Semianalytical Modeling of Concrete Beams Rehabilitated with Externally Prestressed Composites

This study attempts to develop a semianalytical model for the mechanical behavior of reinforced concrete (RC) beams rehabilitated with externally prestressed carbon fiber-reinforced polymers (CFRP) laminates. The main significance of this study is the model of the process of degradation of RC beams until failure and its recovery through externally prestressed CFRP. Experiments have been carried out to observe the load–deflection behavior of fresh RC beams until the load resistance of the beam is exhausted. The beams have been rehabilitated with external CFRP laminates with varying levels of prestress. The rehabilitated beams have been reloaded until failure. The load–deflection behavior of the fresh and rehabilitated beams has been compared. A model for the load–deflection behavior of the fresh and rehabilitated beam has been proposed. The main import of the model is that it incorporates the effect of confinement of concrete. The model shows very good agreement with the experimental results.     

Flexural Strengthening of RC Beams with Prestressed CFRP Sheets: Development of Nonmetallic Anchor Systems

This paper presents a novel anchoring technique for strengthening reinforced concrete beams with prestressed carbon fiber- reinforced polymer (CFRP) sheets. Permanent steel anchors are commonly used for the application of prestressed CFRP sheets. The steel anchors are, however, susceptible to corrosion and may not blend into the aesthetics of the original structure. As a result, it may be preferable to remove the steel anchors after transferring the required prestress to the structure with minimal losses of sustained prestress. A technique for replacing the steel anchors with nonmetallic anchors is investigated and reported herein. Nine doubly reinforced concrete beams are tested with various types of nonmetallic anchor systems such as nonanchored U-wraps, mechanically anchored U-wraps, and CFRP sheet-anchored U-wraps. The developed nonmetallic anchorages successfully transfer the sustained prestress in the CFRP sheets with insignificant prestress losses. A closed-form solution for the transfer of prestress is developed and compared to the experimental results.     

Flexural Behavior and Deformability of Fiber Reinforced Polymer Prestressed Concrete Beams

After a brief review of the ductility and deformability indices currently used in the design of concrete beams reinforced or prestressed with steel or fiber reinforced polymer (FRP) tendons, a new definition of a deformability index (factor) for prestressed concrete beams is proposed. The new factor is defined in terms of both a deflection factor and a strength factor. The deflection factor is the ratio of the deflection at failure to the deflection at first cracking, while the strength factor is the ratio of the ultimate moment (or load) to the cracking moment (or load). The proposed deformability factor is verified not only by test results obtained by the writer, but also by other test results available in the literature and it appears to be a suitable measurement of the deformability of concrete beams prestressed with either FRP tendons or steel tendons.     

Effects of Gradually Anchored Prestressed CFRP Strips Bonded on Prestressed Concrete Beams

Four prestressed concrete beams were constructed and tested to investigate the effectiveness of flexural post-strengthening with prestressed carbon fiber-reinforced polymer (CFRP) strips. One of the beams served as a reference beam, another was bonded with an unstressed CFRP strip, and the remaining two specimens were strengthened with prestressed CFRP strips at two prestressing levels. The gradient method was used for the anchorage of the prestressed CFRP strips. Experimental and analytical calculations are compared with the test results. Further, different failure modes are explained. On the basis of this investigation, recommendations for the use of prestressed CFRP strips anchored with the gradient method are given.     

Prestressed Carbon Fiber Reinforced Polymer Sheets for Strengthening Concrete Beams at Room and Low Temperatures

A technique for strengthening damaged concrete beams using prestressed carbon fiber reinforced polymer (CFRP) sheets was developed at Queen’s University and the Royal Military College of Canada. As part of this study, an anchorage system was developed to directly prestress the CFRP sheets by jacking and reacting against the strengthened concrete beam itself. The feasibility and effectiveness of using bonded prestressed CFRP sheets to strengthen precracked concrete beams at both room (+22°C,+72°F) and low (?28°C,?20°F) temperatures have been investigated experimentally. Materials and prestress changes due to temperature variations that would affect and cause changes in flexural behavior were studied. The strengthened beams showed significant increases in flexural stiffness and ultimate capacity as compared to the control-unstrengthened beams. The flexural behavior of the strengthened beams was not adversely affected by short-term exposure to reduced temperature (?28°C,?20°F). In addition to the experimental investigation, analytical models were developed to predict the overall flexural behavior of the strengthened beams during prestressing of the CFRP sheets and under external loading at both room and low temperatures. The model accurately predicted the flexural beam behavior. Improved serviceability behavior and higher strength were predicted for beams strengthened with the bonded prestressed CFRP sheets.     

Numerical Analysis of Continuous Beams Prestressed with External Tendons

This paper presents a numerical model conceived to simulate the behavior up to collapse of continuous concrete beams prestressed with bonded or external tendons. Its most valuable feature is the ability to automatically determine the most suitable extent of each load increment according to the actual stiffness of all the segments that form the discretized beam. A crucial problem of nonlinear structural analysis is numerical evaluation of the rotation capacity of plastic hinges, especially when dealing with concrete beams prestressed with external tendons, which is a technology nowadays increasingly adopted in new continuous bridges and in the rehabilitation or strengthening of old or damaged structures. This problem is discussed in depth and a simple rule, which differs from those usually discussed in the scientific literature, is adopted to subdivide the beam into discrete elements. The effectiveness of the numerical model is tested by comparing its numerical output with the outcomes of 14 experimental tests. This comparison looks promising since the mean value of the error on load carrying capacity is only 0.1%, with a 2.4% standard deviation.     

Recurrent Single Delaminated Beam Model for Vibration Analysis of Multidelaminated Beams

Free vibration analysis of a through-width multidelaminated beam is performed in the present study. Multiple delaminations are assumed to spread from the top through the thickness direction of the beam. The natural frequencies of the multidelaminated beams are obtained from a recurrent single delaminated beam (RSDB) model, which is the subsingle delaminated beam from the top surface of a global beam. Each frequency equation for the RSDB with unknown boundary conditions is obtained through continuity conditions. Then this result is updated to the next one. With these sequential operations, the final frequency equation of the multidelaminated beams is obtained for both end boundary conditions of the global beam. The numerical results for the beams are compared with those of finite element analysis to give the reliance on the proposed model and to investigate the effects of the shape, number, and size of multidelaminations on the natural frequency. It was shown that the variations in the natural frequency for the multidelaminated beams were significantly affected by the delamination length.     

Nonlinear Zigzag Theory for Buckling of Hybrid Piezoelectric Rectangular Beams under Electrothermomechanical Loads

A new efficient electromechanically coupled geometrically nonlinear (of von Karman type) zigzag theory is developed for buckling analysis of hybrid piezoelectric beams, under electrothermomechanical loads. The thermal and potential fields are approximated as piecewise linear in sublayers. The deflection is approximated as piecewise quadratic to explicitly account for the transverse normal strain due to thermal and electric fields. The longitudinal displacement is approximated as a combination of third order global variation and a layerwise linear variation. The shear continuity conditions at the layer interfaces and the shear traction-free conditions at the top and bottom are used to formulate the theory in terms of three primary displacement variables. The governing coupled nonlinear field equations and boundary conditions are derived using a variational principle. Analytical solutions for buckling of symmetrically laminated simply supported beams under electrothermal loads are obtained for comparing the results with the available exact two-dimensional (2D) piezothermoelasticity solution. The comparison establishes that the present results are in excellent agreement with the 2D solution which neglects the prebuckling transverse strain effect.     

New Approach for Seismic Nonlinear Analysis of Inelastic Framed Structures

A novel approach for seismic nonlinear analysis of inelastic framed structures is presented in this paper. The nonlinear analysis refers to the evaluation of structural response considering P-delta effect, which is in the form of geometric nonlinearity, and inelastic behavior refers to material nonlinearity. This novel approach uses finite element formulation to derive the elemental stiffness matrices, particularly to derive the geometric stiffness matrix in a general form. At the same time, this approach separates the inelastic displacement from total deflection of the structure by applying two additional constant matrices, namely, the force–recovery matrix and the moment-restoring matrix in the force analogy method. The benefit behind this treatment is explicitly locating and calculating the inelastic response, together with strategically separating the coupling effect between the material nonlinearity and geometric nonlinearity, during the time history analysis. Comparison with the traditional incremental methods shows that the proposed method is very time efficient as well as straightforward. One portal frame and one five-story frame are used as numerical examples to illustrate and verify the robustness of current approach.     

Ductility and Cracking Behavior of Prestressed Concrete Beams Strengthened with Prestressed CFRP Sheets

This paper investigates the flexure of prestressed concrete beams strengthened with prestressed carbon fiber-reinforced polymer (CFRP) sheets, focusing on ductility and cracking behavior. Structural ductility of a beam strengthened with CFRP sheets is critical, considering the abrupt and brittle failure of CFRP sheets themselves. Cracking may also affect serviceability of a strengthened beam, and may be especially important for durability. Midscale prestressed concrete beams (L = 3.6?m) are constructed and a significant loss of prestress is simulated by reducing the reinforcement ratio to observe the strengthening effects. A nonlinear iterative analytical model, including tension of concrete, is developed and a nonlinear finite-element analysis is conducted to predict the flexural behavior of tested beams. The prestressed CFRP sheets result in less localized damage in the strengthened beam and the level of the prestress in the sheets significantly contributes to the ductility and cracking behavior of the strengthened beams. Consequently, the recommended level of prestress to the CFRP sheets is 20% of the ultimate design strain with adequate anchorages.     

3D Coordinating Relations between Steel Cables and Concrete of Prestressed Concrete Beam Bridges

Interaction between steel cables and concrete is complicated in prestressed concrete bridges, especially in curved prestressed concrete bridges. The most significant behavior of curved beam bridges under the loads is that, at the same time of vertical flexure, torsion occurs on the cross section, which complicates the mechanical analysis to curved beam bridges. Based on coordinating relations of steel cables and concrete (CRSC), the grillage structure finite-element method was adopted to analyze the spatial effect of curved beam bridges. This way, the effect of all prestressing procedures can be simulated properly, including the prestressing loss due to concrete shrinkage and creep, batch prestressing of the cables, etc. Furthermore, it is effective to analyze the integrated behavior of the combined steel cables space out and concrete. The efficiency and reliability of the CRSC method is demonstrated by our analysis system WXQ2.0 developed for curved-skew bridges.     

Analysis of Snap-Back Instability due to End-Plate Debonding in Strengthened Beams

The problem of end-plate debonding of the external reinforcement in strengthened concrete beams is analyzed in this paper. As experimentally observed, this mode of failure is highly brittle and poses severe limitations to the efficacy of the strengthening technique. A numerical analysis of the full-range behavior of strengthened beams in bending is herein proposed to study the stages of nucleation and propagation of interfacial cracks between the external reinforcement and the concrete substrate. This is achieved by modeling the nonlinear interface behavior according to a cohesive law accounting for Mode Mixity. The numerically obtained load versus midspan deflection curves for three- or four-point bending beams show that the process of end-plate debonding is the result of a snap-back instability, which is fully interpreted in the framework of the Catastrophe Theory. To capture the softening branch with positive slope, the interface crack-length control scheme is proposed in the numerical simulations. The results of a wide parametric study exploring the effect of the relative reinforcement length, the mechanical percentage of fiber-reinforced polymer sheets, the beam slenderness, and the ratio between Mode II and Mode I fracture energies are collected in useful diagrams. Finally, an experimental assessment of the proposed model completes the paper.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.     

Cohesive Interface Modeling of Debonding Failure in FRP Strengthened Beams

A theoretical model that incorporates the concept of the cohesive interface approach for the debonding analysis of reinforced concrete beams strengthened with externally bonded fiber reinforced polymer (FRP) strips is presented. The cohesive interface concept is adopted for modeling of the debonding process near the critical adhesive-concrete interface, whereas the adhesive layer itself is modeled as a two-dimensional elastic medium. Thus, the stress and deformation fields within the adhesive layer, the coupling between the shear and normal stresses and, especially, their influence on the tractions across the cohesive interface are taken into account. The nonlinear relations between the tractions and the displacement jumps across the cohesive interface are derived using a potential function and account for the peeling effects and for the coupling between the shear-slip and the peeling-separation laws. Numerical results that examine the capabilities of the model, provide insight into the stability characteristics of the debonding mechanism, and highlight some aspects of the debonding problem are presented. A summary and conclusions close the paper.     

Upper-Bound Solutions for Rigid-Plastic Beams and Plates of Large Deflections by Variation Principles

This paper demonstrates deriving upper-bound solutions of geometrically nonlinear problems for beams and plates from rigid perfectly plastic material by the principles of virtual work in general form and stationary of total energy. Presented noncomplicated examples justify that the first is more appropriate when a kinematically admissible displacement field is defined by several generalized displacements. The second can serve as effective means for comparison in accuracy solutions corresponding to different displacement fields playing the same role as the upper-bound theorem in the limit analysis. Procedures of the latter for obtaining upper-bound solutions mainly remain valid. Solutions for a beam and rectangular plate subjected to uniformly distributed load illustrate importance of taking into account transformation forms of displacements in loading process.     

Computer-Aided Model Generation for Nonlinear Structural Analysis Using a Structural Component Model Database

This paper presents an approach for efficiently building analytical models for nonlinear analysis. The objective has been achieved by establishing structural component model database by collecting various structural component models addressing various structural details. A common data structure and a relational database schema for storing structural component models were proposed in this study. The proposed structural component model database can serve as a decision supporting system for building nonlinear analytical models manually. In addition, the modeling information stored in this database can be presented in XML document format to be parsed and manipulated by computer system for generating nonlinear analytical model in file automatically. A school building database is used as a case study to show the feasibility of automatic modeling for nonlinear analysis using the proposed structural component database. A semiautomatic model generation system was developed to provide an efficient modeling process, which is in the manner of form filling and option selecting on web-based user interfaces, so that the model builder can focus on making engineering decisions. The modeling details are handled automatically by the proposed system based on user selection and setting.     

Nonlinear Analytical Solution for Cable Truss

In this technical note the nonlinear closed-form static solution of the suspended biconvex and biconcave cable trusses with unmovable, movable, or elastic yielding supports subjected to vertical distributed load applied over the entire span is presented. Irvine’s linearized forms of the deflection and the cable equations are modified because the effects of the nonlinear truss behavior needed to be incorporated in them. The concrete form of the system of two nonlinear cubic cable equations is derived and presented. From a solution of a nonlinear vertical equilibrium equation for a loaded cable truss, the additional vertical deflection is determined. The transformation analytical model serves to determine the response, i.e., horizontal components of cable forces and deflection of the geometrically nonlinear truss, due to the applied loading, considering effects of elastic deformations, temperature changes, and elastic supports. The deflection of asymmetric prestressed cable trusses has been compared with Irvine’s linear solution as well as the nonlinear finite element model results.     

Spatial Stability of Shear Deformable Nonsymmetric Thin-Walled Curved Beams: A Centroid-Shear Center Formulation

An improved shear deformable curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled stability analysis of thin-walled curved beams with nonsymmetric cross sections. For this, the displacement field is introduced considering the second order terms of semitangential rotations. Next the elastic strain energy is newly derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. Then the potential energy due to initial stress resultants is consistently derived with accurate calculation of the Wagner effect. Finally, equilibrium equations and force–deformation relations are obtained using a stationary condition of total potential energy. The closed-form solutions for in-plane and out-of-plane buckling of curved beams subjected to uniform compression and pure bending are newly derived. Additionally, finite-element procedures are developed by using curved beam elements with arbitrary thin-walled sections. In order to illustrate the accuracy and the practical usefulness of this study, closed-form and numerical solutions for spatial buckling are compared with results by available references and ABAQUS’ shell elements.     

Constitutive Model for Rockfill Materials and Determination of Material Constants

Two types of rockfill materials collected from seven sites are modeled and tested under triaxial loading. A constitutive model based on a disturbed state concept is used to characterize the behavior of modeled rockfill materials. The model is shown to provide satisfactory prediction of the observed behavior of the modeled materials. Characteristics of the particles of the rockfill materials are determined. Relationships are developed between the material constants of the modeled rockfill materials and the characteristics of the particles and these are used to predict the material constants for the prototype size rockfill materials.     

Application of Differential Operator with Servo-Order Function in Model of Viscoelastic Deformation Process

The aim of the present paper is the application of a differential operator of variable order in constitutive relations for viscoelastic material. The dependence of the order function on the strain and strain rate is evaluated on the basis of known experimental results on deformation of polymeric materials. Established dependences are used for studying the vibrations of a 1-degree-of-freedom oscillator, in which the viscoelastic deformation is governed by a servo order function.