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A Proposed Formula for Predicting Size Effect on Shear Strength of Concrete Beams Without Coarse Aggregate

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In this research, the size effect on shear strength of concrete beams without coarse aggregate has been studied by evaluating the ACI 318-14, ACI 318-19, and Eurocode 2 formulas. The beam specimens had the width, length, a/d, and maximum aggregate size of 6 cm, 110 cm, 2.744, and 0.6 mm, respectively. The beam's depths had been set to have a range from 6 to 18 cm. The compressive strengths of the beam were in between 58.51 and 99.80 MPa. The beams had been tested under two concentrated loads. The longitudinal reinforcement consisted of two diameter 16 mm. The beams were designed without any stirrups. Based on the analysis, the ACI 318-19 approach provides the best prediction with the mean strength ratio and coefficient of variation of 1.5086 and 0.26, respectively. The ACI 318-19 also indicates insignificant downward trend on the strength ratio vs. effective depth. The test results show that the size effect is in good agreement with the Bažant’s size effect law. In this paper, modifications to the existing formula are given to provide more accurate prediction.
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ACI 318; Coarse Aggregate; Concrete Shear Strength; Eurocode 2; Size Effect

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Tavio, B. Kusuma, Strength and Ductility Enhancement of Reinforced HSC Columns Confined with High-Strength Transverse Steel, Eleventh East Asia-Pacific Conference on Structural Engineering and Construction (EASEC-11), Taipei, Taiwan, 2008.

D. Christianto, Tavio, D. Kurniadi, Effect of Steel Fiber on the Shear Strength of Reactive Powder Concrete, IOP Conference Series: Materials Science and Engineering, vol. 508, 2019, pp. 1-10.

B. Sabariman, A. Soehardjono, Wisnumurti, A. Wibowo, Tavio, Stress-Strain Behavior of Steel Fiber-Reinforced Concrete Cylinders Spirally Confined with Steel Bars, Advances in Civil Engineering, vol. 2018, 2018, pp. 1-8.

B. Sabariman, A. Soehardjono, Wisnumurti, A. Wibowo, Tavio, Stress-Strain Model for Confined Fiber-Reinforced Concrete under Axial Compression, Archives of Civil Engineering, vol. 66, no. 2, 2020, pp. 119-133.

M. Wulandari, M. F. Sofianto, Tavio, Split Tensile and Flexural Strength of Concrete with Artificial Lightweight Aggregate (ALWA) and Steel-Fiber, Journal of Physics: Conference Series, IOP Publishing, vol. 1569, 2020, pp. 1-7.

Murad, Y., Abu Zaid, J., Finite Element Modelling of Reinforced Concrete Beams Strengthened with Different Configuration of Carbon Fiber Sheets, (2019) International Review of Civil Engineering (IRECE), 10 (4), pp. 188-196.

Tavio, M. Rafani, I G. P. Raka, V. Ratnasari, Flexural Capacity Predictions and Comparisons of GFRP Reinforced Beams, Journal of Physics: Conference Series, IOP Publishing, vol. 1477, 2020, pp. 1-5.

M. Rafani, A. Suhardjono, Wisnumurti, A. Wibowo, Tavio, A Theoretical Study of GFRP RC Beams Deflection, Journal of Physics: Conference Series, IOP Publishing, vol. 1477, 2020, pp. 1-5.

D. Pinto, Tavio, I G. P. Raka, Axial Compressive Behavior of Square Concrete Columns Retrofitted with GFRP Straps, International Journal of Civil Engineering and Technology, vol. 10, no. 1, 2019, pp. 2388-2400.

Patuti, I., Rifa'i, A., Suryolelono, K., Siswosukarto, S., Model of Timber Crib Walls Using Counterweight in Bone Bolango Regency Gorontalo Province Indonesia, (2018) International Review of Civil Engineering (IRECE), 9 (3), pp. 98-104.

Almasri, A., Halahla, A., Effect of Tension Stiffening on the Deflection of a Tapered Reinforced Concrete Cantilever Under a Concentrated Load, (2019) International Review of Civil Engineering (IRECE), 10 (2), pp. 56-62.

J. K. Wight, Reinforced Concrete: Mechanics and Design. (Pearson Education, Inc., 2016).

Tavio, Interactive Mechanical Model for Shear Strength of Deep Beams, Discussion, Journal of Structural Engineering, ASCE, vol. 132, no. 5, May 2006, pp. 826-827.

Joint ACI-ASCE Committee 445, Recent Approach to Shear Strength of Structural Concrete (ACI 445R-99) (American Concrete Institute, 1999).

D. Christianto, C. A. Makarim, Tavio, Influence of Longitudinal Reinforcement Ratio on Shear Capacity of No Coarse-Aggregate Concrete, International Journal of GEOMATE, vol. 21, Oct. 2021, pp. 122-130.

D. Christianto, Tavio, C. A. Makarim, Effect of Longitudinal Steel Reinforcement on Shear Capacity of SFRC Beams without Coarse Aggregate, Technology Report of Kansai University, vol. 63, no. 1, Jan. 2021, pp. 6909-6917.

D. Christianto, C. A. Makarim, Tavio, I. D. Pratama, Influence of Longitudinal Reinforcement on Shear Strength of Concrete without Coarse Aggregate according to Eurocode 2, IJASEIT, Feb. 2021.

F. Leonhardt, R. Walther, Contribution to the Treatment of Shear in Reinforced Concrete, Beton-und Stahlbetonbau, pp 54-58.

G. N. J. Kani, How Safe are Our Large Reinforced Concrete Beams, ACI Journal, March 1967, pp. 128-141.

Z. P. Bažant, J. K. Kim, Size Effect in Shear Failure of Longitudinally Reinforced Beams, ACI Journal, Sept.-Oct. 1984, pp. 456-468.

D. Christianto, C. A. Makarim, Tavio, Y. U. Liucius, Size Effect on Shear Stress of Concrete Beam without Coarse Aggregate, Journal of Physics: Conference Series, vol. 1477, 2020, pp. 1-7.

Z. P. Bažant, J. Planas, Fracture and Size Effect in Concrete and Other Quasibrittle Materials (CRC Press, 1998).

ACI Committee 446, Fracture Mechanics of Concrete: Concepts, Models and Determination of Material Properties (ACI 446.1R-91) (American Concrete Institute, 1991).

Z. P. Bažant, Q. Yu, W. Gerstle, J. Hanson, J. W. Ju, Justification of ACI 446 Proposal for Updating ACI Code Provisions for Shear Design of Reinforced Concrete Beams, ACI Structural Journal, Sept.-Oct. 2007, pp. 601-610.

European Committee for Standardization, Eurocode 2: Design of Concrete Structures - part 1-1: General Rules and Rules for Buildings (European Committee for Standardization, 2004).

ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19) (American Concrete Institute, 2019).

R. J. Frosch, Q. Yu, G. Cusatis, Z. P. Bažant, A Unified Approach to Shear Design, Concrete International, vol. 39, no. 9, Sept. 2017, pp. 47-52.

ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14) (American Concrete Institute, 2014).

D. A. Kuchma, S. Wei, D. H. Sanders, A. Belarbi, L. C. Novak, Development of the One-Way Shear Design Provisions of ACI 318-19 for Reinforced Concrete, ACI Structural Journal, vol. 116, no. 4, July 2019, pp. 285-295.

Al-Quraishi, H., Abdulkhudhur, R., Abdulazeez, A., Shear Strength Behavior of Fiber Reinforced Recycled Aggregate Concrete Beams, (2021) International Review of Civil Engineering (IRECE), 12 (5), pp. 314-322.

Chairunnisa, N., Satyarno, I., Muslikh, M., Aminullah, A., Parametrical Study in Non-Linear Numerical Analysis of a Coupling Beam with Steel Truss Configuration in Shear Wall System, (2019) International Review of Civil Engineering (IRECE), 10 (4), pp. 197-206.

Vaghefi, M., Mobaraki, B., Evaluation of the Effect of Explosion on the Concrete Bridge Deck Using LS-DYNA, (2021) International Review of Civil Engineering (IRECE), 12 (3), pp. 135-142.


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