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Effect of Tension Stiffening on the Deflection of a Tapered Reinforced Concrete Cantilever Under a Concentrated Load

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Tapered cantilever concrete beams are widely used in various types of applications. However, deflections for these types of beams are usually estimated using numerical techniques. In this research, an analytical solution is obtained for a non-prismatic tapered cantilever concrete beam that has a varying depth along the length when subjected to a concentrated load at its end. The dependence of the solution on the steel reinforcement ratio is simplified in order to obtain the solution. An effective moment of inertia model with tension stiffening is used in the formulation to obtain a better prediction for deflection. The obtained equation of deflection has the advantage of practicality and ease of use for designers and engineers. The finite element method is used to verify the analytical solution. A smeared cracking model with a tension softening effect was incorporated in the finite element model in order to obtain better simulation results. Despite the fact that the model predicted deflection well, the model lacks the ability to accurately predict the location of the neutral axis.
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Cantilever; Concentrated Load; Deflection; Reinforced Concrete; Finite Element; Tension Softening

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D. E. Branson, Instantaneous and Time-Dependent Deflections of Simple and Continuous Reinforced Concrete Beams. HPR Report No. 7, Part 1, Alabama Highway Department, Bureau of Public Roads, Montgomery, AL, 78, 1965.

Ghali, T. Hall, and W. Bobey, Minimum Thickness Of Concrete Members Reinforced With Fibre Reinforced Polymer Bars. Canadian Journal of Civil Engineering, 28~41, 583–592, 2001.

P. H. Bischoff, Re-Evaluation of Deflection Prediction for Concrete Beams Reinforced with Steel and Fibre Reinforced Polymer Bars. Journal of Structural Engineering, ASCE, 131(5): 752–767, 2005.

M. Khuntia, and S. K. Ghosh, Flexural Stiffness of Reinforced Concrete Columns and Beams: Analytical Approach. ACI Structural Journal, 101(3), 351-363, 2004.

M. Fikry, and C. Thomas, Development of a Model for the Effective Moment of Inertia of One-way Reinforced Concrete Elements. ACI Structural Journal, 95(4), 445–455, 1998.

Akmaluddin, and C. Thomas. Experimental Verification of Effective Moment of Inertia Used in the Calculation of Reinforced Concrete Beam Deflection. International Civil Engineering Conference "Towards Sustainable Civil Engineering Practice" Surabaya, August 25-26, 2006.

H. K. Ammash, and M. H. Muhaisin, Advanced Model for the Effective Moment of Inertia Taking into Account Shear Deformations Effect. Al-Qadisiya Journal For Engineering Sciences, 2, 108-128, 2009

F. Romano, S. Ganduscio, and G. Zingone, Elastoplastic Deflections for Prismatic and Nonprismatic Beams. Journal of Engineering Mechanics, 119, 1117-1135, 1993.

K. Galal, and Q. Yang, Experimental and Analytical Behavior of Haunched Thin-Walled RC Girders and Box Girders. Thin-Walled Structures, 47, 202–218, 2009.

M. Sharifi, and M. Kamali, Evaluating the Concrete Tensions Softening Model in Flexural Behavior. International Journal of Civil Engineering, 15(5), 791–807, 2017.

Yang, K. Kim, and C. Joh, Flexural Strength of Hybrid Steel Fiber-Reinforced Ultra-High Strength Concrete Beams. Journal of the Korea Concrete Institute, 27(3), 283-290, 2015.

Ramachandra Murthy, P. Ganesh, S. Sundar Kumar, and Nagesh R. Iyer. Fracture energy and tension softening relation for nano-modified concrete. Structural Engineering and Mechanics. 54(6), 1201-1216, 2015.

Akhil, M. K. M. V. Ratnam, K. Suseela, U. RangaRaju, Tension Softening Behavior of Fiber Reinforced Concrete. International Journal of Scientific Research in Science, Engineering and Technology. 2(3), 919-925, 2016.

D. Yoo, Y. Yoon, and N. Banthia, Predicting the post-cracking behavior of normal- and high-strength steel-fiber-reinforced concrete beams. Construction and Building Materials. 93, 477-485, 2015.

Z. Taqieddin, G. Voyiadjis, A. Almasri, Formulation and Verification of a Concrete Model with Strong Coupling between Isotropic Damage and Elastoplasticity and Comparison to a Weak Coupling Model. Journal of Engineering Mechanics, 138(5), 530-541, 2011.

Y. Yao, F. A. Silva, M. Butler, V. Mechtcherine, and B. Mobasher, Tension stiffening in textile-reinforced concrete under high speed tensile loads. Cement and Concrete Composites. 64, 49-61,2015.

T. G. Mondal, and S. SuriyaPrakash, Effect of tension stiffening on the behaviour of reinforced concrete circular columns under torsion. Engineering Structures, 92, 186-195, 2015.

Mattar, I., FE Model for R.C Beams Strengthened/Retrofitted with FRP, (2015) International Review of Civil Engineering (IRECE), 6 (1), pp. 10-20.

P. H. Bischoff, and S. P. Gross, Equivalent Moment of Inertia Based on Integration of Curvature. Journal of Composites for Construction, 15(3), 263-273, 2011.

Tenek, L., Aifantis, E., Deformation of a Two-Dimensional, Shear Deformable Cantilever Beam Using Gradient Elasticity and Finite Differences, (2016) International Review of Civil Engineering (IRECE), 7 (3), pp. 79-86.

Bekkar, I., Djermane, M., Bounoua, T., Repairing of Reinforced Concrete Beam by Composite Plate, (2016) International Review of Civil Engineering (IRECE), 7 (1), pp. 1-4.

Sapountzakis, E., An Improved Model for the Analysis of Plates Stiffened by Parallel Beams Including Creep and Shrinkage Effects: Application to Concrete or to Composite Steel-Concrete Structures, (2018) International Journal on Engineering Applications (IREA), 6 (2), pp. 57-70.

Abaqus 6.10 user manual, Dassault Systèmes, 2010.


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