Earthquakes and Structures

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Large deformations of a flexural frame under nonlinear P-delta effects

  • Afshar, Dana (Department of Technology and Engineering, Imam Khomeini International University) ;
  • Afshar, Majid Amin (Department of Technology and Engineering, Imam Khomeini International University)
  • Received : 2021.11.14
  • Accepted : 2022.04.20
  • Published : 2022.05.25
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Abstract

In this paper, nonlinear P-delta effects are studied on the seismic performance, and the modal responses of a flexural frame, considering large deformations. Using multiple scales method, the nonlinear differential equations of motion are estimated, and the nonlinear interactions between the frame's degrees of freedom are outcropped. The results of time and frequency domain analyzes of a dynamic model are examined under internal resonance cases, and the linear and nonlinear responses are investigated in each modal cases. Also, changing the modal responses with respect to the amplitude and frequency of the harmonic forces is evaluated. It is shown that the dominant absorption of energy is in the first natural frequency of the frame, in the case of earthquake excitation, and when a harmonic force is applied to the frame, the peaks of the frequency domain responses depending on the frequency of harmonic force are in the first, and second or third natural frequency of the structure.

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References

  1. Adam, C. and Jager, C. (2012a), "Dynamic instabilities of simple inelastic structures subjected to earthquake excitation", Advanced Dynamics and Model-Based Control of Structures and Machines, 11-18, Springer, Vienna. https://doi.org/10.1007/978-3-7091-0797-3_2.
  2. Adam, C. and Jager, C. (2012b), "Simplified collapse capacity assessment of earthquake excited regular frame structures vulnerable to P-delta", Eng. Struct., 44, 159-173 https://doi.org/10.1016/j.engstruct.2012.05.036.
  3. Afaneh, A.A. and Ibrahim, R.A. (1993), "Nonlinear response of an initially buckled beam with 1: 1 internal resonance to sinusoidal excitation", Nonlinear Dynam., 4(6), 547-571. https://doi.org/10.1007/BF00162232.
  4. Au, F.T.K., and Yan, Z.H. (2008), "Dynamic analysis of frames with material and geometric nonlinearities based on the semirigid technique", J. Struct. Stability Dynam., 8(03), 415-438. https://doi.org/10.1142/S0219455408002727.
  5. Belhadj, A.H. and Meftah, S.A. (2015), "Simplified finite element modelling of non uniform tall building structures comprising wall and frame assemblies including P-delta effects", Earthq. Struct., 8(1), 253-273. https://doi.org/10.12989/eas.2015.8.1.253.
  6. Chen, W.K. (2018). Stability Design of Steel Frames, CRC press, Boca Raton, USA.
  7. Deniz, D., Song, J., Hajjar, J.F. and Nguyen, T.H. (2013). "Probabilistic assessment of dynamic instability of frame structures under seismic excitations", The 11th International Conference on Structural Safety and Reliability (ICOSSAR 2013), New York, June.
  8. Gupta, A. and Krawinkler, H. (2000), "Dynamic P-delta effects for flexible inelastic steel structures", J. Struct. Eng., 126(1), 145-154. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:1(145).
  9. Iu, C. K., Chen, W. F., Chan, S. L. and Ma, T. W. (2008), "Direct second-order elastic analysis for steel frame design" KSCE J. Civil Eng., 12(6), 379-389. https://doi.org/10.1007/s12205-008-0379-3.
  10. Khanlari, K., Naderzadeh, E. and Adhami, B. (2012), "Evaluation of P-delta dynamic effects in steel frames with eccentric braced system by second order dynamic", Proceedings of the 15th World Conference on Earthquake Engineering (15WCEE), Lisbon, September.
  11. Liu, W. and Li, Y. (2021), "Stability analysis for parametric resonances of frame structures using dynamic axis-force transfer coefficient", Structures, 34, 3611-3621. https://doi.org/10.1016/j.istruc.2021.09.095
  12. Lopez, S.E., Ayala, A.G. and Adam, C. (2015), "A novel displacement-based seismic design method for framed structures considering P-delta induced dynamic instability", Bullet. Earthq. Eng., 13(4), 1227-1247. https://doi.org/10.1007/s10518-014-9688-8
  13. Mamouri, S., Mourid, E. and Ibrahimbegovic, A. (2015), "Study of geometric non-linear instability of 2D frame structures", Europ. J. Comput. Mech., 24(6), 256-278. https://doi.org/10.1080/17797179.2016.1181028.
  14. Merter, O. and Ucar, T. (2021), "An energy-based approach to determine the yield force coefficient of RC frame structures", Earthq. Struct., 21(1), 37-49. https://doi.org/10.12989/eas.2021.21.1.037.
  15. Sakar, G., Ozturk, H. and Sabuncu, M. (2012), "Dynamic stability of multi-span frames subjected to periodic loading", J. Construct. Steel Res., 70, 65-70. https://doi.org/10.1016/j.jcsr.2011.10.009.
  16. Sardar, S. and Hama, A. (2018), "Evaluation of p-delta effect in structural seismic response", MATEC Web of Conferences, 162, 04019. https://doi.org/10.1051/matecconf/201816204019.
  17. Shakya, A.M. (2011), "P-delta effects on steel moment frames with reduced beam section connection", M.Sc. Dissertation, Southern Illinois University at Carbondale, Carbondale.
  18. Shehu, R., Angjeliu, G. and Bilgin, H. (2019), "A Simple approach for the design of ductile earthquake-resisting frame structures counting for P-delta effect", Buildings, 9(10), 216. https://doi.org/10.3390/buildings9100216.
  19. Turker, K. and Gungor, I. (2018), "Seismic performance of low and medium-rise RC buildings with wide-beam and ribbed-slab", Earthq. Struct., 15(4), 383-393. https://doi.org/10.12989/eas.2018.15.4.383.
  20. Ucar. T. and Merter, O. (2018), "Derivation of energy-based base shear force coefficient considering hysteretic behavior and P-delta effects", Earthq. Eng. Eng. Vib., 17(1), 149-163. https://doi.org/10.1007/s11803-018-0431-3.
  21. Verma, A. and Verma, S. (2019), "Seismic analysis of building frame using p-delta analysis and static and dynamic analysis: a comparative study", i-Manager's J. Struct. Eng., 8(2), 52. https://doi.org/10.26634/jste.8.2.15462.
  22. Xue, Q. and Meek, J.L. (2001), "Dynamic response and instability of frame structures", Comput. Methods Appl. Mech. Eng., 190(40-41), 5233-5242. https://doi.org/10.1016/S0045-7825(01)00166-9.