Non-Linear Strut and Tie Modelling Approach of Retrofitted Reinforced Concrete Beam Column Joint by Prestress Joint Enlargement

Document Type : Original Article

Authors

• S.Ahmad Nezami ¹
• Jalil Shafaei ²

¹ Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran

² Faculty of Civil engineering, Shahrood university of technology.

10.22067/jfcei.2024.85341.1271

Abstract

The need to retrofitted beam-to-column joints, which are made without observing seismic details, is definitely a live and important issue. Connection damage is reported as one of the most worrying causes of building chain collapse in effective earthquakes. The absence of transverse reinforcement and insufficient bond length of the beam bottom bars in the joint area are still existing seismic weaknesses, which are still the subject of investigation and presentation of a corresponding improvement plan. The strut and tie method based on the knowledge based on the finite element method is a powerful and developable tool in the nonlinear field. In this research, analytical models are presented for the evaluation of reinforced concrete side beam-column joints with seismic, non-seismic and strengthened details based on the method of joint enlargement based on the strut and tie methods. The results of the nonlinear modeling of the strut and tie of retrofitted and un-retrofitted specimen show that this model has the ability to detect the effect of shear reinforcement of the joint area on the shear capacity and activated nonlinear mechanisms, including partial and total slip of the longitudinal beam reinforcements in the joint. Also, the influence of the dimensions of the enlargement of the joint in the design of rehabilitation and deterioration of stiffness and resistance is one of the other capabilities of the proposed equivalent truss-type model.

Keywords

• Beam-Column Joints
• Reinforced Concrete Structures
• Strut and Tie Method
• Joint Enlargement
• Equivalent Non-Linear Truss

---

References

[1] J. Shafaei, S.A. Nezami, “Effect of different size of joint enlargement on seismic behavior of gravity load designed RC beam‐column connections”, The Structural Design of Tall and Special Buildings, vol. 28, no. 14 pp. 1653-1674, (2019).

[2] C. Lima, E. Martinelli and C. Faella, “Capacity models for shear strength of exterior joints in RC frames: state-of-the-art and synoptic examination”, Bulletin of Earthquake Engineering, vol. 10, no. 3, pp. 967-983, (2012).https://doi.org/10.1007/s10518-012-9340-4

[3] K. Parate, R. Kumar, “Investigation of shear strength models for exterior RC beam-column joint”, Structural Engineering and Mechanics, vol. 58, no. 3, pp. 475-514, (2016).

[4] S. Sritharan, M.N. Priestley and F. Seible, “Nonlinear finite element analyses of concrete bridge joint systems subjected to seismic actions”, Finite elements in analysis and design, vol. 36, no. 3-4, pp. 215-233, (2000). https://doi.org/10.1016/S0168-874X(00)00034-2

[5] J. Zhao, S. Sritharan, “Modeling of strain penetration effects in fiber-based analysis of reinforced concrete structures”, ACI structural journal, vol. 104, no. 2, pp. 133, (2007).

[6] D.-C. Feng and J. Xu, “An efficient fiber beam-column element considering flexure–shear interaction and anchorage bond-slip effect for cyclic analysis of RC structures,” Bulletin of Earthquake Engineering, vol. 16, no. 11, pp. 5425-5452, (2018). https://doi.org/10.1007/s10518-018-0392-y

[7] D. C. Feng, G. Wu and Y. Lu, “Finite element modelling approach for precast reinforced concrete beam-to-column connections under cyclic loading”, Engineering Structures, vol. 174, pp. 49-66, (2018). https://doi.org/10.1016/j.engstruct.2018.07.055

[8] D. C. Feng, X. D. Ren and J. Li, “Softened damage-plasticity model for analysis of cracked reinforced concrete structures”, Structural Engineering, vol. 144, no. 6, pp. 1804-1824, (2018). https://doi.org/10.1061/(ASCE)ST.1943-541X.0002015

[9] H. Behnam, J. Kuang and B. Samali, “Parametric finite element analysis of RC wide beam-column connections”, Computers & Structures, vol. 205, pp. 28-44, (2018).https://doi.org/10.1016/j.compstruc.2018.04.004

[10] J. Schlaich, K. Schäfer and M. Jennewein, “Toward a consistent design of structural concrete”, PCI journal, vol. 32, no. 3, pp. 74-150, (1987).

[11] M. F. Ruiz, A. Muttoni, “On development of suitable stress fields for structural concrete,” ACI Structural journal, vol. 104, pp. 495-502, (2007).

[12] ACI Committee 318, Building code requirements for structural concrete: American Concrete Institute, Michigan: Farmington Hills, (2019).

[13] B.K. Breen J, Jirsa JO and Kreger M. “Detailing for Structural Concrete,” University of Texas at Austin, Texas, United States. Report. 1127-3F, (1993).

[14] S.A. Haugerud, J. Blaauwendraad, S. Bousias, L. Cao Hoang, J. Mata Falcón, C. Meléndez Gimeno, B. Mihaylov, M. Pedrosa Ferreira and Q. Roubaty, “Design and assessment with strut-and-tie models and stress fields: from simple calculations to detailed numerical analysis,” fib Bulletin, vol. 100, (2021).

[15] A. Muttoni, J. Schwartz and B. Thürlimann, “Design of concrete structures with stress fields”, Springer Science & Business Media, (1996).

[16] M. S. Lourenço, J. F. Almeida, “Adaptive Stress Field Models: Formulation and Validation”, ACI Structural Journal, vol. 110, no. 1 , (2013).https://doi.org/10.14359/51684331

[17] S. A. Nezami, J. Shafaei, “Parametric Finite Element Evaluation of RC Beam-Column Joints”, Advance Researches in Civil Engineering, vol. 3, no. 2, pp. 16-26, (2021). https://doi.org/10.30469/arce.2021.135123

[18] W. Kassem, “Strut-and-tie modelling for the analysis and design of RC beam-column joints”, Materials and Structures, vol. 49, no. 8, pp. 3459-3476, (2016).https://doi.org/10.1617/s11527-015-0732-1

[19] R. Ketiyot, C. Hansapinyo and B. Charatpangoon, “Nonlinear strut and tie model with bond-slip effect for analysis of RC beam-column joints under lateral loading,” International Journal, vol. 15, no. 47, pp. 81-88, (2018). https://doi.org/10.21660

[20] P. Chaimahawan and A. Pimanmas, “Application of nonlinear link in strut and tie model for joint planar expansion”, Engineering Journal of Research and Development, vol. 24, no. 4, pp. 1-11, (2013).

[21] N.H. To, S. Sritharan and J.M. Ingham, “Strut-and-tie nonlinear cyclic analysis of concrete frames”, Journal of structural engineering, vol. 135, no. 10, pp. 1259-1268, (2009). https://doi.org/10.1061

[22] A. Marchisella, G. Muciaccia, “Haunch retrofit of RC beam–column joints: Linear stress field analysis and Strut‐and‐Tie method application”, Earthquake Engineering & Structural Dynamics, vol. 52, no. 12, pp. 3575-3599, (2023). https://doi.org/10.1002/eqe.3921

[23] G. Genesio, “Seismic assessment of RC exterior beam-column joints and retrofit with haunches using post-installed anchors”, University of Stuttgart, (2012).

[24] S. J. Hwang, H. J. Lee, “Analytical Model for Predicting Shear Strengths of Exterior Reinforced Concrete Beam-Column Joints for Sesimic Resistance”, ACI Structural Journal, vol. 96, pp. 846-857, (1999). https://doi.org/ 10.14359/831

[25] S. Park, K. M. Mosalam, “Parameters for shear strength prediction of exterior beam–column joints without transverse reinforcement”, Engineering Structures, vol. 36, pp. 198-209, (2012). https://doi.org/10.1016/j.engstruct.2011.11.017

[26] M. Pauletta, D. Di Luca and G. Russo, “Exterior beam column joints–Shear strength model and design formula”, Engineering Structures, vol. 94, pp. 70-81, (2015). https://doi.org/10.1016/j.engstruct.2015.03.040

[27] W. M. Hassan, J. P. Moehle, “Shear Strength of Exterior and Corner Beam-Column Joints without Transverse Reinforcement”, ACI Structural Journal, vol. 115, no. 6, (2018).

[28] S. J. Hwang, W. H. Fang, H. J. Lee and H. W. Yu, “Analytical model for predicting shear strength of squat walls”, Journal of Structural Engineering, vol. 127, no. 1, pp. 43-50, (2001).
https://doi.org/10.1061/(ASCE)0733-9445(2001)127:1(43)

[29] S. J. Hwang, R. J. Tsai, W. K. Lam and J. P. Moehle, “Simplification of softened strut-and-tie model for strength prediction of discontinuity regions”, ACI Structural Journal, vol. 114, no. 5, pp. 1239-1258, (2017).

[30] N. Zhang and K. H. Tan, “Direct strut-and-tie model for single span and continuous deep beams,” Engineering Structures, vol. 29, no. 11, pp. 2987-3001, (2007).

[31] P. Chetchotisak, J. Teerawong, S. Yindeesuk and J. Song, “New strut-and-tie-models for shear strength prediction and design of RC deep beams”, Computers and Concrete, vol. 14, no. 1, pp. 19-40, (2014).

[32] P. Chetchotisak, E. Arjsri, J. Teerawong, “Strut-and-tie model for shear strength prediction of RC exterior beam–column joints under seismic loading”, Bulletin of Earthquake Engineering, pp. 1-22, (2019). https://doi.org/10.1007/s10518-019-00756-4

[33] A. Dammika, N. Anwar, “Extraction of strut and tie model from 3D solid element mesh analysi”, presented at International Conference on Sustainable Built Environment, Kandy, (2010).

[34] W. Nukulchai, N. Anwar, “Space Truss Model for Design of Pile Caps,” Asian Institute of Technology, (1996).

[35] ACI Committee 318, Building Code Requirements for Structural Concrete: American Concrete Institute, (2014).

[36] J. R. Cagley, J. M. LaFave, P. Paultre, M. E. Criswell, D. D. Lee, M. S. Saiidi, C. E. French, R. T. Leon, B. M. Shahrooz and L. E. Garcia, “Recommendations for Design of Beam-Column Connections in Monolithic Reinforced Concrete Structures”, ACI Structural Journal, vol. 352, (2002).

[37] A. Doǧangün, “Performance of reinforced concrete buildings during the May 1, 2003 Bingöl Earthquake in Turkey”, Engineering Structures, vol. 26, no. 6, pp. 841-856, (2004).

[38] A. Ghobarah, M. Saatcioglu and I. Nistor, “The impact of the 26 December 2004 earthquake and tsunami on structures and infrastructure”, Engineering structures, vol. 28, no. 2, pp. 312-326, (2006). https://doi.org/10.1016/j.engstruct.2005.09.028

[39] T. Gur, A. Pay, J. A. Ramirez, M. A. Sozen, A. M. Johnson, A. Irfanoglu and A. Bobet, “Performance of school buildings in Turkey during the 1999 Düzce and the 2003 Bingöl Earthquakes”, Earthquake Spectra, vol. 25, no. 2, pp. 239-256, (2009). https://doi.org/10.1193/1.3089367

[40] D. K. Miller, “Lessons learned from the Northridge earthquake”, Engineering structures, vol. 20, no. 4-6, pp. 249-260, (1998). https://doi.org/10.1016/S0141-0296(97)00031-X

[41] J. P. Moehle, S. A. Mahin, “Observations on the behavior of reinforced concrete buildings during earthquakes”, Special Publication, vol. 127, pp. 67-90, (1991). https://doi.org/ 10.14359/3007

[42] T. Paulay, M.N. Priestley, “Seismic design of reinforced concrete and masonry buildings”, Seismic Design Book, (1992).

[43] H. Sezen, A.S. Whittaker, K.J. Elwood and K.M. Mosalam, “Performance of reinforced concrete buildings during the August 17, 1999 Kocaeli, Turkey earthquake, and seismic design and construction practise in Turkey”, Engineering Structures, vol. 25, no. 1, pp. 103-114, (2003). https://doi.org/10.1016/S0141-0296(02)00121-9

[44] B. Zhao, F. Taucer and T. Rossetto, “Field investigation on the performance of building structures during the 12 May 2008 Wenchuan earthquake in China,” Engineering Structures, vol. 31, no. 8, pp. 1707-1723, (2009). https://doi.org/10.1016/j.engstruct.2009.02.039

[45] J. Shafaei, A. Hosseini and M. S. Marefat, “Seismic retrofit of external RC beam–column joints by joint enlargement using prestressed steel angles”, Engineering Structures, vol. 81, pp. 265-288, (2014). https://doi.org/10.1016/j.engstruct.2014.10.006

[46] J. Shafaei, A. Hosseini, M. S. Marefat and J. M. Ingham, “Rehabilitation of earthquake damaged external RC beam‐column joints by joint enlargement using prestressed steel angles”, Earthquake Engineering Structural Dynamics, vol. 46, no. 2, pp. 291-316, (2017).  https://doi.org/10.1002/eqe.2794

[47] A.S. Genikomsou, M. A. Polak, “Finite element analysis of punching shear of concrete slabs using damaged plasticity model in ABAQUS”, Engineering structures, vol. 98, pp. 38-48, (2015). https://doi.org/10.1016/j.engstruct.2015.04.016

[48] British Standard, Eurocode 8: Design of structures for earthquake resistance, (2004).

[49] E. Thorenfeldt, “Mechanical properties of high-strength concrete and applications in design”, Utilization of High-Strength Concrete, (1987).

[50] D. Systèmes, ABAQUS/CAE user’s guide, Vol. 3, (2014).

[51] AIJ, “Standard for structural Calculation of Reinforced concrete Structures–Based on Allowable Stress Concept”, Architectural Institute of Japan, (1999).

[52] ASCE/SEI 41, Seismic Evaluation and Retrofit of Existing Buildings: American Society of Civil Engineers, (2017).

[53] ACI Committee 318, Building Code Requirements for Structural Concrete: American Concrete Institute, (2014).