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.     

FRP-strengthened RC beams under sustained loads and weathering

Glass FRP-strengthened RC beams were subjected to sustained loads and placed for different periods outdoors, indoors, and in chambers that accelerate the effects of outdoor tropical weathering by a factor of six. Beams subjected to outdoor weathering had up to 18% larger crack widths and 16% larger deflections compared to those kept indoors at the end of 1 and 2¾ years, respectively. The increase in deflections and crack widths was lesser for beams with a higher FRP reinforcement ratio. The residual flexural strength and ductility of the beams decreased with longer weathering periods. Also, the failure mode of the beams changed from concrete crushing to FRP rupture, indicating a deterioration in the mechanical properties of the FRP laminates. Analytical methods which account for material degradation in concrete and FRP laminates are presented and found to predict the long-term flexural characteristics of the beams well.     

Interfacial shear transfer of RC beams strengthened by bonded composite plates

In this paper an analytical method is proposed to predict the distributions of interfacial shear stress in concrete beams strengthened by composite plates. Non-linear behaviour of concrete under compression is considered in the analysis. The solutions show significant shear stress concentration near the cut-off end of plates. A parametrical study is carried out to show the effects of some design variables, e.g., thickness of adhesive layer, material properties and the distance from support to cut-off end of bonded plates.     

Collapse loads of cantilever beams under end shear

Summary Results ofOnat andShield and ofGreen on the collapse loads of symmetrically tapered cantilever beams under a uniformly distributed end shear are extended to cover the entire range of geometric parameters. Close bounds are obtained except for very short beams. In addition, the effect of a parabolic distribution of end shear upon the lower bound is investigated and found to be small. For large beams complete solutions are exhibited. Finally, an optimum design problem is considered: for fixed beam length and end load find the angle of taper which minimizes the weight. The minimum is always achieved for a taper angle (top and bottom) between zero and fifteen degrees.

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Traglast eines einseitig eingespannten, durch Querkraftverteilung, belasteten Balkens

Zusammenfassung Ergebnisse vonOnat undShield, sowie vonGreen, über die Traglast von symmetrisch sich verjüngenden, einseitig eingespannten Balken, die durch eine an ihrem Ende angreifende uniform verteilte Querkraft belastet sind, werden erweitert um den gesamten Bereich der geometrischen Parameter zu erfassen. Mit Ausnahme sehr kurzer Balken werden eng zusammenliegende Schranken erhalten. Zusätzlich wird der Einfluß einer parabolischen Verteilung der Querkraft untersucht und als klein befunden. Für den Fall sehr langer Balken wird eine vollständige Lösung gegeben. Abschließend wird ein optimales Entwurfsproblem betrachtet: Für eine vorgegebene Balkenlänge und Belastung finde man den Verjüngungswinkel, der das Gewicht zu einem Minimum macht. Dieses Minimum wird immer für einen Verjüngungswinkel (zwischen Ober-und Unterseite) zwischen O und 15° angenommen.

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With 3 Figures

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This investigation was supported by the National Research Council of Canada     

Failure analysis of RC shear walls with staggered openings under seismic loads

Reinforced concrete shear walls are used to design buildings located in seismic areas, because of their rigidity, bearing capacity and high ductility. Until now many theoretical and experimental tests on shear walls with or without openings have been made, therefore their failure modes have been analysed and are rather very well-known; the research results being confirmed by real failure modes of RC walls after earthquakes.Design codes and standards based on the knowledge of the failure modes of the reinforced concrete walls were developed in order to obtain the ductile failure mechanisms.A special case is the failure mode of the reinforced concrete shear walls with vertical staggered openings. If at coupled walls the elements must be designed so that the plastic hinges appear at the ends of the coupled beams and then in the pier, this thing is more difficult at shear walls with staggered openings.Theoretical and experimental studies on structural walls with staggered openings, lamellar walls and walls with bulbs at the end have been made recently. There have also been studied the followings: the degradation of the stiffness, the ductility function to the intensity of the seismic force, the presence of the vertical forces, the position and the size of the openings and the reinforcing ways.The article presents the results of the theoretical and experimental tests on failure modes of three types of reinforced concrete shear walls with staggered openings which are compared to those obtained from walls with vertical ordered openings as far as the seismic response is concerned.The failure modes of the structural walls under seismic stress have been identified using calculus programs and cyclic alternated experimental tests.The theoretical research on the failure modes was the basis for the elaboration of a simplified methodology for the calculus of the maximum theoretical seismic force that produces the concrete crushing in the ultimate limit stage. The results theoretically obtained with the help of the calculus programs have been confirmed experimentally. The analysis of the failure modes, obtained with the computing methodology proposed, contributed to the completion of the seismic design codes for shear walls with staggered openings.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.     

Performance of CFRP-strengthened RC beams subjected to repeated loads

In this paper, the effects of fatigue leading to crack formation and potential durability-bonding problems in reinforced concrete (RC) beams strengthened by carbon fiber reinforced polymer (CFRP) are studied. These effects are shown to cause CFRP de-bonding and loss of load carrying capabilities under static or low cyclic loading. Two series of RC beams with CFRP strengthening system are constructed and designed to fail in shear and flexural failures, respectively, under static loading. Repeated loading tests are conducted according to various loading ranges and loading cycles, and the experimentally determined fatigue properties are discussed. The test results show that it is possible to eliminate the debonding modes for longitudinally bonded CFRP using a U-wrap CFRP combination. The fatigue loads tested showed a significant effect on concrete rather than the CFRP system especially for the strengthened beams bearing a higher shear level. Moreover, the proposed equation to fit the testing S–N curve and the discussion of the stress in the component materials could be used for fatigue life predictions of beams with CFRP strengthening systems.     

Fatigue lives of RC beams strengthened with CFRP at different temperatures under cyclic bending loads

Fatigue performance of reinforced concrete (RC) components strengthened with fibre reinforced polymer (FRP) is largely improved. However, temperature changes of service environment have a great effect on the fatigue behaviour of RC components strengthened with FRP. Concerning about temperature variations in subtropical areas such as South China, this paper analyses the fatigue behaviour of RC beams strengthened with carbon fibre laminate (CFL) from experimental studies and theoretical analysis under four different temperatures (5 °C, 20 °C, 50 °C, 80 °C) and five different stress levels (0.60, 0.66, 0.72, 0.78, 0.84). The paper discusses temperature fatigue behaviour of RC beams strengthened with CFL under cyclic bending loads in different service environments, and proposes a calculation formula of fatigue lives of RC beams strengthened with CFL under environmental temperatures and external forces coupling. Experimental results show that the formula not only effectively predicts the fatigue lives of the RC beams strengthened with CFL under environmental temperatures and bending loads coupling but also estimates the fatigue limits.     

Interfacial shear stress in SiC fibre-reinforced cordierite

An analytical model based on a consistent shear-lag theory was developed to predict the interfacial shear stress in single fibre pull-out tests. The calculations show that the stress is highly dependent on the specimen thickness and the method of testing. Data for the debond stress and the interfacial shear stress were measured for single SiC fibres embedded in a magnesium aluminium silicate (cordierite) matrix. The effect of fibre embedded length, processing schedule, and matrix toughening were investigated. For a fixed sample support configuration during testing, good agreement was obtained between the model predictions and experimental data.     

Effective strain of RC beams strengthened in shear with FRP

The failure modes of Reinforced Concrete (RC) beams strengthened in shear with Fiber Reinforced Polymer (FRP) sheets or strips are not well understood as much as those of RC beams reinforced with steel stirrups. When the beams are strengthened in shear with FRP composites, beams may fail due to crushing of the concrete before the FRP reaches its rupture strain. Therefore, the effective strain of the FRP plays an important role in predicting the shear strength of such beams. This paper presents the results of an analytical and experimental study on the performance of reinforced concrete beams strengthened in shear with FRP composites and internally reinforced with conventional steel stirrups. Ten RC beams strengthened with varying FRP reinforcement ratio, the type of fiber material (carbon or glass) and configuration (continuous sheets or strips) were tested. Comparisons between the observed and calculated effective strains of the FRP in the tested beams failing in shear showed reasonable agreement.     

复合材料或钢板加固RC梁的板端剥离破坏承载力

 对受拉表面粘贴纤维增强复合材料( Fibre reinforced polymer/ plastic , FRP)或钢板的抗弯加固钢筋混凝土(Reinforced concrete , RC)梁的板端剥离破坏承载力进行了较为细致的研究。在分析关键参数、 试验数据及现 有计算模型的基础上 , 提出了一个简单、 合理的板端剥离破坏承载力计算新模型。该模型首先给出板端位于纯弯 区的弯曲剥离和板端位于弯矩为零或接近于零的主剪区的剪切剥离的承载力计算公式 , 进而采用简洁的相关曲线 确定板端在弯2剪共同作用区的剥离承载力。新模型通过包含未加固梁的抗剪承载力和几个物理意义明确的重要 参数 , 充分反映了抗弯加固梁的剥离破坏机制 , 与试验结果吻合良好 , 使用方便 , 可供制订规范和实际加固工程 设计时参考应用。     

Numerical simulation of reinforced concrete beams with different shear reinforcements under dynamic impact loads

The behavior of concrete/reinforced concrete structures is strongly influenced by the loading rate. Reinforced concrete structural members subjected to impact loads behave quite differently as compared to the same subjected to quasi-static loading. This difference is attributed to the strain-rate influence on strength, stiffness, and ductility as well as to the activation of inertia forces. These influences are clearly demonstrated in experiments. Moreover, for concrete structures, which exhibit damage and fracture phenomena, the failure mode and cracking pattern depend significantly on loading rate. In general, there is a tendency that with the increase of loading rate the failure mode changes from mode-I to mixed mode. Furthermore, theoretical and experimental investigations indicate that after the crack reaches critical speed of propagation there is crack branching. The present paper focuses on 3D finite-element study of reinforced concrete beams with different amount of shear reinforcement under impact. The experiments reported in literature are numerically simulated using the rate sensitive microplane model as constitutive law for concrete, while the strain-rate influence is captured by the activation energy theory. Inertia forces are implicitly accounted for through dynamic finite element analysis. However, the impact was modeled not by explicit modeling of two bodies but by incrementing the load point displacement till the maximum value and at the rate reported from the test. The results of the numerical study show that the numerical analysis using the procedure followed in this work can very well simulate the impact behavior of reinforced concrete beams. The static and dynamic reactions, crack patterns and failure modes as predicted in analysis are in close agreement with their experimentally observed counterparts. It was concluded that under impact loads, of the order as simulated in this work (blunt impact with velocity of around 1 m/s), the shear reinforcement does not get activated and therefore the dynamic reactions, unlike static reactions, are almost independent of the amount of shear reinforcement in the beams. However, the presence of shear reinforcement significantly affects the crack pattern and the cracks are well distributed in the presence of shear reinforcement, thus avoiding the formation of shear plugs.     

HPFL加固受火RC梁抗剪性能研究

 对高性能复合砂浆钢筋混凝土加固受火RC梁的抗剪承载力进行理论推导,并结合实验数据和工程实例验证理论公式的合理性．结合国内外对火灾后钢筋混凝土结构中混凝土和钢筋强度变化的研究,考虑火灾和火灾后冷却条件对混凝土和钢筋强度及性能的影响,提出计算模型．假定钢筋和混凝土之间无相对滑移,忽略混凝土的抗拉强度,不考虑温度—应力的耦合作用,采用等效截面法得到等效截面为T形截面,以桁架 拱模型和软化桁架理论为基础,结合极限平衡原理,考虑拉应变存在条件下混凝土抗压强度的软化．分析结果表明,推导所得的计算公式与试验数据比较吻合,高性能复合砂浆钢筋网加固方法能使梁的抗剪承载力得到显著提高,能满足实际工程的应用．     

Improved model for plate-end shear of CFRP strengthened RC beams

In case of RC members strengthened by means of externally bonded reinforcement, a premature failure can be detected in addition to the conventional modes of failure observed in RC unstrengthened beams. The premature failure occurs mainly due to both shear and normal stresses induced in either the external reinforcement–concrete interface or at the level of steel reinforcement. This research is part of a complete programme aiming to set up design formulae to predict the strength of CFRP strengthened beams, particularly when premature failure through laminates-end shear or concrete cover delamination occurs. Series of RC beams were strengthened with carbon-fiber-reinforced plastic (CFRP) laminates and tested to estimate the extent of the applicability of the formulae proposed by the authors, as well as to study the influence of the layout of the external reinforcement in terms of unsheeted length (the distance between CFRP laminates-end and the nearer support) and cross-sectional area, on the behaviour of strengthened beams. The predictions using the proposed formulae are compared with the obtained experimental results, as well as with the calculated design limit states. The interfacial shear stress and the maximum deflection corresponding to the predicted values at maximum and service loads are also studied.     

Fatigue performance of RC beams strengthened with CFRP under coupling action of temperatures and vehicle random loads

Considering significant influence of servicing environments and vehicle random loads on fatigue performance of main load‐bearing members of bridges, in this paper, fatigue performance of reinforced concrete bridge structures strengthened with carbon fibre–reinforced polymer under coupling action of environmental temperatures and vehicle random loads was studied. A vehicle random loading spectrum for fatigue tests was simulated and compiled. A fatigue testing method with coupling action of random loads and temperatures was proposed, and 3‐point bending fatigue tests of the reinforced concrete beams strengthened with carbon fibre–reinforced polymer under coupling action of temperatures and vehicle random loads were performed. Effects of temperatures and loading form on the fatigue damage mechanism were preliminarily discussed. A modified Palmgren‐Miner rule and semiempirical fatigue equations were proposed and proved effective.     

Improving shear capacity of existing RC T-section beams using CFRP composites

This paper presents the shear performance of reinforced concrete (RC) beams with T-section. Different configurations of externally bonded carbon fiber-reinforced polymer (CFRP) sheets were used to strengthen the specimens in shear. The experimental program consisted of six full-scale, simply supported beams. One beam was used as a bench mark and five beams were strengthened using different configurations of CFRP. The parameters investigated in this study included wrapping schemes, CFRP amount, 90°/0° ply combination, and CFRP end anchorage. The experimental results show that externally bonded CFRP can increase the shear capacity of the beam significantly. In addition, the results indicated that the most effective configuration was the U-wrap with end anchorage. Design algorithms in ACI code format as well as Eurocode format are proposed to predict the capacity of referred members. Results showed that the proposed design approach is conservative and acceptable.     

Behaviour of shear connectors under dynamic loads

The details of an experimental investigation of the fatigue strength of stud type shear connectors are described. A new type of test set-up called ‘New Standard Test Method’ has been employed to assess the fatigue strength of an individual shear connector. The results of the fatigue tests are discussed and a simple relationship between the stress range and the number of cycles has been obtained. This relationship is compared to the one obtained by Slutter on the basis of his experiments.     

Elasticity analysis of orthotropic beams under concentrated loads

A stress analysis is performed, within the framework of the classical theory of elasticity, on orthotropic beams subjected to concentrated loads. Both three-point and four-point bending are considered. Concentrated loads are represented by a uniform stress distributed over a very small length of the beam. Stresses developed in interlaminar beam tests are examined in detail. Considerable departure from classical beam theory over large portions of such beam specimens is observed.     

Interfacial shear stress in a short glass fibre-reinforced polypropylene sheet

The interfacial shear stress, τ, in an extruded short glass fibre-reinforced polypropylene sheet having good fibre alignment is evaluated using two approaches. The first approach considers the matrix to be elastic and results in τ increasing linearly with composite strain. The second approach assumes that the interfacial shear stress is directly proportional to the composite stress. On this scheme, up to 0·8% composite strain, τ is quantitatively identical to that predicted by the first model and it also increases linearly with composite strain. At higher strains, however, the rate of increase of τ is smaller. It is observec that the dependence of τ on composite strain is very similar to the tensile stress-strain behaviour of the homopolymer extruded sheet. The possible implications of this observation are briefly discussed.