Long-Term Behavior of Prestressed Old-New Concrete Composite Beams

This paper presents both theoretical and experimental studies of the long-term behavior of prestressed old-new concrete composite beams under sustained loads. General differential equations governing the relationship between the incremental deflection and incremental internal forces of the composite beams were deduced in the theoretical study. Closed-form solutions for simply supported composite beams were obtained and validated using test results reported in previous literature on steel-concrete composite beams. The experimental investigation consisted of static long-term load tests carried out on four prestressed old-new concrete composite beams. The behavior of the old-to-new concrete interface, time-dependent deflections, concrete strains, and prestress losses was carefully observed over 260?days. The long-term test program showed that the midspan deflections and concrete strains increased with time because of creep and shrinkage of the new prestressed concrete. The slip strains at the old-to-new concrete interface were found to be relatively small, indicating that the interface bond was sound enough to prevent slip and that the prestressing loads were effectively transferred to the old concrete. The proposed theoretical models predicted the long-term behavior of the prestressed old-new concrete composite beams with an acceptable degree of accuracy.     

Preflex Beams: A Method of Calculation of Creep and Shrinkage Effects

This paper presents a method of calculation of creep and shrinkage effects for composite beams. It is particularly applicable to Preflex and Flexstress beams, which are composed of a steel I-girder with the bottom flange encased by concrete. The concrete is prestressed by predeflection of the steel beam and the subsequent release after hardening of the concrete flange or by means of prestressing cables. The presented approach using concrete age-adjusted modular ratios allows the calculation of time-dependent stresses in the concrete flange due to creep and shrinkage, with sufficient accuracy for practical applications and without carrying out cumbersome numerical computations. The results can be extended directly to the analysis of ordinary steel–concrete composite beams. The main goal of the present paper is the calibration of the parameters which must be introduced to simplify the equations describing the system. This calibration is discussed and its sensitivity to some calculation inputs is presented. The conclusions are very encouraging and the simplified approach seems to agree very well with the results of the numerical approach.     

Block FEM for Time-Dependent Shear-Lag Behavior in Two I-Girder Composite Bridges

This paper presents a time-dependent finite-element analysis of a two I-girder composite bridge with a concrete slab. The creep and shrinkage of the concrete slab are considered as sources of time-dependent behavior. This analysis, unlike others, includes the shear-lag effect of the concrete slab on the time-dependent behavior of two I-girder bridges. An example calculation is given for a two-span continuous composite bridge with a cracking region in the concrete deck near the interior support. It is shown that the shear-lag effect becomes significant at the edge of the cracking region and at the bridge ends.     

Fatigue Strength of Repaired Prestressed Composite Beams

Composite steel-concrete bridges constitute a major portion of the national bridge inventory. Many of these structures are approaching or have passed their service lives and are in need of repair and rehabilitation. External prestressing by means of high-strength bars or cables attached to the steel beams has been used as an effective technique for upgrading the load carrying capacity of composite steel-concrete girders. While several researchers have investigated the static behavior of prestressed composite beams, few have reported on the fatigue strength of this structural system. The writers present the results of the experimental and analytical study of ten composite girders that were prestressed with seven-wire strands and then fatigue tested to failure. Three methods of extending the fatigue life of cracks were then explored: (1) drilling a hole at the crack tip and installing a high-strength bolt; (2) splicing the web at the cracked section; and (3) increasing the prestressing force of the tendon. The efficacy of the three methods is compared.     

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.     

Time-Dependent Behavior of RC Beams Retrofitted with CFRP Straps

A retrofitting technique that uses prestressed unbonded carbon-fiber-reinforced polymer (CFRP) straps to provide additional shear capacity has previously been shown to be successful under short-term static loading conditions. The current study explores the longer-term behavior of this retrofitting technique through two experiments (a sustained load and a cyclic load experiment) and the development of a model based on the modified compression field theory. The experiments indicated that the strain in the CFRP straps changes with time due to changes in the load sharing with the concrete (caused by creep) and the steel stirrups (caused by yield of these elements). The predictive model was initially validated against static experimental results before being applied to the longer-term experiments. The model predicts the trends in behavior well although it is conservative in its estimates of strap strain. The model was then used to determine the influence of stirrup yielding, the load level before and after retrofitting, and the duration of loading on the CFRP strap strains. The initial results suggest that the largest increases in long-term strap strain will occur when the straps are installed early in the structure’s service life although further experimental validation is required.     

Flexural Behavior of Continuous GFRP Reinforced Concrete Beams

The results of testing two simply and three continuously supported concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars are presented. The amount of GFRP reinforcement was the main parameter investigated. Over and under GFRP reinforcements were applied for the simply supported concrete beams. Three different GFRP reinforcement combinations of over and under reinforcement ratios were used for the top and bottom layers of the continuous concrete beams tested. A concrete continuous beam reinforced with steel bars was also tested for comparison purposes. The experimental results revealed that over-reinforcing the bottom layer of either the simply or continuously supported GFRP beams is a key factor in controlling the width and propagation of cracks, enhancing the load capacity, and reducing the deflection of such beams. Comparisons between experimental results and those obtained from simplified methods proposed by the ACI 440 Committee show that ACI 440.1R-06 equations can reasonably predict the load capacity and deflection of the simply and continuously supported GFRP reinforced concrete beams tested.     

Control of Creep and Shrinkage Effects in Steel Concrete Composite Bridges with Precast Decks

Creep and shrinkage in concrete deck of steel-concrete composite bridges can result in significant redistribution and consequent increase in bending moments at continuity supports and also increase in deflections. Studies are presented for the control of creep and shrinkage effects in steel-concrete composite bridges with precast concrete decks. A hybrid procedure recently developed by the authors has been used for carrying out the studies. The procedure accounts for creep, shrinkage and progressive cracking in concrete decks. Single span, three span and five span bridges have been analyzed for different thicknesses of concrete decks and grades of concrete. Both the shored and unshored constructions have been considered. It is shown that, for both constructions, the increase in bending moments and midspan deflections can be controlled to a significant degree, without putting constraints on design parameters, by simply delaying the time of mobilization of composite action between the precast concrete deck panels and the steel section. It is also observed that though the percentage change in bending moments due to creep and shrinkage is similar for shored and unshored constructions, the percentage change in midspan deflection is significantly higher for shored construction.     

Repair of Steel Composite Beams with Carbon Fiber-Reinforced Polymer Plates

One significant cause of deterioration of steel bridge structures is the corrosion due to extensive use of deicing salts in winter weather. The investigation presented in this paper focused on the behavior of steel composite beams damaged intentionally at their tension flange to simulate corrosion and then repaired with carbon fiber-reinforced polymer (CFRP) plates attached to their tension areas side. Damage to the beams was induced by removing part of the bottom flange, which was varied between no damage and loss of 75% of the bottom flange. All beams were tested to failure to observe their behavior in the elastic, inelastic, and ultimate states. To help implement this strengthening technique, a nonlinear analytical procedure was also developed to predict the behavior of the section/member in the elastic, inelastic, and ultimate states. The test results showed a significant increase in the strength and stiffness of the repaired beams. Through the use of CFRP plates, all damaged beams were fully restored to their original (undamaged state) strength.     

Boundary-Layer Effect in Composite Beams with Interlayer Slip

An apparent analytical peculiarity or paradox in the bending behavior of elastic-composite beams with interlayer slip, sandwich beams, or other similar problems subjected to boundary moments exists. For a fully composite beam subjected to such end moments, the partial composite model will render a nonvanishing uniform value for the normal force in the individual subelement. This is from a formal mathematical point of view in apparent contradiction with the boundary conditions, in which the normal force in the individual subelement usually is assumed to vanish at the extremity of the beam. This mathematical paradox can be explained with the concept of boundary layer. The bending of the partially composite beam expressed in dimensionless form depends only on one structural parameter related to the stiffness of the connection between the two subelements. An asymptotic method is used to characterize the normal force and the bending moment in the individual subelement to this dimensionless connection parameter. The outer expansion that is valid away from the boundary and the inner expansion valid within the layer adjacent to the boundary (beam extremity) are analytically given. The inner and outer expansions are matched by using Prandtl’s matching condition over a region located at the edge of the boundary layer. The thickness of the boundary layer is the inverse of the dimensionless connection parameter. Finite-element results confirm the analytical results and the sensitivity of the bending solution to the mesh density, especially in the edge zone with stress gradient. Finally, composite beams with interlayer slip can be treated in the same manner as nonlocal elastic beams. The fundamental differential equation appearing in the constitutive law associated with the partial-composite action in a nonlocal elasticity framework is discussed. Such an integral formulation of the constitutive equation encompassing the behavior of the whole of the beam allows the investigation of the mechanical problem with the boundary-element method.     

Local Delamination Buckling of Laminated Composite Beams Using Novel Joint Deformation Models

Local delamination buckling formulas for laminated composite beams are derived based on the rigid, semirigid, and flexible joint models with respect to three bilayer beam (i.e., conventional composite, shear-deformable bilayer, and interface-deformable bilayer, respectively) theories. Two local delamination buckling modes (i.e., sublayer delamination buckling and symmetrical delamination buckling) are analyzed and their critical buckling loads based on the three joint models are obtained. A numerical finite-element simulation is carried out to validate the accuracy of the formulas, and parametric studies of delamination length ratio, the transverse shear effect, and the influence of interface compliance are conducted to demonstrate the improvement of the flexible joint model compared to the rigid and semirigid joint models. The explicit local delamination buckling solutions developed in this study facilitate the design analysis and optimization of laminated composite structures and provide simplified and improved practical design equations and guidelines for buckling analyses.     

Displacement-Based and Two-Field Mixed Variational Formulations for Composite Beams with Shear Lag

Displacement-based and two-field mixed beam elements are proposed for the linear analysis of steel–concrete composite beams with shear lag and deformable shear connection. The kinematics of the shear lag relies on a parabolic shear warping function of uniform shape along the slab. These assumptions are verified by comparing a closed-form solution of the composite beam problem with the results provided by the ABAQUS code. Moreover, three displacement-based finite elements and two mixed elements where both variables, forces, and displacements are approximated within the elements are developed especially for very coarse discretizations. All models neglect uplift and consider shear connectors using distributed interface elements. Locking problems that arise in the 10 degrees-of-freedom (DOF) displacement-based element which ensures the lowest regularity required by the problem are detected. Then, a locking-free element which relies on a reduced integration and a scaling factor method is proposed and analyzed for fine mesh discretizations. Energy errors and convergence rates of the proposed elements are illustrated while numerical examples dealing with a fixed-end steel–concrete composite beam and a simply supported concrete Tee beam are considered to confirm the validity of the closed-form solution and illustrate the performance of the proposed elements, especially of the ones with 10 and 13 DOF.     

Multiscale Nonlinear Framework for the Long-Term Behavior of Layered Composite Structures

This paper presents an integrated micromechanical–structural framework for local–global nonlinear and time-dependent analysis of fiber reinforced polymer composite materials and structures. The proposed modeling approach involves nested multiscale micromodels for unidirectional and continuous filament mat (CFM) layers. In addition, a sublaminate model is used to provide a three-dimensional (3D) effective anisotropic and continuum response to represent the nonlinear viscoelastic behavior of a through-thickness periodical multilayered material system. The 3D multiscale material framework is integrated with a displacement-based finite-element code to perform structural analyses. The time-dependent responses in the unidirectional and CFM layers are exclusively attributed to their matrix constituents. The Schapery nonlinear viscoelastic model is used with a newly developed recursive–iterative integration method applied for the polymeric matrix. The fiber medium is linear and transversely isotropic. The in situ long-term response of the matrix constituents is calibrated and verified using long-term creep coupon tests. Good prediction ability is shown by the proposed framework for the overall viscoelastic behavior of the layered material. Material and geometric nonlinearities of I-shape thick composite columns, having vinylester resin reinforced with E-glass unidirectional (roving) and CFM layers, are studied to illustrate the capability of the multiscale material-structural framework. Nonlinear elastic behavior and creep collapse analyses of the I-shape column are performed. The recursive–iterative and stress correction algorithms, which are implemented and executed simultaneously at each material scale, enhance equilibrium and avoid misleading convergent states.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

Flexural Behavior of Concrete Beams Reinforced with Hybrid (GFRP and Steel) Bars

Reinforcing concrete with a combination of steel and glass fiber-reinforced polymer (GFRP) bars promises favorable strength, serviceability, and durability. To verify its promise and to support design of concrete structures with this hybrid type of reinforcement, we have experimentally and theoretically investigated the load-deflection behavior of concrete beams reinforced with hybrid GFRP and steel bars. Eight beams, including two control beams reinforced with only steel or only GFRP bars, were tested. The amount of reinforcement and the ratio of GFRP to steel were the main parameters investigated. Hybrid GFRP/steel-reinforced concrete beams with normal effective reinforcement ratios exhibited good ductility, serviceability, and load carrying capacity. Comparisons between the experimental results and the predictions from theoretical analysis showed that the models we adopted could adequately predict the load carrying capacity, deflection, and crack width of hybrid GFRP/steel-reinforced concrete beams.     

Simple Mechanical Model of Curved Beams by a 3D Approach

Starting from three-dimensional (3D) continuum mechanics, a simple one-dimensional model aimed at analyzing the whole static behavior of nonhomogeneous curved beams is proposed. The kinematics is described by four one-dimensional (unknown) functions representing radial, tangential, and out-of-plane displacements of the beam axis, which are due to flexures and extension, and the twist of the cross section due to torsion. The flexural and axial displacements fit with the classical Euler–Bernoulli beam theory of straight beams, and nonuniform torsion is also considered. The relevant elastogeometric parameters have been determined, and the system of governing equilibrium equations is obtained by means of the principle of minimum potential energy. Finally, the general theory is illustrated with examples.     

Flexural Behavior of Continuous FRP-Reinforced Concrete Beams

Continuous concrete beams are commonly used elements in structures such as parking garages and overpasses, which might be exposed to extreme weather conditions and the application of deicing salts. The use of the fiber-reinforced polymers (FRP) bars having no expansive corrosion product in these types of structures has become a viable alternative to steel bars to overcome the steel-corrosion problems. However, the ability of FRP materials to redistribute loads and moments in continuous beams is questionable due to the linear-elastic behavior of such materials up to failure. This paper presents the experimental results of four reinforced concrete beams with rectangular cross section of 200×300?mm continuous over two spans of 2,800 mm each. The material and the amount of longitudinal reinforcement were the main investigated parameters in this study. Two beams were reinforced with glass FRP (GFRP) bars in to different configurations while one beam was reinforced with carbon FRP bars. A steel-reinforced continuous concrete beam was also tested to compare the results. The experimental results showed that moment redistribution in FRP-reinforced continuous concrete beams is possible if the reinforcement configuration is chosen properly. Increasing the GFRP reinforcement at the midspan section compared to middle support section had positive effects on reducing midspan deflections and improving load capacity. The test results were compared to the available design models and FRP codes. It was concluded that the Canadian Standards Association Code (CSA/S806-02) could reasonably predict the failure load of the tested beams; however, it fails to predict the failure location.     

Composite Action and Adhesive Bond between Fiber-Reinforced Polymer Bridge Decks and Main Girders

This paper describes the behavior of hybrid girders consisting of fiber-reinforced polymer (FRP) bridge decks adhesively connected to steel main girders. Two large-scale girders were experimentally investigated at the serviceability and ultimate limit state as well as at failure. One of the girders was additionally fatigue loaded to 10 million cycles. Compared to the behavior of a reference steel girder, deflections of the two girders at the SLS were decreased by 30% and failure loads increased by 56% due to full composite action in the adhesive layer. A ductile failure mode occurred: Deck compression failure during yielding of the steel girder. The adhesive connections were able to prevent buckling of the yielding top steel flanges. Thus, compared to the reference steel girder, the maximum deflections at failure could be increased up to 130%. No deterioration due to fatigue loading was observed. Based on the experimental results, a conceptual design method for bonded FRP/steel girders was developed. The proposed method is based on the well-established design method for hybrid girders with concrete decks and shear stud connections. The necessary modifications are proposed.     

Determination of Nonlinear Softening Behavior at FRP Composite/Concrete Interface

For concrete beams and slabs, the bonding of fiber reinforced plastic (FRP) plates to the bottom surface is an effective and efficient technique for flexural strengthening. Failure of strengthened members often occurs due to stress concentrations at the FRP/concrete interface. For debonding failure initiated at the bottom of shear or shear/flexural cracks in the concrete, experimental results clearly indicate a progressive failure process accompanied by gradual reduction in shear transfer capability at the interface. Several existing models for FRP debonding have taken interfacial shear softening into account. However, the assumed shear stress versus slip relations employed in the models have never been properly measured. In this investigation, a combined experimental/theoretical approach for the extraction of interfacial stress versus slip relation is developed. With loading applied to a bonded FRP plate, strain is measured at various points along its length. Based on the strain measurements, the interfacial softening curve is derived from a finite element analysis. The present paper will present the proposed approach in detail, demonstrate its application to typical experimental data, and discuss the implications of the results.     

Flexural Behavior of GFRP-Reinforced Concrete Masonry Beams

An experimental and analytical study is conducted in order to investigate the flexural behavior of masonry beams that are internally reinforced using glass fiber-reinforced polymers (GFRP) rebars. Seven reinforced masonry beams with 4.0- and 2.4-m spans were tested under four-point bending setup. The beams were loaded monotonically up to failure. One had two courses of hollow concrete masonry units and the remaining six beams had three courses. Two masonry beams were reinforced using conventional steel rebars and were considered as the control specimens. The remaining five beams were internally reinforced using GFRP rods with different reinforcement ratios. Beams were detailed to have sufficient shear reinforcement such that they do not fail in shear. Flexural capacity, deformation, curvature, and strains of the tested GFRP-reinforced and steel-reinforced masonry beams were compared and discussed. Using the acquired data from the experimental and analytical studies, effectiveness of GFRP rods as internal reinforcement for concrete masonry beams is demonstrated.