Studies on ductility and evaluation of minimum flexural reinforcement in RC beams

Some experimental investigations on ductility and prediction of minimum flexural reinforcement in reinforced concrete (RC) beams are reported. The minimum flexural reinforcement was evaluated using optimum ductility in RC beams. Beams of size 100 mm, 200 mm and 400 mm were tested, which were designed with varying percentages of flexural reinforcement i.e. 0.15, 0.30, 0.60 and 1.0. The beams were tested under four-point loading to study the flexural behaviour under uniform bending moment. The experimentally obtained average compressive strength of concrete was 30 MPa. The influence of beam size (depth) on cracking and normalised ultimate flexural strength, ductility and overall average rotation has been studied. The cracking in RC beams is complex phenomenon in small size beams, while the cracking strength decreases as the depth increases beyond 200 mm. The flexural strength of RC beams, from the present study, appears to decrease as the depth increases. The ductility of RC beams increases as the percentage of flexural reinforcement increases. The ductility number has been derived from dimensional analysis using fracture mechanics principles. The ductility of RC beams decreases as the depth of beams increases. An optimum percentage of flexural reinforcement has been established using optimum ductility number, N_p, which is equal to 0.20. The minimum flexural reinforcement was found to decrease as the beam depth increases, and decreases as the yield strength of reinforcement increases.     

钢绞线(丝)网-聚合砂浆加固钢筋混凝土梁受弯性能研究

钢绞线(丝)网-聚合砂浆加固技术是一项新型加固工艺,具有耐火、耐腐蚀、耐老化、施工速度快等优点,已被逐渐应用于钢筋混凝土结构的加固补强中。采用该技术抗弯加固钢筋混凝土梁的受力性能可分为三个阶段:未裂阶段、裂缝阶段和破坏阶段。已有研究多数集中于加固混凝土梁正常使用阶段的抗弯性能分析,对受力纵筋屈服后破坏阶段的抗弯性能分析则鲜有涉及。该文在以往试验研究的基础上,采用换算截面法计算加固钢筋混凝土梁屈服阶段和极限阶段的等效刚度,对加固梁在集中荷载作用下抗弯性能全过程进行受力分析,并通过10根加固梁的试验数据对其验证,吻合良好。     

A numerical approach to modelling size effects on the flexural ductility of RC beams

The problem of evaluating the rotation capacity of reinforced concrete (RC) beams in bending has been largely investigated from both the experimental and the analytical point of view during the last decades. Since the development of ductility is influenced by several design parameters, it is difficult to develop a predictive model that can fully describe the mechanical behaviour of RC beams. In particular, the role of the size-scale effect, which has been evidenced by some experimental tests, is not yet completely understood. One of the main reasons is the inadequacy of the traditional models based on ad hoc stress–strain constitutive laws. In the present paper, a new model based on the concept of strain localization is proposed, which is able to describe both cracking and crushing growths in RC beams during the loading process. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which describes the strain localization due to crushing by means of a material interpenetration. With this algorithm in hand, it is possible to effectively capture the flexural behaviour of RC beams by varying the reinforcement percentage and/or the beam depth. An extensive comparison with experimental results demonstrates the effectiveness of the proposed approach.     

The effect of CFRP and CFRP/concrete interface models when modelling retrofitted RC beams with FEM

Concrete structures retrofitted with fibre reinforced plastic (FRP) applications have become widespread in the last decade due to the economic benefit from it. This paper presents a finite element analysis which is validated against laboratory tests of eight beams. All beams had the same rectangular cross-section geometry and were loaded under four point bending, but differed in the length of the carbon fibre reinforced plastic (CFRP) plate. The commercial numerical analysis tool Abaqus was used, and different material models were evaluated with respect to their ability to describe the behaviour of the beams. Linear elastic isotropic and orthotropic models were used for the CFRP and a perfect bond model and a cohesive bond model was used for the concrete–CFRP interface. A plastic damage model was used for the concrete. The analyses results show good agreement with the experimental data regarding load–displacement response, crack pattern and debonding failure mode when the cohesive bond model is used. The perfect bond model failed to capture the softening behaviour of the beams. There is no significant difference between the elastic isotropic and orthotropic models for the CFRP.     

Flexural strength of palm oil clinker concrete beams

This paper presents an experimental program on the flexural behaviour of reinforced concrete beams produced from palm oil clinker (POC) aggregates. POC is obtained from by-product of palm oil milling. Utilisation of POC in concrete production not only solves the problem of disposal of this solid waste but also helps to conserve natural resources. An experimental work was conducted involving eight under-reinforced beams with varying reinforcement ratios (0.34–2.21%) which were fabricated and tested. The data presented include the deflection characteristics, cracking behaviour and ductility indices. It was found that although palm oil clinker concrete (POCC) has a low modulus of elasticity, the test results revealed that the deflection of singly reinforced POCC beams, with reinforcement ratio less than 0.524, under the design service load is acceptable as the span-deflection ratios range between 250 and 257 and these values are within the allowable limit provided by BS 8110. In addition, the results reported in this paper indicate that the BS8110 based design equations can be used for the prediction of the flexural capacity of POCC beams with reinforcement ratio up to 2.23%.     

Composite bonded systems for renovations of orthotropic steel bridge decks

The renovation solution for orthotropic steel bridge decks studied consists of bonding a second steel plate to the existing steel deck in order to reduce the stresses and increase the lifespan of the orthotropic bridge deck. A parametric study was carried out on the flexural behaviour of beams representing the renovation solution using experimental and analytical studies. The influence of different thicknesses, temperatures and spans was tested. The results obtained for the stress reduction factor show that it is independent of temperature. More efficient solutions can be achieved when minimizing the second steel plate thickness and maximizing the adhesive layer thickness reducing the weight and increasing the stiffness of the composite structure. Both elastic behaviour and yield load of the composite beams are dominated by the steel plate properties and therefore not affected significantly by temperature. However, the ultimate failure of the beams occurs by shear of the adhesive layer, the properties of which are affected by temperature.     

RC beams strengthened with composite material: a limit analysis approach and experimental study

This paper deals with the flexural strengthening of reinforced concrete beams by means of thin carbon fibre reinforced plastic (CFRP) plates. A simplified laminated plate model is used to describe the behaviour of three-layered plate in cylindrical bending which were subjected to third-point line loads. The upper bound theorem of limit analysis is used to approximate the ultimate load capacity for multi-layered plates and identify different collapse mechanisms. A reinforced concrete beam strengthened by CFRP is designed as a three-layered plate. Experimental results are obtained and a comparison with theoretical predictions made.     

GFRP筋橡胶集料混凝土梁受弯性能

为提高纤维增强聚合物复合材料(FRP)筋混凝土梁抗裂性能,改善其脆性破坏特征,将玻璃纤维增强聚合物复合材料(GFRP)筋与橡胶集料混凝土共同应用于梁构件中。采用ABAQUS对GFRP筋橡胶集料混凝土梁的受弯性能进行有限元模拟及参数分析,探究了橡胶掺量、GFRP筋配筋率、混凝土强度等级及截面高度对梁受弯性能的影响。结果表明:增加混凝土中橡胶颗粒的掺量可提高梁的开裂荷载,当橡胶掺量为15%时,开裂荷载提高了29%;增加配筋率可提高梁的开裂荷载和承载力,当受拉筋直径由10 mm增加至18 mm时,橡胶掺量为10%的GFRP筋橡胶混凝土梁开裂荷载提高了约15%,承载力提高了约85%,但配筋率增加至一定数值后,其影响不再明显;提高橡胶混凝土强度等级,可提高梁的开裂荷载及承载力,当橡胶混凝土强度等级由C25提高至C40时,开裂荷载提了高约53.7%,承载力提高了约23%;为更好地满足正常使用极限状态,GFRP筋橡胶混凝土梁的截面高度宜适当增加。      

钢丝网复合砂浆加固混凝土受弯构件非线性分析

对用钢丝网复合砂浆加固的钢筋混凝土梁进行了正截面抗弯试验研究。试验包括16根用钢丝网加固的梁和两根未加固的对比梁,采用U形三面的加固方式(钢丝网复合砂浆包裹了梁的受拉面及两个侧面)。试验中对比了加固与未加固构件的裂缝开展情况、跨中挠度以及极限荷载。试验结果表明,钢丝网复合砂浆薄层可以明显地提高钢筋混凝土梁的抗弯承载力,提高抗裂性能,增强构件的抗弯刚度。理论部分采用非线性的方法得到加固构件的荷载-挠度曲线,与试验结果比较,有较好的吻合。     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Investigation into the time-dependent behaviour of reinforced concrete specimens strengthened with externally bonded CFRP-plates

This paper deals with the influence of an external CFRP-reinforcement on the time dependent behaviour of flexural concrete beams. For this purpose, four reinforced concrete beams are tested in relaxation under three-point bending. Three of the four are strengthened with a composite plate bonded to their tensile soffit. The latter is not strengthened. The phenomenon of relaxation leads to a decrease in the loading force in the course of time. The test results are analysed in three ways: the first is a comparison between the global behaviour of the four beams. The second is a detailed analysis of the internal equilibrium of the beams in the course of time. The third is a global approach based on an incremental method suited to time analysis of composite structures. It can be concluded that composite reinforcement has a positive influence on the long term behaviour of strengthened beams. Their time dependent behaviours are different depending on whether the beam is pre-cracked before being strengthened. This difference may be taken into account using a coefficient of influence applied to the composite reinforcement. The existence of a period of loading before strengthening has a positive influence on the long-term behaviour of the beam.     

Structural behaviour of RC beams with external flexural and flexural–shear strengthening by FRP sheets

This paper presents experimental research on reinforced concrete (RC) beams with external flexural and flexural–shear strengthening by fibre reinforced polymer (FRP) sheets consisting of carbon FRP (CFRP) and glass FRP (GFRP). The work carried out has examined both the flexural and flexural–shear strengthening capacities of retrofitted RC beams and has indicated how different strengthening arrangements of CFRP and GFRP sheets affect behaviour of the RC beams strengthened. Research output shows that the flexural–shear strengthening arrangement is much more effective than the flexural one in enhancing the stiffness, the ultimate strength and hardening behaviour of the RC beam. In addition theoretical calculations are developed to estimate the bending and shear capacities of the beams tested, which are compared with the corresponding experimental results.     

Cracking behaviour of concrete beams reinforced with a combination of ordinary reinforcement and steel fibers

The paper presents an experimental and theoretical study on the cracking behaviour of concrete beams having longitudinal tension reinforcement and various combinations of volume and aspect ratio of steel fibers. Five full-scale beams with a concrete compressive strength of 42 MPa were tested. The mechanical properties of the steel fiber concrete under tension were determined by means of the four-point bending test specified in the Belgian standard NBN B15-238. The experimental results show that the addition of steel fibers decreases both the crack spacing and the crack width. A modification of the model of Nemegeeret al. to predict crack widths is suggested.     

An integrated cohesive/overlapping crack model for the analysis of flexural cracking and crushing in RC beams

In the present paper, a new fracture-mechanics based model is proposed for the analysis of reinforced concrete beams in bending describing both cracking and crushing growths taking place during the loading process by means of the concept of strain localization. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which considers a material interpenetration when the elastic limit is overcome, in close analogy with the Cohesive Crack Model, routinely adopted for modelling the tensile behaviour of concrete. On the basis of different nonlinear contributions due to concrete and steel, a numerical finite element algorithm is proposed. According to this approach, the flexural behaviour of reinforced concrete structural elements is analyzed by varying the main geometrical and mechanical parameters. Particular regard is given to the role of the size-scale effects on the ductility of plastic hinges, which is available at the ultimate load conditions.     

钢筋混凝土梁受弯破坏及尺寸效应的细观模拟分析

钢筋混凝土构件破坏的尺寸效应取决于混凝土材料的非均质性以及钢筋/混凝土相互作用。该文借助混凝土细观结构特征,基于非线性弹簧单元来描述钢筋与混凝土之间的相互作用,建立了钢筋混凝土梁破坏行为模拟的三维细观数值模型。在模拟结果与试验结果吻合良好的基础上,拓展模拟了更大尺寸梁的弯曲大变形破坏行为,并分析了单调及循环加载模式对不同尺寸悬臂梁受弯破坏及名义抗弯强度影响规律。模拟结果分析表明:1)该文工况下钢筋混凝土悬臂梁的弯曲破坏存在尺寸效应,弯曲强度随梁深增大而减小; 2)循环加载下,混凝土、钢筋以及两者间的粘结性能由于低周疲劳而使得梁的弯曲破坏呈现出脆性特征; 3)相比于单调加载,循环加载条件下,悬臂梁的破坏具有更强的脆性,名义抗弯强度尺寸效应更明显。     

Response of steel fiber reinforced high strength concrete beams: Experiments and code predictions

The shear-flexure response of steel fiber reinforced concrete (SFRC) beams was investigated.Thirty-six reinforced concrete beams with and without conventional shear reinforcement (stirrups) were tested under a four-point bending configuration to study the effectiveness of steel fibers on shear and flexural strengths, failure mechanisms, crack control, and ductility.The major factors considered were compressive strength (normal strength and high strength concrete up to 100 MPa), shear span-effective depth ratio (a/d = 1.5, 2.5, 3.5), and web reinforcement (none, stirrups and/or steel fibers).The response of RC beams was evaluated based on the results of crack patterns, load at first cracking, ultimate shear capacity, and failure modes.The experimental evidence showed that the addition of steel fibers improves the mechanical response, i.e., flexural and shear strengths and the ductility of the flexural members.Finally, the most recent code-based shear resistance predictions for SFRC beams were considered to discuss their reliability with respect to the experimental findings. The crack pattern predictions are also reviewed based on the major factors that affect the results.     

Mechanical characterisation and impact behaviour of concrete reinforced with natural fibres

It is well known that high strength concrete displays a brittle behaviour and less tough characteristics than normal strength concrete. This type of behaviour can be enhanced by incorporating various types of fibres which lead to better mechanical properties and impact resistance. In this paper, an experimental study conducted on high strength concrete reinforced with glass fibres and natural fibres (palm tree leaves), both used at a relatively low volume fraction, is presented. Compressive, splitting, three-point bending and impact test methods have been used to characterise reinforced concrete materials, and the results are analysed statistically. It is observed that natural fibres enhanced the mechanical properties and impact resistance of concrete and exhibit comparable response to the glass fibres. A finite element model using ANSYS was employed to study the flexural behaviour of fibre reinforced concrete. It is concluded that both experimental and numerical results are in good agreement.     

Layer model for long-term deflection analysis of?cracked?reinforced concrete bending members

A numerical technique has been proposed for the long-term deformation analysis of reinforced concrete members subjected to a bending moment. The technique based on the layer approach in a simple and rational way deals with such complex issues as concrete cracking and tension-stiffening as well as creep and shrinkage. The approach uses the material stress-strain relationships for compressive concrete, cracked tensile concrete and steel. Such effects as linear and nonlinear creep, cracking, tension-stiffening as well as the reduction in concrete tension strength due to sustained loading have been taken into account. The shrinkage effect has been modeled by means of adequate actions of axial force and bending moment. A statistical deflection calculation analysis has been carried out for 322 experimental reinforced concrete beams reported in the literature. The comparative analysis of the experimental and the modeling results has shown that the proposed technique has well captured the time-deflection behavior of reinforced concrete flexural members. The results of the predictions by ACI 318 and Eurocode 2 design codes have been also discussed.     

氯盐环境下锈蚀预应力混凝土梁抗弯性能试验

为探讨氯盐环境下锈蚀预应力混凝土梁的抗弯性能,制作了5根先张预应力混凝土梁,采用电化学法分别对其进行了0 d、7 d、14 d、28 d及42 d的快速腐蚀,随后进行了四点弯曲试验。研究了不同锈蚀程度对预应力混凝土梁自振频率、钢绞线滑移、结构变形、弯曲开裂、破坏模式及极限承载力等性能的影响。结果表明:氯盐环境下锈蚀对预应力混凝土梁高阶频率影响较小,导致一阶频率逐渐增大,28 d后锈蚀裂缝较大且局部混凝土脱落,一阶频率迅速减小;轻微腐蚀对预应力混凝土梁的抗弯性能影响较小,腐蚀程度增大,抗弯性能明显降低,腐蚀42 d后,极限挠度减小了18.7%,抗弯承载力减小了17.3%,延性降低了19%;锈蚀钢绞线与混凝土间滑移速率增大,极限滑移值由5 μm增加至11.4 μm;钢筋锈蚀对弯曲裂缝高度发展的影响不大,但促进了裂缝宽度的扩展,结构屈服后,底部裂缝开裂速率由0.0062 mm/kN增加至0.0252 mm/kN。在试验研究基础上,采用有限元软件ANSYS对各锈蚀梁的受载全过程进行了有限元模拟计算,极限荷载和钢绞线滑移量的模拟值与实测值误差分别小于5%和10%,吻合较好。      

Simplified analysis of shear-lag in framed-tube structures with multiple internal tubes

 A simple numerical modelling technique is proposed for estimating the shear-lag behaviour of framed-tube systems with multiple internal tubes. The system is analysed using an orthotropic box beam analogy approach in which each tube is individually modelled by a box beam that accounts for the flexural and shear deformations, as well as the shear-lag effects. The method idealises the tube(s)-in-tube structure as a system of equivalent multiple tubes, each composed of four equivalent orthotropic plate capable of carrying loads and shear forces. The numerical analysis so developed is based on the minimum potential energy principle in conjunction with the variational approach. The shear-lag phenomenon of such structures is studied taking into account the additional bending stresses in the tubes. Structural parameters governing the shear-lag behaviour in tube(s)-in-tube structures are also investigated through a series of numerical examples. Received 8 December 1999