High-Order Analysis of Reinforced Concrete Slabs Strengthened with Circular Composite Laminated Patches of General Layup

A high-order model for the analysis of reinforced concrete (RC) slabs strengthened with externally bonded composite laminated patches of a general layup is presented. The model follows the concepts of the high-order theory and it is based on variational principles, equilibrium, and compatibility requirements. The classical lamination theory is adopted for the composite patch and it yields a set of coordinate dependent constitutive relations. The governing equations form a set of partial differential equations with variable coefficients. The solution procedure adopts the Galerkin and the multiple-shooting methods in the circumferential and radial directions, respectively. The proposed model is used for the numerical study of a square RC slab strengthened with a circular cross-ply laminated patch. The results focus on the overall behavior of the slab and the localized shear and vertical normal stresses near the edge of the bonded patch. Comparison with results obtained using a simplified axisymmetric model is also presented and discussed. The study reveals that the anisotropy of the bonded patch affects the overall and the localized response of the strengthened slab. It also shows that the simplified axisymmetric analysis tends to underestimate the stresses and stress resultants, and thus may be considered unsafe.     

Finite Element Analysis of Concrete Pavements Over Culverts

Accelerated distress of Portland cement concrete pavements (PCCP) over structures such as culverts, pipes, and tunnels beneath roadways is a common occurrence. In this article, finite element analysis is employed to analyze the response of concrete pavements over such structures. The factors that influence the overlying pavement slabs include: (1) cover depth, (2) pavement slab thickness and length, (3) cement concrete elastic modulus, (4) foundation modulus, and (5) backfill soil modulus. The tensile stresses at the bottom and top of the slab induced by wheel loads are predicted. In the traditional pavement design only the tensile stress at the bottom of the slab is considered to be significant. However, this study shows that the tensile stress at the top surface of pavement slabs over culverts may also cause the concrete pavements to fail. A laboratory model was employed to study the mechanical characteristics of Portland cement concrete pavement slabs over culverts and to verify the theoretical analysis.     

3D Finite Element Analysis of Temperature‐Induced Stresses in Dowel Jointed Concrete Pavements

A detailed 3D finite element (3DFE) model is developed to investigate the applicability of Westergaard’s curling stress equations to doweled jointed concrete pavements. The model does not rely on any of Westergaard’s assumptions and is capable of handling nonlinear and/or time‐dependent temperature profiles. However, only linear gradient is applied to facilitate the comparison with Westergaard’s results. The transverse stress calculated using Westergaard’s formula was found to be within 10% of that computed using 3DFE. Westergaard’s longitudinal stress equation required a correction. The 3DFE results confirm Westergaard’s finding that the slab curling stresses are independent of slab length. Thus, curling stress does not explain the field‐observed dependency of mid‐slab cracking on the slab length. Through the examination of the mechanism of dowel‐concrete interaction, it is shown that uniform temperature changes play the major role in mid‐slab transverse cracking of relatively long slabs. Due to built‐in slab curling as well as temperature or moisture curling, the dowel bars bend restricting the slab from free contraction due to uniform temperature drop. This gives rise to a large component of stress that has not been considered in previous investigations. Application of a combined temperature gradient and uniform temperature drop to slabs of different lengths revealed the dependency of mid‐slab transverse cracking on slab length.     

变厚度轧制过程力平衡微分方程

 生产节材型产品LP板和TRB板需要解决变厚度轧制参数计算问题,为此利用作用在微元体上的力平衡关系分别推导了趋薄轧制和趋厚轧制的力平衡微分方程,称为VGR方程。推导过程中考虑了轧辊在垂直方向上刚性位移速度vy的影响,获得了VGR方程对趋薄、趋厚轧制的统一表达形式,验证了Karman方程是VGR方程在vy=0时的特例。本研究为变厚度板材轧制参数的理论研究奠定了基础。     

Design Recommendations for Externally Restrained Highway Bridge Decks

A severe maintenance penalty exists for composite multibeam highway bridges in areas where the use of deicing chemicals is prevalent. This maintenance concern is largely due to the corrosion of embedded steel reinforcing bars and the attendant concrete degradation in the deck slab. Transverse steel straps, placed below the concrete slab, eliminate the deleterious effects of corrosion on the concrete. Further, the straps can be designed to provide the restraint necessary to promote the development of internal arching in the concrete slab in response to a concentrated load. A design procedure is presented for an externally restrained highway bridge deck. The method has been developed, based on the Canadian Limit States design philosophy, considering both the strength and serviceability requirements. It is demonstrated that the ultimate strength requirements dictate the external restraint requirements, and a numerical example of the design procedure is given.     

Postbuckling Analysis of Plates Resting on a Tensionless Elastic Foundation

The buckling and large deflection postbuckling behavior of plates laterally constrained by a tensionless foundation and subjected to in-plane compressive forces are investigated. A nonlinear finite-element formulation based on Marguerre’s nonlinear shallow shell theory, modified by Mindlin’s hypothesis, is employed to model the plate response. To overcome difficulties in solving the plate–foundation equilibrium equations together with the inequality constraints due to the unilateral contact condition, two different approaches are used: (1) the unilateral constraint is accounted for indirectly by a bilinear constitutive law and (2) the problem is formulated as a mathematical programming problem with inequality constraints from which a linear complementarity problem is derived and solved by the Lemke algorithm. To obtain the nonlinear equilibrium paths, the Newton–Raphson algorithm is used together with path-following strategies. Plate–foundation interaction leads to interesting deformation sequences, characterized by the variation of the contact and noncontact zones along the postbuckling path, leading sometimes to sudden changes in the deformation pattern. The results have a remarkable dependence on the plate aspect ratio, foundation stiffness, and buckling shape. The effects of geometric imperfections on the nonlinear response of the plate are also investigated. From these results, a number of insightful conclusions regarding the behavior of such plate–foundation systems are drawn.     

Biparametric Models for Elastic Wedge Foundation

In this paper, some biparametric models for an elastic foundation are proposed. It is assumed that the foundation has the shape of the wedge. The modeling procedure starts from the linear elasticity equations into which we introduce some simplifying assumptions based on the conceptions of decay functions. The simplified models are described by the ordinary differential equations. Stationary and nonstationary Green’s functions for the foundation considered are obtained by applying the Hankel and Laplace transform methods. An example of the interaction between the rigid plate and the elastic wedge foundation is studied.     

Interface Shear Stress: A New Design Criterion for Plate Debonding

This paper critically assesses the applicability and reliability of existing analytical techniques to predict and∕or prevent brittle plate debonding failure that occurs in reinforced concrete (RC) beams strengthened with externally bonded steel or fiber-reinforced-polymer composite plates. The experimental results, available to date in literature, have been very carefully reviewed and analyzed for this purpose. A new approach, very different from existing methods, and based on the interface shear stress obtained form elastic analysis of RC beam cross section and the fundamentals of force transfer mechanism in a bonded joint, is presented to predict the premature plate debonding phenomenon. The paper identifies important structural, material, and force parameters that influence this critical interface shear stress value between the bonded plate and concrete. The relations between these parameters and interface shear stress value are also examined and found to be consistent and logical to predict plate debonding at the plate cutoff end. The validity of this new design-oriented approach and scope for further research are also discussed.     

Ductile Design of Reinforced Concrete Beams Retrofitted with Fiber Reinforced Polymer Plates

For reinforced concrete beams retrofitted with fiber-reinforced polymer (FRP) plates, an analytical method is derived for determining the allowable plate area to achieve a targeted value of ductility. Nonlinear models for concrete and reinforcement are applied, and the effects of concrete confinement and spalling and of FRP plate rupture are considered. The derivation of equilibrium and compatibility equations for a rectangular cross section is presented, and the solution to the nonlinear equation for determining the allowable plate area is demonstrated with examples. Analytical results are compared with numerical and experimental data reported in the literature. Subsequently a simplified version of the method is derived, based on regression analysis, to relate the curvature ductility to the FRP plate ratio. It is noted that additional conditions need to be checked to ensure ductile performance, such as local failure of the concrete layer between tension reinforcement and FRP plate or debonding of the plate itself.     

Modeling of Steel-Concrete Composite Beams under Negative Bending

Negative bending moments acting in the support regions of continuous composite beams generate tensile stresses in the concrete slab and compressive stresses in the lower steel profile. As a result the mechanical behavior of these beams is strongly nonlinear even for low stress levels, due not only to the slip at the beam-slab interface, but also to cracking in the slab. Therefore, an adequate theoretical modeling should take account of the interactions between the structural steel and the concrete slab by shear connectors and also between steel rebars and concrete in tension by bond phenomenon. In this paper a model of steel and concrete composite beams subjected to negative bending is presented. It accounts for the slip occurring at both the beam-slab interface and the steel reinforcement-concrete interface. Some numerical results, obtained using a suitable numerical procedure, are discussed to show the capacity of the model.     

Concrete Beams Strengthened with Externally Bonded FRP Plates

The structural behavior of reinforced concrete beams strengthened with adhesively bonded fiber-reinforced plastics (FRP) is presented. The experimental work included flexural testing of 2.3-m-long concrete beams with bonded external reinforcements. The test variables included the amount of conventional (internal) reinforcement and also the type and amount of external reinforcement. For comparison, some of the beams were strengthened with bonded steel plates. Theoretical analyses included 2D nonlinear finite-element modeling incorporating a “damage” material model for concrete. In general there were reasonably good correlations between the experimental results and nonlinear finite-element models. It is suggested that the detachment of bonded external plates from the concrete, at ultimate loads, is governed by a limiting principal stress value at the concrete∕external plate interface.     

A Higher Order Shear Deformation Model for Bending Analysis of Functionally Graded Plates

In this paper, the static response of simply supported functionally graded plates subjected to a transverse uniform load and resting on an elastic foundation is examined by using a new higher order displacement model. The present theory exactly satisfies the stress boundary conditions on the top and bottom surfaces of the plate. No transverse shear correction factors are needed, because a correct representation of the transverse shear strain is given. The material properties of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of material constituents. The foundation is modeled as a two-parameter Pasternak-type foundation, or as a Winkler-type one if the second parameter is zero. The equilibrium equations of a functionally graded plate are given based on the new higher order shear deformation theory of plates presented. The effects of stiffness and gradient index of the foundation on the mechanical responses of the plates are discussed. It is established that the elastic foundations significantly affect the mechanical behavior of thick functionally graded plates. The numerical results presented in the paper can serve as benchmarks for future analyses of thick functionally graded plates on elastic foundations.     

3D Finite Element Study on Load Transfer at Doweled Joints in Flat and Curled Rigid Pavements

This study examines load transfer across doweled joints in rigid pavements using 3D finite element analysis. A recently developed dowel modeling strategy is employed that allows the efficient and rigorous consideration of dowel/slab interaction. Parametric studies on the response of a typical, dowel‐retrofitted pavement system subjected to axle loads and varying degrees of slab curling are conducted. To examine the effect of slab support on pavement response, the studies consider two different foundation types: layered elastic with an asphalt‐treated base and a dense liquid foundation. The results of the studies are discussed with emphasis on the effect of slab curling and foundation type on joint load transfer and the potential for joint distress. While there are significant differences in response for the ATB‐supported slabs and the slabs founded on a dense liquid, slab curling does generally increase dowel shears and dowel/slab bearing stresses. However, further examination of the parametric study results that accounts for compressive fatigue of the concrete at the dowel/slab interface indicates that slab curling may not significantly increase the potential for damage to the slab concrete surrounding the dowels.     

Thermoelastic Analysis of Functionally Graded Ceramic-Metal Cylinder

The pseudodynamic thermoelastic response of functionally graded ceramic-metal cylinders is studied. This paper presents the finite-element formulation of the 1D, axisymmetric heat transfer equation and the thermoelastic radial boundary value problem. A two-step solution of the governing equations of thermoelasticity is presented. Thermoelastic coupling is considered by taking into effect the temperature dependence of the constitutive equations. Nonlinearity due to the temperature dependence of the material properties of the constituent ceramic and metal is considered. A parametric study with respect to varying volume fraction of the metal is conducted. Temperature and radial∕hoop stress distributions arising due to rapid heating of the inner surface of the functionally graded cylinder are presented.     

Damping and Viscoelastic Dynamic Response of RC Flexural Members Strengthened with Adhesively Bonded Composite Materials

A theoretical approach for the dynamic viscoelastic response of reinforced concrete (RC) beams and one-way slabs strengthened with adhesively bonded composite materials is developed. The analytical model is based on variational principles, dynamic equilibrium, and compatibility of deformations between the structural components (RC beam/slab, adhesive, composite material). The model accounts for the deformability of the adhesive layer and for its high order stress and displacement fields. The equations of motion and the boundary, continuity, and initial conditions are derived via the extended Hamilton’s principle. The Kelvin-Voigt approach is adopted for the consideration of the viscoelastic response of the adhesive material and the internal damping in the composite material and the RC member. The Rayleigh damping model is used for the external viscous damping of the RC member. The dynamic governing equations are solved using the Newmark time integration and a multiple shooting algorithm is used for the solution in space. A numerical example is presented to examine the capabilities of the model, to highlight the unique phenomena associated with the viscoelastic response of the adhesive material, and to demonstrate its influence on the local and global behavior. The results obtained using the analytical model show that the viscoelastic response of the adhesive material may significantly modify the critical shear and peeling stresses at the interfaces of the adhesive layer.     

Delamination Effects in Reinforced Concrete Slabs Strengthened with Circular Composite Patches

The behavior of reinforced concrete slabs strengthened with fully or partially bonded (delaminated) circular patches is analytically investigated. The model derived follows the concepts of the high-order theory, and uses variational principles, equilibrium, and compatibility requirements, the constitutive equations of reinforced concrete (RC) members and composite laminates, and the fracture-mechanics concept of energy release rate. A substructuring approach, in which the localized response of the strengthened area is modeled assuming circular axis-symmetric behavior, is adopted. The investigated substructure consists of fully bonded and delaminated regions, where the delaminated faces can slip horizontally one with respect to another. A distinction is made between delaminations with contact, in which the delaminated faces accommodate vertical normal compressive stresses, and delaminations without vertical contact, in which the cracked interface is free of stresses on any kind. The field and governing equations of the fully bonded, delaminated (with or without contact), and unstrengthened regions, as well as the boundary/continuity conditions that combine these regions together, are derived. The influence of the existence of a delaminated area at the center of the slab and the effect of its size on the localized and overall behavior are investigated numerically. The elastic energy release rates associated with the growth of the delaminated area and their influence on the failure mode of the strengthened structure are also studied. The investigation reveals that the formation of a delaminated region reduces the composite action of the RC slab and the bonded patch, is involved with stress concentrations near the edge of the region, and may trigger an unstable delamination failure of the strengthened slab.     

Dynamic Behavior of Reinforced Concrete Beams Strengthened with Composite Materials

The dynamic behavior of reinforced concrete (RC) beams strengthened with externally bonded composite materials is analytically investigated. The analytical model is based on dynamic equilibrium, compatibility of deformations between the structural components (RC beam, adhesive, composite material) and the concept of the high order approach. The equations of motion along with the boundary and continuity conditions are derived using Hamilton’s variational principle and the kinematic relations of small deformations. The mathematical formulation also includes the constitutive laws that are based on beam and lamination theories, and the two-dimensional elasticity representation of the adhesive layer including the closed form solution of its stress and displacement fields. The Newmark time integration method, which is directly applied to the resulting set of coupled partial differential equations, is adopted. This procedure yields a set of ordinary differential equations, which are analytically or numerically solved in every time step. The response of a strengthened beam to different dynamic loads that include impulse load, harmonic load, and seismic base excitation is numerically investigated. The numerical study highlights some of the phenomena associated with the dynamic response and explores the capabilities of the proposed model. The paper closes with a summary and conclusions.     

Multicomponent Model of Reinforced Concrete Joints for Cyclic Loading

Efficient simplified models are available for reinforced concrete beams and columns, with the assumption of a perfectly rigid connection. However, interior beam∕column joints have been shown to be the area of strong deformation and degradation mechanisms, involving mainly the cyclic behaviors of concrete under shear and of bond under push-pull loading. In this paper, a global component-based model is proposed for the beam∕column connections of reinforced concrete frame structures that can be directly connected to beam elements. This model incorporates explicitly the modeling of concrete, steel, and steel∕concrete bond. Thus, the key mechanisms of deformation and degradation of the connection, as well as various interactions can be taken into account naturally. In particular, the effect of push-pull-type loading on the flexural steels can be captured. On the basis of a local finite-element modeling of the connection, simplifying assumptions are proposed and implemented leading to the component-based model. Both approaches (local and component-based) are compared on an application example.     

浅谈钢筋砼现浇板裂缝的预防

分析钢筋混凝土现浇板产生裂缝的原因,主要论述温度-收缩应力对钢筋混凝土现浇板产生裂缝的影响。对温度-收缩应力作用产生裂缝提出预防措施。     

Analysis of Adhesive-Bonded Joints, Square-End, and Spew-Fillet—High-Order Theory Approach

The analysis of adhesive-bonded joints using a closed-form high-order theory (CFHO theory) is presented, and its capabilities are demonstrated numerically for the case of single lap joints with and without a “spew-fillet.” The governing equations based on the CFHO theory are presented along with the appropriate boundary∕continuity conditions at the free edges. The joints consist of two metallic or composite laminated adherends that are interconnected through equilibrium and compatibility requirements by a 2D linear elastic adhesive layer. The CFHO theory predicts that the distributions of the displacements through the thickness of the adhesive layer are nonlinear in general (high-order effects) and are a result of not presumed displacement patterns. The spew-fillet is modeled through an equivalent tensile bar, which enables quantification of the effects of the spew-fillet size on the stress fields. Satisfactory comparisons with two-parameter elastic foundation solution (Goland-Reissner type) results and finite-element results are presented.