Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Determining elastic lateral stiffness of steel moment frame equipped with elliptic brace

  • Habib Ghasemi, Jouneghani (School of Civil and Environmental Engineering, University of Technology Sydney) ;
  • Nader, Fanaie (Department of Civil Engineering, K. N. Toosi University of Technology) ;
  • Mohammad Talebi, Kalaleh (Department of Civil and Environmental Engineering, University of Alberta) ;
  • Mina, Mortazavi (School of Civil and Environmental Engineering, University of Technology Sydney)
  • Received : 2022.03.23
  • Accepted : 2023.01.02
  • Published : 2023.02.10
⟨ Previous Next ⟩

Abstract

This study aims to examine the elastic stiffness properties of Elliptic-Braced Moment Resisting Frame (EBMRF) subjected to lateral loads. Installing the elliptic brace in the middle span of the frames in the facade of a building, as a new lateral bracing system not only it can improve the structural behavior, but it provides sufficient space to consider opening it needed. In this regard, for the first time, an accurate theoretical formulation has been developed in order that the elastic stiffness is investigated in a two-dimensional single-story single-span EBMRF. The concept of strain energy and Castigliano's theorem were employed to perform the analysis. All influential factors were considered, including axial and shearing loads in addition to the bending moment in the elliptic brace. At the end of the analysis, the elastic lateral stiffness could be calculated using an improved relation through strain energy method based on geometric properties of the employed sections as well as specifications of the utilized materials. For the ease of finite element (FE) modeling and its use in linear design, an equivalent element was developed for the elliptic brace. The proposed relation was verified by different examples using OpenSees software. It was found that there is a negligible difference between elastic stiffness values derived by the developed equations and those of numerical analysis using FE method.

Keywords

References

  1. Dawe, D.J. (1974), "Curved finite element for the analysis of shallow and deep arches", J. Comput. Struct., 4, 559-580. https://doi.org/10.1016/0045-7949(74)90007-8.
  2. Dawe, D.J. (1974), "Numerical studies using circular arch finite elements", J. Comput. Struct., 4, 729-740. https://doi.org/10.1016/0045-7949(74)90041-8.
  3. Dahlberg (2004), "Procedure to calculate deflections of curved beams", Int. J. Engng Ed., 20(3), 503-513. https://doi.org/10.5923/j.jmea.20150501.02.
  4. Fateh, A., Hejazi, F., Saleh Jaafara, M. and Bin Adnan, A. (2016), "Design of a variable stiffness bracing system: Mathematical modeling, fabrication, and dynamic analysis", J. Soil Dyn. Earth. Eng., 80, 87-101. https://doi.org/10.1016/j.soildyn.2015.10.009.
  5. Gimena, F.N., Gonzaga, P. and Gimena, L. (2008), "3D-curved beam element with varying cross-sectional area under generalized loads", J. Eng. Struct., 30, 404-411. https://doi.org/10.1016/j.engstruct.2007.04.005.
  6. Gimena, L., Gimena, F.N. and Gonzaga, P. (2008), "Structural analysis of a curved beam element defined in global coordinates", J. Eng. Struct., 30, 3355-64. https://doi.org/10.1016/j.engstruct.2008.05.011
  7. Grande, E. and Rasulo, A. (2013), "Seismic assessment of concentric X-braced steel frames", J. Eng. Struct., 49, 983-995. https://doi.org/10.1016/j.engstruct.2013.01.002.
  8. Ghasemi J.H., Haghollahi A., Moghaddam H. and Sarvghad Moghadam. A.R. (2016), "Study of the seismic performance of steel frames in the elliptic bracing", JVE Int. LTD. J. Vibro Eng., 18(5), 2974-2985. https://doi.org/10.21595/jve.2016.16858.
  9. Ghasemi, J.H., Haghollahi, A., Moghaddam, H. and Sarvghad Moghadam., A.R. (2019), "Assessing seismic performance of elliptic braced moment resisting frame through pushover method", J. Rehab. Civil Eng., 2, 1-17. https://doi.org/10.22075/JRCE.2018.13030.1232.
  10. Ghasemi, J.H. and Haghollahi, A. (2020), "Assessing the seismic behavior of Steel Moment Frames equipped by elliptical brace through incremental dynamic analysis (IDA)", J. Earth. Eng. Eng. Vib., 19(2), 435-449. https://doi.org/10.1007/s11803-020-0572-z.
  11. Ghasemi, J.H. and Haghollahi, A. (2020), "Experimental study on hysteretic behavior of steel moment frame equipped with elliptical Brace", J. Steel Comp Struct., 34(6), 891-907. https://doi.org/10.12989/scs.2020.34.6.891.
  12. Ghasemi, J.H., Haghollahi, A. and Beheshti-Aval, S.B. (2020), "Experimental study of failure mechanisms in elliptic-braced steel frame", J. Steel Comp Struct., 37(2), 175-191. https://doi.org/10.12989/scs.2020.37.2.175.
  13. Ghasemi, J.H. and Haghollahi, A. (2020), "Experimental and analytical study in determining the seismic demand and performance of the ELBRF-E and ELBRF-B braced frames", Steel Comp Struct., 37(5), 571-587. https://doi.org/10.12989/scs.2020.37.5.571.
  14. Ghasemi, J.H., Haghollahi, A., Talebi Kalaleh., M. and Beheshti-Aval, S.B. (2021), "Nonlinear seismic behavior of elliptic-braced moment resisting frame using equivalent braced frame", Steel Comp Struct., 40(1), 45-64. https://doi.org/10.12989/scs.2021.40.1.045 45.
  15. Ghasemi, J.H., Haghollahi, A. and Mortazavi, M. (2022), "Pushover analysis for estimating seismic demand of elliptic braced moment resisting frames", J. Gradevinar, 74(11), 941-955. https://doi.org/10.14256/JCE.2311.2017.
  16. Ghasemi, J.H., Fanaie, N., and Haghollahi, A. (2022), "Theoretical formulation for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic", Steel Compos. Struct., 45 (3), 437-454. https://doi.org/10.12989/scs.2022.45.3.437.
  17. Ghasemi, J.H., Haghollahi, A. and Mortazavi, M. (2022), "Analiza postupnog guranja za procjenu seizmickih zahtjeva okvira s elipticnim vezovima", J. Gradevinar, 74 (11), 941-955. https://doi.org/10.14256/JCE.2311.2017.
  18. Hadi, W.K. (2002), Elastic Plastic Analysis of Reinforced Concrete Shallow Arched Frames Using Curved Beam Element, Master Thesis, Department of Civil Engineering, University of Babylon-Iraq.
  19. Haktanir, V. (1995), "The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes", Int J. Numer Meth Eng., 38, 1031-1056. https://doi.org/10.1002/nme.1620380611.
  20. Hibbeler, R.C. (2018), Structural Analysis, University of Louisiana", Lafayette.
  21. Holmes, A.M.C. (1957), "Analysis of helical beams under symmetrical loading", J. Struct. Div., 83(6), 1-37. https://doi.org/10.1061/JSDEAG.0000165.
  22. Horibe, T. and Mori, K. (2015), "In-plane and out-of-plane deflection of J-shaped beam", J. Mech. Eng. Automation, 5(1), 14-19.
  23. Just, D.J. (1982), "Circularly curved beams under plane loads", J. Struct. Div., 11(8), 1858-1873. https://doi.org/10.1061/JSDEAG.0006024.
  24. Kardestuncer, H. (1974), Elementary Matrix Analysis of Structures, New York: McGraw-Hill, https://doi.org/10.1016/j.engstruct.2008.05.011.
  25. Li, X., Zhao, Y., Zhu, C. and Chen, C. (2012), "Exact solutions of stiffness matrix for curved beams with pinned - pinned ends", J. Adv. Mater. Res., 368-373, 3117-3120. https://doi.org/10.4028/www.scientific.net/AMR.368-373.3117.
  26. Litewka, P. and Rakowski, J. (1998), "The exact thick arch finite element", J. Comput. Struct., 68, 369-379. https://doi.org/10.1016/S0045-7949(98)00051-0.
  27. Love, A.E.H. (1994), A Treatise on the Mathematical Theory of Elasticity, New York: Dover.
  28. MacRae, G.A., Kimura, Y. and Roeder, C. (2016), "Effect of column stiffness on braced frame seismic behavior", J. Soil Dyn. Earth. Eng., 80, 87-101. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(381).
  29. Marquis, J.P. and Wang, T.M. (1989), "Stiffness matrix of parabolic beam element", J. Comput Struct., 6, 863-870. https://doi.org/10.1016/0045-7949(89)90271-X.
  30. Mazzoni, S., McKenna, F., Scott, M.H., Fenves, G.L. and Jeremic, B. (2013), OpenSees Command Language Manual.
  31. Michalos, J.P. (1958), Theory of Structural Analysis and Design, New York: Ronald Press Company.
  32. Morris, D.L. (1968), "Curved beam stiffness coefficients", J. Struct. Div., 94, 1165-1178. https://doi.org/10.1061/JSDEAG.0001949.
  33. Muhaisin, M.H. (2003), Influence of Moving Load upon Deformations of Reinforced Concrete Frames, Master Thesis, Department of Civil Engineering, University of Babylon-Iraq.
  34. Palaninathan, R. and Chandrasekharan, P.S. (1958), "Curved beam stiffness coefficients", J. Comput. Struct., 21, 663-669. https://doi.org/10.1061/JSDEAG.0001949.
  35. Pan, W., Eatherton, M.R., Nie, X. and Fan, J. (2018), "Design of pre-tensioned cable-stayed buckling restrained braces considering interrelationship between bracing strength and stiffness requirements", J. Struct. Eng., 144, 4018169. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002162.
  36. Pan, W.H. and Tong, J.Z. (2020), "A new stiffness-strength-relationship-based design approach for global buckling prevention of buckling-restrained braces", J. Adv. Struct. Eng., 1-14. https://doi.org/10.1177/1369433220974780.
  37. Pan, W.H., Tong, J.Z., Guo, Y.L. and Wang, C.M. (2020), "Optimal design of steel buckling-restrained braces considering stiffness and strength requirements", J. Eng. Struct., 211, 110437. https://doi.org/10.1016/j.engstruct.2020.110437.
  38. Petrolo, A.S. and Casciaro, R. (2004), "3D beam element based on Saint Venant's rod theory", J. Comput Struct., 82, 2471-81. https://doi.org/10.1016/j.compstruc.2004.07.004.
  39. Rezaiee-Pajand, M. and Rajabzadeh-Safaei, N. (2016), "An explicit stiffness matrix for parabolic beam element", J. Latin Amer. J. Solids Struct., 13, 1782-1801. https://doi.org/10.1590/1679-78252820. 
  40. Sabelli, R., Mahin, S. and Chang, C. (2003), "Seismic demands on steel braced frame buildings with buckling restrained braces", J. Eng. Struct., 25, 655-666. https://doi.org/10.1016/S0141-0296(02)00175-X.
  41. Todd, A., Helwig, M. and Joseph, A. (2008), "Shear Diaphragm Bracing of Beams. I: Stiffness and Strength Behavior". J. Struct. Eng.,134 (3), 348-356. https://doi.org/10.1061/(ASCE)07339445(2008)134:3(348).
  42. Upadhyay, H., Rao, N. and Desai, P. (2018), "Direct stiffness method for a curved beam and analysis of a curved beam using SAP", Interdiscipl. J. Navrachana University, 2(1), 1-10.
  43. Xie, X., Xu, L. and Li, Zh. (2020), "Hysteretic model and experimental validation of a variable damping self-centering brace", J. Construc. Steel Res., 167, 105965. https://doi.org/10.1016/j.jcsr.2020.105965.
  44. Xu, L., Chen, P. and Li, Z. (2021), "Development and validation of a versatile hysteretic model for pre-compressed self-centering buckling-restrained brace", J. Construc. Steel Res., 177, 106473. https://doi.org/10.1016/j.jcsr.2020.106473.
  45. Xu, L., Lin. Z. and Xie, X. (2022), "Assembled self-centering energy dissipation braces and a force method-based model", J. Construct. Steel Res., 190, 107121. https://doi.org/10.1016/j.jcsr.2021.107121.
  46. Yamada, Y. and Ezawa, Y. (1977), "On curved finite element for the analysis of circular arches", Int J Numer. Meth. Eng., 4, 1635-1651. https://doi.org/10.1002/nme.1620111102.
  47. Yu, A.M. (2004), "Solution of the integral equations for shearing stresses in two-material curved beams", Mech. Res. Commun, 31, 137-146. https://doi.org/10.1016/S0093-6413(03)00090-9.
  48. Yu, A.M. and Nie, G.H. (2005), "Explicit solutions for shearing and radial stresses in curved beams", J. Mech. Res. Commun, 32, 323-331. https://doi.org/10.1016/j.mechrescom.2004.10.006.
  49. Yu, A.M., Yang, X.G. and Nie, G.H. (2006), "Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes", Int J Solids Struct., 43, 2853-2867. https://doi.org/10.1016/j.ijsolstr.2005.05.045.
  50. Yu, A.M. and Nie, G.H. (2007), "Tangential stresses in two-material curved beams", Meccanica, 42, 307-311. https://doi.org/10.1007/s11012-007-9056-8.