Using integrated displacement method to time-history analysis of steel frames with nonlinear flexible connections

  • Hadianfard, M.A. (Department of Civil and Environmental Engineering, Shiraz University of Technology)
  • Received : 2010.12.11
  • Accepted : 2012.02.04
  • Published : 2012.03.10


Most connections of steel structures exhibit flexible behaviour under cyclic loading. The flexible connections can be assumed as nonlinear rotational springs attached to the ends of each beam. The nonlinear behaviour of the connections can be considered by suitable moment-rotation relationship. Time-history analysis by direct integration method can be used as a powerful technique to determine the nonlinear dynamic response of the structure. In conventional numerical integration, the response is evaluated for a series of short time increments. The limitations on the size of time intervals can be removed by using Chen and Robinson improved time history analysis method, in which the integrated displacements are used as the new variables in integrated equation of motion. The proposed method permits longer time intervals and reduces the computational works. In this paper the nonlinearity behaviour of the structure is summarized on the connections, and the step by step improved time-history analysis is used to calculate the dynamic response of the structure. Several numerical calculations which indicate the applicability and advantages of the proposed methodology are presented. These calculations illustrate the importance of the effect of the nonlinear behaviour of the flexible connections in the calculation of the dynamic response of steel frames.


  1. Abolmaali, A., Kukreti, A.R. and Razavi, H. (2003), "Hysteresis behavior of semi-rigid double web angle steel connections", J. Constr. Steel Res., 59, 1057-1082.
  2. Chan, S.L. and Mingho, G.W. (1994), "Nonlinear vibration analysis of steel frames with semi-rigid connections", J. Struct. Eng., 120(4), 1075-1087.
  3. Chen, C.C. and Robinson, A.R. (1993), "Improved time-history analysis of structural dynamics. I: Treatment of rapid variation of excitation and material nonlinearity", J. Eng. Mech., 119(12), 2496-2513.
  4. Chen, W.F. and Lui, E.M. (1991), Stability Design of Steel Frames, CRC Press, Inc.
  5. Clough, R.W. and Penzien, J. (2003), Dynamics of Structures, Computers & Structures, Inc.
  6. Elghazouli, A.Y., Malaga-Chuquitaype, C., Castro, J.M. and Orton, A.H. (2009), "Experimental monotonic and Cyclic behavior of blind-bolted angle connections", Eng. Struct., 31, 2540-2553.
  7. Elnashai, A.S. and Izzuddin, B.A. (1993), "Modeling of material nonlinearities in steel structures subjected to transient dynamic loading", J. Earthq. Eng. Struct. D., 22, 509-532.
  8. Hadianfard, M.A. and Rahnema, H. (2010), "Effects of RHS face deformation on the rigidity of beam-column connection", J. Steel Compos. Struct., 10(6), 491-502.
  9. Hadianfard, M.A. and Razani, R. (2003), "Effects of semi-rigid behavior of connections in the reliability of steel frames", J. Struct. Saf., 25, 123-138.
  10. Healey, T.J. and Robinson, A.R. (1984), "Successive Symmetric Quadratures: A new approach to the integration of ordinary differential equations", Proc. 5th ASCE -Eng. Mech. Div. Specially Conf., ASCE.
  11. Kishi, N. and Chen, W.F. (1990), "Moment-rotation relations of semi-rigid connections with angles", J. Struct. Eng.-ASCE, 116(ST7), 1813-1834.
  12. Kishi, N., Chen, W.F., Goto, Y. and Matsuoka, K.G. (1993), "Design aid of semi-rigid connections for frame analysis", Eng. J., AISC, 30(3), 90-107.
  13. Lee, S.S. and Moon T.S. (2002), "Moment-rotation model of semi-rigid connections with angles", Eng. Struct., 24, 227-237.
  14. Nader, M.N. and Astaneh, A. (1991), "Dynamic behavior of flexible, semi rigid and rigid steel frames", J. Constr. Steel Res., 18, 179-192.
  15. Pirmoz, A., Khoei, A.S., Mohammadrezapour, E. and Daryan, A.S. (2009), "Moment-rotation behavior of bolted top-seat angle connections", J. Constr. Steel Res., 65, 973-984.
  16. Popov, E.P. and Takhirov, S.M. (2002), "Bolted large seismic steel beam-to-column connections part 1: experimental study", Eng. Struct., 24, 1523-1534.
  17. Richard, R.M. and Abbott, B.J. (1975), "Versatile elastic-plastic stress-strain formula", J. Eng. Mech. Div.-ASCE, 101(EM4), 511-515.
  18. Robinson, A.R. and Chen, C.C. (1993), "Improved time-history analysis of structural dynamics. II: Reduction of effective number of degrees of freedom", J. Eng. Mech., 119(12), 2514-2530.
  19. Sekulovic, M. and Nefovska, M. (2008), "Contribution to transient analysis of inelastic steel frames with semirigid connections", Eng. Struct., 30, 976-989.
  20. Sekulovic, M., Salatic, R. and Nefovska, M. (2002), "Dynamic analysis of steel frames with flexible connections", Comput. Struct., 80, 935-955.
  21. Silva, J.G.S., Lima, L.R.O., S.Vellasco, P.C.G., Andrade, S.A.L. and Castro, R.A. (2008), "Nonlinear dynamic analysis of steel portal frames with semi-rigid connections", Eng. Struct., 30, 2566-2579.
  22. Yang, C.M. and Kim, Y.M. (2007), "Cyclic behavior of bolted and welded beam-to-column joints", Int. J. Mech. Sci., 49, 635-649.

Cited by

  1. Evaluation of energy response of space steel frames subjected to seismic loads vol.54, pp.4, 2015,
  2. Improved formulation for a structure-dependent integration method vol.60, pp.1, 2016,
  3. Nonlinear P-Δ analysis of steel frames with semi-rigid connections vol.14, pp.1, 2013,
  4. A family of dissipative structure-dependent integration methods vol.55, pp.4, 2015,