Abstract

In order to evaluate the shear strength and behavior of high-strength concrete beams without web reinforcing, eight high-strength continuous concrete beams with cross sections of 200 mm by 300 mm were cast and tested to failure. The ultimate load-carrying capability and shear behavior are presented. The applicability of the Sudheer et al. equations and ACI 318M-14 is examined. In addition, the effects of the compressive strength () and shear span to effective depth ratio (a/d) on the shear strength and behavior of HSRC beams without stirrups are also studied. 63 MPa, 78.8 MPa, 85.9 MPa, and 92 MPa were the concrete’s compressive strengths, while 2.41 and 3.33 were its shear span to effective depth ratios. There were two equal spans of continuous beams, and at each span, they were evaluated under a single-point load. It was found that with increasing compressive strength, the failure load was increased. But the deflection did not affect it significantly. While increasing, (a/d) led to a decrease in failure load but increased deflection. It was also found that both ACI 318 M-14 and Sudheer et al. equation were more conservative.

1. Introduction

Reinforced concrete has been the most extensively utilized material in building since the eighteenth century because of its desirable excellent qualities. The main property of concrete is its compressive strength, which will be classified as normal strength concrete (NSC) and high strength concrete (HSC) by some publications. High-strength concrete is defined as concrete that has a compressive strength that is significantly greater than that used in normal practice [1, 2]. Beams made of reinforced concrete could fail in a variety of different ways. Shear is one of the most common failures in reinforced concrete buildings because it happens unexpectedly and without warning to the user. This might be due to the difficulty in anticipating some other kinds of collapse, or the catastrophic nature of some of the failures if they occur [3]. Because shear defeat is sudden and brittle, the shear design must ensure that shear strength matches or exceeds flexural strength at every part of the beam. When high-strength concrete is rapidly loaded in uniaxial compression cracks, it can generate a smooth failure surface that is virtually planar. Unlike lower-strength concrete, which has a rough failure surface, high-strength concrete has a smooth failure surface [4]. Dependent on the strength and location of coarse aggregates, the crack may go through or pass by them, resulting in a quite different shear behavior. Once shear cracking is initiated, both the normal and the tangential displacements occurred at the interface of the cracks. As the aggregates are strong, the crack would pass by them. Aggregate interlock caused by friction and collision will be activated in this situation, preventing the tangential displacement. However, if the crack penetrates through the aggregates, a relatively smooth crack surface would be formed, as shown in Figure 1 [5].

The crack development mechanism is difficult to completely comprehend, even though it appears to be the simplest; yet, shear failure of reinforced concrete beams is a very complex occurrence due to the participation of too many variables [6]. Five shear transfer mechanisms had been identified: residual tensile stresses transmitted directly across cracks; shear stress in the uncracked compression zone (the flexural compression zone); interfacial shear transfer caused by aggregate interlock or crack friction; dowel action of the longitudinal reinforcing bars; and arch action [7]. After cracks occur due to flexure the amount of shear force is taken compression zone. Since the concrete is uncracked, failure is due to a combination of shear and compressive stresses. This means that the shear force can be represented by the compressive strength of the concrete. When fractures appear as a result of flexure, the compression zone is accountable for the amount of shear force. This means that the concrete’s compressive strength may be used to represent the shear force. Kani [8] concluded that small (a/d) beams had higher shear strength. The term (M/Vd) contains a theoretical representation involving bending moment (M), shear force (V), and effective depth (d). (M/Vd) still has physical significance at any cross-section of a beam. In addition, Brian et al. [9] showed that regardless of the kind of the coarse aggregate material employed, the shear span-to-depth ratio was found to significantly influence the shear strength of beams. Because continuous beams constitute the majority of the actual construction, understanding the effect of continuity on shear behavior is critical. Rodriguez et al. [10] had studied the effects of continuity on the shear strength of statically indeterminate parts, the function of web reinforcement in shear strength, and the minimal amount of web reinforcement required to prevent shear failures. The test’s parameters included loading type, flexural reinforcement grade, spacing and percentage of web reinforcement, cut-off or extension of longitudinal reinforcement, and a nominal compressive strength of 3500 psi (24.1 MPa). A study on the behavior of simple and continuous fiber-reinforced polymer beams was published by Grace et al. [11]. The concrete’s compressive strength was 48.26 MPa. They came to the conclusion that the use of GFRP stirrups significantly enhanced beam deflections and deformed shear. Furthermore, the use of GFRP stirrups rather than steel stirrups resulted in a significant number of small, inclined cracks that covered roughly two-thirds of the span. Michael [12] released an article describing a thorough experimental study to identify the critical variables influencing the degree of the size effect in shear. They looked at the variables that affect how strong flexural beams with big, light reinforcements are in shear. They came to the conclusion that, as the beams grew larger, members without stirrups failed in shear at lower shear stresses. Moreover, high-strength concrete structures could collapse at unexpectedly low shear levels and were more vulnerable to the size effect in shear. They recommended making a few minor changes to the current ACI shear design equation. The influence of concrete strength contribution on continuous reinforced concrete beams with two spans was the subject of Michael McCarty’s [13] M.Sc. thesis. He has made an effort to determine whether shear reinforcement at maximum spacing can regulate shear forces and avert a shear failure. Concrete had a compressive strength range of 4948 psi (34 MPa) to 6255 psi (43 MPa). Motamed [14] had presented a Ph.D. dissertation about the behavior of a monolithic beam at external column joints and the effect of the central vertical bar (CVB) on joint shear behavior. They employed two different types of concrete: high-strength concrete, whose compressive strength ranged from 87.2 MPa to 94.48 MPa, and normal-strength concrete, whose compressive strength ranged from 32.8 MPa to 38.16 MPa. He came to the conclusion that the shear capacity of NSC beams with the same geometry and reinforcement and an a/d = 3.02 span/depth ratio was lower or equal to the shear capacity of HSC beams. In a research study by Nwofor et al. [15], the most economical design for six continuous reinforced concrete beams was compared to that of Eurocode 2 and BS 810-97. They came to the conclusion that the BS8110 shear forces at supports surpassed the Eurocode2 by an average of around 1.19% for both the top and lower limits of shear force. And, the Eurocode 2 is more cautious in terms of partial factors of safety for loadings. For the combination of live and dead loads examined in this study, the maximum design loads required by the BS 8110 were almost 1.3% higher than those required by the Eurocode 2. The necessary margin of safety was maintained while a more cost-effective design was possible thanks to Eurocode 2. Twelve reinforced concrete beams, eight without stirrups, and four with shear reinforcement, had been tested by Aguilar et al. [16]. The compressive strength of concrete varied from 48 to 105 MPa. They wanted to know if high-strength concrete could use the minimum and maximum shear reinforcement levels indicated in the AASHTO LRFD 14 standards and the ACI Code 318-14. They came to the conclusion that both AASHTO LRFD and ACI 318’s conservatism had diminished as the amount of shear reinforcement increased. Ahmad et al.’s [17] investigation of moment redistribution behavior under flexural and shear stresses in continuous concrete beams reinforced with glass fiber-reinforced polymer (GFRP). The analysis system (ANSYS) was used to generate a finite element model. The predictive shear capabilities of the analytical model, the produced finite element model, and the data from the literature were all compared. This study demonstrated the effectiveness of ANSYS software as a tool for simulating GFRP reinforcement. It was found that the results of the experiments and the finite element analysis were in perfect accord.

As was previously mentioned, a variety of factors affect how strong shear beams made of high-strength reinforced concrete are. It is challenging to analyze one component and isolate it from other factors since the impacts of different factors interact with one another. There are many studies on simply supported beams, but fewer studies than simply supported ones cover continuous beams. Therefore, the main objective of this study is to determine the effect of continuity on the shear strength of statically indeterminate beams.

2. Objectives of the Study

(1)To measure the shear strength of continuous beams made of high-strength reinforced concrete without web reinforcement(2)To study how the a/d ratio and compressive strength affect the shear strength of high-strength reinforced concrete beams without stirrups when subjected to a concentrated loads

3. Methodology

To fulfill the above-given objectives, a research program that includes experimental and numerical phases is proposed. The experimental phase consists of casting and testing 8 concrete beams continuously over two spans. Also, the comparison made between the ultimate shear strength acquired from test data with values calculated from ACI and other researchers’ predictions.

4. Experimental Program

4.1. Materials

To reach the required mix design of high-strength concrete mixtures, instructions and directions of ACI 211.4R [18] and ACI 363.2R [2] guides have been followed. To reach the required concrete strengths, four types of mixes were used. These mixes were obtained after conducting more than thirty trials. The mixed proportions are summarized in Table 1.

The selection of the raw components for concrete had been controlled by ASTM regulations. Ordinary Portland cement, locally manufactured at the Tasluja factory in Sulaimani, North Iraq, locally natural sand from river, whose properties shown in Figure 2, which conforms to ASTM C33 [19] limits, crushed stone with 12.5 mm maximum size, the grading conformed ASTM C33 [19] specifications, shown in Figure 3, and ordinary drinking tap water were used. Also, to achieve the workability and strength of concrete, a water reducing admixture, Sika ViscoCrete 5930 L super plasticizer, was needed to make the concrete mix workable, in addition to the Silica fume. Finally, deformed steel bars with nominal diameters of 20 mm and 538 MPa yield strength were used as flexural reinforcements and 8 mm with 520 MPa yield strength were used for shear reinforcements, whose properties shown in Table 2.

4.2. Beam Details

The variables are concrete compressive strength and shear span to effective depth ratio. All the beams have the same cross-section (200 mm width and 300 mm height) and longitudinal reinforcement ratio (). Beam details are explained in the Table 3. The specimens were divided into four groups A, B, C, and D according to their concrete compressive strengths. In Figures 4 and 5 reinforcement details were explained. All the beams were designed so that failure will occur due to shear. Also, they were so chosen that they do not fail in the exterior support regions.

4.3. Mechanical Properties of Concrete

Figure 6 show curves of stress-strain diagrams. To obtain Compressive Strength three 150 × 300 mm cylinders were taken according to ASTM C 39/C 39M [20]. Three 100 × 100 × 500 mm prisms were taken in accordance with ASTM C78/C78M [21] utilizing simple beams with third-point stress in order to obtain the modulus of rupture. Elasticity modulus were made in accordance with ASTM C 469/C 469M [22]. Finally, to determine splitting tensile strength, three additional 100 × 200 mm cylinders were obtained in compliance with ASTM C 496/C 496M [23]. Table 4 presents the results for the control specimens.

4.4. Instruments

After the preparation of the molds using plywood sheets, the next stage began with the construction of the cage, by assembling the main reinforcement bars with the stirrups as shown in Figure 7, and they were explained previously in the figures and tables. Then, the strain gauges were fixed to the predetermined location on the reinforcements using glue. After that the strain gauges were covered with special tape, made for electrical joints, to protect their moisture, impact, or damage during casting. Finally, the cage was placed inside the plywood mold after brushing inside with oil to make the removal of the forms easy after casting the beams.

Casting was started along the length of the beams and was filled in two layers each layer was compacted using an internal vibrator. The upper surface of the molds was leveled with a steel trowel. This process was continued until the casting of the group was completed. Side by side of this process, nine cylinders () mm and three prisms () mm were cast to obtain compressive strength, splitting tensile strength, modulus of rupture, and modulus of elasticity. After 24 hours, the sides of the molds and control specimens were removed. The curing process for the beams and the control specimens started and all of them were covered with wet burlap and kept wet for more than 90 days. The beams were tested under a universal machine with a hydraulic jack of 2000 kN (200 ton), 700 bar, and maximum capacity as explained in Figures 8 and 9.

To obtain reactions and loads, load cells of type S8920 were placed beneath the exterior reaction and loaded. As shown in Figure 10, these load cells were manufactured by SEWHACNM. Three (linear variable displacement transducer) LVDT were used, the first one along the inclined strut location, the second on the compression fiber of the load, and the third one along the compression fiber of the middle support. Also, precision electronic strain gauges were used along the diagonal strut between the middle support and loading points. For measuring the strain of stirrups and main reinforcements, precision electronic strain gauges were used. The positions of strain gauges were shown in Figures 1114.

A linear variable displacement transducer (LVDT) was used under the point load to measure the deflection that occurred during the loading process. And, a data logger of the type Windmill 851 was used to collect all the data from the strain gauges, LVDTs, and loads cells.

4.5. Test Procedure

All the beams were tested in a loading frame through one hydraulic jack of 2000 kN capacity, with three support reactions. Load cells had been put beneath the left support to determine the support reactions in addition to total load accurately to determine the shear force in each span. A wide flange steel beam was used to divide the hydraulic jack force into two-point loads. A thick plate () mm was used to prevent the local bearing failure at the point of load application.

The test was started under force control with a specific load increase of 10 kN to 15 kN once the preceding processes had been finished. A visual inspection was conducted at each load increase, and any cracks were marked. The crack propagation was examined at each load increment, and the location, load size, and newly formed cracks were noted and documented. The weight was increased incrementally during this procedure until the beam finally failed.

5. Test Results and Discussions

5.1. Crack Propagation and Failure Load

At beginning of the loading process, with loads, all the beams behaved elastically. The stresses were small and below proportional limits, consequently, the beams were free of cracks and the deflections were small. The first crack was vertical, due to flexural stress. After the formation of the first crack, they were followed by more similar flexural cracks. Further new flexural cracks formed in both the hogging and sagging flexural regions as the load was increased. With increasing the loads, the flexural cracks near the supports propagated diagonally toward the loading point. The cracks grew wider and propagated toward each other. Before the beams fail, a diagonal crack is initiated at the midheight of the beam. Before the failure, as the load increased, the number of cracks did not increase, but the depth and width of the cracks had increased. The failure loads of the beams are shown in Table 5. The crack pattern of beams is shown in Figures 1518 for casting groups A, B, C, and D, respectively.

5.2. Effect of Compressive Strength on Load-Deflection Behavior and Ultimate Load

The relation between deflection and load is shown in Figures 19 and 20. In general, when the concrete compression strength increases, the ultimate load of failure of the beams increases too. The experimental results showed that for beam series 1, beams with shear span to depth ratio (a/d) 2.41 when the compression of the concrete increased from 63 MPa to 78.8 MPa the ultimate load increased 121.6%. By changing the compressive strength from 63 MPa to 85.9 MPa the ultimate load increased 132.4%. While the changing of compressive strength from 63 MPa to 92 MPa lead to an increase in the ultimate load by 1.523%. For shear span to depth ratio (a/d) 3.33, beam series 2, when the compressive strength increased 1.25% as well as the ultimate load increased 1.106%. The increase in concrete strength of 136.4% was followed by the increase in the ultimate load of the beam by 123.1%. Also, raising the compressive strength by 146% was reasoned to increase the ultimate load by 134.7%.

In contrast to the ultimate load, it was found that with increasing concrete compressive strength the deflection response was not in the same attitude. In some groups, we observed that with increasing concrete strength displacement decreases, but not in a constant proportion while in some other groups increasing compressive strength caused to increase in the deflection of the beam. We noted that the load-deflection curves could be divided into two distinct stages, precracking and postcracking. In the first stage, the curve was almost linear. After formation of the cracks causes a reduction in the beam stiffness and leads to a changing slope of the curve. Also, it was observed that when the compressive strength of the concrete was increased the slope of the first stage of the curve, precrack, became steeper.

5.3. Effect of Shear Span to Effective Depth Ratio on Load-Deflection Behavior and Ultimate Load

The shear span to effective depth ratio is one of the most essential aspects affecting the beam’s resistance and behavior. The influence of the force moment increases as the distance between the load and the support increases, and in the presence of the force moment, the fractures in the section expand and the effective depth of the section falls, reducing the section’s resistance to shear. In this study, we got two shear span to effective depth ratios (a/d) 2.41 and 3.33. The results of the tested beams showed that for beams with compressive strength of concrete 63 MPa, changing a/d from 2.41 to 3.33 the ultimate load decreased from 356.1 kN to 264.55 kN, 74.3%, as shown in Figure 21. For beams, with concrete compressive strength of 78.8, MPa changing a/d led to a decrease in the ultimate load by 67.57%, from 433.1 MPa to 292.64 MPa, as shown in Figure 22. Beams of type C, with concrete compressive strength of 85.9 MPa, changing in shear span to effective depth ratio reduced the ultimate load 69.07%, from 471.6 MPa to 325.74%, as shown in Figure 23. The last group was beams of type D, with concrete compressive strength of 92 MPa. When the aspect ratio, a/d, changed the ultimate load changed too, from 542.2 MPa to 356.26 MPa, 65.71%, as shown in Figure 24.

It is commonly known that the deflection grew along with the span. The moment of force increases as the distance between the supports increases, increasing the deflection as a consequence. We came to the conclusion that raising the aspect ratio, a/d, produced an increase in the deflection under the point load after examining the curves of the relationship between load and deflection of the tested beams. These increases were varied rather than consistent.

6. Comparing Test Results with Other Provisions

In this article, the results of the tests are compared to the ACI code, with two different researcher approaches presented. The ACI 318M-19 equation for calculating the shear strength provided by concrete for nonprestressed members The modified Zsutty equation and the equation proposed by Sdheer et al. were compared.

6.1. ACI 318M Equation for Shear Prediction

For member subjected to shear and flexure ACI 318M-14 proposed the following equation [24]:where ; Nominal shear strength provided by concrete, N ; Compressive strength of Concrete, N/mm2, ; Longitudinal flexural reinforcement ratio, , ; Shear force at the section considered, N, ; Moment at the section considered, N·mm, ; Web width, mm, ; and Effective depth, mm

ACI stated that shall not be greater than 1.0. Table 6 presents the calculated shear strength versus tested shear.

6.2. The Equation Proposed by Sudheer et al. for Shear Prediction [25]

In 2010, Sudheer et al. developed the linear regression equation in power series to calculate the shear resistance of high-strength concrete beams while accounting for the concrete’s tensile strength, flexural reinforcement, and the (a/d) ratio:where , Shear strength provided by concrete, N, , Tensile strength of concrete, N/mm2, , Shear span to depth ratio. Longitudinal flexural main reinforcement ratio, and , d Web width, effective depth, mm

The predicted results based on equation (2) are presented in Table 7, along with a comparison of the predicted and test results.

The values measure the equation’s conservation, and if this number is less than 1.0, the equation is on the safe side because it overestimates the true value of the beam. The following broad conclusions can be drawn based on the information in these tables:(1)For the ACI equation, when a/d increased, the values became less conservative; this may be because of the effect of the flexural moment(2)The equation proposed by Sudheer et al. was more conservative, and the predicted values decreased as the tensile strength of concrete increased

7. Conclusions

The results of a study on the strength and behavior of reinforced high-strength continuous concrete beams were summarized in this paper. The following conclusions may be taken from the scope of this study:(1)As the compressive strength of concrete was increased, the concrete became more fragile and the corresponding strain decreased. And, increasing the compressive strength led to an increase in the ultimate load of the beams.(2)The increase of concrete compressive strength caused a slight decrease in the deflection of the beams because the increasing concrete strength caused to increase in stiffness and this led to a decrease the deflection. Also, when the concrete became stronger, the ductility reduced and the concrete became more brittle.(3)In beams with a/d = 2.41, Increasing compressive strength by 125% caused the ultimate to increase by 121%. And, ultimate load 132% because of increasing compressive strength 136%. Also, this increase continued and reached 152% when compressive strength increased by 146%. Also, when a/d = 3.33, the increase in ultimate load was 111%, 123%, and 135% when the compressive strength increased 125%, 136, and 146%, respectively.(4)When a/d increased, the deflection of the beams increased, too.(5)For concrete strength of 63 MPa, increasing a/d from 2.41 to 3.33 caused to decrease in the ultimate strength of 74%, and deflection increased by 137%.(6)For beams group B (78.8 MPa) changing a/d led to a decrease in ultimate load of 68% and increased deflection by 143%.(7)For beams group C (85.9 MPa) the ultimate load decreased 69% and deflection increased 152% because of changing a/d from 2.41 to 3.33.(8)For beams group D (92 MPa) the ultimate load decreased 66% and deflection increased 123%.(9)The values for the ACI equation became less conservative as a/d increased; the flexural moment might have had something to do with this.(10)The values predicted by Sudheer et al.’s equation decreased as concrete’s tensile strength increased, and they were more conservative.

8. Further Study Recommendations

The following suggestions may be useful for further work:(1)Experimental and analytical studies about the shear behavior of continuous beams with different cross-sections, such as L-shaped and T-shaped sections.(2)In this study, specimens were tested under one-point loads in each span. It is better to test a series of continuous beams under different loading arrangements than a one-point load in each span.(3)Experimental and analytical study about the effect of unsymmetrical spans on shear strength of reinforced high-strength continuous beams.

Data Availability

The data used to support the study are available from the corresponding author upon request.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The study was supported by University of Sulaimani, College of Engineering, Sulaymaniyah, Kurdistan Region, Iraq.