- Original article
- Open Access
Experimental Investigation on Flexural Crack Control for High-Strength Reinforced-Concrete Beam Members
- Chien-Kuo Chiu^{1}Email author,
- Kai-Ning Chi^{1} and
- Bo-Ting Ho^{1}
https://doi.org/10.1186/s40069-018-0253-8
© The Author(s) 2018
- Received: 10 May 2017
- Accepted: 30 January 2018
- Published: 29 May 2018
Abstract
The purpose of this study is to investigate the flexural crack development of high-strength reinforced concrete (HSRC) beams and suggest the design equations of the flexural crack control for HSRC beams. This study conducts two full-size simply-supported beam specimens and seven full-size cantilever beam specimens, and collects the experimental data of twenty full-size simply-supported beams from the past researches. In addition to high-strength reinforced steel bars of specified yielding stresses of 685 and 785 MPa, these specimens are all designed with the high-strength concrete of a specified compressive stress of 70 or 100 MPa. The experimental data is used to verify the application of the flexural crack control equations recommended in ACI 318-14, as reported by AIJ 2010, as reported by JSCE 2007 and as reported by CEB-fib Model Code 2010 on HSRC beam members; then, this study concludes the design equations for the flexural crack control based on ACI 318-14. Additionally, according to the experimental data, to ensure the reparability of an HSRC beam member in a medium-magnitude earthquake, the allowable tensile stress of the main bars can be set at the specified yielding stress of 685 MPa.
Keywords
- high-strength reinforced concrete
- beam members
- flexural crack
- serviceability
- reparability
1 Introduction
Over the last six decades, the use of high-strength concrete (HSC) has been gradually transformed with its scope of application as mentioned by the American Concrete Institute (ACI 2010). HSC has a continuously expanding range of applications, owing to its highly favorable characteristics, including the high early age strength, low deformation under the loading owing to its high modulus of elasticity, and high load resistance per unit weight (including shear and moment). HSC is thus very useful for constructing skyscrapers and span suspension bridges. HSC commonly refers to concrete whose compressive strength is at least 60 MPa and less than 130 MPa (FIP/CEB 1990). High-strength reinforcement is increasingly common in the construction industry. In Taiwan, high-strength reinforced concrete (HSRC) includes HRC with a specified compressive strength of at least 70 MPa and high-strength reinforcement with a specified yield strength of at least 685 MPa. As the most commonly applied specification for concrete engineering design in Taiwan, ACI 318-14 (ACI 2014) sets an upper bound of 420 MPa on the yield strength of reinforcing steel bars. Owing to the high strength of concrete and reinforcing steel, the mechanical behavior of HSRC structural members differs from that of normal-strength RC members. Furthermore, few full-scale experimental studies have addressed the mechanical behaviors of HSRC beam and column members. Therefore, mechanical models of HSRC members that accurately capture the lateral force–deformation relationship must be developed since the conventional model of normal-strength RC members may be unfeasible for evaluating the performance of HSRC members or structures.
The Architectural Institute of Japan (AIJ 2010) has stated that building performance is a function of serviceability, safety and reparability. Accordingly, as well as serviceability and safety, the performance-based design of buildings should consider reparability. As a major determinant of the cost of a building over its life cycle, reparability can also be regarded as a basic economic performance metric of a building; its importance has become evident in several seismic disaster events, including the Northridge Earthquake (USA, 1994), the Kobe Earthquake (Japan, 1995), and the Chi–Chi Earthquake (Taiwan, 1999). Obviously, reparability can reduce reconstruction costs after a seismic disaster. Generally, a crack-based damage assessment has a major role in estimating the cost of repairing a building. However, despite various assessments of crack-based damage to RC members or structures, related investigations (Silva et al. 2008; Shimazaki 2009) have focused mainly on normal-strength RC while paying little attention to HSRC structural members. A crack-based damage assessment can also be performed to estimate post-earthquake residual seismic capacity or facilitate performance-based design for a building structure (Soltani et al. 2013; Chiu et al. 2015).
Chiu et al. (2014) and (2016) proposed formulas for determining the allowable stresses of stirrup that ensure the serviceability and reparability of HSRC beam members. However, with respect to controlling flexural cracks of HSRC beam specimens, the development of such cracks must be investigated by performing full-scale experiments. Therefore, in this work, two four-point loading simply-supported beam tests and seven cantilever beam tests are performed, and 20 four-point loading simply-supported beam tests that were performed previously are considered. All specimens herein include a high-strength main reinforcement (with a specified yielding strength of 685 MPa) with high-strength stirrups (with a specified yielding strength of 785 MPa), and the specified compressive strengths of the concrete that is used herein are 70 and 100 MPa. The purpose of this work is to investigate flexural crack control with a view to ensure the serviceability and reparability of HSRC beam members.
The usefulness of the flexural crack control equations, recommended by ACI 318-14, fib Model Code (2010), AIJ (2010) and JSCE (2007), in ensuring the serviceability of HSRC beam members, is investigated in this work. Based on comparisons among various specifications and for reasons of convenience for engineers or designers, the provisions of ACI 318-14 are modified to control the width of flexural cracks in HSRC beam members. Additionally, AIJ (2010) recommends the allowable stress of main bars to ensure the reparability of HSRC beam members that are subjected to short-term loading. On the basis of AIJ (2010) with respect to reparability, this work investigates the experimental data to identify a ratio of the residual maximum flexural crack width to the maximum flexural crack width at the peak deformation angle n_{ max }. To maintain the residual maximum flexural crack width ≦ 0.4 mm to ensure reparability, this work uses the ratio n_{ max } to determine the allowable stress of the main bars in HSRC beam members that are subjected to short-term loading.
2 References Related to the Flexural Crack Width Control
For the purpose of controlling flexural cracks in an RC beam member, the Architectural Institute of Japan (AIJ; AIJ 2010) sets allowable stresses of the concrete and reinforcement under a long-term loading. Based on experimental data, the allowable stress allows a maximum crack width of 0.2–0.25 mm indoors and 0.3–0.4 mm outdoors. Equation (18) provided in the appendix of AIJ (2010) can be used to calculate the average flexural crack width of a beam or plate under a long-term load w_{ av }. Since the average flexural crack width that is calculated using Eq. (18) is assumed to be in the concrete close to the tensile reinforcement, it can be used to calculate the average width of flexural cracks at the concrete surface by applying the strain gradient amplification coefficient β_{ s }, as defined in Eqs. (3) or (4).
Along with average strain of tensile reinforcing bars ε_{ s,av } and the dry shrinkage of the concrete ε_{ sh } (second term in Eq. 18), the thicknesses of the side and bottom concrete covers c_{ b } (mm) and c_{ s } (mm), the effective tensile reinforcement ratio p_{ e }, the spacing of the tensile reinforcement s (mm), and the diameter of the tensile reinforcement \( \phi_{b} \)(mm), are all included in the first item in Eq. (19), which yields average crack spacing l_{ av } in Eq. (18) (mm). According to AIJ (2010), these equations are applicable to high-strength concrete with a compressive strength of 60–100 MPa. AIJ (2010) also recommends a maximum flexural crack width w_{ max } of the average crack width multiplied by 1.5.
\( \varepsilon^{\prime}_{csd} \) accounts for the effect of the concrete shrinkage and creep on the flexural crack width. Since \( \varepsilon^{\prime}_{csd} \) is influenced by the shape of a member section, environmental conditions and stress, it must be determined with reference to various structural performance requirements, such as serviceability and durability. Based on the JIS testing method, the strain of concrete shrinkage and creep \( \varepsilon^{\prime}_{csd} \) is 1000 × 10^{−6}; a value of 300–450 × 10^{−6} is recommended if the age of the concrete is 30–200 days.
3 Experimental Setup and Results
This section describes the setup for testing HSRC beam specimens. Nine full-size beam specimens are tested to investigate the relationship between flexural crack development and deformation of the member. Some of the experiments that were conducted by Chiu et al. (2014, 2016) are also investigated in this work. All tests were performed at the National Center for Research on Earthquake Engineering, Taiwan (NCREE).
3.1 HSRC Beam Specimens Conducted in Previous Research (Chiu et al. 2014, 2016)
Spec. | N | C _{ c } (mm) | S (cm) | f _{y} (MPa) | f _{yt} (MPa) | \( f^{\prime}_{c}\) (MPa) | a/d | ρ_{ t } (%) | ρ_{ s } (%) | ||
---|---|---|---|---|---|---|---|---|---|---|---|
Left | Right | Left | Right | ||||||||
8H70 | 8 | 40 | 20 | 30 | 685 | 785 | 88.7 | 3.33 | 1.7 | 0.32 | 0.21 |
8H100 | 8 | 40 | 20 | 30 | 685 | 785 | 98.6 | 3.33 | 1.7 | 0.32 | 0.21 |
8N70 | 8 | 40 | 20 | 30 | 685 | 420 | 93.5 | 3.33 | 1.7 | 0.32 | 0.21 |
8N100 | 8 | 40 | 20 | 30 | 685 | 420 | 103.5 | 3.33 | 1.7 | 0.32 | 0.21 |
8NS100 | 8 | 40 | Non-stirrup | 685 | – | 105.1 | 3.33 | 1.7 | – | ||
12H70 | 12 | 40 | 20 | 30 | 685 | 785 | 88.7 | 3.33 | 2.5 | 0.32 | 0.21 |
12H100 | 12 | 40 | 20 | 30 | 685 | 785 | 98.6 | 3.33 | 2.5 | 0.32 | 0.21 |
12N70 | 12 | 40 | 20 | 30 | 685 | 420 | 93.5 | 3.33 | 2.5 | 0.32 | 0.21 |
12N100 | 12 | 40 | 20 | 30 | 685 | 420 | 103.5 | 3.33 | 2.5 | 0.32 | .021 |
12NS100 | 12 | 40 | Non-stirrup | 685 | – | 105.1 | 3.33 | 2.5 | – | ||
6W70 | 6 | 40 | 20 | 30 | 685 | 785 | 73.7 | 3.33 | 2.02 | 0.32 | 0.21 |
6H70 | 6 | 40 | 20 | 30 | 685 | 785 | 70.7 | 3.33 | 2.02 | 0.32 | 0.21 |
175R70 | 6 | 40 | 30 | 685 | 785 | 87.9 | 1.75 | 3.5 | 0.24 | ||
200R70 | 6 | 40 | 30 | 685 | 785 | 91.2 | 2 | 3.5 | 0.24 | ||
275R70 | 6 | 40 | 30 | 685 | 785 | 76.8 | 2.75 | 3.5 | 0.24 | ||
325R70 | 6 | 40 | 30 | 685 | 785 | 75.5 | 3.25 | 3.5 | 0.24 | ||
175R100 | 6 | 40 | 30 | 685 | 785 | 90.4 | 1.75 | 3.5 | 0.24 | ||
200R100 | 6 | 40 | 30 | 685 | 785 | 92.3 | 2 | 3.5 | 0.24 | ||
275R100 | 6 | 40 | 30 | 685 | 785 | 83.1 | 2.75 | 3.5 | 0.24 | ||
325R100 | 6 | 40 | 30 | 685 | 785 | 87.1 | 3.25 | 3.5 | 0.24 |
Chiu et al. (2016) used ten simply-supported beam specimens and the loading system that was used in their earlier work (Chiu et al. 2014). The main bars were SD685 of D32, while the stirrups were SD785 of D13. The equivalent shear regions on the right and left-hand sides of the beam specimens were designed with the stirrup spacing of 300 mm. The length of the specimens was 6600, 4600 and 2600 mm, and the size of the section of the specimens was 350 mm (width) × 500 mm (depth) and 400 mm (width) × 700 mm (depth). Additionally, the shear span-to-depth ratios of the specimens were 3.33, 3.25, 2.75, 2.0 and 1.75. The measured compressive strength of concrete was approximately 70.7–92.3 MPa.
In the symmetric monotonic loading test, the mechanical behavior of the equivalent shear region is similar to that of a beam member with a single curvature. It can also be assumed to be a half of the middle region of a beam member in the antisymmetric loading test based on the moment and shear distribution diagrams. Zakaria et al. (2009) used the symmetric monotonic loading method to investigate the shear crack behavior of RC beams with shear reinforcement. Therefore, Chiu et al. (2014, 2016) adopted the symmetric monotonic loading test to investigate shear crack behavior. For the 20 specimens listed in Table 1, the spacing of flexural cracks in the equivalent moment regions is investigated in this work. Additionally, some flexural-shear cracks in the equivalent shear regions are used to investigate the relationship between crack width and the stress of the reinforcement.
3.2 Experiment Setting
HSRC beam specimens conducted in this work.
Spec. | N | C _{ c } (mm) | S (cm) | f _{ y } (MPa) | f _{ yt } (MPa) | \( f^{\prime}_{c}\) (MPa) | a/d | ρ _{ t } (%) | ρ_{ s } (%) | ||
---|---|---|---|---|---|---|---|---|---|---|---|
Left | Right | Left | Right | ||||||||
2C100 | 12 | 20 | 20 | 30 | 685 | 785 | 124.4 | 3.33 | 2.42 | 0.32 | 0.21 |
3C100 | 12 | 30 | 20 | 30 | 685 | 785 | 133 | 3.33 | 2.45 | 0.32 | 0.21 |
2C15S | 6 | 20 | 15 | 685 | 785 | 99.9 | 3.5 | 1.94 | 0.42 | ||
2C20T | 6 | 20 | 20 | 685 | 785 | 101.9 | 3.5 | 1.94 | 0.41 | ||
3C15S | 6 | 30 | 15 | 685 | 785 | 87.4 | 3.5 | 1.98 | 0.42 | ||
3C20T | 6 | 30 | 20 | 685 | 785 | 90.9 | 3.5 | 1.98 | 0.41 | ||
4C15S | 6 | 40 | 15 | 685 | 785 | 95.4 | 3.5 | 2.01 | 0.42 | ||
4C20T | 6 | 40 | 20 | 685 | 785 | 89.4 | 3.5 | 2.01 | 0.41 | ||
5C15S | 6 | 50 | 15 | 685 | 785 | 84.6 | 3.5 | 2.04 | 0.41 |
- 1.
Flexural crack cracking occurs where the bending moment stress is at its maximum.
- 2.
Shear crack cracking occurs where the shear stress is at its maximum. Furthermore, the width at the intersection between the shear crack and the stirrup, which includes the shear crack width and the width parallel to the stirrup, is measured.
3.3 Experimental Results
In this work, two four-point loading simply-supported beam tests and seven cantilever beam tests are conducted. In the experiment herein, the development of the shear and flexural cracks is observed at various peak deformations angle of each specimen. When the applied loading is set back to be zero at a peak deformation angle, the residual shear and flexural crack widths are also measured.
4 Flexural Crack Control for HSRC Beam Members
4.1 Flexural Crack Spacing
Various specifications for the average flexural crack width.
Specifications | Average/maximum | Recommended equations |
---|---|---|
ACI-318 (2014) | Average spacing | \( 1.5\sqrt {d_{c}^{2} + \left( {\frac{s}{2}} \right)^{2} } \) |
AIJ (2010) | Average spacing | \( 2\left( {\frac{{c_{b} + c_{s} }}{2} + \frac{s}{10}} \right) + 0.1\frac{{\phi_{b} }}{{p_{e} }} \) |
JSCE (2007) | Maximum spacing | \( 1.1k_{1} k_{2} k_{3} [4c + 0.7(s - \phi_{b} )] \) |
CEB-fib Model Code (2010) | Maximum spacing | \( 2 \times \left( {k \times c + \frac{1}{4} \times \frac{{f_{ctm} }}{{\tau_{bms} }} \times \frac{{\phi_{b} }}{{\rho_{s,ef} }}} \right) \) |
Required parameters in Eq. (6).
Spec. | Required parameters in Eq. (6) | |||
---|---|---|---|---|
d_{ c } (mm) | s (mm) | d _{ 1 } ^{ * } (mm) | d _{ 2 } ^{ * } (mm) | |
2C100 | 45.4 | 61.84 | 64.2 | 71.3 |
3C100 | 55.4 | 57.84 | 78.3 | 62.5 |
2C15S | 48.6 | 151.425 | 68.7 | 90.0 |
2C20T | 48.6 | 151.425 | 68.7 | 90.0 |
3C15S | 58.6 | 141.425 | 82.8 | 91.8 |
3C20T | 58.6 | 141.425 | 82.8 | 91.8 |
4C15S | 68.6 | 131.425 | 97.0 | 95.0 |
4C20T | 68.6 | 131.425 | 97.0 | 95.0 |
5C15S | 78.6 | 121.425 | 111.1 | 99.3 |
8H70 | 65.37 | 89.753 | 92.5 | 79.29 |
8H100 | 65.37 | 89.753 | 92.5 | 79.29 |
8N70 | 65.37 | 89.753 | 92.5 | 79.29 |
8N100 | 65.37 | 89.753 | 92.5 | 79.29 |
8NS100 | 65.37 | 89.753 | 92.5 | 79.29 |
12H70 | 65.37 | 53.852 | 92.5 | 70.7 |
12H100 | 65.37 | 53.852 | 92.5 | 70.7 |
12N70 | 65.37 | 53.852 | 92.5 | 70.7 |
12N100 | 65.37 | 53.852 | 92.5 | 70.7 |
12NS100 | 65.37 | 53.852 | 92.5 | 70.7 |
6W70 | 68.8 | 131.2 | 97.3 | 95.1 |
6H70 | 68.8 | 131.2 | 97.3 | 95.1 |
175R70 | 68.8 | 84.2 | 97.3 | 80.7 |
200R70 | 68.8 | 84.2 | 97.3 | 80.7 |
275R70 | 68.8 | 84.2 | 97.3 | 80.7 |
325R70 | 68.8 | 84.2 | 97.3 | 80.7 |
175R100 | 68.8 | 84.2 | 97.3 | 80.7 |
200R100 | 68.8 | 84.2 | 97.3 | 80.7 |
275R100 | 68.8 | 84.2 | 97.3 | 80.7 |
325R100 | 68.8 | 84.2 | 97.3 | 80.7 |
4.2 Flexural Crack Width
4.3 Flexural Crack Control for HSRC Beam Members
According to Fig. 18, for HSRC beam specimens, the maximum flexural crack width can still be controlled well in the way recommended by ACI 318. However, in order to solve the non-conservative phenomenon under the low stress and not to change the pattern of the original equation (Eq. 9), a correction coefficient should be introduced in the stress ratio of the tensile reinforcement, as (\( \phi \) × (f_{ s }/f_{ y })). Restated, the non-conservative maximum flexural crack width in the low stress state can be solved by the constraint of the stress of the tensile reinforcement. According to the experimental results, the stress ratio of the tensile reinforcement considering the correction coefficient \( \phi \) is in the range of 0.0–0.45. This work suggests the modified stress ratio of the tensile reinforcement is 0.4 based on its mean value of 0.36. As shown in Fig. 19e, if f_{ s } = 0.4fy is used instead of Eq. (25) when f_{ s } < f_{ y } in Eq. (26), the average ratio of the measured to the calculated maximum flexural crack width using Eq. (26) is 0.72. Therefore, engineers or designers can calculate the maximum flexural crack width of a HSRC beam under the service loading according to ACI 318 (Eq. (26)). Additionally, if the calculated stress of the tensile reinforcement is lower than 0.4f_{ y }, then 0.4f_{ y } shall be substituted in Eq. (26).
If s is smaller than 2d_{ c }, Eq. (26) can be used to derive a maximum value of d_{ c } for controlling the maximum flexural crack width as Eq. (27). Taking the maximum flexural crack width of 0.4 mm for an example, when the stress of the tensile reinforcement is 0.4f_{ y } and, the maximum value of d_{ c } is 105 mm calculated using Eq. (27). Additionally, Fig. 20 shows the allowable values of s remarked as Zone II for s < 2d_{ c }. Therefore, for the maximum flexural crack width of 0.4 mm, Zone I and Zone II remarked in Fig. 20 are the allowable design region of s when the stress of the tensile reinforcement is set at 0.4f_{ y } or 0.6f_{ y }.
To ensure the reparability of an HSRC beam member in a medium-magnitude earthquake, the residual maximum flexural crack width of a member following an earthquake does not exceed 0.4 mm based on the reference. However, it is difficult to develop the relationship between the residual maximum flexural crack with and tensile stress of main bars based on the mechanical behaviors of RC members. Therefore, this work uses the experimental data to suggest the allowable stress of main bars to ensure the reparability of an HSRC beam member.
5 Conclusions
In this work, nine full-size HSRC beam specimens are utilized to investigate the relationship between flexural crack development and deformation. Some HSRC experiment data collected from Chiu et al. (2014, 2016) are also investigated. Experimental results are compared with various specifications that are related to flexural crack width control and modified equations for ACI 318-14 related to flexural crack width control are suggested. Designers or engineers can adopt the proposed equations (Eqs. (28), (29)) to design the spacing of tensile 1reinforcements or the thickness of the concrete cover, to control the flexural crack width of an HSCR beam member under service-level loading. Additionally, the minimal calculated stress of the tensile reinforcement in the proposed equations is 0.4f_{ y }.
According to the experimental data, when the residual maximum flexural crack width is limited to 0.4 mm, the allowable maximum flexural crack width at the peak deformation angle is 0.8 mm. According to the relationship between the maximum flexural crack width and the maximum stress of the tensile reinforcement, the latter reaches the yielding stress before the maximum flexural crack width exceeds 0.8 mm. Therefore, to ensure the reparability of an HSRC beam member in a medium-magnitude earthquake, the allowable tensile stress of the main bars can be set at the specified yielding stress of 685 MPa.
Since the specimens are all designed with the high-strength reinforcing bars with specified yielding stresses of 685 MPa (main bars) and 785 MPa (transverse reinforcement) and the high-strength concrete with the compressive strength of 70 or 100 MPa (measured compressive strength is in the range of 70–133 MPa), the proposed equations herein are applicable in the flexural crack control for HSRC beams. In the future, the experimental data of concrete and reinforcement with various strength should be added to extend the application of the proposed models.
Declarations
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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