Strut-and-Tie Method for Prediction of Ultimate Shear Capacity of Shear-Strengthened RC deep beams with FRP

Document Type : Regular Paper


1 M.Sc, Structural Engineering, Razi University, Kermanshah, Iran

2 Assistant Professor, Structural Engineering, Razi University, Kermanshah, Iran


The main objective of this study is to propose the Strut-and-Tie method (STM) to predict the shear capacity of simply supported RC deep beams shear-strengthened with carbon fiber reinforced polymers (CFRP). It is assumed that, the total carried shear force by shear-strengthened RC deep beam provided by three independent resistance, namely diagonal concrete strut due to Strut-and-tie mechanism, and the equivalent resisting force resulted by with web reinforcement and FRP layer. The STM approach is regressioned with 104 specimens shear-strengthened with different scheme which are modelled and analyzed through the Non Linear finite elements method and analyzed according under Push over load. For verifying of the accuracy of proposed method, it was used to determine the shear capacity of specimens which have been tested by other researchers. Obtained results were compared with experimental data, that this comparison indicate the proposed method is capable to predict the shear strength of strengthened deep beams with externally bonded (EB) CFRP with acceptable accuracy.


Main Subjects

[1] ACI 318-02. (2002) “Building Code Requirements for Structural Concrete and Commentary”, American Concrete Institute
[2] ACI 318-14. (2014) “Building Code Requirements for Structural Concrete and Commentary”, American Concrete Institute
[3] ACI 440.2R-08. (2008), “Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures”, American Concrete Institute
[4] Adhikary, B.B., Mutsuyoshi, H. and Ashraf, M. (2004), “Shear Strengthening of Reinforced Concrete Beams Using Fiber-Reinforced Polymer Sheets with Bonded Anchorage”, ACI STRUCTURAL JOURNAL, V101, 660-668
[5] Arabzadeh, A., Rahaie, A. R., Aghayari, R.  (2009), “A Simple Strut-and-Tie Model for Prediction of Ultimate Shear Strength of RC Deep Beams”, International Journal of Civil Engineering, Vol. 7, No. 3, 141-153
[6] Arabzadeh, A., Mirzaei, M. (2008), “Evaluation of shear strength of deep beams that strength and repair with CFRP sheets”, Eighth International Congress of Civil Engineering, Shiraz university, (Persian).
[7] Brown, M., and Bayrak, O. (2007), “Minimume transvers reinforcement for bottle – shaped strut”, ACI STRUCTURAL JOURNAL, Vol.103, No.6, 813-821.
[8] Chaallal, O., Shahawy, M. and Hassan, M. (2006), “Behavior of Reinforced Concrete T-Beams Strengthened in Shear with Carbon Fiber-Reinforced Polymer— An Experimental Study”, ACI STRUCTURAL JOURNAL, V103, 339-347.
[9] Eom, T.S., Park, H.G. (2010), “Secant Stiffness Method for Inelastic Design of Strut-and-Tie Model”, ACI STRUCTURAL JOURNAL, V107, 689-698.
 [10] Foster, S.J, and Gilbert, R.I. (1998), “Experimental Studies on High –Strength Concrete Deep beam”, ACI STRUCTURAL JOURNAL, V. 95, No. 4,382-390.
[11] Foster, S.J., and Malik, A.R., 2002, Evaluation of Efficiency Factor Models used in Strut-and-Tie Modeling of Non-flexural Members, ASCE Journal of Structural Engineering, Vol. 128, No. 5, 569-577.
[12] Gaetano, R., Raffaele, V., and Margherita, P. (2005), “Reinforced Concrete Deep Beams—Shear Strength Model and Design Formula”, ACI STRUCTURAL JOURNAL, V. 102, No. 3, 429-437.
[13] Godat, A. and Chaallal, O. (2013), “Strut- and- Tie Method for externally FRP Shear Strengthened Large scale RC Beams”, Composite Structural, 99, 327-338.
[14] Hwang, S., Lu, W., and Lee, H. (2000), “Shear Strength Prediction for Deep Beams”, ACI STRUCTURAL JOURNAL, Vol. 97, No. 3, 367-376
[15] Kachlakev, D.I. and Barnes, W.A. (1999), “Flexural and Shear Performance of   Concrete Beams Strengthened with Fiber Reinforced Polymer Laminates”, ACI STRUCTURAL JOURNAL, V188, 959-972.
[16] Khalifa, A., Tumialan, G., Nanni, A. and Belarbi, A. (1999), “Shear Strengthening of Continuous Reinforced Concrete Beams Using Externally Bonded Carbon Fiber Reinforced Polymer Sheets”, ACI STRUCTURAL JOURNAL, SP-188, 995-1008.
[17] Lu, W., Lin, I. and Yu, Hsin. (2013), “Shear Strength of Reinforced Concrete Deep Beams”, ACI STRUCTURAL JOURNAL, V110, 671-680.
[18] Maaddavwy, T.EI. and Sherif, S. (2009), “FRP composites for shear strengthening of reinforced concrete deep beams with opening”, Compos Struct J, 89, 60-69.
[19] Park, J.W. and Kuchma, D. (2007) “Strut-and-Tie Model Analysis for Strength Prediction of Deep Beams”, ACI STRUCTURAL JOURNAL, Vol.105, No. 6, 657-666.
[20] Shin, S., Lee, K., Moon, J., and Ghosh, S. K. (1999) “Shear Strength of Reinforced High-Strength Concrete Beams with Shear Span-to-Depth Ratios between 1/5 and 2/5”, ACI Structural Journal, V.96, NO.4, 549-556.
[21] Sherif H. Al-Tersawy. (2013), “Effect of fiber parameters and concrete strength on shear behavior of strengthened RC beams”, Construction and Building Material, V44, 15-24.
[22] Sim, J., Kim, G., Park, C., Ju, M. (2005), “Shear Strengthening Effects with Varying Types of FRP Materials and Strengthening Methods”, ACI STRUCTURAL JOURNAL, V230, 1665-1680.
[23] Simon, C., Ianniruberto, U. and Rinaldi, Z. (2010), Redistribution of Bending Moment in Continuous Reinforced Concrete Beams Strengthened with Fiber-Reinforced Polymer”, ACI STRUCTURAL JOURNAL, V105, 318-326.
[24] Yungon, K., Kevin, Q., Wassim M. G. and James O. J. (2011), “Shear Strengthening RC T-beams Using CFRP Laminates and Anchors”, ACI STRUCTURAL JOURNAL, V111, 1027-1036.
  • Receive Date: 02 September 2015
  • Revise Date: 25 February 2016
  • Accept Date: 27 February 2016
  • First Publish Date: 27 February 2016