Lowes, L. N. & Altoontash, A. Modeling reinforced-concrete beam-column joints subjected to cyclic loading. J. J. Struct. Eng. 12, 1686–1697 (2003).
Shi, K. et al. Numerical simulation on seismic behavior of steel fiber reinforced concrete beam-column joints. J. Materials 14(17), 4883 (2021).
Vecchio, F. J. & Collins, M. P. The modified compression–field theory for reinforced concrete elements subjected to shear. J. ACI J. 83, 219–231 (1986).
Xue, R. et al. Modeling method for steel fiber reinforced concrete beam column joints. J. Vibration Shock 41, 96–102 (2022).
Ritter, W. Die bauweise hennebique. J. Schweizerische Bauzeitung 33, 59–61 (1899).
Morsch, E. Concrete-Steel Construction, (Der Eisenbetonbau), English translation of the 3rd Vol. 33 (McGraw-Hill Book Co., German, 1909).
Schlaich, J. & Schafer, K. Design and detailing of structural concrete using strut–and–tie models. J. Struct. Eng. 69, 113–125 (1991).
Schlaich, J., Schafer, K. & Jennewein, M. Toward a consistent design of structural concrete. J. PCI J. 32, 74–150 (1987).
Cai, J. H., Ding, H. B. & Huang, L. Topology optimization method of strut-and-tie composite structure under uncertain load conditions. J. Adv. Eng. Softw. 203, 103886 (2025).
Xia, Y. et al. Comparison of ground-structure and continuum based topology optimization methods for strut-and-tie model generation. J. Eng. Struct. 316, 118498 (2024).
Yang, X., Wu, T., Liu, X. & Liu, Y. Influence of web reinforcement on shear behavior and size effect of lightweight aggregate concrete deep beams: Experimental and theoretical studies. J. Eng. Struct. 322, 119119 (2025).
Kevinly, C., Du, P. W., Teoh, B. K. & Tan, K. H. Shear behaviour of continuous fibre-reinforced lightweight aggregate concrete beams. J. Eng. Struct. 323, 119141 (2025).
Shabanlou, M., Meghdadi, Z. & Ghaffar, S. H. Experimental and analytical study of the residual performance of reinforced concrete deep beams with circular web openings. J. Results Eng. 25, 104229 (2025).
Tu, R. H., Yuan, P., Cai, Y. F. & Wang, L. Reusability diagnosis method for demolished bridge girders based on topological evolution of load paths. J. Eng. Struct. 330, 119893 (2025).
Xiong, L. Q., Luo, Q., He, J. & Cheng, L. F. Shear strength prediction of interior RC column and steel beam composite joints using the modified softened strut-and-tie model. J. J. Build. Eng. 88, 109250 (2024).
Ye, M. et al. Shear behavior of precast ultrahigh-performance concrete (UHPC) segmental beams with external tendons and dry joints. J. Arch. Civ. Mech. Eng. 23(3), 143 (2023).
Shi, X. F. et al. Experimental and numerical study on tensile capacity of composite cable-girder anchorage joint. J. Steel Compos. Struct. 49, 215–230 (2023).
Chetchotisak, P., Teerawong, J. & Hansapinyo, C. Strut-and-tie – and – tie model including shear-flexure – flexure interaction for predicting shear capacity of reinforced concrete short coupling beams. J. ACI Struct. 66, 800230 (2024).
ACI A. ACI CODE-318–19 (22): Building Code Requirements for Structural Concrete and Commentary (Reapproved 2022). United States: American Concrete Institute, 2022.
NZS 3101:2006, Design of Concrete Structures, Concrete Structures Standards: Wellington, New Zealand, 2016.
CEN. Design of structures for earthquake resistance, Part 1: General rules, seismic actions and rules for buildings. EN 1998–1, Eurocode 8. Vol. 3. Brussels: European Committee for Standardization, 2004.
AASHTO, LRFD bridge design specifications. 10th ed Washington, DC: American Association of State Highway and Transportation Officials, 2024.
CSA (Canadian Standards Association). 2019b. Design of concrete structures. CSA A23.3:19. Rexdale, Ontario: CSA, 2019.
Fib (International Federation for Structural Concrete), fib model code for concrete structures 2010. Wiley, Lausanne, Switzerland: Ernst & Sohn, 2013.
Hwang, H. J. & Lee, H. J. Analytical model for predicting shear strengths of exterior reinforced concrete beam–column joints for seismic resistance. J. ACI Struct. J. 96, 846–857 (1999).
You, X. H., Wang, P., Shi, Q. X., Wang, Q. W. & Rong, C. Shear mechanism and bearing capacity calculation of steel fiber reinforced concrete beam-column joints. J. Struct. 70, 107752 (2024).
Anwar, M. M., Ismail, M. K., Hodhod, H. A., El-Dakhakhni, W. & Ibrahim, H. H. A. Mechanics guided data-driven model for seismic shear strength of exterior beam-column joints. J. Struct. 69, 107320 (2024).
Zhang, C. et al. Cyclic behavior and shear strength of exterior reinforced concrete beam-column joints with inclined columns. J. J. Build. Eng. 90, 109341 (2024).
Mitra, N. An analytical study of reinforced concrete beam–column joint behavior under seismic loading. Ph.D. Thesis, University of Washington, Seattle, (2007).
Xia, Y., Langelaar, M. & Hendriks, M. A. N. Optimization-based strut-and-tie model generation for reinforced concrete structures under multiple load conditions. J. Eng. Struct. 266, 114501 (2022).
Mashhadi, R., Diznab, M. A. D. & Tehrani, F. M. A strut-and-tie model for predicting the shear strength of exterior beam-column joints strengthened with fiber-reinforced polymers. J. J. Compos. Constr. 27(1), 04022097 (2023).
Yang, H., Zhao, W. T., Zhu, Z. Z. & Fu, J. P. Seismic behavior comparison of reinforced concrete interior beam-column joints based on different loading methods. J. Eng. Struct. 166, 31–45 (2018).
GB 50010–2010, Code for design of concrete structures, Construction Ministry of China, 2015.
Chang, B., Hutchinson, T., Wang, X. & Englekirk, R. Seismic Performance of Beam-Column Subassemblies with High Strength Steel Reinforcement. J. ACI Struct. J. 111, 1329–1338 (2014).
Mander, B., Priestley, M. J. N. & Park, R. Theoretical stress–strain model for confined concrete. J. J. Struct. Eng. 114, 1804–1826 (1988).
Wang, T., Su, X. & Fang, J. Application of STMs for calculation of reinforced concrete frame joints. J. Chin. Civ. Eng. J. 40, 36–40 (2007).
Xing, G., Liu, B. & Niu, D. Shear strength of reinforced concrete frame joints using modified softened strut–and–tie model. J. Eng. Mech. 11, 60–66 (2013).
Rudra, P. Getting Started with MATLAB 7: A Quick Introduction for Scientists and Engineers (Oxford University Press, 2006).
Zhao, W., Yang, H., Fu, J. & Li, B. Calibration of beam–column joint element model and comparison of loading methods of beam–column subassemblages. J. Build. Struct. 38, 133–142 (2017).
Fu, J. Seismic Behaviour and Design of Joints in a Reinforced Concrete Frame. Ph.D. Thesis, Chongqing University, Chongqing (2002).
Supaviriyakit, T. & Pimanmas, A. Comparative performance of sub-standard interior reinforced concrete beam–column connection with various joint reinforcing details. J. Mater. Struct. 41, 543–557 (2008).
Kusuhara, F., Azukawa, K., Shiohara, H., Otani, S. Tests of reinforced concrete interior beam–column joint subassemblage with eccentric beams. C. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, BC, Canada, 1–6 (August 2004).
Zaid, S., Shiohara, H., Otani, S. Test of a Joint Reinforcing Detail Improving Joint Capacity of R/C Interior Beam–Column Joint. C. In Proceedings of the 1st Japan-Korea Joint Seminar on Earthquake Engineering for Building Structures, Seoul National University, Seoul, South Korea, 29 (October 1999).
Joh, O, Goto, Y. Beam–column joint behavior after beam yielding in R/C ductile frames. C. In Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zeland, 30 (January 2000).
Durrani, A. J. Experimental and analytical study of internal beam to column connections subjected to reversed cyclic loading. Ph.D. Thesis, University of Michigan, Ann Arbor (1982).
Hwang, H. J., Eom, T. S. & Park, H. G. Design considerations for interior RC beam–column joint with additional bars. J. Eng. Struct. 98, 1–13 (2015).
Noguchi, H., Kurusu, K. Correlation of bond and shear in RC beam-column connections subjected to seismic forces. C. In Proceedings of the 9th World Conference on Earthquake Engineering, Tokyo-Kyoto, Japan, 2–9 (August 1988).
Mitra, N. & Lowes, L. N. Evaluation, calibration and verification of a reinforced concrete beam–column joint model. J. J. Struct. Eng. 133, 105–120 (2007).
