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Manual for Design and Detailing of Reinforced Concrete to the September 2013 Code of Practice for Structural Use of Concrete 2013 2.0 Some Highlighted Aspects in Basis of Design 2.1 Ultimate and Serviceability Limit states The ultimate and serviceability limit states used in the Code carry the normal meaning as in other codes such as BS8110. May 18, 2017 The angle 0 of the equivalent concrete struts is the same for both torsion and shear design. (5) For a solid, approximately rectangular section no shear and torsion reinforcement is necessary, apart from the minimum reinforcement given in section 5.4.2.2(5), Table 5.5, if the following conditions are satisfied: 4.3.3.3 Warping torsion.
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Torsional Behavior of High-Strength Concrete Beams with Minimum Reinforcement Ratio
1Research Fellow, Korea Institute of Civil Engineering and Building Technology, Department of Infrastructure Safety Research, Goyang, Gyeonggi 10223, Republic of Korea
2Senior Researcher, Korea Institute of Civil Engineering and Building Technology, Department of Infrastructure Safety Research, Goyang, Gyeonggi 10223, Republic of Korea
3Professor, Kunsan National University, Department of Civil Engineering, Kunsan, Jeonbuk 54150, Republic of Korea
4Senior Research Fellow, Korea Institute of Civil Engineering and Building Technology, Department of Infrastructure Safety Research, Goyang, Gyeonggi 10223, Republic of Korea
2Senior Researcher, Korea Institute of Civil Engineering and Building Technology, Department of Infrastructure Safety Research, Goyang, Gyeonggi 10223, Republic of Korea
3Professor, Kunsan National University, Department of Civil Engineering, Kunsan, Jeonbuk 54150, Republic of Korea
4Senior Research Fellow, Korea Institute of Civil Engineering and Building Technology, Department of Infrastructure Safety Research, Goyang, Gyeonggi 10223, Republic of Korea
Correspondence should be addressed to ; rk.er.tcik@hojc
Received 25 April 2018; Revised 18 September 2018; Accepted 18 October 2018; Published 17 January 2019
Academic Editor: Constantin Chalioris
Copyright © 2019 Changbin Joh et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Although there is a growing trend to use higher strength for concrete and steel in reinforced concrete structures due to the lightness and slenderness of these members together with the simplified arrangement of their reinforcement, there is still the necessity to inspect the reduction of ductility resulting from the gain in strength. Taking into account that this also concerns the design for torsion, this study intends to investigate the regulations related to the torsional minimum reinforcement ratio in view of the minimum ductility requirement with focus on Eurocode 2. To that goal, the relation between the torsional cracking moment and the ductile behavior is discussed for the beam reinforced with the minimum torsional reinforcement ratio to examine the eventual properness of the minimum torsional reinforcement ratio recommended by Eurocode 2. Moreover, a pure torsion test is performed on 18 beams made of 80 MPa concrete reinforced by high-strength bars with rectangular section and various test variables involving the minimum torsional reinforcement ratio, the transverse-to-longitudinal reinforcement ratio, and the total reinforcement ratio. As a result, for the high-strength concrete beams, the minimum torsional reinforcement ratio recommended by Eurocode 2 was insufficient to prevent the sudden loss of strength after the initiation of the torsional cracking. But with regard to the compatibility torsion of statically indeterminate structure, the adoption of the minimum torsional reinforcement ratio recommended by Eurocode 2 might secure enough deformability under displacement-controlled mode to allow the redistribution of the torsional moment.
1. Introduction
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There is a growing trend to use higher strength for concrete and steel in reinforced concrete structures. The near future will see wider application of members applying concrete with the compressive strength higher than 80 MPa and reinforced by steel with the yield strength of 600 MPa. This new popularity is due to the lightness and slenderness of these members together with the simplified arrangement of their reinforcement. However, there is still the necessity to inspect the reduction of ductility resulting from the gain in strength. Need is thus to verify if the current design codes under force are capable to control adequately the strength-ductility balance. Particularly, the regulations related to the minimum reinforcement ratio should be examined in view of the minimum ductility requirement.
This also concerns the design for torsion. In general, similar to the minimum reinforcement for shear and flexure, the minimum torsional reinforcement intends to provide the member with sufficient postcracking torsional resistance. This means controlling the crack width and securing enough ductility to prevent sudden loss of the torsional strength after cracking. Numerous researchers, however, already pointed out the issues resulting from the behavioral change brought by the increase of the strength or related to the minimum torsional reinforcement ratio recommended by ACI 318-14 Code or Eurocode 2 (EC 2) [1–19].
Rasmussen and Baker [3] and Lopes and Bernardo [4] compared the torsional characteristics of reinforced beams made of normal concrete and high-strength concrete and concluded that the use of high-strength concrete was favorable with respect to the torsional stiffness and the stress in the reinforcement but increased the brittle tendency after cracking. Chiu et al. [5] performed pure torsion tests on beams made of normal concrete and high-strength concrete to investigate the effect of the minimum reinforcement ratio in the longitudinal and transverse directions. Based upon their experimental results, these authors reported that the postcracking strength, i.e., the ductile failure mode, depended significantly on the total reinforcement ratio in the longitudinal and transverse directions as well as the ratio of the longitudinal to the transverse reinforcement. This dependency was more marked in the high-strength concrete members than in those made of normal concrete. Ismail [6], who performed a literature review on previous torsion tests, and Yoon et al. [7], who studied experimentally the effect of high-strength reinforcement, also reported that the use of high-strength concrete favored the occurrence of the brittle behavior beyond the torsional strength.
Numerical methods were also studied. Rahal and Collins [8, 9] successfully applied the modified compression field theory to estimate the torsional behavior of concrete beams, and Chalioris [10] combined the smeared crack model and the softened truss model to predict the initial torsional stiffness, torsional cracking moment, and strength of concrete beams. Bernardo and Lopes [11] proposed a parameter for the plastic behavior and twist capacity of high-strength concrete hollow beams based on the analysis of their test.
In concern with the minimum torsional reinforcement ratio, Koutchoukali and Belarbi [12] stated that the minimum torsional reinforcement of ACI 318-95 Code [13] was inadequate for high-strength concrete beams and stressed the necessity to provide at least 20% reserve of strength after cracking to prevent the brittle failure. Both Ali and White [14] and Kim et al. [15] indicated the problems of the minimum torsional reinforcement ratio and proposed new minimum reinforcement ratios enabling to maintain the postcracking strength.
Accordingly, this study intends to investigate the appropriateness of the current design codes for torsion with focus on EC 2. To that goal, the relation between the minimum torsional reinforcement ratio and the torsional cracking moment is analyzed theoretically, and the pure torsion test is performed on beams made of 80 MPa concrete reinforced by high-strength reinforcement. Moreover, the relation between the torsional cracking moment and the ductile behavior is discussed for the beam reinforced with the minimum torsional reinforcement ratio to examine the eventual properness of the minimum torsional reinforcement ratio recommended by EC 2.
2. Minimum Torsional Reinforcement Ratio and Torsional Cracking Moment
Since the torsional design methods of EC 2 and ACI 318-14 Code provide conceptually identical minimum torsional reinforcement, this study analyzes theoretically the relation between the minimum torsional reinforcement and the torsional cracking moment () with reference to EC 2.
In EC 2, the torsional load is decomposed into shear forces applied in each face of the member, and design is performed only with respect to these shear forces. Therefore, can be expressed as follows in function of the tensile strength of concrete and the yield strength of the stirrups:where = cross-sectional area of minimum shear reinforcement; = spacing of stirrups; = width of the cross section; = compressive strength of concrete; and = yield strength of shear and torsional reinforcement.
Besides, according to the theory of the thin-walled tube and the space truss analogy, the torsional cracking strength () and the torsional strength () can be expressed as follows [1, 20]:where = effective thickness of the tube resisting to torsion; = internal area inside the central axis of effective thickness; = tensile strength of concrete; = cross-sectional area of closed torsional stirrup; and = angle of crack.
In Equation (2), the tensile strength of concrete can be assumed as [1, 20]. The beam in torsion can be seen to be in a biaxial state under the simultaneous occurrence of compression and tension, and accordingly, the concrete tensile strength can be lowered compared to the uniaxial tension state. Following, Equation (2) can be rewritten as
Besides, if is accepted in the usual way as the minimum reinforcement ratio enabling the member to maintain ductility without sudden loss of the torsional strength after cracking, and the following equation is obtained by equaling Equations (3) and (4):
If the beam is not prestressed and is reinforced equally in the transverse and longitudinal directions, the crack angle can be assumed to be . Consequently, Equation (5) can be rewritten as follows:
According to EC 2 (EN 1992-1-1:2004 6.3.2 (1)), the effective thickness, t, may be taken as the total cross-sectional area (,h = height of the section) divided by the outer circumference of the cross section (). To make the discussion as simple and practical as possible, only rectangular members are considered here. Considering the aspect ratio of the cross section ,t ranges between and . Accordingly, the reinforcement ratio resisting to can be obtained by the following equation:
This value corresponds to about 2 to 3.7 times the minimum reinforcement ratio given in Equation (1) as suggested by EC 2.
From Equation (7), can be expressed as a function of . This function is plotted in Figure 1 together with the values recommended by EC 2, ACI 318-14, CSA-04, MC2010, and KCI by applying the condition [21–24].