Rehabilitation of Cracked and Corroded Reinforced Concrete Beams with Fiber-Reinforced Plastic Patches

The behavior under static loading of fiber-reinforced plastic (FRP) retrofitted reinforced concrete beams, possessing a high chloride content and rebar corrosion, was studied both experimentally and analytically. The test beams were characterized as falling into three different groups according to the state of their corrosion damage: (1) natural corrosion, (2) cathodic protection, and (3) accelerated corrosion. The load carrying capacities of the beams, with or without FRP patching, were tested in the laboratory. The experimental results show that the state of corrosion of the steel, the water/cement ratio of the concrete material, and the arrangement and the number of FRP patches all affect the strength as well as the failure mechanisms of retrofitted RC beams. Some simple analytical models and a design concept for retrofitting cracked and corroded RC beams with FRP sheets are also presented and discussed.     

Role of Fiber Reinforced Plastic Sheets in Shear Response of Reinforced Concrete Beams: Experimental and Analytical Results

The paper is principally aimed at analyzing the role of externally applied fiber reinforced plastic (FRP) sheets in the shear ultimate behavior of reinforced concrete elements. A theoretical model for predicting the shear resisting contribution of FRP sheets is illustrated. The proposal is based on a complete equilibrium/compatibility approach for reinforced concrete beams failing in shear and considers the possible interactions between the composite contribution and the resisting mechanisms of an ordinary reinforced concrete beam. The proposal is discussed and tested by means of an experimental investigation carried out on beams reinforced by glass FRP composite sheets with a shear span to depth ratio equal to 3. Further comparisons are then performed that consider the predictions of other existing approaches reported in the literature.     

Identification of Cracking in Beam Structures Using Timoshenko and Euler Formulations

Timoshenko and Euler beam formulations, using energy approach, have been used to estimate the influence of crack size and location on the natural frequencies of cracked beams. Fracture mechanics approach has been used to consider the effect of cracking on the dynamic response of the beam. Galerkin’s approach has been used to solve the problem numerically. It is shown that for slender beams the deep beam influence is felt only when the [(basic?bending?length)/h] ratio of the fundamental sinusoid of a beam becomes very small for higher modes. When the (l/h) ratio becomes small (<10), the influence of shear rotation and rotary inertia effects become dominant; the inclusion of these effects makes the beam less stiff than a Euler beam. The crack influence on Euler and Timoshenko beams are similar for beams with l/h>10; but when l/h<10, the results of cracked Euler and Timoshenko beams slowly become different and diverge. The frequency contour method identifies the crack size and location properly, using the lower order frequencies. When structural symmetry gives an ambiguity regarding the crack location, the vibration behavior of the same beam with an asymmetrically placed mass, in conjunction with the frequency contour method, would uniquely identify the crack size and location.     

Effect of z-Pins on Fracture in Composite Cocured Double Cantilever Beams

The paper illustrates a new approach to the evaluation of the effect of z-pins on deformations and the strain energy release rate in composite double cantilever beams (DCB) subject to a standard fracture toughness test. The effect of z-pins is modeled by an elastic foundation, based on previously published work. The approach to the solution is based on a separate analysis of the intact and delaminated parts of DCB. The rotational stiffness of the intact part is obtained from the Rayleigh-Ritz solution for this part subjected to a force couple, rather than modeling the rotational restraint by introducing an elastic foundation, as has been done in the previous studies. Subsequently, the deformation of the delaminated part of DCB is analyzed exactly by solving the equation of equilibrium with the appropriate boundary conditions. Based on this solution, the compliance, the rate of change of compliance, and the strain energy of the specimen can be evaluated. The results illustrate the beneficial effect of z-pins on the resistance of DCB to delamination cracking.     

Carbon-Fiber-Reinforced Polymer Repair to Extend Service Life of Corroded Reinforced Concrete Beams

This paper presents the results of an experimental study designed to investigate the viability of using externally bonded carbon-fiber-reinforced polymer (CFRP) laminates to extend the service life of corroded reinforced concrete (RC) beams. A total of 14 beams, 152×254×3,200?mm each, were tested. Three beams were not corroded; two of them were strengthened by CFRP laminates, while one specimen was kept as a virgin. The remaining 11 beams were subjected to different levels of corrosion damage up to a 31% steel mass loss using an impressed current technique. Six of the corroded beams were repaired with CFRP laminates, whereas the remaining five beams were not repaired. Eventually, all specimens were tested to failure under four-point bending. Corrosion of the steel reinforcement significantly reduced the load-carrying capacity of RC beams. At all levels of corrosion damage, CFRP repair increased the ultimate strengths of the corroded beams to levels higher than the strength of the virgin beam but significantly reduced the deflection capacity.     

Unilateral Contact Problem for Aging Viscoelastic Beams

The frictionless unilateral contact problem of a viscoelastic Bernoulli–Euler beam resting on a viscoelastic soil is studied. The mathematical formulation involves equilibrium equations, compatibility equations, and constitutive laws, with an aging integral-type form. The unilateral nature of the contact is imposed through a compatibility inequality, which allows the determination of the contact imprint at each time. Further, the governing integro-differential equation for the unknown contact pressure is derived. As special cases, the elastic Winkler-type soil and the rigid soil conditions are discussed. A numerical approach is presented, which employs the finite difference method along space and an adaptive step-by-step algorithm along time. The procedure allows for time discontinuities of both external loads and contact pressure. Several selected numerical examples are presented and the influence of the most important material and geometrical parameters are shown. For the simplest situations, it was possible to compare the results obtained with known analytical solutions.     

Generalized Damped Wave Approach for Evaluating Seismic Shear Demands

This paper presents a new analytical approach for simple and explicit computation of the seismic base shear demand of structural systems that can be idealized by a uniform shear-beam model. The approach is based on a Green’s function representation for the relative displacement response that is assumed to be composed of exponentially decaying wave sequences. Explicit solutions for both the strain and displacement response are derived in terms of an effective ground velocity and displacement that can be computed incrementally from the ground acceleration. A physical interpretation for the damping mechanism is proposed. The method is further generalized to form a class of physically motivated shear-beam systems referred to as the continuous spring-dashpot (CSD) model. The response characteristics of three cases of the CSD model along with a shear beam equipped with a mass-proportional external damping are compared and discussed for the case of near-field earthquake excitation.     

钢-混凝土组合梁挠度研究发展概述

文章较为系统地分别阐述了钢-混凝土组合梁挠度在国内和国外的研究进程和发展状况,列举了一些具有代表性的重要理论与公式,并将各种理论的优缺点进行了分析评述,同时提出了有关组合梁挠度计算的值得进一步研究的问题。     

Lateral buckling strengths of cold-formed Z-section beams

This paper is concerned with the inelastic lateral buckling strengths of cold-formed Z-section (CFZ) beams. The point symmetry of the cross-section of a CFZ beam introduces characteristics that are not encountered in a doubly symmetric I-beam. Firstly, the effective section rotates after yielding, so that a CFZ beam under in-plane bending about the geometrical major principal axis is subjected to bending moments about the effective minor axis and bimoments. Secondly, the minor axis bending and warping strain distributions and therefore the lateral inelastic buckling behaviour and strengths of CFZ beams are related to the twist rotation and minor axis displacement directions. The stress–strain curves, residual stresses, initial imperfections, and lipped flanges of CFZ beams are all different to those of hot-rolled I-beams. This paper develops a realistic finite element model for the analysis of CFZ beams and uses it to investigate the elastic lateral-distortional buckling, inelastic behaviour, and strengths of CFZ beams with residual stresses and initial imperfections. The results of the study are used to develop improved design rules which are suitable for CFZ beams. The effects of moment distribution and load height on the lateral buckling strengths are also studied.     

Distortional theory of thin-walled beams

The classic thin-walled beam theory for open and closed cross-sections is generalized to include one distortional mode of deformation. Distortional cross-section parameters are introduced and the new orthogonality conditions for uncoupling of the axial displacement modes are given. A normalization technique for the distortional modes leads to unique distortional cross-section properties. The theoretical formulations for torsion and distortion are nearly similar and result in nearly identical equilibrium equations. However, for closed single- or multi-cell cross-sections the torsional and distortional shear flows may couple. A study of the order of magnitude of the governing torsional and distortional parameters shows the difference between open and closed cross-sections and the related solution types. The difference in the order of magnitude of the governing cross-section parameters also leads to approximate solution techniques. In the examples, section three cross-sections are used to illustrate variations of the theoretical parameters.