SHEAR STRENGTH OF RC BEAMS WITH HIGH-STRENGTH STIRRUPS

INTRODUCTION

Many building codes, including the current, IS 456:2000 do not recommend the use of nominal yield strengths of high-strength rebars in the shear design of concrete members and limit the design yield strength to a value of 420 MPa [1-2]. The primary reasons for limiting the yield strength of shear reinforcement are to control the width of diagonal shear cracks and to ensure the yielding of stirrups before the sudden shear failure of members. Despite numerous past studies on high-strength steel as shear reinforcements, there is a lack of consistency in the shear design of RC beams worldwide. The Eurocode-02 [4] limits the design yield strength of shear reinforcement to 600 MPa for all grades of concrete, whereas the Japanese Guidelines for Concrete [5] allow the yield strength of shear reinforcement to reach up to 800 MPa, when the compressive strength of concrete is greater than 60 MPa. This limit of restricting the yield strength of stirrups to 420MPa has been raised to 550 MPa in the current ACI 318-19 code [3] while computing the shear strength of concrete members.

In recent years, several researchers conducted studies on high-strength shear reinforcement higher than 550MPa. As mentioned earlier, the use of high-strength shear reinforcement in large-scale structures will not only reduce the amount of shear reinforcement but also improve workability due to the wider stirrup spacing. However, members with high-strength shear reinforcement are more likely to cause the crushing of concrete compression struts. In addition, it may lead to widened diagonal cracks before the failure of members. In particular, when high-strength shear reinforcement is used for large-scale reinforced concrete beams, the size effect and the characteristics of high-strength steel bars may affect the shear behavior of large-scale reinforced concrete beams.

RECENT EXPERIMENTAL RESULTS 

Sahu and Sahoo (2022)[6] recently tested six reinforced concrete (RC) beams of two different concrete grades and three grades of reinforcing steel. The type of steel includes the high-strength rebars of Fe-500D, Fe-550D, and Fe-600 grades conforming to the IS:1786 (2008) [7]. All reinforcement bars were made up of thermo-mechanically treated (TMT) steel having a tough outer core and a soft inner core. These TMT bars have higher tensile strengths and better elongation (ductility) and hence, are also suitable for seismic applications. Two different concrete grades having cube compressive strengths of 50 MPa and 35 MPa were adopted in the casting of test specimens.

Based on the test results Sahu and Sahoo (2022) have come to the following conclusions

1. All beam specimens reinforced with high-strength steel as longitudinal and transverse reinforcement resisted significantly higher peak shear loads as compared to their respective design strengths. The measured peak shear loads were found to be 4.0 times the design shear strengths predicted using the ACI 318-19 and the IS 456: 2000 provisions for beams having the shear span-to-depth (a/d) ratio of 1.05. The concrete strut action being predominant led to a higher difference between the measured and design shear strengths of beams with low a/d ratios. This also highlighted the enhanced shear strength of concrete beams in sections near to supports.

2. Beams with a low grade of concrete and reinforced with Fe500D grade longitudinal steel failed in the diagonal shear, as expected, for all grades of transverse steel with a maximum yield strength of 600 MPa. However, the beam specimens with high concrete compressive strength and Fe-550D grade longitudinal steel failed in flexure mode even though they were designed to fail in the diagonal shear. This showed that the shear design provisions of the current codes were very conservative for these types of beams.

3) All tested beams did not show the diagonal shear cracks at 60 % of their design loads (taken as the service load) and thus, the serviceability criteria were satisfied in the beams reinforced with high-strength transverse steel of yield strengths in the range of 500-600 MPa. Irrespective of the failure modes, the yielding of longitudinal steel followed by the yielding of transverse reinforcement was noted in all test specimens except the beam having the shear-span ratio of 1.7 in which the yielding of Fe-600 grade steel stirrups was observed.

4. The peak shear loads in test specimens having a/d ratios less than 1.7 exceeded the maximum shear strengths allowed in the ACI 318-19 code. The shear design provisions of CSA A23.3-04[9], ACI 318-19, and also the proposed equation for the IS 456 by Sahoo (2020)[10] are adequate for reinforced concrete beams with high-strength stirrups for the low a/d ratios as well.

SIZE EFFECTS IN LARGE BEAMS

The shear behavior of large-scale RC beams is affected by the size effect, while the main factors influencing the size effect are the effective depth of cross section and the shear span ratio. Until about 2008, the rationale for not introducing the size effect into the ACI code was that no tests of three-point loaded beams had shown a strength less than that required by the code. In other words, the safety margins implied by the design code were thought to provide adequate protection from the size effect. However, Bažant and Yu (2009)[11] showed that, if the size effect is ignored, an increase of beam depth from 0.3 m to 1 m raises the shear failure probability of beams without stirrups from 10^(-6) to 10^(-3) per lifetime.  The value of 10^(-6) is considered acceptable by safety experts as the maximum tolerable for buildings, bridges, aircraft, and ships . But the value of 10^(-3), which means that one in 1,000 very large beams is expected to fail, is considered unacceptable. In addition, one test of a 1.89 m deep beam without stirrups at the University of Toronto was found to have a shear strength, that was 50% lower than that predicted by the then, 2008 version of the ACI code.

Based on these observations,  it was simply decided to introduce into ACI 318 [Sec. 11.4.6.1(d)] a mandatory requirement that RC beams deeper than 250 mm must contain at least the specified minimum amount of stirrups. The assumption in adopting this resolution was a widespread conviction that the use of stirrups, even minimum stirrups, eliminates the size effect (Lubell et al. 2004).

However,  according to fracture mechanics, the failure is caused by the energy release associated with stress redistribution caused by a large crack and approximately follows Bažant’s (1984)[12] energetic size effect law:

v= v0/[Sq. root (1-d/d0)]

in which parameters v0 and d0 depend only on structure geometry. Although this formula has been shown to apply to beams without stirrups, it was shown by  Yu and Bažant (2011) [13]that it can be applied to beams with stirrups also.  They showed that although stirrups mitigate the size effect on the shear strength of RC beams, they cannot suppress it completely, regardless of the stirrup ratio. In addition, it was learnt that although the spacing of stirrups significantly affects the inclination of the diagonal shear crack, it has a negligible effect on the shear strength of beam. Based on the research by Bažant and his associates, the ACI 318:19 code introduced a size effect factor of

Deltas = sq. root [2/(1+d/250)] < 1.0

However, Shaoo(2020) proposed a size effect factor of (taken from BS 8110)

Deltas =(400/d)^0.25

It is of interst to note that The Japan Society of Civil Engineers (JSCE)[5] pioneered the size effect for design code long ago. It adopted a power-law, vc ∝ d^(–1/4), which was proposed by Okamura and Higai(1980)[15] as early as 1980 before the energetic size effect was discovered and was motivated by the Weibull statistical theory, at a time when this classical theory was the only theory of size effect.

Shin et al. (2019) recently carried out tests on  19 RC beams with high stength stirrups specimens to evaluate the shear behavior of large-scale RC beams. The primary parameters of tests were the size of cross section, yield strength of stirrups (fyt), and shear reinforcement ratio (ρt). Experimental tests were carried out in two series.

In the first series of experiments, eleven RC beam specimens with four different cross-sectional sizes were chosen: 490 x 600 mm, 495 x 900 mm , 480 x 1200 mm, and 540 x 1500 mm . Meanwhile, the second series of experiments consisted of eight RC beams with two cross-sectional sizes: 500 x 850 mm and 500 x 1100 mm. Considering the intended shear failure mode, the specimens were designed to have a relatively short shear span-depth ratio (a/d) of 2.5. The longitudinal reinforcement ratio was designed to be at least 1.53% to prevent flexure failure prior to shear failure. 

To evaluate the effect of high-strength steel on the shear strength of large-scale RC beams, specimens with normalstrength stirrups were tested and compared with specimens reinforced with high-strength shear reinforcement. In the first series, the normal-strength stirrups had yield strengths of 480 and 505 MPa , respectively, while the high-strength shear reinforcement had a yield strength of 667 MPa . In the second series, the yield strengths of stirrups were 460 and 581 MPa , respectively, and ultimate tensile strengths of stirrups were 582 and 699 MPa, respectively. All specimens were designed according to the shear design formulas given in ACI 318-14.

Shin et al.(2019) found that large-scale RC beams with high-strength shear reinforcement failed in shear tension failure mode, as the strain of stirrups reached the yield strain before reaching maximum shear strength. However, when high-strength shear reinforcement was used, the margin between observed shear strength and predicted shear strength by ACI 318-14[1] of the large-scale RC beams was lower than that of specimens with a section depth of 600 mm . In particular, in the case of specimens having the same ρt fyt/√fc′, the margin between observed shear strength and predicted shear strength by ACI 318-14[1] of the large-scale RC beams was the lowest, compared to beams with normal cross-sectional size. Because ACI 318-14[1] does not consider the size effect in its shear evaluation formulation, the shear strength of large-scale RC beams calculated by ACI 318-1416 may be higher than the actual value.

Shin et al.(2019) also found that for specimens with a large cross section and a large amount of shear reinforcement, the average crack width exceeded the limit value suggested in the ACI 224R.3 [16] Therefore, considering the serviceability limit state, they cautioned that attention should be paid to the use of high-strength steel bars in large-scale RC beams.

References

 [1] ACI Committee 318 (2008, 2014). Building code requirements for structural concrete (ACI 318-08 and 318-14) and commentary, American Concrete Institute, Farmington Hills, MI, USA.

[2] IS: 456 (2000). Plain and reinforced concrete - code of practice, Bureau of Indian Standards, New Delhi, India.

[3] ACI Committee 318 (2019). Building code requirements for structural concrete (ACI 318-19) and commentary, American Concrete Institute, Farmington Hills, MI, USA.

[4] Eurocode 2 (2004). Design of concrete structures, part 1: General rules and rules for buildings, EN 1992-1-1, European Committee for Standardization, Brussels Belgium, pp. 425

[5] JSCE Guidelines for Concrete No. 15 (2010).Standard specifications for concrete structures -2007: Design, Japanese Society of Civil Engineers (JSCE), Tokyo, Japan

[6]Sahu, S.K. and Sahoo, D.R.(2022) “Shear Performance Of Concrete Beams Of Low Shear Spans Reinforced With High-Strength Steel” The Indian Concrete Journal, Vol. 96, No. 6, pp. 14-29

[7] IS: 1786 (2008). High strength deformed steel bars and wires for concrete reinforcement- specification, Bureau of Indian Standards, New Delhi, India.

[8] Shin, D., Haroon, M., Kim, C., Lee, B. S., and Lee, J. Y. (2019). “Shear strength reduction of large-scale reinforced concrete beams with high-strength stirrups”, ACI Structural Journal, Vol. 116, No. 5, pp. 161-179.

[9] CSA Committee A23.3 (2004). Design of concrete structures (CSA A23.3-04), Canadian Standards Association, Rexdale, ON, Canada

[10]Sahoo, D. R. (2020). “Development of IS: 456 shear design provisions-II: Members with shear reinforcement”, Indian Concrete Journal, Vol. 94, No. 4, pp. 33-43. 

[11] Bažant and Yu (2009) “Does strength test satisfying code requirement for nominal strength justify ignoring size effect in shear?” ACI Structural Journal, Vol.106, No. 1, pp. 14–19.

[12] Lubell, A., Sherwood, T., Bentz, E., and Collins, M. P. (2004). “Safe shear design of large, wide beams.” Concrete International, Vol. 26, No. 1, pp. 67–78, with discussions (letter to ed.) by Bažant and Yu.

[13] . Bažant, Z. P., “Size Effect in Blunt Fracture: Concrete, Rock, Metal,” Journal of Engineering Mechanics, ASCE, V. 110, 1984, pp. 518-535.

[14] Yu, Q., and Bažant, Z. P. (2011). “Can stirrups suppress size effect on shear strength of RC beams?” ASCE Journal Structural Engineering, Vol. 137, No. 5, pp. 607-617.

[15] Okamura, H., and Higai, T., “Proposed Design Equation for Shear Strength of Reinforced Concrete Beams without Web Reinforcement,” Proceedings of the Japanese Society of Civil Engineers, Vol. 300, 1980, pp. 131-141.

[16] ACI Committee 224, Control of Cracking in Concrete Structures (ACI 224R-01), American Concrete Institute, Farmington Hills, MI, 2001, 46 pp