DOI QR코드

DOI QR Code

Theoretical formulation for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic brace

  • Jouneghani, Habib Ghasemi (School of Civil and Environmental Engineering, University of Technology Sydney) ;
  • Fanaie, Nader (Department of Civil Engineering, K. N. Toosi University of Technology) ;
  • Haghollahi, Abbas (Department of Civil Engineering, Shahid Rajaee Teacher Training University)
  • Received : 2021.10.02
  • Accepted : 2022.09.02
  • Published : 2022.11.10

Abstract

Elliptic-braced simple resisting frame as a new lateral bracing system installed in the middle bay of frame in building facades has been recently introduced. This system not only creates a problem for opening space from the architectural viewpoint but also improves the structural behavior. Despite the researches on the seismic performance of lateral bracing systems, there are few studies performed on the effect of the stiffness parameters on the elastic story drift and calculation of period in simple braced steel frames. To overcome this shortcoming, in this paper, for the first time, an analytical solution is presented for calculating elastic lateral stiffness in a simple steel frame equipped with elliptic brace subjected to lateral load. In addition, for the first time, in this study, a precise formulation has been developed to evaluate the elastic stiffness variation in a steel frame equipped with a two-dimensional single-story single-span elliptic brace using strain energy and Castigliano's theorem. Thus, all the effective factors, including axial and shear loads as well as bending moments of elliptic brace could be considered. At the end of the analysis, the lateral stiffness can be calculated by an improved and innovative relation through the energy method based on the geometrical properties of the employed sections and specification of the used material. Also, an equivalent element of an elliptic brace was presented for the ease of modeling and use in linear designs. Application of the proposed relation have been verified through a variety of examples in OpenSees software. Based on the results, the error percentage between the elastic stiffness derived from the developed equations and the numerical analyses of finite element models was very low and negligible.

Keywords

References

  1. Akiyama, H. (1985), Earthquake Resistant Limit State Design for Buildings, University of Tokyo Press.
  2. Alavi, E. and Nateghi, F. (2013), "Experimental study on diagonally stiffened steel plate shear walls with central perforation", J. Constr. Steel Res., 89, 9-20. https://doi.org/10.1016/j.jcsr.2013.06.005.
  3. Bradford, M.A. and Pi, Y.L. (2002), "Elastic flexural-torsional buckling of discretely restrained arches", J. Struct. Eng., 128, 719-727. https://doi.org/10.1061/(ASCE)0733-9445(2002).
  4. Bertero, V.V. and Popov, E.P. (1997), "Seismic behaviour of ductile moment-resisting reinforced concrete frames. Reinforced concrete structures in seismic zones", Detroit: ACI Publication SP-53, American Concrete Institute. 247-291.
  5. Chun Cui, J., Xu, J.D., Xu, Z.R. and Huo, T. (2020), "Cyclic behavior study of high load-bearing capacity steel plate shear wall", J. Constr. Steel Res., 172, 1-12. https://doi.org/10.1016/j.jcsr.2020.106178.
  6. Dahlberg, T. (2004), Procedure to Calculate Deflections of Curved Beams. 20(3), 503-513.
  7. Dowrick, D.J. (1997), Earthquake Resistant Design: A Manual for Engineers and Architects. New York, Wiley.
  8. Fateh, A., Hejazi, F., Jaafar, M.S., Karim, I.A. and Adnan, A.B. (2016), "Design of a variable stiffness bracing system: Mathematical modeling, fabrication, and dynamic analysis", Soil Dyn. Earthq. Eng., 80, 87-101. https://doi.org/10.1016/j.soildyn.2015.10.009.
  9. Ghasemi Jouneghani, H., Haghollahi, A., Moghadam, H. and Sarvghad Moghaddam, A.R. (2016), "Study of the seismic performance of steel frames in the elliptic bracing", J. Vibroeng., 6(2), 232-243. https://doi.org/10.21595/jve.2016.16858.
  10. Ghasemi Jouneghani, H., Haghollahi, A., Moghadam, H. and Sarvghad Moghaddam, A.R. (2019), "Assessing seismic performance of elliptic braced moment resisting frame through pushover method", J. Rehab. Civil Eng., 7(2), 68-85. https://doi.org/10.22075/JRCE.2018.13030.1232.
  11. Ghasemi Jouneghani, 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.
  12. Ghasemi Jouneghani, 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.
  13. Ghasemi Jouneghani, H., Haghollahi, A. and Beheshti-Aval, S.B. "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.
  14. Ghasemi Jouneghani, 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", J. Steel Comp. Struct., 37(5), 571-587. https://doi.org/10.12989/scs.2020.37.5.571.
  15. 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.
  16. Hadi, W.K. (2002), Elastic Plastic Analysis of Reinforced Concrete Shallow Arched Frames Using Curved Beam Element, Master Thesis, University of Babylon-Iraq.
  17. 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.
  18. Hosseinzadeh, S.A.A. and Tehranizadeh, M. (2012), "Introduction of stiffened large rectangular openings in steel plate shear walls", J. Constr. Steel Res,. 77, 180-192. https://doi.org/10.1016/j.jcsr.2012.05.010.
  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. Just, D.J. (1982), "Circularly curved beams under plane loads", J. Struct. Div., 11(8), 1858-1873. https://doi.org/10.1061/JSDEAG.0006024.
  22. Kardestuncer, H. (1974), Elementary Matrix Analysis of Structures. NewYork, McGraw-Hill.
  23. 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., 3117-3120. https://doi.org/10.4028/www.scientific.net/AMR.368-373.
  24. Litewka, P. and Rakowski, J. (1998), The Exact Thick Arch Finite Element. J. Computer and Struct., 68, 369-379. https://doi.org/10.1016/S0045-7949(98)00051-0.
  25. Helwig, T.A. and Yura, J.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)0733-9445(2008)134.
  26. Love, A.E.H (1944), A Treatise on the Mathematical Theory of Elasticity, New York: Dover.
  27. 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.
  28. 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.
  29. Mazzoni, S., McKenna, F., Scott, M.H., Fenves, G.L. and Jeremic, B. (2013), OpenSees Command Language Manual.
  30. Michalos, J.P. (1958), Theory of Structural Analysis and Design. New York, Ronald Press Company.
  31. Moradipour, P., Chan, T. and Gallage, C. (2015), "An improved modal strain energy method for structural damage detection, 2D simulation", J. Struct. Eng. Mech., 54(1), 105-119. https://doi.org/10.12989/sem.2015.54.1.105.
  32. Morris, D.L. (1968), "Curved beam stiffness coefficients", J. Struct. Div., 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, University of Babylon-Iraq.
  34. Naderpour, M.N. and Aghakouchak, A. (2018), "Probabilistic damage assessment of concentrically braced frames with built up braces", J. Constr. Steel Res., 147, 191-202. https://doi.org/10.1016/j.jcsr.2018.04.011.
  35. Palaninathan, R. and Chandrasekharan, PS. (1985), "Curved beam stiffness coefficients", J. Comput. Struct., 21, 663-669. https://doi.org/10.1016/0045-7949(85)90143-9
  36. Pan, W.H. and Tong, J.Z. (2020), "A new stiffness-strengthrelationship-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. 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.
  39. Paulay, T. and Priestley, M.J.N. (1995), Seismic Design of Reinforced Concrete and Masonry Buildings. New York, Wiley.
  40. Petrolo, A.S. and Casciaro, R. (2004), "3D beam element based on Saint Venant's rod theory", J. Comput. Struct., 82, 2471-2481. https://doi.org/10.1016/j.compstruc.2004.07.004.
  41. Pi, Y.L. and Bradford, M.A. (2002), "Elastic flexural-torsional buckling of continuously restrained arches", Int. J. Solids Struct., 39, 2299-2322. https://doi.org/10.1016/S0020-7683(02)00006-9.
  42. Rezaiee-Pajand, M. and Rajabzadeh-Safaei, N. (2016), "An explicit stiffness matrix for parabolic beam element", Latin Amer. J. Solids Struct. 13, 1782-1801. http://dx.doi.org/10.1590/1679-78252820.
  43. Rosenblueth, E. (1980), Design of Earthquake Resistant Structures. London, Pentech Press.
  44. Rostami, P. and Mofid, M. (2019), "Steel plate shear walls having door openings with different arrangements of stiffeners", J. Adv. Struct. Eng., 10, 1-14. https://doi.org/10.1177/13694332198362.
  45. 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.
  46. Sabouri-Ghomi, S., Mamazizi, S. and Alavi, M. (2015), "An investigation into linear and nonlinear behavior of stiffened steel plate shear panels with two openings", J. Adv. Struct. Eng., 687-700. https://doi.org/10.1260/1369-4332.18.5.687.
  47. Selvaraj, S. Madhavan, M. and Lao, H.H. (2021), "Sheathingfastener connection strength based design method for sheathed CFS point-symmetric wall frame studs", J. Struct., 33, 1473-1494. https://doi.org/10.1016/j.istruc.2021.04.052.
  48. Selvaraj, S., Madhavan, M. and Lao, H.H. (2021), "Direct stiffness-strength method design for sheathed cold-formed steel structural members - Recommendations for the AISI S100", J. Thin-Wall. Struct., 162, 107282. https://doi.org/10.1016/j.tws.2020.107282.
  49. Selvaraj, S. and Madhavan, M. (2020), "Influence of sheathingfastener connection stiffness on the design strength of coldformed steel wall panels", J. Struct. Eng., 146(10), 04020202. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002709.
  50. Selvaraj, S. and Madhavan, M. (2019), "Investigation on sheathing-fastener connection failures in cold-formed steel wall panels", J. Struct., 20, 176-188. https://doi.org/10.1016/j.istruc.2019.03.007.
  51. Selvaraj, S. and Madhavan, M. (2019), "Bracing effect of sheathing in point-symmetric cold-formed steel flexural members", J. Constr. Steel Res., 157, 450-462. https://doi.org/10.1016/j.jcsr.2019.02.037.
  52. Wakabayashi, M. (1986), Design of Earthquake Resistant Buildings. New York, McGraw-Hill.
  53. Wang, S., Zhang, M. and Liu, F. (2013), "Estimation of semi-rigid joints by cross modal strain energy method", J. Struct. Eng. Mech., 47(6), 757-771. https://doi.org/10.12989/sem.2013.47.6.757.
  54. Xu, L.H., Chen, P. and Li, Z. (2021), "Development and validation of a versatile hysteretic model for pre-compressed self-centering buckling-restrained brace", J. Constr. Steel Res., 177, 106473. https://doi.org/10.1016/j.jcsr.2020.106473.
  55. Xu, L.H., Fan, X.W. and Li, Z.X. (2016), "Cyclic behavior and failure mechanism of self-centering energy dissipation braces with pre-pressed combination disc springs", J. Earth. Eng. Struct. Dyn., 46(7), 1065-1080. https://doi.org/10.1002/eqe.2844.
  56. Xu, L.H., Xiea, X.S. and Li, Z.X. (2018), "Development and experimental study of a self-centering variable damping energy dissipation brace", J. Eng. Struct., 160, 270-280. https://doi.org/10.1016/j.engstruct.2018.01.051.
  57. Yu, AM. (2004), "Solution of the integral equations for shearing stresses in two-material curved beams", J. Mech. Res. Commun., 31, 137-146. https://doi.org/10.1016/S0093-6413(03)00090-9.
  58. 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.
  59. 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.
  60. Yu, A.M. and Nie, G.H. (2007), "Tangential stresses in twomaterial curved beams", Meccanica, 42, 307-311. https://doi.org/10.1007/s11012-007-9056-8.
  61. 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.
  62. Zhang, G., Xu, L.H. and Li, Z.X. (2021), "Development and seismic retrofit of an innovative modular steel structure connection using symmetrical self-centering haunch braces", J. Eng. Struct., 229, 111671. https://doi.org/10.1016/j.engstruct.2020.111671.