A numerical method for estimating the curvature, deflection and moment capacity of FRPreinforcedconcretebeams is developed. Force equilibrium and strain compatibility equations for a beam section divided into a number of segments are numerically solved due to the non- linear behaviour of concrete. The deflection is then obtained from the flexural rigidity at mid- span section using the deflection formaule for various load cases. A proposed modification to the mid-span flexural rigidity is also introduced to account for the experimentally observed wide cracks over the intermediate support of continuous FRPreinforcedconcretebeams. Comparisons with experimental results show that the proposed numerical technique can accurately predict moment capacity, curvature and deflection of FRPreinforcedconcretebeams. The ACI-440.1R-06 equations reasonably predicted the moment capacity of FRPreinforcedconcretebeams but progressively underestimated the deflection of continuous ones. On the other hand, the proposed modified formula including a correction factor for the beam flexural rigidity reasonably predicted deflections of continuous FRPreinforcedconcretebeams. It was also shown that a large increase in FRP reinforcement slightly increases the moment capacity of FRP over-reinforcedconcretebeams but greatly reduces the defection after first cracking.
7) The derived formulae have been applied to predict the results of 112 shear tests on FRPreinforcedconcretebeams with FRP stirrups. Predictions made by other existing formulations and some provisions of current guidelines have been also compared with the experimental results. The results obtained by the proposed method are very good, in terms of mean value (1 .08 ) and coefficient of variation (19.5%) of the ratio between the experimental and the predicted values, V exp/Vpred . The coefficient of variation (COV) obtained is the lowest of all the methods studied. This fact is relevant, since the model with similar results  is based on genetic algorithms while the proposed method has been rationally derived, without any adjustment to the database.
The use of fiber-reinforced polymer (FRP) as an alternative of reinforcing materials has become accepted in construction industry. Not like steel, properties of FRP reinforcement offers an outstanding performance for concrete that have high strength-to-weight ratios (10 to 15 times than steel), non-magnetic and provides excellent corrosion resistant which can lead to lower life-cycle costs [1-2]. Commercially, FRP bars are available in different types of fiber including carbon (CFRP), aramid (AFRP) and glass (GFRP). Among these types of fiber, GRFP is the least expensive and the lowest tensile modulus of elasticity (typically 40 to 55 GPa) which possibly applied as non-prestressed reinforcement [3,4]. Several investigations has been conducted to reveal that FRP bars can be used as alternative of reinforcing materials in concrete structures [5–8]. However, due to brittle elastic failure and low modulus of elasticity of FRP, the performance of FRP RC beams Manuscript received February 10, 2013. This work was supported in part by the University Teknologi Mara under Grant 600-RMI/ST/DANA 5/3/Dst (449/2011).
effective moment of inertia to describe the reduced stiffness of a cracked element, has proven effective in determining service deflections of steel reinforcedconcrete elements and has also been adopted for FRPreinforcedconcrete elements. ACI 440.1R-06 , for example, has adopted a modified form of the effective moment of inertia equation included in ACI 318  and originally developed by Branson . Although a similar model is also discussed in the design manual published by ISIS Canada , the use of an equation derived by implementing the tension stiffening effect included in Model Code 90  is proposed as a more reliable model for concrete elements reinforced with different types of FRP reinforcements. The tension stiffening model of Model Code 90 also underlies the method recommended in Eurocode 2  to estimate service deflections for steel RC elements, and was shown to lead to acceptable results also for FRP RC elements . CAN/CSA-S806  recommends determining deflections by integration of curvatures along the span, but ignores the tension stiffening effect provided by the FRP reinforcement. Instead it proposes the use of a gross and cracked moment of inertia to represent the stiffness of un-cracked and cracked portions of the element, respectively.
The beams were tested monotonically under four point bending by means of 500 and 1000 kN hydraulic actuator. Each beam was loaded continuously to failure with each load increments approximately 5% from its theoretical ultimate load. A part of operation was manually controlled and some necessary adjustments were made to keep the load constantly during the test. The electrical-resistance strain gauges were used to measure tensile strains along reinforcing bars, stirrups and compressive area in concrete with a 5 mm long, 3 mm long and 60 mm long, respectively. Fig. 2 shows the strain gauge positions along the reinforcing bars and denoted as B1, B2 and B3. Whereas strain gauges denoted as SG were attached on selected stirrups. Concrete strain gauges were also bonded at the top compression surface at the mid-span and indicated as C. All the strain gauges were fully wrapped and waterproofed before casting. To measure the deflection of the beam, three linear variable displacement transducers (LVDTs) with a 50 mm stroke were placed at the mid-span and under the load positions. During the test, all crack formation and propagation on both sides of the beam surfaces were marked and labelled with the corresponding incremental loads.
The investigation on flexural creep of high performance fibre reinforcedconcrete (HPFRC) is still scarce. Even though the presence of fibres in concrete help to control the deformations, these may increase under the effect of a sustained load. To analyse the effect of creep in pre-cracked HPFRC elements, twelve beamsreinforced with either glass or steel fibres with dimensions 40 x 80 x 1200 mm were tested under a three-point configuration. For that, a new type of frame was designed and constructed to test the HPFRC beams under flexural load in a climate-controlled room with constant temperature and relative humidity. The loading mechanism was based on a lever system, applying sustained load ranging between 25% and 50% of the load at which the first crack appeared. The deflection at the mid-span was registered by means of LVDT transducers. Additionally, the influence of the curing procedure (with or without aluminium tape wrap) was assessed. In general, glass fibre reinforcedbeams presented higher deflections than steel fibres, even though at low load levels the type of fibre did not have significant influence on the deformation.
Concrete beam with an opening is constructed to allow the easy passage of utility services such as air-conditioning services, water supply as well as electricity. The use of this overall dead space helps save structure height and leads to a more economical design. The opening can be provided in various shapes and sizes which depend on the size or type of pipe or duct which passes through the opening (Mansur & Tan, 199). The most common shapes used in practice are circular and rectangular openings.
Group two contains three beams with characteristic strength 25Mpa and 10% Nano-Metakaolin and different ratios of flexural reinforcement as shown in table (1). Group three contains two beams with characteristic strength 25Mpa and 10% Nano-Metakaolin and different ratios of compression reinforcement as shown in table (1). Group four contains a beam with characteristic strength 35Mpa and 10% Nano-Metakaolin and reinforcement (As=2Φ12mm) and (AS \ =2Φ8mm) and ø6mm @20cm shear reinforcement as shown in figs. (2-5).
The results for residual flexural strength predicted by the present method are plotted in Figure 10 as a function of the corrosion level and compared with the published experimental data. Here, the normalized residual flexural strength is calculated by dividing the flexural capacity of the corroded beam by the capacity of the non-corroded beam. The reduction in cross-sectional area of the reinforcing bar due to corrosion is considered in calculations. As observed in Figure 10, the results by the present study shows very good agreement with the experimental data of Mangat and Elgarf  and the data published in other experimental investigations [18, 20]. At the initial corrosion stage, the flexural strength of the corroded beam remains almost the same as that for the un- corroded beam. When corrosion level reaches about 5%, considerable strength deterioration occurs. The reduction in flexural strength is due to significant decrease in bond strength, which is required to prevent the RC beam from bond failure. In addition, the residual flexural strength of the beam is calculated by ignoring the bond strength loss and by using the standard expression for the moment of resistance of under-reinforcedbeams given in Eurodcode 2 , as plotted in Figure 10. It can be seen that in the case without bond strength influence, the reduction in flexural strength follows approximately linear relation with corrosion level. The reduction in flexural strength for the case without bond strength influence is relatively low in comparison with the case with influence of bond strength loss. For instance, at a corrosion level of 20%, the residual flexure strength by using conventional method is about 80% of the original strength, whereas the corresponding flexural strength with considering influence of bond strength loss is only about 25%. This indicates that at relatively high corrosion level (>5%), bond strength reduction at the steel-concrete interface is the primary factor responsible for the deterioration of the flexural strength of the corroded beam rather than the reduction in cross sectional area of the rebar.
This paper compares the flexuralperformance of reinforcedconcrete (RC) beams strengthened with textile-reinforced mortar (TRM) and fibre-reinforced polymers (FRP). The investigated parameters included the strengthening material, namely TRM or FRP; the number of TRM/FRP layers; the textile sur- face condition (coated and uncoated); the textile fibre material (carbon, coated basalt or glass fibres); and the end-anchorage system of the external reinforcement. Thirteen RC beams were fabricated, strength- ened and tested in four-point bending. One beam served as control specimen, seven beams strengthened with TRM, and five with FRP. It was mainly found that: (a) TRM was generally inferior to FRP in enhancing the flexural capacity of RC beams, with the effectiveness ratio between the two systems varying from 0.46 to 0.80, depending on the parameters examined, (b) by tripling the number of TRM layers (from one to three), the TRM versus FRP effectiveness ratio was almost doubled, (c) providing coating to the dry textile enhanced the TRM effectiveness and altered the failure mode; (d) different textile materials, having approximately same axial stiffness, resulted in different flexural capacity increases; and (e) providing end-anchorage had a limited effect on the performance of TRM-retrofitted beams. Finally, a simple for- mula proposed by fib Model Code 2010 for FRP reinforcement was used to predict the mean debonding stress developed in the TRM reinforcement. It was found that this formula is in a good agreement with the average stress calculated based on the experimental results when failure was similar to FRP- strengthened beams.
Researches on new building materials have been on for the past decades, with the sole aim of developing low cost construction materials that can be affordable to the people. Cheap and standard building materials are necessary for the construction of low-cost housing estates, and other structures. Composites are a versatile and valuable family of materials that can solve problems of different applications and facilitate the introduction of new properties in materials (Gon et al., 2012). Park (2009) carried out a series of unconfined compression tests on samples reinforced with fibres. He reported that a fibre reinforced specimen was twice as strong as a non-fibre- reinforced specimen. The author also reported that a specimen with five fiber inclusion layers was 1.5 times stronger than a specimen with one fibre inclusion layer. According to Aho and Ndububa, (2015) concretebeamsreinforced with raffia palm fruit peel fibres improved their flexural strength but resulted in reduction of their compressive strength. Ahmad et al. (2014) reported that the flexural strength of beam increases when we use bamboo stick as reinforcement in concrete. The flexural strength of doubly bamboo reinforcedbeams reached up to 80MPa as compare to 48MPa for concretebeams without any reinforcements. The maximum deflection at the mid span reaches up to 1mm approximates. Mostafa and Uddin, (2015) studied the behaviour of mortar reinforced with different percent of coconut and banana fibres. They observed that the maximum tensile strength and modulus of rupture of mortar composite increased up to certain fibre content (percent), before the values dropped as the fibre volume increases. Similarly, Estabragh et al. (2012) studied the effects of fibre volume, cement volume, and curing age on the unconfined compressive strength of cement-stabilized clay. They
Focus has increased recently on strengthening reinforcedconcrete structures that deteriorate due to aging, corrosion of steel reinforcing bars, excessive loading, or severe environmental conditions. The strengthening of RC structures has been successfully implemented using fabric reinforced cementitious matrix (FRCM) systems for the flexure strengthening of RC beams. There is, however, a problem of premature debonding which is observed in high fabric strength FRCM systems which does not allow full utilization of the strengthening material. It has also been a problem in FRCM systems to use multiple layers for strengthening, where using more than two layers causes premature failure in the strengthened beams. This work aims to counter the problem of premature failure by investigating the relatively new concept of near surface embedded (NSE) strengthening where the strengthening material is embedded within the concrete cover at the soffit of the beam thus allowing the FRCM to be better utilized. Three different types of FRCM systems have been investigated, namely: Carbon, Polyparaphenylene Benzobisoxazole (PBO), and Glass. The potential of combining both NSE strengthening and the traditional externally bonded (EB) methods resulting in the hybrid near surface embedded/externally bonded (NSE/EB) is also examined in this work to investigate the efficient application of multiple FRCM layers in flexure. Part of the results of this work have been successfully published proving that it is a viable strengthening application .
Some researchers have been developed plasticity based models for HPFRCC material [7, 9, 10]. But, there are some computer programs for modeling of concrete and cement composites. The experimental beams which were tested in this paper, also analyzed using the available nonlinear finite element software called ABAQUS. In a nonlinear analysis, ABAQUS automatically chooses appropriate load increments and convergence tolerances and continually adjusts them during the analysis to ensure
Approximate value was evaluated for crack spacing as 0.5t to 0.8t (Lim et al., 1987; Laura C., 2007). • The compressive and post-cracking strengths of HSFRC are evaluated by the empirical functions given before in Section 2. 3-2 FORMULATIONS OF THE APPROACH b t d d ' As d -c c s tu cu=0.003 N.A. T T s f f pp k 3 f cuf k 2 c Cc t- c c a = B 1 c T T s f f pp 0.67f a /2 Cc= 0.67f ab cuf cuf Strain Actual Stress Idealized Stress Distribution Distribution Distribution a) Fully Reinforced SFRC Section t f 0.67f Cc= cu cu d d ' b As N.A. d -c c s cu=0.003 c t f a = B 1 c T s f pp T f a /2 Strain Idealized Stress Distribution Distribution b) Partially Reinforced SFRC Section Fig. 7. Ultimate stress and strain distribution Based on the above assumptions, the ultimate strain and stress distribution is shown in Fig. (7-a) for the fully reinforced HSFRC section, and in Fig. (7-b) for the partially reinforced HSFRC section; where the steel fiber is included only in the tension side over a depth of t f , From the force equilibrium condition and strain compatibility condition, the depth of the compression block can be determined as follows: C c = T s + T f (13)
The experimental results show that the ultimate moment resistance of reinforcedconcrete beam is increased by 4.0 to 7.5 % with the addition of randomly distributed FibraFlex fibers. Fiber action to stop propagation of cracks at micro or macro level strongly depends on the properties of fiber (geometry, strength and stiffness) and on the bond between fibers and concrete matrix. For the bond between matrix and fiber, matrix compactness also plays an important role. Among the two fibers used in this study; FibraFlex fibers develop good bond with the matrix because of their rough surface and large specific surface area. According to a study carried out by Turatsinze et al , micro-cracking occurs inside the matrix before the peak load in flexure, in this context, FibraFlex fibers act as soon as the first micro-cracks open and immediately restrain their propagation due to good bond with concrete matrix. By this way, they enhance the response prior and just after the peak load. With further increase of crack opening, the fibers contribute to carry tension along with steel bar and response of the composite is improved in term of load bearing capacity, reduced deflection and smaller crack opening (Fig.9 and Fig.10). With regard to the failure of the FibraFlex fibers is concerned, when the stress in the fiber exceeds its tensile strength with the increase of crack opening, the fibers break instead of pulling out from the matrix and the post-peak residual load bearing capacity approaches to a value equal to RC beam without fibers (Fig.5).
The average crack height, for beams BS-I and BS-II only, is calculated as a fraction of the overall depth of the beam at each damage level and plotted against load levels in Fig. 19. It is worth noting that the crack height was not recorded properly for beam BS-III and hence is not included in the analysis. The curves are contrasted with the estimation of the model for the average crack height. It can be seen that the model overestimates the average crack height in comparison to the beams by about 30% of the overall depth. This is due to the fact that the cracks in the beams were captured by the naked eye. The authors  found with the aid of digital image correlation techniques that cracks become visible to the naked eye when the width is more than 0.2mm. Hence, when this value is used to correct the model’s prediction of the average crack height, the trend of increase in the average crack height is comparable. Between 15% and 45% of the failure load, there is a steep increase in the average crack height for both the model and the experimental data. After that, the average crack height gradually increased to about 50% of the overall depth of the beam. However, the model’s predictions show that at 30% of the failure load the average crack height is almost half the overall depth of the beam. This may explain previous results of vibration measurements which revealed that resonant frequencies experience the greatest reduction in early stages of damage (20% − 30%) of the failure load . The experimental results also indicate that visual inspection methods might lead to underestimation of the true crack height in structures.
In this investigation, the main steel in reinforcedconcretebeams was subjected to an accelerat- ed corrosion technique in the laboratory using one of the several methods available. The gal- vanostatic method was used in this study to simulate the field conditions. The method involves passing a direct current through the reinforcement to accelerate corrosion. The galvanostatic corrosion is carried out whilst the beam is unloaded, which is different from the corrosion in ac- tual structures. The corrosion by galvanostatic method is general, whereas actual structures have some specific areas that are more prone to corrosion. Thus in the latter case, there is al- ways the possibility of pitting corrosion whereby the cross-sectional area of the reinforcing bars could be significantly reduced, thus reducing the tensile strength of the reinforcing bars. How- ever, to ensure consistency of results in this investigation, the steel reinforcement was subjected to general corrosion only, which allows easier repeatability compared to pitting corrosion.
comparison with steel, are a lower modulus of elasticity and a linear elastic behaviour up to rupture, which implies the lack of plasticity in the behaviour of FRP . From among research studies conducted on flexural behavior and serviceability performance of concretebeamsreinforced with FRP bars one can refer to [5-15]. Among the research studies conducted on pullout behavior of GFRP bars in concrete and bond stress-slip behavior of GFRP bars in concrete respectively one can refer to  and , and Studies conducted on shear behavior of concretebeamsreinforced with GFRP bars include references [18, 19]. The present study focuses on investigating the effectiveness of FRP reinforcing on the pushover behaviour of RC beams using FE modeling technique. The FE meshes, boundary conditions and nonlinearity implementation methods have been calibrated/validated by comparing the predictions of the available experimental data. Subsequently, effects from FRP reinforcing on the bending response of RC beams were studied. Moreover, two groups of FRP and steel reinforcedbeams, with same reinforcement ratio, have been selected to investigate the effect of FRP reinforcement on the moment capacity of RC beams. Geometrical and material nonlinearities in the concrete material, steel reinforcements and also FRP reinforcement have been taken into consideration. In the study effects from the variation of span/depth ratio, the reinforcement ratio and the effective depth of the beam are that the new issues that have been addressed.
The theory of stress analysis for metalic/plastic structural elements with cemented joints subjected to both axial and bending deformation was first established by Goland and Reissner . Volkersen  provided governing equations for normal and shear stress distributions in double-lap cemented joints which were later improved in 1970’s as reviewed in . Roberts  further developed governing equations valid for different adhesive joint configurations subjected to bending and axial forces and indicated the role of practical details such as spew fillets of adhesive on reduction of stress concentration. Most of these early studies preceeded the application of bonded steel-plates for concrete strengthenening and the development of Roberts and Haji-Kazemi’s solution based on the partial interaction theory  which relaxed bondary condition for zero shear stress on the free edge of adhesive. With the introduction of FRP-materials to plate-bonding of concrete elements, the work of Roberts  was followed by a number of analytical solutions based on linear elastic method [7-10]. These solutions were found to produce very similar stress magnitudes in the debonding zone . Still, their ability to predict debonding failures has not yet been verified against experimental data from published works although several concrete design guidelines are already being extended to comprise the FRP-plate strengthening technique [11-12].
A.Muthadhi and S. Kothandaraman (1) (2013), the authors investigated on experimental performance characteristics of rice husk ash–blended concrete. In this paper, four concrete mixtures were considered to identify the effect of RHA (produced under controlled conditions) on performance characteristics of the concrete. RHA was added as partial replacement of ordinary Portland cement from 10 to 30%. The properties investigated include compressive strength, chloride permeability, water absorption, and sorptivity of RHAblended concrete. Based on the results, it was found that RHA addition upto 20% in partial replacement of ordinary Portland cement lead to increased compressive strength of concrete compared with that of reference mixtures. However, the durability of RHA concrete was on the higher side for all doses compared with the reference mixtures. The compressive strength is well correlated with chloride permeability of RHA-blended concrete mixtures. Rice husk ash proves to be highly reactive pozzolana, which contributes to higher strength and improved performance characteristics.