T-beams are acknowledged as economic and efficient structural members widely used for floor slab construction systems. In many cases, according to practice in some countries, the beams do not present transverse reinforcement, and their shear strength is governing for dimensioning the width of the web. Although experimen- tal investigations have shown that the presence of the compression flange enhances the shearcapacity with respect to equivalent rectangular cross sections, most cur- rent design codes neglect this phenomenon, which leads to the overdesign of these members. In this paper, the role of the compression flange of slender T-beams with concentrated loads is investigated with reference to its influence on the shape of the critical shear crack and to the associated shear transfer actions (STA) of the beam. The flanges are considered elements that allow the smearing of applied loads over a certain length of the web. This consideration, in combination with the mechanical model of the Critical Shear Crack Theory (CSCT), allows a consistent treatment of the phenomenon and leads to simple design expressions accounting for the role of flanges. The results of the proposed model are compared together with design codes (Model Code 2010, Eurocode 2, and ACI 318-11) and other shear design approaches to a database of 239 beams on T-shaped members. The comparison shows that the role of flanges is finely accounted with the proposal based on the CSCT, leading to consistent agreement and to strength predictions that are more suitable for design purposes than the other investigated design models.
This paper reports the testing of fifteen reinforcedconcrete deep beams with openings. All beams tested had the same overall geometrical dimensions. The main variables considered were the opening size and amount of inclined reinforcement. An effective inclined reinforcement factor combining the influence of the amount of inclined reinforcement and opening size on the structural behaviour of the beams tested is proposed. It was observed that the diagonal crack width and shear strength of beams tested were significantly dependent on the effective inclined reinforcement factor that ranged from 0 to 0.318 for the test specimens. As this factor increased, the diagonal crack width and its development rate decreased, and the shear strength of beams tested improved. Beams having effective inclined reinforcement factor more than 0.15 had higher shear strength than that of the corresponding solid beams. A numerical procedure based on the upper bound analysis of the plasticity theory was proposed to estimate the shear strength and load transfer capacity of reinforcement in deep beams with openings. Predictions obtained from the proposed formulas have a consistent agreement with test results.
equations. For the ACI318-11 provisions the ratio equals 1.44, 1.26 for EC-2, 1.35 for Model Code 2010 and 1.33 for CSA A23.3-14, using for the Model Code the better results obtained for the different levels of approximation. The CoV is 18.6% for the simplified model proposed in this paper. For ACI318-04, EC-2, MC- 2010 and CSA A23.3-14 the CoV equals 35.3%, 34.1%, 31.4% and 26.9% respectively. A recently published paper studied the scatter in the shearcapacity of slender RC members withoutwebreinforcement . The authors concluded that the scatter of the shearcapacity seems to be mainly due to the randomness of the tensile strength of concrete. Also recently, other authors confirmed that a comparison with different shear design models revealed that models that use the concrete tensile strength predict the shearcapacity of continuous prestressed concretebeams with external prestressing more accurately  that the models that do not explicitly consider the tensile strength of the concrete. In this sense, the coefficient of variation of the predictions by the Compression Chord Capacity Model for the beam tests included in the four databases is not much higher than the coefficient of variation of the splitting tensile strength. In a published database of 78 splitting tensile tests , the coefficient of variation (COV) for the prediction of the tensile strength was 15.1%. This fact seems to indicate that the shear transfer mechanisms at failure have been well captured by the model.
Abstract: For shear-critical structural elements where the use of stirrups is not desirable, such as slabs or beams with reinforcement congestion, steel fibers can be used as shearreinforcement. The contribution of the steel fibers to the shearcapacity lies in the action of the steel fibers bridging the shear crack, which increases the shearcapacity and prevents a brittle failure mode. This study evaluates the effect of the amount of fibers in a concrete mix on the shearcapacity of steel fiber reinforcedconcretebeams with mild steel tension reinforcement and without stirrups. For this purpose, twelve beams were tested. Five different fiber volume fractions were studied: 0.0%, 0.3%, 0.6%, 0.9%, and 1.2%. For each different steel fiber concrete mix, the concrete compressive strength was determined on cylinders and the tensile strength was determined in a flexural test on beam specimens. Additionally, the influence of fibers on the shearcapacity is analyzed based on results reported in the literature, as well as based on the expressions derived for estimating the shearcapacity of steel fiber reinforcedconcretebeams. The outcome of these experiments is that a fiber percentage of 1.2% or fiber factor of 0.96 can be used to replace minimum stirrups according to ACI 318-14 and a 0.6% fiber volume fraction or fiber factor of 0.48 to replace minimum stirrups according to Eurocode 2. A fiber percentage of 1.2% or fiber factor of 0.96 was observed to change the failure mode from shear failure to flexural failure. The results of this presented study support the inclusion of provisions for steel fiber reinforcedconcrete in building codes and provides recommendations for inclusion in ACI 318-14 and Eurocode 2, so that a wider adoption of steel fiber reinforcedconcrete can be achieved in the construction industry.
failed shear span was the only output of the NNs developed. Table 1 gives the ranges of input data in training, validation and test subsets used to develop the NNs. In the database, beam width of deep and slender beams ranged from 20 to 300 mm and from 100 to 457 mm, respectively, effective section depth is between 80 and 1,559 mm for deep beams and between 110 and 1,090 mm for slender beams, and longitudinal reinforcement ratio ranged between 0.0011 and 0.066 for deep beams and between 0.0028 and 0.066 for slender beams. The maximum ver- tical webreinforcement indices for deep and slender beams were 0.964 and 0.14, respectively, and the maximum horizontal webreinforcement index for deep beams was 1.847. The test speci- mens were made of concrete having a very low compressive strength of 11.2 MPa and 14.7 MPa for deep and slender beams, respectively, and a high compressive strength of 120 MPa and 125 MPa for deep and slender beams, respectively. Training, vali- dation and test subsets had 50%, 25%, and 25% of all specimens in the database, respectively. The input data in each subset were selected at equally spaced points throughout the database so that the range of input in training subset would cover the entire distri- bution of database and input in validation subset would stand for all points in training subset as shown in Table 1.
Since the beams were prepared with different shear span length, significant influence can be seen from two types of failure mode. It is clearly shown that the beams with lesser a/d ratio (i.e.; BSM-01 to BSM-04) experienced higher capacity compared to beams which have greater a/d ratios (i.e.; BSM-05 to BSM-08). Similar results was found in beams which reinforced with GFRP bars i.e.; BGM-01 with 1.6 a/d ratios exhibit high capacity up to 233.2 kN rather than BGM-05 with a/d=3.1 that only reached 99.0 kN when it failed. It is shown that the ultimate capacity increases as the shear span-to-depth ratios decreases. In addition, two modes of failure, shear and flexure were observed from the test results. Sudden formation of diagonal crack can be found in the shear span zone followed by beam failure (BSM-03, BSM-04, BGM-03 and BGM-04). Additionally, the inclination of shear cracks growth rapidly as the load increase. While, beam failed in flexure experienced by one of the following condition i.e.; rupture of tensile longitudinal reinforcement for beam BGM-01, BGM-05, BGM-06, BGM-07 and BGM-08 and also concrete crushing on the top of
Concrete is known for its good compressive strength and low tensile strength. Researchers are continuously striving to improve its tensile capacity, as it is being the most accepted composite used for all structural applications. In this course, usage of steel fiber reinforcedconcrete (SFRC) emerged and many studies having been undertaken over the past four decades. Numerous research‟s (e.g. Narayanan. R et al.,; Kwak et al., ) has been conducted on the shear behavior of FRC over the past decades and the general conclusion is that, with proper mixture design FRC is capable of considerably increasing performance in terms of shear strength and ductility when compared to plain concrete. From most of the reviews, it may be concluded that Steel Fiber ReinforcedConcrete (SFRC) is a composite material with significantly better tensile strength and higher resistant to crack formation and propagation. Research on the high strength concrete showed that the cube compressive strength has less significance than the fracture energy for the description of the material behavior of structural elements.
In this study, three reinforcedconcretebeams were tested using the new shearreinforcement swimmer bar system and the traditional stirrups system. Several shapes of swimmer bars are used to study the effect of swimmer bar configuration on the shear load carryingcapacity of the beams (Al-Nasra et al 2013). Only three beams will be presented in this study. The first beam, BC, is used as a reference control beam where stirrups are used as shearreinforcement. The other two beams were reinforced by swimmer bars. Beam, WSB is the beam which is reinforced by two swimmer bars welded to the longitudinal top and bottom bars. Beam, SSB is the beam which is reinforced by swimmer bars spliced with the longitudinal steel reinforcement. Extra stirrups were used to make sure that the prepared beams will fail by shear in the swimmer bars side. In this investigation, all of the beams are supposed to fail solely in shear, so adequate amount of tension reinforcement were provided to give sufficient bending moment strength. This study aims at investigating a new approach of design of shearreinforcement through the use of splicing swimmer bars provided in the high shear region. The main advantages of this type of shearreinforcement system are: flexibility, simplicity, efficiency, and speed of construction. AlNasra and Asha (2013) studied the use of swimmer bars welded to the longitudinal steel reinforcement, and concluded that the beam reinforced with welded swimmers bars exhibit better shear resistance compared with the control sample beam reinforced with regular stirrups.
Moody et.al [28 & 29] in 1954 presented experimental works on 40 NWC beams casted withoutshearreinforcement and 2 NWC beams casted with shearreinforcement, which were segregated into three series to observe the influence of the variables: (i) percentage of longitudinal and webreinforcement and method of anchorage, (ii) size and percentage of longitudinal reinforcement and cylindrical concrete strength and (iii) concrete mixture and method of curing. The concept of redistribution of internal stresses was introduced for the predictions of shear failure for NWC beams. For each of the 3 series, the sizes of the beams were different and the beams were tested with one or two concentrated load. It was observed that all beams failed in shear. It is observed that the shearcapacity of the NWC beam specimens increased with the increment of concrete strength and percentage of longitudinal steel. It was also noted that the test results indicated that the beam strength tested at higher a/d ratio is governed by the first cracking load whilst the beam strength tested at lower a/d ratio is governed by the load, which caused destruction to the concrete compression zone. Hence, it is suggested by Moody et. al that instead of cracking load, ultimate load should be taken as the measured value for shearcapacity.
combined action of moment and shear taking the size effect into consideration is evaluated at the formation of diagonal tension cracks and at ultimate shear failure by using a method that combines both dimensional analysis and statistical analysis. Several sets of experimental data were carefully selected such that the influence of each basic variable (i.e., longitudinal steel ratio , concrete compressive strength f c ' , shear span to depth ratio a / d or beam size d ) can be separately evaluated. Comparison with existing experimental results as well as with four existing models supports the validity of the two proposed models in predicting and explaining the observed behavior of slender RC beams ( a / d 2 . 5 ) withoutwebreinforcement.
Abstract—This study presents test results of simply supported concretebeams longitudinally reinforced either by steel or glass fiber-reinforced polymer (GFRP). A total of sixteen large-scale concretebeams with steel stirrups were constructed and tested under four-point monotonic loading until failure. Half of the beams were longitudinally reinforced with GFRP bars, while the other half was reinforced with conventional steel bars as control specimens. To examine the shear behavior of the GFRP reinforcedconcrete (RC) beams, the main parameters investigated in the study included shear span-effective depth ratios, longitudinal reinforcement ratios and stirrup ratios. Two modes of failure, namely flexure and shear were observed. Due to low modulus elasticity of FRP bars, it was found that lesser shear strength resulted in concretebeamsreinforced with GFRP bars compared to beamsreinforced with steel bars. Moreover, the influence of the shear span-effective depth ratios and longitudinal reinforcement ratios significantly affect the distribution of internal forces in GFRP reinforcedconcretebeams. The test results correlated well with the prediction values provided by standard codes and design guidelines except in the case of GFRP reinforcedconcretebeams failed on shear.
Comparisons between test results and predictions obtained from the strut-and-tie model recommended by ACI 318-05 as developed above are shown in Table 3 and Fig. 11: Fig. 11 (a) for simple deep beams given in appendix A and Fig. 11 (b) for continuous deep beams including Rogowsky et al.’s and Ashour’s test results. In simple deep beams, the width of strut can be calculated from w t ' cos ( l p ) E sin , and the total load is 2 F E sin . Although Eq. (7) proposed by ACI 318-05 is recommended for deep beams having concrete strength of less than 40 MPa, the load capacity of H-series beams were also predicted using this equation to evaluate its conservatism in case of high-strength concrete deep beams. The mean and standard deviation of the ratio,
Abstract— This study presents test results of simply supported concretebeams longitudinally reinforced either by steel or glass fiber-reinforced polymer (GFRP). A total of sixteen large-scale concretebeams with steel stirrups were constructed and tested under four-point monotonic loading until failure. Half of the beams were longitudinally reinforced with GFRP bars, while the other half was reinforced with conventional steel bars as control specimens. To examine the shear behavior of the GFRP reinforcedconcrete (RC) beams, the main parameters investigated in the study included shear span-effective depth ratios, longitudinal reinforcement ratios and stirrup ratios. Two modes of failure, namely flexure and shear were observed. Due to low modulus elasticity of FRP bars, it was found that lesser shear strength resulted in concretebeamsreinforced with GFRP bars compared to beamsreinforced with steel bars. Moreover, the influence of the shear span-effective depth ratios and longitudinal reinforcement ratios significantly affect the distribution of internal forces in GFRP reinforcedconcretebeams. The test results correlated well with the prediction values provided by standard codes and design guidelines except in the case of GFRP reinforcedconcretebeams failed on shear.
Abstract There is no general consensus or accepted theory for evaluating the ultimate shearcapacity of reinforcedconcretebeamswithoutwebreinforcement as a result the requirements in most of Codes of practice are provided in the form of empirical equations for predicting the shearcapacity of reinforcedconcretebeams. In this paper, a study is conducted to evaluate the predictive accuracy of 6 empirical equations used in different Code of practice to predict the shearcapacity of reinforcedconcrete slender beams. Empirical equations used in some Codes are identified to be superior to other equations. In addition, a study was also conducted to assess predictive accuracy of 17 empirical equations proposed in the literature by several researchers to predict the shearcapacity of reinforcedconcrete slender beams. Among these 17 empirical equations some equations are identified to be superior to the other proposed equations. On the basis of experimental results of reinforcedconcretebeams having shear span to depth ratio a/d ≥2.5, empirical equations are proposed which include basic parameters i.e. concrete compressive strength , shear
The effect of small circular opening on the shear and flexural and ultimate strength of beams were investigated. The main factors of the test are the diameter changes and the opening position. In this study, five beams were casted and tested using C20 concrete and Fy415 steel. The first beam was solid and was used as control for comparison with other beams with an opening. The second beam opened at distance of L/8 by 110mm (0.55D), third beam opened at distance of L/8 by 90mm (0.45D). Beam number four and beam number five had openings at distance L/4 as mentioned above. The tested beams were loaded with two concentrated and symmetrical load as simple beam. They conclude that the reduction of ultimate strength increased and cracking patterned as well as the beam failure mode when the opening diameter increased. To increase the ultimate shear strength of the beam, they recommended the use of diagonal reinforcement and stirrups in top and bottom chords of opening. They also concluded that the most critical opening position to achieve the ultimate strength in beams is near the support and that the best opening place in these beams is mid span (flexure zone) .
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.
Asghari et al. (2013), presented an experimental investigation on shear strength enhancement of reinforcedconcrete lightweight deep beams externally reinforced with vertical CFRP sheets. The shear span/depth ratio was taken equal to 1, and the percentage of shear strength improving by strengthening was 30%. Khudair and Atea (2015), studied the shear behavior of self-compacting concrete deep beams strengthened with CFRP sheets. The experimental work includes testing of reinforcedconcrete self-compacting concrete (SCC) deep beams with shear span/depth ratio of 2. The tested results show that the specimens strengthened by vertical CFRP sheets provided enhancement in ultimate loads reached 30%.
In this study, the failure modes of BSM are governs by steel yielding before the concrete strain at the compression area reached the maximum permissible value of 0.0035 . For shearreinforcement, 2-legged steel stirrups of 8 mm diameter (mild steel) were spaced at 50 mm and 150 mm centre to centre at the shear region. These two kinds of spacing were calculated based on BS8110 code provisions in order to investigate the shear performance of the beams with minimum and adequate amount of stirrups. In each specimen, strain gauges were position at selected locations at longitudinal bars, stirrups and concrete which were labelled as X (see Fig. 1). The deflection of the beam was measured by at mid-span and two loading points.
Moreover, in order to picture confirmation of the SR development model, a parametric analysis was accomplished based on the procedure that proposed in . The mentioned procedure examines the response of the developed formulae to a set of assumed data. Based on this method, one input is changed while the other inputs are remained constant at their average. If this analysis yields conformed results to the underlying of problem, the strength of developed formulae is proved. For this study, the results of the mentioned parametric analysis show in Fig. 3. In fact, Fig. 3 illustrates the tendency of the shearcapacity of SFRC beams to the variations of 𝑉 𝑓 , 𝑙 𝑓 ⁄ 𝑑 𝑓 , 𝜌 𝑙 , 𝑑, 𝑎 𝑑 ⁄ and 𝑓 𝑐 ′ . Therefore,