Journal of Engineering Mechanics

Prevention of structures against progressive collapse has become a concern of increasing significance and the alternative load path method (ALPM) is the extensively acknowledged approach in this area of research. With the basis of ALPM and by amalgamation of the Monte Carlo simulation method and an iterative algorithm, a new approach is developed in this paper to assess the reliability of ductile RC frame structures when subjected to one column failure. This paper focuses on the construction and solution of the performance function of the damaged structure under static service loadings. With this intention, three types of critical zones are identified and an optimum model is presented to determine the possible failure modes for each zone. By employing the virtual work principle and critical collapse mechanism criterion, the performance function is established in terms of minimum internal virtual work and external virtual work done by service loadings. Three equations containing the interaction between the axial forces and bending strength of structural members are evolved to calculate this function, and by solving these equations from the top floor to the floor of the failed column the performance of the damaged structure can be appraised.

The fiber-reinforced polymer (FRP) plate or sheet debonding or cover delamination (concrete cover separation) failure mode in externally strengthened reinforced concrete beams has attracted a lot of attention. In this paper, a closed-form analytical solution is developed to determine the nonlinear shear stress distribution along the laminate interface and cover area for any load stage assuming a perfect bond. Trilinear moment-curvature and moment-extreme compression fiber strain is assumed to realize the analytical results. By differentiating the FRP axial tension force with respect to position along the beam, closed-form derivatives in terms of curvature and extreme compressive fiber strain are obtained. The results show three distinct regions of constant or stepwise linear shear distribution in each. These correspond to the uncracked, postcracked, and postyielded zones of the shear span. The results are shown to yield an exact match to those numerically obtained by dividing the shear spans into a large number of small segments and applying nonlinear sectional analysis in the middle of each segment. The analytical solution also compares well with the finite-element results using ABAQUS. The analysis of a number of strengthened beams at experimental debonding or cover delamination failure load show that the interface shear stress distribution varies from cases having no cracking at the plate tip (three regions) to those encountering two regions only (postcracked and postyielded) when the FRP plates or sheets extend close to the supports. It also shows that this distribution, at failure, consists of two regions in most of the cases and may only have a postcracked region in beams with relatively shorter plates or sheets.

This paper explains the importance of using a nonlinear anisotropic three-dimensional (3D) finite-element (FE) pavement model to simulate the granular base layer and predict viscoelastic pavement responses under moving vehicular loading. The FE model was built using the general-purpose FE software ABAQUS, and a user material subroutine was developed to implement the constitutive model of granular material using a modified Newton-Raphson approach with secant stiffness. The FE model utilizes implicit dynamic analysis and simulates the vehicular loading as a moving load with 3D contact stresses at the tire-pavement interface. The analysis results indicate that it is important to consider the viscoelastic nature of the asphalt layer and the moving load for accurately capturing the nonlinear granular base modulus in the mechanistic pavement model. The modulus distribution in the granular base layer is affected not only by wheel load and pavement structure (such as asphalt layer thickness and subgrade support) but also by temperature and vehicle speed because of the viscoelastic behavior of the asphalt surface layer. Excluding the cross-anisotropic stress-dependent behavior of the granular base layer could cause significant error in predicting fatigue cracking and rutting potential in thin asphalt pavements. In addition, the model results captured the trends of field measurements at different loading and temperature conditions.

In this paper, an analytic solution to the modified mild-slope equation (MMSE) for wave reflection by a submerged rectangular breakwater with two scour trenches is explored. Because of the use of the MMSE with effects of the bottom curvature and the slope-squared terms, the solution is not only valid in the whole wave range from shallow water to deep water, but also valid for topographies not restricted to vary moderately. The present analytic solution includes an existing analytic long-wave solution as its special case, and the computing results show good agreement between two solutions, except for a slight difference when waves approach intermediate-wave range. It is found that this slight difference used to lead to an incorrect conclusion that the reflection coefficient for wave reflection by a rectangular breakwater or trench is a periodic function to the ratio of the breakwater length to the wavelength. This analysis shows that the reflection coefficient is a periodic oscillation function with a variable oscillation amplitude rather than a periodic function with a constant oscillation amplitude. It is also found that the discrepancy between the two solutions, respectively based on the MSE and the MMSE, mainly occurs for intermediate waves. Based on the present MMSE-based solution, the influence of trench dimensions on the reflection effect is investigated. It is shown that in the whole wave range, the phenomenon of zero reflection occurs more frequently for symmetrical bathymetry.

A suitable and simple two-step model able to predict the nonlinear response of fiber-reinforced polymer (FRP)-strengthened three-dimensional masonry structures is presented. In the first step, nonstrengthened masonry is substituted by a macroscopically equivalent homogeneous material through a kinematic model based on finite elements and working on a heterogeneous assemblage of blocks. Nonlinearity is concentrated exclusively on joints reduced to interfaces exhibiting a frictional behavior with limited tensile and compressive strength with softening. The homogenized stress-strain behavior evaluated at the mesoscale is then implemented at a structural level in a finite-element nonlinear code, relying on an assemblage of rigid infinitely resistant six-noded wedge elements and nonlinear interfaces, exhibiting deterioration of the mechanical properties. The FRP-reinforcing strips are modeled through rigid triangles and nonlinear interfaces between adjoining triangles. Delamination from the support is accounted for by modeling the FRP-masonry bond by means of nonlinear softening triangular interfaces. Italian code formulas are used to evaluate peak interface tangential strength and postpeak behavior. In this first part, the theoretical basis of the model and the nonlinear stress-strain behavior at a cell level are discussed. Structural examples will be analyzed in the accompanying paper devoted to the structural scale.

The homogenized masonry nonlinear stress-strain curves obtained through the simple micromechanical model developed in the first part of the paper are here used for the analysis of strengthened masonry walls under various loading conditions. In particular, a deep beam and a shear wall strengthened with fiber-reinforced polymer (FRP) strips are analyzed for masonry loaded in-plane. Additionally, single and double curvature masonry structures strengthened in various ways, namely a circular arch with buttresses and a ribbed cross vault, are considered. For all the examples presented, both the nonstrengthened and FRP–strengthened cases are discussed. Additional nonlinear finite-element analyses are performed, modeling masonry through an equivalent macroscopic material with softening to assess the present model predictions. Detailed comparisons between the experimental data, where available, and numerical results are also presented. The examples show the efficiency of the homogenized technique with respect to (1) accuracy of the results; (2) low number of finite elements required; and (3) independence of the mesh at a structural level from the actual texture of masonry.

While a freestanding high-strength sheet metal subject to tension will rupture at a small strain, it is anticipated that lamination with a ductile sheet metal will retard this instability to an extent that depends on the relative thickness, relative stiffness, and hardening exponent of the ductile sheet. This paper presents an analytical study for the deformability of such a laminate under tensile load within the context of necking instability. Laminates of high-strength sheet metal and ductile low-strength sheet metal are studied assuming (1) the sheets are fully bonded and (2) the metals obey the power-law material model. The effect of the hardening exponent, volume fraction, and relative stiffness of the ductile component has been studied. The stability of both uniform and nonuniform deformations has been investigated. The results have shown retardation of the high-strength layer instability by lamination with the ductile layer. The laminate exhibits marked enhancement in the strength-ductility combination, which is essential in metal-forming applications.