Shape Functions Development for Beam-Column Element with Semi-Rigid Connections in Second-Order Steel Frame Analysis
Vol. 11 No. 1 (2025): January
Research Articles
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Doi: 10.28991/CEJ-2025-011-01-021
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Vu, Q. A., Dung, B. T. L., & Nguyen, H. Q. (2025). Shape Functions Development for Beam-Column Element with Semi-Rigid Connections in Second-Order Steel Frame Analysis. Civil Engineering Journal, 11(1), 369–392. https://doi.org/10.28991/CEJ-2025-011-01-021
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[1] Stelmack, T. W. (1982). Analytical and experimental response of flexibly-connected steel frames. Master Thesis, University of Colorado, Boulder, United States.
[2] Chen, W. F. & Lui, E. M. (1987). Structural stability theory and implementation. Elsevier, Amsterdam, Netherlands.
[3] Anh, V. Q. (2003). Research on analysis and calculation methods of steel frames with elastic connections. Ph.D. Thesis, Hanoi University of Architecture, Hanoi, Vietnam. (In Vietnamese).
[4] Quang, N. H. (2012). Calculation of steel frames with semi-rigid connections according to the elastic-plastic model subjected to dynamic loads. PhD Thesis, Hanoi University of Architecture, Hanoi, Vietnam. (In Vietnamese).
[5] Chan, S. L., & Chui, P. T. (2000). Non-linear static and cyclic analysis of steel frames with semi-rigid connections. Elsevier, Amsterdam, Netherlands.
[6] LRFD (AISC). (2000). Load and Resistance Factor Design Specification for Structural Steel Buildings. American Institute of Steel Construction (AISC), Chicago, United States.
[7] EN 1993-1-1 (CEN) (2005). Design of steel structures - Part 1-1: General rules and rules for buildings. European Committee for Standardization, Brussels, Belgium.
[8] Monforton, G. R. (1962). Matrix analysis of frames with semi-rigid connections, Master Thesis. University of Windsor, Ontario, Canada.
[9] Dhillon, B. S., & Abdel-Majid, S. (1990). Interactive analysis and design of flexibly connected frames. Computers and Structures, 36(2), 189–202. doi:10.1016/0045-7949(90)90118-L.
[10] Xu, L., & Grierson, D. E. (1993). Computer-Automated Design of Semirigid Steel Frameworks. Journal of Structural Engineering, 119(6), 1740–1760. doi:10.1061/(asce)0733-9445(1993)119:6(1740).
[11] Xu, L. (2001). Second-order analysis for semirigid steel frame design. Canadian Journal of Civil Engineering, 28(1), 59–76. doi:10.1139/l00-077.
[12] Lui, E. M., & Chen, W. F. (1986). Analysis and behaviour of flexibly-jointed frames. Engineering Structures, 8(2), 107–118. doi:10.1016/0141-0296(86)90026-X.
[13] Xu, L. (1992). Geometrical stiffness and sensitivity matrices for optimization of semi-rigid steel frameworks. Structural Optimization, 5(1–2), 95–99. doi:10.1007/BF01744701.
[14] Chen, W. F. (2000). Practical Analysis for Semi-Rigid Frame Design. World Scientific, Singapore. doi:10.1142/4277.
[15] Bazant, Z. P., & Cedolin, L. (2010). Stability of structures: elastic, inelastic, fracture and damage theories. World Scientific, Singapore. doi:10.1142/9789814317047.
[16] Dhillon, B. S., & O'Malley III, J. W. (1999). Interactive Design of Semirigid Steel Frames. Journal of Structural Engineering, 125(5), 556–564. doi:10.1061/(asce)0733-9445(1999)125:5(556).
[17] Kim, S. E., & Choi, S. H. (2001). Practical advanced analysis for semi-rigid space frames. International Journal of Solids and Structures, 38(50–51), 9111–9131. doi:10.1016/S0020-7683(01)00141-X.
[18] Nguyen, P. C., & Kim, S. E. (2014). An advanced analysis method for three-dimensional steel frames with semi-rigid connections. Finite Elements in Analysis and Design, 80, 23–32. doi:10.1016/j.finel.2013.11.004.
[19] Chan, S. L., & Ho, G. W. M. (1994). Nonlinear Vibration Analysis of Steel Frames with Semirigid Connections. Journal of Structural Engineering, 120(4), 1075–1087. doi:10.1061/(asce)0733-9445(1994)120:4(1075).
[20] Chan, S. L. (1994). Vibration and modal analysis of steel frames with semi-rigid connections. Engineering Structures, 16(1), 25–31. doi:10.1016/0141-0296(94)90101-5.
[21] Chui, P. P. T., & Chan, S. L. (1997). Vibration and deflection characteristics of semi-rigid jointed frames. Engineering Structures, 19(12), 1001–1010. doi:10.1016/s0141-0296(97)00126-0.
[22] Suarez, L. E., Singh, M. P., & Matheu, E. E. (1996). Seismic response of structural frameworks with flexible connections. Computers and Structures, 58(1), 27–41. doi:10.1016/0045-7949(95)00108-S.
[23] Sekulovic, M., & Salatic, R. (2001). Nonlinear analysis of frames with flexible connections. Computers and Structures, 79(11), 1097–1107. doi:10.1016/S0045-7949(01)00004-9.
[24] Zohra, D. F., & Nacer, I. T. A. (2018). Dynamic analysis of steel frames with semi-rigid connections. Structural Engineering and Mechanics, 65(3), 327–334. doi:10.12989/sem.2018.65.3.327.
[25] Salatic, R. (2019). Seismic analysis of steel frames with semi-rigid and viscous connections. 7th International Conference Contemporary achievements in civil engineering, 23-24 April, 2019, Subotica, Serbia.
[26] Zlatkov, D. (2015). Theoretical and experimental analysis of reinforced concrete frame structures with semi-rigid connections. Ph.D. Thesis, University of NiŠ¡, NiŠ¡, Serbia. (In Serbian).
[27] Milićević, M. (1986). Design of systems with semi-rigid connections by use of slope-deflection method. 17th Yugoslav Congress of Theoretical And Mechanics, Zadar, Croatia.
[28] Zlatkov, D., Zdravkovic, S., Mladenovic, B., & Stojic, R. (2011). Matrix formulation of dynamic design of structures with semi-rigid connections. Facta Universitatis - Series: Architecture and Civil Engineering, 9(1), 89–104. doi:10.2298/fuace1101089z.
[29] Zlatkov, D., Zdravkovic, S., Mladenovic, B., & Mijalkovic, M. (2020). Seismic analysis of frames with semi-rigid connections in accordance with EC8. Facta Universitatis - Series: Architecture and Civil Engineering, 18(2), 203–217. doi:10.2298/fuace201208015z.
[30] Anh, V. Q. (2002). Stability analysis of steel frames with semi-rigid connections and rigid zones by using P-Delta effect. Vietnam Journal of Mechanics, 24(1), 14–24. doi:10.15625/0866-7136/24/1/6605.
[31] Anh, V. Q. (2002). Analysis plane steel frame with semi-rigid connections and rigid-zones with consideration of the second order effect. Advances in Building Technology, II, 1043–1049. doi:10.1016/b978-008044100-9/50131-5.
[32] Nguyen, P.-C., Tran, T.-T., & Nghia-Nguyen, T. (2021). Nonlinear time-history earthquake analysis for steel frames. Heliyon, 7(8), e06832. doi:10.1016/j.heliyon.2021.e06832.
[33] Dang, H. K., Thai, D. K., & Kim, S. E. (2023). Stochastic analysis of semi-rigid steel frames using a refined plastic-hinge model and Latin hypercube sampling. Engineering Structures, 291(116313), 1–16. doi:10.1016/j.engstruct.2023.116313.
[34] De Souza, L. A. F., & Verdade, L. L. (2023). Numerical-Computational Model for Dynamic Nonlinear Analysis of Frames With Semi-Rigid Connection Considering the Damping Effect. Revista de Gestí£o Social e Ambiental, 18(1), e04192. doi:10.24857/rgsa.v18n1-019.
[35] Saadi, M., Yahiaoui, D., Lahbari, N., & Tayeb, B. (2021). Seismic fragility curves for performance of semi-rigid connections of steel frames. Civil Engineering Journal (Iran), 7(7), 1112–1124. doi:10.28991/cej-2021-03091714.
[36] Genovese, F., & Sofi, A. (2024). A novel interval matrix stiffness method for the analysis of steel frames with uncertain semi-rigid connections. Advances in Engineering Software, 192, 103629. doi:10.1016/j.advengsoft.2024.103629.
[37] Jough, F. K. G., & Soori, M. (2024). Considering the Effect of Semi-Rigid Connection in Steel Frame Structures for Progressive Collapse. World Academy of Science, Engineering and Technology International Journal of Structural and Construction Engineering, 18(6), 218–227.
[38] Przemieniecki, J. S. (1985). Theory of matrix structural analysis. Courier Corporation, North Chelmsford, United States.
[39] McGuire, W., Gallagher, R. H., & Saunders, H. (2014). Matrix Structural Analysis. John Wiley & Sons, Hoboken, United States.
[40] Kishi, N., & Chen, W. F. (1990). Moment-rotation relations of semirigid connections with angles. Journal of Structural Engineering, 116(7), 1813-1834. doi:10.1061/(ASCE)0733-9445(1990)116:7(1813).
[41] Richard, R. M., & Abbott, B. J. (1975). Versatile elastic-plastic stress-strain formula. Journal of the Engineering Mechanics Division, 101(4), 511-515. doi:10.1061/JMCEA3.0002047.
[42] Bhatti, M. A., & Hingtgen, J. D. (1995). Effects of connection stiffness and plasticity on the service load behavior of unbraced steel frames. Engineering Journal, 32(1), 21–33. doi:10.62913/engj.v32i1.637.
[43] Abolmaali, A., & Choi, Y. (2004). Nonlinear moment reversal behavior in steel frames. Korean Science Journal, Korea Spatial Information Society (KSIS), 5(22), 3-15.
[44] Stelmack, T. W., Marley, M. J., & Gerstle, K. H. (1986). Analysis and tests of flexibly connected steel frames. Journal of Structural Engineering, 112(7), 1573-1588. doi:10.1061/(ASCE)0733-9445(1986)112:7(1573).
[45] Valipour, H. R., & Bradford, M. A. (2013). Nonlinear P-Δ analysis of steel frames with semi-rigid connections. Steel & Composite Structures, 14(1), 1–20. doi:10.12989/scs.2013.14.1.001.
[2] Chen, W. F. & Lui, E. M. (1987). Structural stability theory and implementation. Elsevier, Amsterdam, Netherlands.
[3] Anh, V. Q. (2003). Research on analysis and calculation methods of steel frames with elastic connections. Ph.D. Thesis, Hanoi University of Architecture, Hanoi, Vietnam. (In Vietnamese).
[4] Quang, N. H. (2012). Calculation of steel frames with semi-rigid connections according to the elastic-plastic model subjected to dynamic loads. PhD Thesis, Hanoi University of Architecture, Hanoi, Vietnam. (In Vietnamese).
[5] Chan, S. L., & Chui, P. T. (2000). Non-linear static and cyclic analysis of steel frames with semi-rigid connections. Elsevier, Amsterdam, Netherlands.
[6] LRFD (AISC). (2000). Load and Resistance Factor Design Specification for Structural Steel Buildings. American Institute of Steel Construction (AISC), Chicago, United States.
[7] EN 1993-1-1 (CEN) (2005). Design of steel structures - Part 1-1: General rules and rules for buildings. European Committee for Standardization, Brussels, Belgium.
[8] Monforton, G. R. (1962). Matrix analysis of frames with semi-rigid connections, Master Thesis. University of Windsor, Ontario, Canada.
[9] Dhillon, B. S., & Abdel-Majid, S. (1990). Interactive analysis and design of flexibly connected frames. Computers and Structures, 36(2), 189–202. doi:10.1016/0045-7949(90)90118-L.
[10] Xu, L., & Grierson, D. E. (1993). Computer-Automated Design of Semirigid Steel Frameworks. Journal of Structural Engineering, 119(6), 1740–1760. doi:10.1061/(asce)0733-9445(1993)119:6(1740).
[11] Xu, L. (2001). Second-order analysis for semirigid steel frame design. Canadian Journal of Civil Engineering, 28(1), 59–76. doi:10.1139/l00-077.
[12] Lui, E. M., & Chen, W. F. (1986). Analysis and behaviour of flexibly-jointed frames. Engineering Structures, 8(2), 107–118. doi:10.1016/0141-0296(86)90026-X.
[13] Xu, L. (1992). Geometrical stiffness and sensitivity matrices for optimization of semi-rigid steel frameworks. Structural Optimization, 5(1–2), 95–99. doi:10.1007/BF01744701.
[14] Chen, W. F. (2000). Practical Analysis for Semi-Rigid Frame Design. World Scientific, Singapore. doi:10.1142/4277.
[15] Bazant, Z. P., & Cedolin, L. (2010). Stability of structures: elastic, inelastic, fracture and damage theories. World Scientific, Singapore. doi:10.1142/9789814317047.
[16] Dhillon, B. S., & O'Malley III, J. W. (1999). Interactive Design of Semirigid Steel Frames. Journal of Structural Engineering, 125(5), 556–564. doi:10.1061/(asce)0733-9445(1999)125:5(556).
[17] Kim, S. E., & Choi, S. H. (2001). Practical advanced analysis for semi-rigid space frames. International Journal of Solids and Structures, 38(50–51), 9111–9131. doi:10.1016/S0020-7683(01)00141-X.
[18] Nguyen, P. C., & Kim, S. E. (2014). An advanced analysis method for three-dimensional steel frames with semi-rigid connections. Finite Elements in Analysis and Design, 80, 23–32. doi:10.1016/j.finel.2013.11.004.
[19] Chan, S. L., & Ho, G. W. M. (1994). Nonlinear Vibration Analysis of Steel Frames with Semirigid Connections. Journal of Structural Engineering, 120(4), 1075–1087. doi:10.1061/(asce)0733-9445(1994)120:4(1075).
[20] Chan, S. L. (1994). Vibration and modal analysis of steel frames with semi-rigid connections. Engineering Structures, 16(1), 25–31. doi:10.1016/0141-0296(94)90101-5.
[21] Chui, P. P. T., & Chan, S. L. (1997). Vibration and deflection characteristics of semi-rigid jointed frames. Engineering Structures, 19(12), 1001–1010. doi:10.1016/s0141-0296(97)00126-0.
[22] Suarez, L. E., Singh, M. P., & Matheu, E. E. (1996). Seismic response of structural frameworks with flexible connections. Computers and Structures, 58(1), 27–41. doi:10.1016/0045-7949(95)00108-S.
[23] Sekulovic, M., & Salatic, R. (2001). Nonlinear analysis of frames with flexible connections. Computers and Structures, 79(11), 1097–1107. doi:10.1016/S0045-7949(01)00004-9.
[24] Zohra, D. F., & Nacer, I. T. A. (2018). Dynamic analysis of steel frames with semi-rigid connections. Structural Engineering and Mechanics, 65(3), 327–334. doi:10.12989/sem.2018.65.3.327.
[25] Salatic, R. (2019). Seismic analysis of steel frames with semi-rigid and viscous connections. 7th International Conference Contemporary achievements in civil engineering, 23-24 April, 2019, Subotica, Serbia.
[26] Zlatkov, D. (2015). Theoretical and experimental analysis of reinforced concrete frame structures with semi-rigid connections. Ph.D. Thesis, University of NiŠ¡, NiŠ¡, Serbia. (In Serbian).
[27] Milićević, M. (1986). Design of systems with semi-rigid connections by use of slope-deflection method. 17th Yugoslav Congress of Theoretical And Mechanics, Zadar, Croatia.
[28] Zlatkov, D., Zdravkovic, S., Mladenovic, B., & Stojic, R. (2011). Matrix formulation of dynamic design of structures with semi-rigid connections. Facta Universitatis - Series: Architecture and Civil Engineering, 9(1), 89–104. doi:10.2298/fuace1101089z.
[29] Zlatkov, D., Zdravkovic, S., Mladenovic, B., & Mijalkovic, M. (2020). Seismic analysis of frames with semi-rigid connections in accordance with EC8. Facta Universitatis - Series: Architecture and Civil Engineering, 18(2), 203–217. doi:10.2298/fuace201208015z.
[30] Anh, V. Q. (2002). Stability analysis of steel frames with semi-rigid connections and rigid zones by using P-Delta effect. Vietnam Journal of Mechanics, 24(1), 14–24. doi:10.15625/0866-7136/24/1/6605.
[31] Anh, V. Q. (2002). Analysis plane steel frame with semi-rigid connections and rigid-zones with consideration of the second order effect. Advances in Building Technology, II, 1043–1049. doi:10.1016/b978-008044100-9/50131-5.
[32] Nguyen, P.-C., Tran, T.-T., & Nghia-Nguyen, T. (2021). Nonlinear time-history earthquake analysis for steel frames. Heliyon, 7(8), e06832. doi:10.1016/j.heliyon.2021.e06832.
[33] Dang, H. K., Thai, D. K., & Kim, S. E. (2023). Stochastic analysis of semi-rigid steel frames using a refined plastic-hinge model and Latin hypercube sampling. Engineering Structures, 291(116313), 1–16. doi:10.1016/j.engstruct.2023.116313.
[34] De Souza, L. A. F., & Verdade, L. L. (2023). Numerical-Computational Model for Dynamic Nonlinear Analysis of Frames With Semi-Rigid Connection Considering the Damping Effect. Revista de Gestí£o Social e Ambiental, 18(1), e04192. doi:10.24857/rgsa.v18n1-019.
[35] Saadi, M., Yahiaoui, D., Lahbari, N., & Tayeb, B. (2021). Seismic fragility curves for performance of semi-rigid connections of steel frames. Civil Engineering Journal (Iran), 7(7), 1112–1124. doi:10.28991/cej-2021-03091714.
[36] Genovese, F., & Sofi, A. (2024). A novel interval matrix stiffness method for the analysis of steel frames with uncertain semi-rigid connections. Advances in Engineering Software, 192, 103629. doi:10.1016/j.advengsoft.2024.103629.
[37] Jough, F. K. G., & Soori, M. (2024). Considering the Effect of Semi-Rigid Connection in Steel Frame Structures for Progressive Collapse. World Academy of Science, Engineering and Technology International Journal of Structural and Construction Engineering, 18(6), 218–227.
[38] Przemieniecki, J. S. (1985). Theory of matrix structural analysis. Courier Corporation, North Chelmsford, United States.
[39] McGuire, W., Gallagher, R. H., & Saunders, H. (2014). Matrix Structural Analysis. John Wiley & Sons, Hoboken, United States.
[40] Kishi, N., & Chen, W. F. (1990). Moment-rotation relations of semirigid connections with angles. Journal of Structural Engineering, 116(7), 1813-1834. doi:10.1061/(ASCE)0733-9445(1990)116:7(1813).
[41] Richard, R. M., & Abbott, B. J. (1975). Versatile elastic-plastic stress-strain formula. Journal of the Engineering Mechanics Division, 101(4), 511-515. doi:10.1061/JMCEA3.0002047.
[42] Bhatti, M. A., & Hingtgen, J. D. (1995). Effects of connection stiffness and plasticity on the service load behavior of unbraced steel frames. Engineering Journal, 32(1), 21–33. doi:10.62913/engj.v32i1.637.
[43] Abolmaali, A., & Choi, Y. (2004). Nonlinear moment reversal behavior in steel frames. Korean Science Journal, Korea Spatial Information Society (KSIS), 5(22), 3-15.
[44] Stelmack, T. W., Marley, M. J., & Gerstle, K. H. (1986). Analysis and tests of flexibly connected steel frames. Journal of Structural Engineering, 112(7), 1573-1588. doi:10.1061/(ASCE)0733-9445(1986)112:7(1573).
[45] Valipour, H. R., & Bradford, M. A. (2013). Nonlinear P-Δ analysis of steel frames with semi-rigid connections. Steel & Composite Structures, 14(1), 1–20. doi:10.12989/scs.2013.14.1.001.
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