including supplemental damping devices such as viscous oil dampers. When creating laboratory scale structures, it is difficult to achieve the target level of damping in the specimen. Solutions such as adding discrete damping devices are costly, while solutions such as adding foam or other dissipative materials may add undesired nonlinear behavior or increase the stiffness. This paper proposes a novel technique to introduce artificial damping to a dynamic specimen through shake table control. Artificial damping (AD) is introduced by designing a feedforward (FF) shake table controller that compensates for both shake table dynamics and achieves target specimen performance; that is, with larger damping than the original specimen. The performance of the proposed artificial damping by FF (AD-FF) is investigated for both traditional shake table testing and shake table real-time hybrid simulation (RTHS) through a uniaxial shake table and a two-story shear building specimen with very low damping. The target level of structural damping is accurately realized through the proposed AD-FF in both traditional shake table testing and RTHS. Moreover, damping can be introduced to specific modes of the structure, a feature that cannot be realized by using physical damping devices. In RTHS, the proposed AD-FF gives researches the ability to increase stability without changing the dominant structural response by adding damping to higher modes, even if they appear in the specimen.

Natural frequencies and mode shapes of a complex shell composed of a circular cylindrical shell and hemispherical shell with variable thickness are determined by the Ritz method using a mathematically three-dimensional (3D) analysis instead of two-dimensional (2D) thin-shell theories or higher-order thick-shell theories. The present analysis is based upon the circular cylindrical coordinates, whereas in traditional shell analyses, 3D shell coordinates have usually been used. Using the Ritz method, Legendre polynomials, which are mathematically orthonormal, are used as admissible functions instead of ordinary simple algebraic polynomials. Natural frequencies are presented for different boundary conditions. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the combined shell. The frequencies from the present 3D method are compared with those from three types of 2D thin-shell theories found by previous researchers. The present method is applicable to very thick shells as well as thin shells and complex shells with variable thickness.

Short-ranged hydration of water on mineral surfaces and capillary condensation in larger pores influences mechanical behavior of unsaturated soil (e.g., strength, stiffness) in different ways. Transition between water retention dominated by surface and cation hydration at high suction into a regime dominated by capillary condensation at low suction corresponds to a transition in soil behavior, yet the occurrence and implications of this transition remain unclear. Results are presented from Brazilian tensile strength (BTS) tests using compacted kaolinite disks equilibrated under controlled relative humidity ($R_H$) conditions. Transition between surface hydration and capillary condensation is evident for specimens compacted to dense and loose conditions as a nonmonotonic relation between tensile strength and $R_H$. Minimum tensile strength occurs in both cases at approximately 80% $R_H$, or corresponding potential of about $-14$ to $-30\mathrm{MPa}$. Transitions in strength, stiffness, and strain at failure are consistent with transition from a hydration-dominated water retention regime to a capillary-dominated water retention regime. A semiquantitative framework accounting for evolution of suction stress is applied to interpret the experimental results. Results provide evidence for the hydration–capillary transition in compacted clay and clarify corresponding implications to macroscopic behavior.

Three methods of stochastic equivalent linearizations defined in the broad framework of structural reliability analysis are presented. These methods are (1) the Gaussian equivalent linearization method (GELM), here defined for the first time as a linear response surface in terms of normal standard random variables; (2) the tail equivalent linearization method (TELM), here reinterpreted as a stochastic critical excitation method; and (3) a novel equivalent linearization called the tail probability equivalent linearization method (TPELM). The Gaussian equivalent linear system (GELS) is the equivalent linear system (ELS) obtained by minimizing the difference between the variance of the GELS and the original nonlinear system. The tail equivalent linear system (TELS) is the ELS having the same critical excitation as the original system. The tail probability equivalent linear system (TPELS) is the ELS obtained by minimizing the difference between the tail probability of the equivalent system and the original nonlinear system. The knowledge of the ELS allows the evaluation of engineering quantities of interest—e.g., first-passage probabilities—through the application of the random vibration analysis to these systems. Shortcomings and advantages of the three methods are presented and illustrated through applications to selected representative nonlinear oscillators. Finally, the methods are applied to an inelastic multi-degree-of-freedom (MDOF) system, showing their scalability to systems of higher complexity.

Unreinforced masonry walls subjected to out-of-plane horizontal bending can fail by two alternate modes: stepped failure along the brick-mortar bond, or line failure cutting directly through the bricks. Because of random variations in material properties throughout a panel and the tendency for failure to occur across the weaker elements, vertical cracks will generally exhibit a combination of the two modes. This paper develops a pair of analytical methodologies that treat this phenomenon using a stochastic approach. The first part deals with calculating the ultimate moment capacity by allowing for the weakening effect associated with the mixed (stepped and line) mode of failure. This effect is quantified in terms of strength-reduction factors for mean and characteristic (0.05 quantile) values of strength, which may be applied toward generic ultimate strength design. The second part deals with estimating the relative probability of each failure mode and the probability distribution for the relative proportions of each failure mode along a crack. This is of particular relevance to seismic performance because the two failure modes lead to significantly different postcracking behavior.

Estimation of statistical moments of performance functions is one of the main topics in structural reliability analysis by moment methods. It is possible to apply the well-developed multiple-dimensional cubature formulas to assess such statistical moments. In this paper, a new criterion is proposed to fulfill the aim. Several efficient cubature formulas are firstly revisited. Then, a new criterion is proposed to select “the best” cubature formula that gives the most accurate statistical moments of performance functions. This criterion is established based on the marginal moments of input random variables. The cubature formula that provides the smallest difference between the estimated values and the exact values of marginal moments is determined as the adopted one for statistical moments of performance functions. Several numerical examples are presented to illustrate the effectiveness of the proposed criterion, in which Monte Carlo simulations are employed for comparison.

An explicit expression for a rational fractional powers Caughey damping series consistent with a set of prescribed modal damping ratios is presented. The result is obtained by use of Adhikari’s approach combined with a Lagrange interpolation of the modal damping constants as a function of the natural frequencies and independently by a modal expansion of the stiffness matrix. The explicit expression for the resulting classical damping matrix circumvents the need for solving an ill-conditioned system of equations for the coefficients in the Caughey series. The general result is specialized to the case of “linear hysteretic damping” in which all the modal damping ratios are equal. Closed-form expressions for the elements of a classical damping matrix for a simple multistory structure are also presented.

Analytical solutions for critical design properties of elastomeric bearings, such as the compression modulus, bending modulus, and maximum shear strain due to compression or rotation, including the compressibility of the elastomer, have been developed for most basic laminated elastomeric bearing geometries. Due to the introduction of extensible fiber reinforcement, these analytical solutions have been expanded to include the extensibility of the reinforcement as an additional design parameter. Extensible reinforcement can have a pronounced effect on these design properties, comparable to the compressibility of the elastomer. These analytical solutions have previously been used to derive simplified approximations appropriate for use in design codes and standards. Thus far, a rectangular bearing geometry, which is in fact the most common in bridge bearing applications, has been largely omitted from these derivations. Simplified approximations for the compression modulus, maximum shear strain due to compression, and bending modulus of a rectangular laminated bearing with extensible reinforcement are proposed and evaluated against the analytical solution, including the effects of compressibility of the elastomer and extensibility of the reinforcement.

Field investigations reveal that railway tracks, pipelines, and pavements are prone to buckling locally as a result of the axial compressive forces caused by thermal loading. These types of structural elements can be simplified as a beam on a nonlinear foundation. A simple and efficient Rayleigh-Ritz method for the postbuckling analysis of an axially loaded column on a nonlinear foundation is proposed herein. The method leads to an integrable formulation of the total potential energy of the column-foundation system and to an expression for the axial shortening in analytical form. The postbuckling deformation consists of an amplitude modulation of the periodic buckle at bifurcation buckling (either symmetric or antisymmetric) in terms of three undetermined coefficients, which can be determined readily. Nonlinear foundation models that include softening and restabilizing behavior are studied, allowing for localization and snaking to be captured in stable and unstable branches of the postbuckling response. The results are shown to agree quite well with numerical studies of the problem.