Previous studies have shown that a uniform distribution of load may increase the shearstrength of a slender member by as much as 40 percent (Leonhardt and Walther 1964). The increase of shearstrength is potentially due to clamping stresses induced from the uniformload, although a mathematical equation to quantify the effect of clamping stress in slender uniformly loaded members has yet to be derived (Acevedo et al. 2009). Only a small percentage of all shear tests on slender specimens withoutshearreinforcement were completed with uniformload. Additionally, the majority of uniformload data consists of specimens with small specimen depths (d) and large longitudinal reinforcement ratios (ρ).
One of possible and discovered reason is the size effect of the structure members, which was introduced by Okamura . Another possible problem is the shear carrying capacity’s design concept used as the strength of concrete at either failure or shear crack load and sum up with shear resistance of web reinforcement. It is possible that a small amount of web reinforcement cannot maintain the shearstrength resist by concrete to be the same up to yielding point of stirrup itself . However, there is still not a simple, albeit analytically derived formula to predict and with accuracy the shearstrength of slenderbeams. In addition many of the factors that influence the determination of the required minimum amount of shearreinforcement are not yet known . Unlike flexural failures, reinforced concrete shear failures are relatively brittle and particularly for members without stirrups can occur without warning because of this, the prime objective of shear design is to identify where shearreinforcement is required to prevent such a failure and then in a less-critical decision how much is required. Shearreinforcement, usually called stirrups links together the flexure tension and flexure compression sides of a member and ensures that the two sides act as a unit.
The behavior of deep beams is different from that of common flexural members; the strength of deep beams is mainly controlled by shear rather flexure when sufficient amounts of tension reinforcement are used (Oh and Shin 2001), and they are classified as non-flexural members, in which the plane sections do not remain plane in bending(Rao, Kunal et al. 2007). Elastic behavior is characterized of deep beams before cracking. After cracking major redistribution of stresses and strains, significant effects of vertical normal stress and shear deformation takes place therefor strength of the beams must be estimated using the nonlinear analysis (Nawy 1985), (Rao, Kunal et al. 2007)and (Ramakrishnan and Ananthanarayana 1968). The high shearstrength is an important specific of such beams; that is because of internal arch action mechanism which is quite deferent from beams of normal proportion (Kalyanaraman, Rayan et al. 1979, Nilson and Winter 1987). Tied arch as a characteristic of deep beams will be formed after appears of diagonal cracking, even though diagonal tension failure mode occurs in the slenderbeams, deep beams carry the additional loads after diagonal cracking due to the behavior of strut and tie which transmissions the load directly to the support through concrete compression struts. The tension reinforcement actions as a tie. Horizontal compression in concrete and the tension in the main reinforcement have to equilibrate the load, adequately anchored of tension bars must be provided to prevent anchorage failure. Also the deep beams are categorized as disturbed regions, in which the nonlinear distribution of strain. However, the bending elementary concept for simple beams may not be appropriate for deep beams even under linear elastic assumption. It is found that using ordinary bending theory of flexure will yield erroneous values of all the stresses
A few researchers namely Kim and Park 1 mentioned that the shear failure of a reinforced concrete beam without web reinforcement is divided into 2 modes, as shown in Fig.2. The inclined cracking load exceeds shear compression load for shear span to depth ratio, a/d, greater than 2.0 – 3.0. The formation of crack, usually known as diagonal tension crack, indicates that the beam is unstable and fails. Shear compression failure on the other hand occurs when failure load exceeds the inclined cracking load, as in the case for a/d less than 2.0 – 3.0. For slenderbeams, shear force is carried by the shear
and SFRC members are shown in order to clarify the differences. The ratios based on theoretical values calculated by predicted equations showed an approximate uniform consistency while the rates based on the codes calculations a great gap. This is due to the fact that the codes neglect the effect of steel fibres in their equations whereas the predicted equations by investigators were specifically designed for SFRC beams. It can be noticeable from 5.6 that the average ratios of the experimental shear strengths to the theoretical code values are conservative for all beams. All ratios are highly conservative for SFRC beams in particular for the reason mentioned previously about ignoring the effect of the presence of steel fibres. ACI and CSA codes slightly underestimated the nominal shearstrength for all beams except NNB sample that showed lower experimental shearstrength than ACI result for the same beam. ACI and CSA did not consider steel fibres in beams in predicting shearstrength. Therefore, experimental shear resitance values of beams with steel fibres were noticeably greater than the codes predictions. This is definitely attributed to the higher flexural capacity gained by the presence of steel fibres in those beams. Those samples in fact failed in flexure without even knowing how much shear stresses they could resist. That is, the actual shearstrength of beams failed in flexure is highly greater than codes prediction. On the other hand, the underestimation predictions by codes for reference RC beams are purposely reduced by codes for safety reasons in order to keep the designed beams in the safe side.
The beams in group D failed in shear. Initially, flexural cracks were observed at mid-span in the un-repaired beams at different loads based on the corrosion level: 61 kN (for non-corroded beam), 57 kN and 64kN (for low of 0.77% actual mass loss and high or 4.39% actual mass loss corrosion levels). The loads at which diagonal cracks initiated and propagated for the different beams are presented in Table 3.2. As the load increased, the diagonal cracks widened and the stirrups started to share in resisting the applied load and consequently the beam lost the aggregate interlock. The failure in the un-repaired corroded beams unexpectedly occurred in the non-corroded shear span possibly because the enhancement of shear friction due to the low achieved mass loss led to increasing the shear resistance in the corroded shear span. At the ultimate strength, the beams exhibited brittle shear failures. The failure modes were diagonal tension splitting failure in the control and the corroded beams as shown in Figure 3.21. The corroded beam with high corrosion level experienced stirrups rupture. However, the CFRP repaired beam experienced debonding of FRP with diagonal tension failure (Figure 3.21).
beams is very essential as shear failure is a sudden failure without any warnings. The NSM technique is one of the techniques newly developed to strengthen a beam in shear. This method also has proved to be efficient than the conventional method like External Bonding of Reinforcement (EBR) method. The NSM technique involves fixing of NSM steel bars using adhesive into pre-cut grooves in the concrete cover of lateral surfaces of the beams. In this paper, the influence on NSM bar orientation and NSM bar diameter on the ultimate load carrying capacity of the RC beam is studied. Results have shown that, the load carrying capacity of the RC beams increases for those having NSM bars at inclined orientation than vertical orientation. Also, an increase in the NSM bar diameter increases the ultimate load carrying capacity of the RC beam.
High-strength concrete (HSC) has gradually transformed in use and scope for more than six decades, as mentioned by the American Concrete Institute (ACI 2010). HSC has a continuously expanding range of applications, owing to its highly desired characteristics such as a sufﬁciently high early age strength, low deﬂections owing to a high modulus elasticity, and high load resistance per unit weight (including shear and moment). HSC is thus highly effective in con- structing skyscrapers and span suspension bridges. HSC commonly refers to concrete whose compressive strength equals or exceeds 60 MPa and less than 130 MPa (FIP/CEB 1990). High-strengthreinforcement is increasingly common in the construction industry. In Taiwan, high-strength rein- forced concrete (HSRC) should include HRC with a speci- ﬁed compressive strength of at least 70 MPa and high- strengthreinforcement with a speciﬁed yield strength of at least 685 MPa. Meanwhile, as the most common speciﬁca- tion for concrete engineering design in Taiwan, ACI 318 (2011) sets an upper bound of the yield strength of
specimen G8N6 are modified to take into account the different loading conditions, i.e., four-point bending for G8N6 versus three- point bending for S0M. Because specimen G8N6 had a pure bend- ing region, the midspan deflection caused by the curvature in this region was subtracted from the total measured deflection. The curvature was evaluated based on the classical plane-sections- remain-plane approach by using the program Response-2000 (Bentz 2000, 2009). Although the classical approach applies to slender members, it is used in this study to provide a measure of the flexural deformations between the applied loads. By compar- ing the thick dashed line and the thick continuous line, the two specimens are shown to exhibit different shear strengths and differ- ent deflections at peak load. Although the GFRP-reinforced speci- men was significantly shorter than specimen S0M, it failed under a smaller normalized shear force and a larger midspan deflection. This result shows that the stiffness of the longitudinal reinforce- ment has a significant effect on the shear behavior of deep beams. Some insight into this result can be gained from Fig. 1(b), which compares the crack diagrams of the two beams near fail- ure. Although the two crack patterns are very similar, the GFRP- reinforced beam had a wider critical diagonal crack than the steel-reinforced member. Wider cracks result in less aggregate in- terlock between the crack surfaces, and therefore smaller shear capacity. The 2PKT, originally developed for members with steel reinforcement, accounts explicitly for the width of the cracks and the shear resisted by aggregate interlock, and therefore has the po- tential to capture the shear behavior of FRP-reinforced deep beams.
with the production of cement: this will have reduction effect on the greenhouse, a major cause of climate change. The web openings of the beam result in the decrease of flexural stiffness, flexural and shear strengths, increase in the deflection of the beam and may lead to cracking. Therefore the reinforcement at the openings is needed to ensure the proper strength and stiffness of the beams (Mansur et al, 2006, Mansur and Tan, 1999a, Vivek, and Madhavi, 2016). Euro Code 2 (BS EN 1992-1-1, 2004) defines a deep beam as a member whose span is less or equal to 3 times the overall section depth. Hence slender beam can be said
This study presents a method that combines both dimensional analysis and statistical regression analysis for predicting the shear capacity of slender reinforced concrete (RC) beamswithout web reinforcement taking the size effect into consideration. This method incorporates the modified Buckingham-PI theorem (Butterfield, 1999, Geotechnique 49(3), 357-366) to formulate two mathematical models for predicting the shear capacity at the formation of diagonal tension cracks and at the ultimate shearstrength. The results of the two models are compared with several sets of existing experimental results. This study shows that the variations in the experimental results of shear capacity of slender RC beams ( a / d 2 . 5 ) defined at the formation of diagonal tension cracks of beams can be explained by the variations of the concrete tensile strength and the variations in the experimental results of ultimate shearstrength of slender RC beams ( a / d 2 . 5 ) can be explained by the variations of the concrete splitting strength.
In case of HSC beams, COR for Euro code EC2  Eq. 4 is 0.974 which is higher as compared to New Zealand Code  Eq. 3 , Canadian Code  Eq. 2 and ACI Code  Eq. 1 which are 0.882, 0.932 and 0.90 respectively. It should be noted that Euro code EC2  Eq. 4 equation uses cubic root function (ƒ'c) ⅓ rather than the square root function (ƒ'c) ½ used by ACI Code  Eq. 1, Canadian Code  Eq. 2 and Newzealand Code  Eq. 3 to reflect the effect of the concrete compressive strength ƒ'c on the shear capacity of reinforced concrete beams. This implies that (ƒ'c)½ function used in the ACI Code  Eq. 1, Canadian Code  Eq. 2 and Newzealand Code  may not be adequate to reflect the effect of the ƒ'c on the shear capacity of high strength reinforced concrete beams.
Beamswithout web reinforcement with a/d = 2, short beams (Fig. 11(b)). ACI Code states that the no- minal concrete shearstrength defined in the equation is based on the shear causing inclined crack. Unlike the shallow beams, which usually fail soon after the formation the inclined crack at the shear span, the short beams can still carried more load due to the arch action. The ultimate loads of the short beams are usually much higher than their inclined cracking load. Therefore, ACI Code gives rather conservative predic- tions for these short beams, but it still can be seen that this conservative trend decreases with the increase of the beam sizes. Both ACI Code and Zsutty’s equation are safe for small beams and tend to be unsafe for the large beams. Bazant’s method predicts the trend of in- fluence of the effective depth is not as well as in shal- low beams. It also underestimates the ultimate strength. Strut-and-Tie model predicts well the trend of influence of effective depth, but it overestimates the shear capacities of HSC deep beams.
a highly random process and very hazardous. For last ten year, experiments have been done to analyze this phenomenon, in order to solve the riddle that shear is. Researchers turn out to be more knowledgeable about the shear and the factors responsible for the same. The present work involved collecting the test data of concrete beams of different depths and consequently different shear span ratio(a/d) and relating the test results to four shear resistance formulas for (beamswithoutshearreinforcement) given by different codes. ACI-318, BS8110, IS-456, and the formula given by the Bazant Zdenek.P and Yu  considering size effect in the beam (ASCE 2011 Paper). An attempt is made to establish the probability distribution to describe the inherent randomness in shear resistance of RC beams. IS 456-2000 adopted the concept of characteristic value for material strength and load. 6 series of beam data from the literatures are collected and the test results are compared with the results obtained from the four empirical formulas. The findings are that, i) Bazant size effect formula gives very conservative results, since it is consider the size effect in the beam. ii) IS-456 and ACI-318 gives reasonable estimates at shearstrength at the failure of section but not for shear resistance at the appearance of first shear crack in the beam in some situation. An attempt has been made to establish the probability of failure or margin of safety of R.C.C beam subjected to shear force in various limit states, and to propose the LRFD design format. As the basic variables in the design of a R.C.C beam have inherent probabilistic variations, the probability of failure can be accessed through reliability analysis. Conducted a sensitivity analysis to establish the statistical influence played by each basic variable on the shear resistance predicted using the different building codes.
In this paper an analytical model is provided for the calculation of the flexural and shear capacity of HSC beams in the presence of transversal reinforcement. The model is given in additive form, assuming two different contributions in the shear resistance, i.e., the shear capacity provided by the concrete and the contribution due to the transversal stirrups. The shearstrength of concrete is calculated following the classical approach originally proposed by Bazant and Kim (1984), determining two resisting mechanisms named “arch” and “beam” action. The model also takes into account the crushing of concrete by introducing an upper limit to the contribution of the material in compression. For the validation of the model, several analytical formulations available in the literature are reviewed and the models are applied for interpreting the results of a set of experimental data in the literature. The comparison shows that there is an increasing underestimation of the flexural capacity of the beam for increasing values of the concrete compressive strength; the results also show that the limit of 2.5% for the steel ratio is excessively conservative to ensure the yielding of the steel reinforcement before the crushing of concrete, even though in seismic areas this limit should be carefully checked. Finally, all models for the prediction of the shearstrength are able to provide quite accurate results. In particular the model proposed by Russo et al. (2013) gives the most accurate mean value of the ratio between experimental and theoretical shear resistance, equal to 1.12, while the current model gives a quite accurate mean value (equal to 1.24) and proves to be the most reliable model with the lowest value of coefficient of variation which is equal to 15.6%. Finally the current model is able to provide the most conservative result in terms of non-dimensional ultimate shear stress with the variation of the mechanical ratio of transversal reinforcement.
Shear failure in reinforced concrete, also known as diagonal tension failure, is difficult to accurately predict. This remains the case despite decades of experimental research, the development of new behavioral theories, and the use of sophisticated analytical tools. The difficulty lies in the fact that shear failure is really the sum of several internal mechanisms of resistance acting within the concrete. These include the uncracked compression zone, aggregate interlock, dowel action, and residual tensile stresses normal to cracks. The uncracked compression zone is the portion of uncracked concrete that is still able to fully resist shear forces. Aggregate interlock refers to the internal friction generated at a crack due to surface roughness, and can account for over one third of the total shear force. Dowel action results from the vertical forces across the longitudinal steel (Nilson et al., 2004). Collins et al. (1996) demonstrated that cracked concrete possesses tensile stresses that can considerably increase the ability of concrete to resist shear forces.
Fig. 5 shows the amount of the load transferred to the end and intermediate supports against the total applied load in L-series beams. On the same figure, the support reactions obtained from the linear 2-D FE analysis are also presented. The relationship between the total applied load and support reaction in H-series beams was similar to that in L-series beams; therefore, not presented here. Before the first diagonal crack, the relationship of the end and intermediate support reactions against the total applied load in all beams tested shows good agreement with the prediction of the linear 2-D FE analysis. However the amount of loads transferred to the end support was slightly higher than that predicted by the linear 2-D FE analysis after the occurrence of the first diagonal crack within the interior shear span. At failure, the difference between the measured support reaction and prediction of the linear 2-D FE analysis was in order of 7% and 12 %, for beams with
Recently, the steel ﬁber-reinforced concrete (SFRC) has been widely used as structural material due to its remarkable mechanical properties compared to conventional concrete. Through the numerous experimental studies, it turns out that the addition of steel ﬁbers can improve the structural capa- bility of concrete (Fanella and Naaman 1985; Sharma 1986; Narayanan and Darwish 1987; Wafa and Ashour 1992; Ashour et al. 1992; Ezeldin and Balaguru 1997; Kwak et al. 2002). Even though SFRC has many advantages as struc- tural material, some limitations still exist in the construction of the large-scale structures that requires very high com- pressive and tensile strength.
Bentz, Vecchio & Collins (2006) observe that the shear behaviour of reinforced concrete continues to be studied, and discussed as there is no agreed basis for a rational theory, and experiments cannot be conducted for concrete beams subjected to pure shear. Shear failures of PSC beam structures are potentially brittle and could occur without warning due to the low level of shearreinforcement which is often associated with these types of beams. This brittle and explosive nature of failure was evident in the testing of PSC beams within this study. This illustrates the increased importance of being able to accurately and safely predict the shear capacities and ductility of bridge beams.