RC two-way slabs strengthened with CFRP strips: experimental study and a limit analysis approach

This paper deals with strengthening of reinforced concrete (RC) two-way slabs with carbon fibre reinforced plastic (CFRP) strips bonded to the tensile face. The first part deals with an experimental study. The fibre reinforced plastics (FRP) strengthened slab test presents a failure mode with debonding of the external FRP strips from the slab. The second part deals with a limit analysis modelling. The strengthened slab is designed as a three-layered plate. A simplified laminated plate model is used to describe the behaviour of three-layered plate supported in four sides, which is subjected to a load in the centre. The upper bound theorem of limit analysis is used to approximate the ultimate load capacity and identify the different collapse mechanisms. Experimental results are compared with theoretical predictions.     

四边简支钢筋混凝土矩形薄板的热屈曲

基于刚性板和小挠度理论,考虑混凝土的材料非线性,推导了热载作用下钢筋混凝土矩形薄板的平衡方程和稳定方程。给出了四边简支钢筋混凝土矩形薄板在横向变温和温度均匀变化时临界屈曲温度变化的封闭解,并对工程中常见的钢筋混凝土矩形薄板在温度均匀变化时的临界屈曲温度变化进行了计算,讨论了板的材料常数、长宽比和相对厚度对临界屈曲温度变化的影响,从而为工程结构中钢筋混凝土矩形薄板的临界屈曲温度变化的计算提供了理论计算依据。     

Use of laminated mechanical joints with metal and concrete plates for precast concrete columns

This study investigated the structural behavior of a mechanical joint with laminated concrete and metal plates for moment connections which can be used for the rapid erection of reinforced concrete precast columns. A concrete filler plate was placed between the metal column plates to transfer loads and protect nuts threaded with rebars. Nonlinear numerical finite element analyses considering concrete damaged plasticity was also performed to evaluate the load–displacement relationship, plate deformation of the joints with concrete filler plates, and rates of strain increase of the structural components. The influence of the column and concrete filler plates on the rate of strain increase of the structural components attached to the column plates was explored to determine how concrete, rebars, and steel sections, were activated relative to the stiffness of the metal plates. The strain values of structural elements that were attached to plates with sufficient stiffness values were found to be higher than those of the structural elements that were attached to plates with smaller stiffness values. These strains were evident in the nonlinear finite element analyses and experimental investigations. It can be inferred that laminated mechanical plates consisting of metal and concrete plates can be implemented and used to replace conventional precast connections.     

粘贴钢板加固钢筋混凝土梁的分离式有限元模型

提出了外粘钢板加固受弯钢筋混凝土梁的非线性有限元模型。该模型中采用了一种特殊的、具有剥离破坏功能的界面单元来模拟混凝土梁和外粘钢板之间的粘结层,这种剥离破坏主要发生在粘贴钢板端部区域和弯曲、剪切裂缝附近。影响这种剥离破坏的主要因素有两个:一是粘贴钢板的端部与加固梁支座距离;二是粘贴钢板的厚度。传统的梁理论不能描述这种加固梁破坏模式,采用有限元方法能全方位地描述这种加固梁的各种性状和破坏模式。数值计算结果与粘贴不同厚度钢板加固梁的试验结果相吻合。     

钢筋混凝土矩形薄板徐变效应分析

基于弹性薄板理论和按龄期调整的有效模量法思想,分析钢筋混凝土矩形薄板徐变效应,建立了考虑混凝土徐变和钢筋约束影响的时变弹性曲面微分方程,并给出了四边简支和四边夹支的钢筋混凝土矩形薄板的徐变效应计算公式,可方便求解任意时刻薄板挠度和混凝土、钢筋的应力.     

Unilateral buckling of elastically restrained rectangular mild steel plates

 This paper considers the elastic unilateral buckling of rectangular mild steel plates that are restrained elastically and subjected to bending and axial actions. A variational formulation of the Ritz method using linear combinations of harmonic functions for the buckling deformations is used to establish an eigenproblem to determine the plate local buckling coefficients. The motivation for the study is the retrofit of reinforced concrete beams by gluing and then bolting steel plates to the sides of the beam. Such plates, when acting compositely with the concrete beam, are subjected to predominantly bending and axial actions which may cause unilateral local buckling. Whereas the bolts provide complete restraint against buckling at discrete points, the glue may also inhibit local buckling between these nodal points since it acts as a continuous elastic restraint. The influence of the glue stiffness, support conditions and plate proportions on the unilateral buckling of such plates are assessed.     

Propagation of Iamb waves in adhesively bonded multilayered media

The effect of introducing attenuation on Lamb wave dispersion curves is studied in this paper. Attenuation is introduced to a three-layered composite plate by an adhesive bond layer with viscous behavior. No changes are required to the transfer matrix formulation for the propagation of elastic waves. By introduction of a complex wavenumber, the model can be used to the propagation of attenuative Lamb waves. Numerical examples for a three-layered aluminium-epoxy-aluminium plate show that attenuation values of each mode in plates are related not only to attenuation, but also to the thickness of the bonded layer, which is in agreement with practical situations.     

Prediction of the behavior of RC Beams Strengthened with FRP Plates

Epoxy-bonding a composite plate to the tension face is an effective technique to repair reinforced concrete beams since it increases their strength and rigidity. In this paper, the structural behavior of reinforced concrete beams with fibre reinforced polymer (FRP) plates is studied numerically. For it, a numerical damage model is used in order to predict their strength, stiffness and failure modes observed in experimental tests taking into account the influence of different variables such as the amount of steel reinforcement, the type and amount of external reinforcement, the plate length, etc. The consideration of concrete cracking and the yielding of the steel rebars allows to predict in a realistic way the behavior of the strengthened beams and especially the debonding failure mode. In that sense both end and midspan debond can be represented since the model is able to reproduce the tension stiffening phenomenon.     

Static strength tests of steel plate strengthened concrete beams

The behaviour of damaged concrete beams strengthened by externally bonded steel plates is experimentally investigated. The study includes an investigation of the mode of failure, including flexural failure and the interface separation of the steel plate. Simply supported beams under monotonically increasing loads are considered exclusively. A total of five plain concrete beams externally reinforced with bonded steel plates were tested under static loads to determine their strength and behaviour. The variables tested were the thickness of the external steel plate, length and location of the interfacial crack, and the degree of surface preparation of the steel plate. In all five beams the thickness of adhesive was kept constant. The results indicate that (i) the behaviour of a damaged open sandwich beam is similar to that of a singly reinforced concrete beam when no debonding occurs between the concrete and the adherent steel plate; (ii) when debonding occurs, the failure is sudden and at loads smaller than for a case where failure is either by yielding of steel or crushing of concrete; (iii) the case with an interfacial crack between the steel and the adhesive is more critical than the case when the interfacial crack is between the adhesive and the concrete; and (iv) the failure load and the mode of failure are dependent on the degree of surface preparation of the steel plate. Analytical investigation to predict the interfacial debonding is summarized, and the results suggest that linear elastic fracture mechanics is suited for predicting the failure load for open sandwich beams which fail by interface debonding.     

不同参数下低屈服点钢剪切板耗能元件受力性能试验研究

低屈服点钢剪切板耗能元件具有良好的耗能能力,可以消耗输入结构中的大部分地震能量,改善和提高结构的抗震性能。为了考察面外初始缺陷对低屈服点钢剪切板耗能元件屈曲后稳定性的影响,开展了1个传统工字钢耗能元件和3个具有面外初始缺陷的低屈服点钢剪切板耗能元件的低周往复循环荷载试验,重点考察了面外初始缺陷、耗能元件宽厚比和钢筋混凝土约束板对其受力性能的影响。研究结果表明:面外初始缺陷对剪切板的受力性能影响较大,钢筋混凝土约束板可有效抑制剪切板的面外局部屈曲变形,翼缘板可有效抑制剪切板的整体扭转屈曲变形,从而提高剪切板耗能元件的耗能能力。     

低配网率纤维编织网增强混凝土轴拉力学性能

通过单束纤维与纤维编织网增强混凝土(Textile reinforced concrete, TRC)薄板的单轴拉伸试验, 研究了纤维编织网增强混凝土这种新型材料的受力特征和影响其极限承载力的主要因素, 提出临界配网率的概念。以配网率为变化参数, 讨论了在低配网率(配网率小于1%)时材料的力学性能。当配网率大于临界配网率时, 纤维编织网增强混凝土薄板的极限承载力大于其开裂荷载, 加载过程中没有承载力突降; 随着配网率增加, 纤维的利用率随着配网率增加呈线性降低, 即纤维丝的强度并不能完全发挥。低配网率时, 随着配网率增加, 薄板的裂缝间距减小, 裂缝宽度下降。根据混合定律和ACK模型把TRC薄板的拉伸应力-应变曲线简化成三线型模型, 从宏观上提出了考虑配网率影响的极限承载力计算公式。      

Interfacial shear stress in FRP-plated RC beams under symmetric loads

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre-reinforced polymer (FRP) plates to their soffits. An important failure mode of such plated beams is debonding of the FRP plates from the concrete due to high level interfacial stresses near the plate ends. A closed-form rigorous solution for the interfacial stresses in simply supported beams bonded with thin plates and subjected to arbitrary loads has been found, in which a non-uniform stress distribution in the adhesive layer was taken into account. This paper uses the rigorous solution to investigate the impact of symmetric loading configurations on the interfacial shear stress distributions, and concludes that the bending moments on the cross sections at the plate ends play a significant role in terms of stress concentration, while the shear forces on the same cross-section contribute little to the concentration. On the basis of this observation, this paper proposes a simplified approximate solution to the shear stress along the interface between concrete and adhesive layer. Compared with the rigorous and other approximate solutions, the simplified solution exhibits sufficient accuracy in terms of stress distribution and stress concentration localized near the plate ends. Due to its compact feature, the simplified solution is more suitable for engineering applications using a portable calculator and to be adopted in the codes of practices.     

钢筋混凝土板裂缝开展角的计算方法

本文研究了钢筋混凝土板固定角（α２）、裂缝开展角（α＇）、转动角（α）和钢筋角（αｓ）之间的关系,建立了钢筋混凝土板的平衡方程、协调方程以及钢筋和混凝土的本构方程,提出了钢筋混凝土板裂缝开展角的计算方法．通过两块板的计算结果与试验结果的比较,本文提出ｒ计算方法的可靠性得到了验证．     

Vibration and damping analysis of a three-layered composite annular plate with a viscoelastic mid-layer

The natural frequencies and modal loss factors of the three-layered annular plate with a viscoelastic core layer and two polar orthotropic laminated face layers are considered. The discrete layer annular finite element is employed to derive the equations of motion for the three-layered annular plate. The viscoelastic material in the central layer is assumed to be incompressible, and the extensional and shear moduli are described by the complex quantities. Complex eigenvalued problems are then solved, and the frequencies and modal loss factors of the composite plate are extracted. The results of the symmetric and non-symmetric composite annular plates are both presented. The effects of material properties, radius to thickness ratio, stacking sequences and thickness of face layers, and thickness of the viscoelastic core layer are discussed.     

Interface stress redistribution in FRP-strengthened reinforced concrete beams using a three-parameter viscoelastic foundation model

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP–concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP–concrete interface can lead to the FRP debonding from the concrete beam. In this study, a novel analytical solution has been developed to predict the interface stress redistribution of FRP-strengthened reinforced concrete beams induced by the viscoelastic adhesive layer. Both the FRP plate and the RC beam are modeled as Timoshenko’s beams, connected through the adhesive layer. The adhesive layer is modeled as a three-parameter viscoelastic foundation (3PVF) using Standard Linear Solid model. The 3PVF model satisfies the equilibrium equation of the adhesive layer and the zero shear-stress boundary condition at the free edge. Closed-form expressions of the time-dependent interface stresses and deflection of the beam are obtained using Laplace transform. Finite element analysis is also conducted to verify the analytical solution using a subroutine UMAT based on the Standard Linear Solid model. Numerical results suggest that the stress concentrations within the FRP–concrete interface relax with time. The axial force in the FRP plate also reduces with time due to the creep of the adhesive layer. However, this relaxation is limited to a small zone close to the end of the FPR plate.     

Numerical analysis of square reinforced concrete plates strengthened by fiber-reinforced plastics with various patterns

Abaqus finite element program is employed to analyze the ultimate load capacities of square reinforced concrete plates strengthened by fiber-reinforced plastics. Appropriate constitutive models are introduced and validated to stimulate nonlinear material behavior of reinforced concrete and fiber-reinforced plastics. The influences of FRP reinforcement, steel reinforcement, and concrete properties on the ultimate strengths of the reinforced concrete plates are investigated. Finally, based on the numerical results, empirical equations are proposed to predict increment of ultimate load capacities of the square reinforced concrete plates strengthened by fiber-reinforced plastics, which would be useful for practical engineering applications.     

Dynamic stability of three-layered annular plates with wavy forms of buckling

The solution to the dynamic stability problem of the three-layered, annular plate with wavy, asymmetric forms of buckling is presented in this paper. The geometric nonlinearity of plate subjected to the linear lateral load increasing in time is considered. The approximate, finite difference method is used in the numeric solution to the formulated stability problem. The critical parameters characterizing the loss of plate stability and plate supercritical behavior depending on the material, geometrical and loading parameters are evaluated. The results of the critical loads of plates with asymmetric forms of critical deformation are analyzed in detail. The significant qualitative and quantitative differences of results obtained for plates with axisymmetric and asymmetric buckling form confirm the rightness of the analysis of the stability plate problem for the general solution without the limitation to the observation of the regular, axially symmetrical forms of deformation only.     

Fatigue behaviour of CFRP L-shaped plates for shear strengthening of RC T-beams

Prefabricated carbon fibre reinforced plastic (CFRP) L-shaped plates can be used to shear strengthen reinforced concrete (RC) T-beams. Previous investigations by EMPA have shown the suitability of the CFRP L-shaped plates for static shear strengthening.In this paper, a large-scale fatigue test is presented which demonstrated the suitability of the CFRP L-shaped plates for shear strengthening of RC T-beams for fatigue reasons. The test beam was subjected to 5 million load cycles at a high load level and a subsequent failure test. Its behaviour is compared with that of a similar, statically tested beam. A fatigue design proposal is presented for users of the CFRP L-shaped plates.     

Interfacial shear stress concentration in FRP-strengthened beams

This paper reports the results of an experimental programme designed to study the interfacial shear stress concentration at the plate curtailment of reinforced concrete (RC) beams strengthened in flexure with externally bonded carbon fibre-reinforced polymer (CFRP). Specifically, the study looks at the relationship between the CFRP plate thickness and the interfacial shear stress concentration at the plate curtailment, the failure modes of the CFRP-strengthened beams as well as the efficiency of the CFRP external reinforcing system. Comparing the experimental results with existing models' predictions is another objective of this study. The experimental programme included five RC beams 115 mm×150 mm in cross-section and 1500 mm in length. Four of the RC beams were reinforced externally with CFRP plates of different thicknesses. Tests in this study showed that the thickness of CFRP plate affects not only the load-carrying and deflection capacities of the strengthened beam, but also the shear stress concentration at the CFRP/concrete interface and the beam failure mode.     

Flexural behavior of steel beams strengthened by carbon fiber reinforced polymer plates – Three dimensional finite element simulation

Debonding, as a mode of failure, is one of the major limitations when using externally bonded carbon fiber reinforced polymer (CFRP) plates in strengthening of steel beams. In this work, mode of failure and flexural behavior of both steel and steel–concrete composite beams strengthened by different lengths of CFRP plates were numerically investigated. The effect of both splicing position (at mid-span and near supports) and CFRP plate ends configuration were studied. Three dimensional finite element analysis (3D FEA) was adopted to simulate the nonlinear behavior of these beams loaded under four point bending configuration. The present numerical analysis assisted by previously valuable experimental results found in the literature succeeded to predict the critical CFRP plate length at which, full efficiency of the adhesively bonded plate is achieved.