Experimental study on shear behavior of reinforced concrete beams with web horizontal reinforcement

Abstract

In determining the shear capacity of reinforced concrete beams, current codes do not provide any calculation method to evaluate the influence of web horizontal reinforcement, although they exist as structural reinforcements (or skin reinforcement). The present paper comprises results of 11 reinforced concrete beams in an effort to investigate the influence of web horizontal reinforcement on the shear behavior of reinforced concrete beams. The primary design variables are the shear-span-depth ratio, different reinforcement ratio of stirrups and web horizontal reinforcement. Influence of web horizontal reinforcement on crack patterns and failure mode was studied. It was found that web horizontal reinforcement can increase the shear capacity of the beams and restrain growth of inclined cracks effectively. Test results are very valuable, as very few references of shear tests can be found focusing on the effect of web horizontal reinforcement on the shear capacity of the beams.

Keywords

reinforced concrete beam / shear strength / web horizontal reinforcement / experiments

Introduction

Research on the shear behavior of reinforced concrete beams started near the end of 19th century. Since then, a lot of shear failure mechanism and calculation models to evaluate the shear strength have been proposed by numerous researchers [ 1]. Currently effective design procedures for reinforced concrete beams in shear are based on several models: modified 45 degree truss model in ACI 318-05 [ 2], Variable Strut Inclination Method in Eurocode 2 [ 3], Modified Compression Field Theory (MCFT) [ 4] in Canadian Building Code [ 5] and AASHTO LRFD Specification [ 6]. In different design codes, only stirrups are designed as shear reinforcement and corresponding shear failure tests are presented in concrete beams reinforced without stirrups [ 7- 10] or with stirrups [ 11- 13]. Actually there exists horizontal reinforcement in most existing codes, but they are only considered as structural reinforcements (or skin reinforcement) and not accounted for in shear strength prediction.

Regarding the contribution of the longitudinal reinforcement, it is to highlight that the unbalanced horizontal forces produced by shear once the concrete cracks diagonally, alters the longitudinal stresses on the top and bottom longitudinal tension reinforcements. Actually, shear force in truss model [ 14, 15] can cause stress increment in longitudinal tensile reinforcement, which will resist shear together with stirrups. According to Eurocode 2 [ 3], AASHTO LRFD Specification [ 6] and Modified Compression Field Theory (MCFT) [ 4], the longitudinal reinforcement should be able to resist the additional tensile force caused by shear. However, there are no such special provisions in ACI318-05 [ 2]. On the other hand, both longitudinal and vertical reinforcements are considered as torsion reinforcement in different codes (ACI318-05; Eurocode 2; AASHTO LRFD Specification). It is found that different codes propose a different reinforcement pattern to resist shear stresses if they are produced by shear (stirrups) or by torque (longitudinal and vertical reinforcement). Hence it is clear that a lack of consistency exists between reinforcement design for shear and torsion in popularly adopted design codes.

In general, webs of concrete beams contain longitudinal reinforcing bars regardless of whether they are subjected to torque or not. Even if no torque is acting on the beam, at least some skin reinforcement is provided in the webs to control cracking. In none of the design rules, this reinforcement is taken into account to evaluate the steel contribution to the shear strength. And only AASHTO LRFD [ 6] takes this reinforcement into account to reduce the size effect.

The aim of the present paper is to study the influence of web horizontal reinforcement on shear behavior of reinforced concrete beams failing in shear. To do so, 11 reinforced concrete beams were tested at the Structural Laboratory of Department of Bridge Engineering at Tongji University, as a part of a research program on shear design of reinforced concrete beams. Some test beams are reinforced with both web horizontal reinforcement and stirrups, which is rather unusual in experimental studies. The primary design variables are the shear-span-depth ratio and the different reinforcement ratio of stirrups and web horizontal reinforcement, and the influence of each design parameter is studied separately. The details of the beam specimens, material properties, instrumentation and the testing procedure used are carefully described in this paper. The test results and their analysis are presented, leading to innovative conclusions. The effect of web horizontal reinforcement on shear strength of reinforced concrete beams is verified. It is found that the presence of web horizontal reinforcement enhances the shear behavior of the beam, both at Service Limit State and at Ultimate Limit State, whereas the codes do not provide any calculation method to evaluate the influence of web horizontal reinforcement on the shear strength of concrete members. It is recommended to account for the web horizontal reinforcement when calculating the shear strength of a beam if present.

Experimental campaign

Eleven reinforced concrete beams were tested under flexure and shear up to failure. The main objectives of the experimental campaign carried out were:

1) To study the influence of shear-span-depth ratio on the shear strength of concrete beams reinforced with web horizontal reinforcement and stirrups;

2) To study the influence of the web horizontal reinforcement on the shear strength of beams. Only stirrups are considered as shear reinforcement in most current design codes [ 2, 3, 5, 6];

3) To study the influence of the web horizontal reinforcement on diagonal crack width in reinforced concrete beams;

4) To study the effect of different ratio of web horizontal reinforcement and stirrups on the shear capacity of thin-webbed T beams.

Design of the test specimens

To achieve the prior objectives, a total of 11 beam specimens were designed and tested: eight beams were rectangular cross section and three beams were T cross section. Length of the beams ranged from 2400 to 3500 mm and depth ranged from 320 to 400 mm.

The test program consisted of three series of beams:

1) Series R40: rectangular cross section beams with concrete strength of 40 MPa. Four beam specimens numbered R40-1/2/3/4 were tested under a four point scheme (Fig. 1). All of them shared the same cross section (200 mm wide × 400 mm deep) and the same reinforcement layout. Shear-span-depth ratio (a/d = 2, 2.5, 2.5, 3 for R40-1, R40-2, R40-3, R40-4 respectively) were different for all of them, though. Flexural longitudinal reinforcement consisted of eight 20 mm diameter bars (ρ_l = 3.6%), with a characteristic yielding stress of 363 MPa. Both web horizontal reinforcement and stirrups were provided. This consisted of two-legs stirrups spaced 80 mm (ρ_t = 0.63%) and eight horizontal rebars distributed along the web with spacing 80 mm (ρ_h = 0.63%). Bars were 8 mm in diameter and the steel yielding stress was 234 MPa. The objective of this series was to study the influence of the shear-span-depth ratio on the shear capacity of concrete beams reinforced with web horizontal reinforcement and stirrups.

2) Series R25: rectangular cross section beams with concrete strength of 25 MPa. Four beams specimens R25-1/2/3/4 were tested, having same rectangular cross section (120 mm wide × 320 mm deep), same stirrup ratio (ρ_t = 0.59%) and shear-span-depth ratio (a/d = 2). The longitudinal flexural reinforcement consisted of eight 16 mm diameter bars (ρ_l = 3.5%), with a characteristic yielding stress of 363 MPa. Horizontal 6 mm reinforcements spaced 60mm and vertical 6 mm stirrups spaced 80mm were provided for beams R25-1 and R25-2 (Fig. 2(a)); only 6mm stirrups spaced 80mm were provide for beams R25-3 and R25-4 (Fig. 2(b)). Steel yielding stress was 242 MPa. The objective of this series was to study the effect of the web horizontal reinforcement on the shear capacity of reinforced concrete beams.

3) Series T40: T section beams with concrete strength of 40 MPa. Three T beams T40-1/2/3 were tested, having the same cross section and shear-span-depth ratio (a/d = 2). The longitudinal flexural reinforcement provided was a 20 mm diameter bar (ρ_l = 1.4%). Rebars used as shear reinforcement were 3.5 mm in diameter and steel yielding stress was 335 MPa. T40-1 was reinforced only with vertical stirrups set at 80mm horizontal spacing (ρ_t = 0.34%, ρ_h = 0.0%), see Fig. 3(a); T40-2 was reinforced with web horizontal reinforcements and vertical stirrups, both of them set at 80mm spacing (ρ_t = ρ_h = 0.34%), see Fig. 3(b); T40-3 was reinforced only with vertical stirrups set at 55 mm horizontal spacing, see Fig. 3(c). In this way, the stirrup ratio was increased up to (ρ_t = 0.5%, ρ_h = 0.0%). This series aimed to study the effect of different ratio of web horizontal reinforcement and stirrups on the shear capacity of thin-webbed T beams.

Detailed parameters of these beam specimens are shown in Table 1.

Materials

All tested beams were cast at the Structural Laboratory of Department of Bridge Engineering at Tongji University, Shanghai, China. Wooden formwork was used. The concrete for the beam specimens was elaborated at the laboratory. It is to highlight that a maximum aggregate size of 20 mm was used. Six standard [ 16] 150 mm × 150 mm × 150 mm cubes were cast with the specimens to obtain the compressive strength and six 100 mm × 100 mm × 300 mm prisms were cast to get the elastic modulus for each test series. The cubes and prisms were kept under the same environmental conditions as the beam specimens until the time of testing. The actual concrete strength from the cubes at the timing of testing (more than 28-days curing) is shown in Table 1 for different series. The mix composition and the elastic modulus from the prisms can be observed in Table 2.

Corrugated steel bars with different diameters (16 mm and 20 mm) were used as longitudinal flexural reinforcement; and plain round bars (3.5 mm, 6 mm and 8 mm) were used as shear reinforcement. Table 3 lists the actual yield stress, f_y, and the ultimate stress, f_u, for the reinforcing bars. All the reinforcements were properly anchored in test beams.

Instrumentation

A detailed measuring set-up was elaborated to obtain information throughout the development of the tests. Beams deflections were measured by means of linear variation differential transducers (LVDTs). Reinforcement and concrete strains were measured by strain gauges attached to the surface of steel and concrete. Load was applied and measured by a 500kN capacity hydraulic testing system. A general sketch of the instrumentation set-up is shown in Fig. 4. More than 100 channels were used. Most of the variables were monitored continuously by the data acquisition system. Photography equipment was also utilized. It is to highlight that diagonal crack widths were measured at the mid-depth of the beams when test beams were near collapse point (or near ULS).

Testing procedure

Two symmetric point loads were applied to the beam through a steel beam beard on two steel cylinders. The actuator loaded this beam under a spherical bearing and a 150 mm × 150 mm and 28 mm thick neoprene pad. The beam specimen was supported by a sliding pin bearing on one side and a fixed pin bearing on the other side, both of 40 mm diameters. Tests were carried out under displacement control using a hydraulic compression actuator with a loading capacity of 500 kN. Load increments were 10 kN before the first diagonal crack occurred and then changed to 5 kN until beam collapsed. After every load increment, cracking pattern was checked manually. The test layout is shown in Fig. 5.

Behavior of the beams during the test

All beams specimens failed in shear except beam specimen R40-4, which failed in flexure because of its bigger shear span. Figures 6-8 show the cracking patterns at failure and crack width observed in the experimental campaign.

In Series R40: similar sequence of cracking was observed in beams R40-1/2/3. First vertical flexural cracks occurred at the bottom surface of test beams near the loading point; then web-shear cracks appeared; eventually, one of the web-shear cracks developed into the critical diagonal crack and beam collapsed. At failure, the compressed zone of the beams R40-1/2/3 was crushed due to the combination of compressive and shear stresses. The spalling of the concrete next to the crack can be best observed in Fig. 6(b), Fig. 6(c); Beam R40-4 failed in flexure because of its bigger shear span, see Fig. 6(d).

In Series R25: for beams R25-1 and R25-2, first vertical flexural cracks occurred at the bottom surface of test beams; then, some web-shear cracks appeared (see Fig. 7(a) and (b)), eventually the compressed zone of the beam were crushed due to the combination of compressive and shear stresses; for beams R25-3 and R25-4, after the formation of the first shear crack, stirrups started to carry load and shear cracks grew quickly. At failure, shear compression failure happened abruptly in the compression zone of the beam; the critical diagonal crack separated the beam into two parts and stirrups were bent through the wider inclined cracks, as shown in Fig. 7(d).

In Series T40: for beam T40-1, first vertical flexural cracks occurred at the bottom surface of test beam near the loading point; the first inclined crack was developed from flexural crack; inclined cracks grew quickly and the inclination of critical diagonal crack was near 45 degree, finally the compressed zone of flange were crushed due to the combination of compressive and shear stresses and the beam was separated into two parts by the critical diagonal crack at failure, see Fig. 8(a); for beam T40-2, the first inclined crack was flexural-shear crack and critical diagonal crack developed from web-shear crack with 45 degree inclination, more than one shear cracks appeared and a more ductile response was shown compared with beam T40-1, the width of inclined cracks was smaller and all the inclined cracks grew completely, finally shear compression failure happened near the junction of web and upper flange, the spalling of the concrete next to the crack was observed at failure, see Fig. 8(b); for beam T40-3, the critical diagonal crack was developed from flexural-shear crack and grew quickly, at last spalling of web concrete near the upper flange was observed and the critical diagonal crack separated the beam into two parts, stirrups were bent through the wider inclined cracks at failure, as shown in Fig. 8(c) and (d).

Shear strength for all test beams are shown in Table 1.

Discussion and analysis of the test results

Shear capacity of test beams

From the analysis of the shear strengths for all test beams shown in Table 1, it is found that:

1) From the analysis of series R40, where shear-span-depth ratio increased in test beams from 2 in R40-1, to 2.5 in R40-2 and R40-3, keeping the longitudinal and shear reinforcement ratio constant, the failure shear strengths are 320, 240, and 245 kN respectively. Therefore, there is a decrease in failure shear strength as the shear-span-depth ratio increases. This implies that for small shear span-depth ratio beams, arch effect is also relevant to shear transfer mechanism in beams reinforced with both web horizontal reinforcement and stirrups.

2) For test series R25, comparing failure load of beams R25-1 (R25-2) to the beams R25-3 (R25-4) without web horizontal reinforcement, the latter failed at a lower value (see Table 1). This is mainly attributed to the thicker web in these concrete beams and to the low shear span. This enabled the formation of an “arch” effect to continue to carry shear after cracking.

3) In series T40, beam specimen T40-1 failed at 62.5 kN and T40-3 failed at 80 kN, and beam T40-2 failed at 87.5 kN. The failure mechanism was considerably different for beam T40-2 with web horizontal reinforcement when compared with similar beams without web horizontal reinforcement T40-1. Beam specimens T40-1 and T40-3 failed suddenly after the formation of the flexural shear crack. Beam T40-2 developed more than one shear crack and failure shear strength is 30% higher than that of T40-1. From which it can be found that web horizontal reinforcement can increase the shear capacity of concrete beams greatly.

Width of critical diagonal crack

In this paragraph, T40 series are taken as an example to explain the influence of web horizontal reinforcement on the growth of diagonal cracks. From the occurrence of inclined cracks to the final collapse of test beams, diagonal cracks of beam specimen T40-1 (only reinforced with stirrups) grew rapidly and width of critical diagonal crack was the biggest one (23 mm), see Fig. 8(a); but for beam specimen T40-2 with both web horizontal reinforcement and stirrups, there were more inclined cracks (see Fig. 8(b)) and width of critical diagonal crack, 6mm, was much smaller compared to beam T40-1 (23 mm) and T40-3 (12 mm), and the occurrence of critical diagonal crack was later (V = 50 kN for T40-2) than that in the other two beams (V = 30kN for T40-1/3). So from these experimental results, it can be proved that, stirrups can’t restrain the growth of diagonal cracks caused by principal tensile stress effectively, even the amount of stirrups is increased (beam T40-3); combination of web horizontal reinforcement and stirrups works much better than only vertical stirrups in restraining growth of inclined cracks and delaying the occurrence of critical diagonal crack. Even though the crack width was only measured near collapse (near ULS) and not monitored continuously during the test, the same conclusions apply to SLS: Cracks were much smaller and more abundant in beam T40-2.

Stress in web horizontal reinforcement

In this paragraph, test beam R40-1 (reinforced with web horizontal reinforcement) is taken as an example to show the stress of web horizontal reinforcement during the development of diagonal cracks. As shown in Fig. 9(a), there are 40 strain gauges attached to web horizontal reinforcement. Experimental values of ten strain gauges (No.6~No.10 and No11~No.15) in shear span are shown in Fig. 9(b). In which, the vertical axis stands for the number of strain gauge (No.) attached to the web horizontal reinforcement along the depth of the section, and the horizontal axis stands for the measured values of the corresponding strain gauge. As shown in Fig. 9(b), when applied load equals to 190KN, the critical diagonal crack occurred in beam R40-1, corresponding strain in No.6~No.10 (No.11~No.15) changed from compression strain to tension strain and distributed linearly along the depth of the test beam; when applied load reached 325 kN, beam R40-1 collapsed, corresponding strain in No.6~No.10 (No.11~No.15) remained similar linear distribution. For the strain gauge value of web horizontal reinforcement in shear span of other test beams reinforced with both web horizontal reinforcement and stirrups, the same conclusions can also be gotten from the experimental results: from SLS to ULS, strain changes from compression strain to tension strain and distributes linearly along the depth of the test beam.

The development process of stress in web horizontal reinforcement and stirrups is very similar. Once cracking, the stress in web horizontal reinforcement crossing inclined cracks will increase immediately; especially for web horizontal reinforcement located in shear span, in which strain increases much faster than that in pure flexure span; and most web horizontal reinforcement yield when beam fails. It means that web horizontal reinforcement carries axial tension force caused by shear force, in other words, it carries horizontal component of principal tensile stress and resists shear together with stirrups.

Stress in longitudinal flexural reinforcement

Because of existence of web horizontal reinforcement, increased tension force in longitudinal flexural reinforcement caused by shear force is reduced greatly. For beams without web horizontal reinforcement, the increase of tension force caused by shear force should be carried by top and bottom longitudinal flexural reinforcement completely. Here test series T40 are taken as an example to explain the relationship between applied loadings and strains in longitudinal flexural reinforcement. The strain gauge distribution in longitudinal flexural reinforcement is shown in Fig. 10(a). For beam T40-1 (only reinforced with stirrups), see Fig. 10(b), the strain of longitudinal flexural reinforcement in shear span increases much faster than that in pure flexure span; the longitudinal flexural reinforcement is supposed to yield at 52kN when only resisting flexure, but in fact it yield at 40 kN due to the increased tensile force caused by shear force. But it is different for T40-2 (reinforced with both web horizontal reinforcement and stirrups), see Fig. 10(b), the longitudinal flexural reinforcement is supposed to yield at 52 kN when only resisting flexure, but in fact it yield at 53 kN due to the effect of web horizontal reinforcement.

Comparison of test results with different design approaches

The comparisons between the theoretical calculations from different design codes and experimental results are also shown. To obtain a fair comparison of shear code predictions and experimentally observed failure loads, a filter to eliminate those beams failing in flexure was applied. So beam R40-4 is removed from the comparison. Table 4 summaries the shear procedures included in the ACI 318-05 [ 2], AASHTO LRFD [ 6] and Eurocode 2 [ 3]. To calculate the predictions (shown in Table 5) all the safety factors were taken equal to 1.00. The amount of web reinforcement was obtained by considering the stress state of the stirrups during the test just before reaching the failure load (Table 1). For the beams with web reinforcement, the Eurocode 2 [ 3] predicted failure loads depend on the angle of the concrete struts, ρ. It has been taken as cotθ changing from 1.0 to 2.5 (Table 4). For the ACI318-05 [ 2] the angle is fixed to 45 degree (cotθ = 1). For the AASHTO LRFD [ 6] shear procedure, the angle of the concrete strut is obtained by compatibility conditions (Table 4), which is based on the Modified Compression Field Theory, here the program RESPONSE [ 4, 17] is adopted to get the shear resistance.

For the ten beam specimens, the average V_exp/V_cal ratio is 1.47 for the ACI 318-05 [ 2] formulation, 1.22~3.05 for the Eurocode 2 [ 3], and 1.35 for the AASHTO LRFD [ 6]. The coefficient of variation (standard deviation over the average) is 0.13 for the ACI 318-05, 0.21 for the AASHTO LRFD and 0.15 for the Euro code 2.

For members only reinforced with stirrups, the ACI318-05 is more conservative; Eurocode 2 correlates better than ACI318-05 and AASHTO LRFD when cotθ is taken as 2.5. But for members reinforced with web horizontal reinforcement and stirrups, all results from the design codes presents a great scatter. Actually there exists web horizontal reinforcement in most existing codes, but they are only considered as structural reinforcements (or skin reinforcement) and not accounted for during shear strength prediction.

Conclusions

In this paper, some shear tests of simply-supported reinforced concrete beams were undertaken. Beams were shear reinforced either only with stirrups or with both web horizontal reinforcement and stirrups. Tests were performed to investigate the influence of web horizontal reinforcement on the shear behavior of reinforced concrete beams and to compare the behavior of these with the ones only reinforced with traditional stirrups. No such experiments have been documented in the past 40 years. Based on the test results of the 11 beam specimens, the following conclusions can be drawn:

1) Web horizontal reinforcement carries the axial tension force induced by shear force across the cross section, in other words, it carries the horizontal component of the principal tensile stress and resists the shear together with stirrups.

2) Combination of web horizontal reinforcement and stirrups works much better than only stirrups in restraining the development of inclined cracks and delaying the occurrence of critical diagonal crack.

3) For concrete beams with web horizontal reinforcement, existing design codes cannot consider the contribution from such reinforcement, although they exist as structural reinforcement in practical engineering.

4) Shear capacity of reinforced concrete beams can be increased when reinforced with web horizontal reinforcement.

This study presents the effect of web horizontal reinforcement on shear strength of reinforced concrete beams. More researches are needed to quantify the contributions of web horizontal reinforcement and to accelerate the introduction of web horizontal reinforcement as shear reinforcement in RC members.

References

[1] Joint ACI-ASCE Committee 445. Recent approaches to shear design of structural concrete. Journal of Structural Engineering, 1998, 124(12): 1375-1417

[2] ACI Committee 318. Building Code requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05). American Concrete Institute, Farmington Hills, Mich, 2005

[3] European Committee for StandardizationUNE-ENV 1992-1-1:2004 Eurocode 2. Deisgn of concrete structures. Part 1-1: General Rules and Rules for Buildings. Brussels, 2004

[4] Collins M P, Mitchell D. Prestressed concrete Structures. Prentice Hall, Englewood Cliffs, N J, 1991

[5] Committee C S A. A23.3. Design of concrete structures (CSA A23.3-04). Canadian Standards Association, Mississauga, 2004

[6] AASHTO LRFD. Bridge Design Specification and Commentary, 3rd Edition, American Association of State Highway and Transportation Officials, Washington D C, 2004

[7] Choi K K, Sherif A G, Reda-Taha M M, Chung L. Shear Strength of Slender Reinforced Concrete Beams without Web Reinforcement: A Model using Fuzzy Set Theory. Engineering Structures, 2009, 31(3): 768-777

[8] Jung S, Kim K S. Knowledge-based prediction of shear strength of concrete beams without shear reinforcement. Engineering Structures, 2008, 30(6): 1515-1525

[9] Reineck K H, Kuchma D A, Kim K S, Marx S. Shear database for reinforced concrete members without shear reinforcement. ACI Structural Journal, 2003, 100(2): 240-249

[10] El-Chabib H, Nehdi M, Said A. Predicting shear capacity of NSC and HSC slender beams without stirrups using artificial intelligence. Computers and Concrete, 2005, 2(1): 79-96

[11] Cladera A, Mari A R. Experimental Study on High-strength Concrete Beams Failing in Shear. Engineering Structures, 2005, 27(10): 1519-1527

[12] Teoh B K, Mansur M A, Wee T H. Behaviour of high-strength concrete I-beams with low shear reinforcement. ACI Structural Journal, 2002, 99(3): 299-307

[13] Fournier B, Razaqpur A G, Abbas A, Fathifazl G, Foo S, Isgor O B. Shear Strength of Reinforced Recycled Concrete Beams with Stirrups. Magazine of Concrete Research, 2010, 62(10): 685-699

[14] Ritter W. Die Bauweise Hennebique. Switzerland: Schweizerische Bauzeitung, Switzerland1899

[15] Mörsch E. Concrete-Steel Construction (Der Eisenbetonbau). English translation of the 3rd German edition, McGraw-Hill Book Co., New work. 1909.

[16] JTG D62-2004 Code for Design Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts. Beijing: China Communications Press, Beijing, 2004 (in Chinese)

[17] Bentz E C. Sectional analysis of reinforced concrete members. Dissertation for the Doctoral Degree. Toronto: University of Toronto, 2000

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