Previous studies have shown that a **uniform** distribution of **load** may increase the **shear** **strength** of a **slender** member by as much as 40 percent (Leonhardt and Walther 1964). The increase of **shear** **strength** is potentially due to clamping stresses induced from the **uniform** **load**, 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 **without** **shear** **reinforcement** were completed with **uniform** **load**. Additionally, the majority of **uniform** **load** data consists of specimens with small specimen depths (d) and large longitudinal **reinforcement** ratios (ρ).

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One of possible and discovered reason is the size **effect** of the structure members, which was introduced by Okamura [2]. 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 **shear** **strength** resist by concrete to be the same up to yielding point of stirrup itself [4]. However, there is still not a simple, albeit analytically derived formula to predict and with accuracy the **shear** **strength** of **slender** **beams**. In addition many of the factors that influence the determination of the required minimum amount of **shear** **reinforcement** are not yet known [3]. 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 **shear** **reinforcement** is required to prevent such a failure and then in a less-critical decision how much is required. **Shear** **reinforcement**, 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.

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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 **shear** **strength** 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 **slender** **beams**, 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

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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 **slender** **beams**, **shear** force is carried by the **shear**

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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 **shear** **strength** for all **beams** except NNB sample that showed lower experimental **shear** **strength** than ACI result for the same beam. ACI and CSA did not consider steel fibres in **beams** in predicting **shear** **strength**. 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 **shear** **strength** 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.

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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).

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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-**strength** **reinforcement** 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- **strength** **reinforcement** 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

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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**.

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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

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This study presents a method that combines both dimensional analysis and statistical regression analysis for predicting the **shear** capacity of **slender** reinforced concrete (RC) **beams** **without** 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 **shear** **strength**. 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 **shear** **strength** of **slender** RC **beams** ( a / d 2 . 5 ) can be explained by the variations of the concrete splitting **strength**.

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In case of HSC **beams**, COR for Euro code EC2 [7] Eq. 4 is 0.974 which is higher as compared to New Zealand Code [6] Eq. 3 , Canadian Code [5] Eq. 2 and ACI Code [4] Eq. 1 which are 0.882, 0.932 and 0.90 respectively. It should be noted that Euro code EC2 [7] Eq. 4 equation uses cubic root function (ƒ'c) ⅓ rather than the square root function (ƒ'c) ½ used by ACI Code [4] Eq. 1, Canadian Code [5] Eq. 2 and Newzealand Code [6] 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 [4] Eq. 1, Canadian Code [5] Eq. 2 and Newzealand Code [6] may not be adequate to reflect the **effect** of the ƒ'c on the **shear** capacity of high **strength** reinforced concrete **beams**.

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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 (**beams** **without** **shear** **reinforcement**) given by different codes. ACI-318, BS8110, IS-456, and the formula given by the Bazant Zdenek.P and Yu [2] 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 **shear** **strength** 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.

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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 **shear** **strength** 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 **shear** **strength** 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**.

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performance of these high-strength lightweight coarse aggregate – normal weight fine aggregate concrete beams without transverse reinforcement against design equations[r]

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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

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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**.

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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 **shear** **reinforcement** 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**.

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