Structural Engineering and Mechanics

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Free vibration analysis of asymmetric shear wall-frame buildings using modified finite element-transfer matrix method

  • Bozdogan, Kanat B. (Department of Civil Engineering, Kirklareli University)
  • 투고 : 2012.06.03
  • 심사 : 2013.02.19
  • 발행 : 2013.04.10
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초록

In this study, the modified finite element- transfer matrix methods are proposed for free vibration analysis of asymmetric structures, the bearing system of which consists of shear wall-frames. In the study, a multi-storey structure is divided into as many elements as the number of storeys and storey masses are influenced as separated at alignments of storeys. The shear walls and frames are assumed to be flexural and shear cantilever beam structures. The storey stiffness matrix is obtained by formulating the governing equation at the center of mass for the shear walls and the frames in the i.th floor. The system transfer matrix is constructed in the dimension of $6{\times}6$ by transforming the obtained stiffness matrix. Thus, the dimension, which is $12n{\times}12n$ in classical finite elements, is reduced to the dimension of $6{\times}6$. To study the suitability of the method, the results are assessed by solving two examples taken from the literature.

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참고문헌

  1. Aksoğan, O., Arslan, H. M. and Choo, B.S. (2003), "Forced vibration analysis of stiffened coupled shear walls using continuous connection method", Eng. Struct., 25, 499-506. https://doi.org/10.1016/S0141-0296(02)00192-X
  2. Baikov, V. and Sigalov, E. (1983), Reinforced Concrete Structures Volume 2, Mir Publisher, Moscov.
  3. Balendra, T., Swaddiwudhipong, S. and Quek, S.T. (1984), "Free vibration of asymmetric shear wall-frame buildings", Earth. Eng. Struct. Dyn., 12(5), 629-650. https://doi.org/10.1002/eqe.4290120505
  4. Basu, A., Nagpal, A.K., Bajaj, R.S. and Guliani, A. (1979), "Dynamic characteristics of coupled shear walls", J. Struct. Eng. -ASCE, 105, 1637-1651.
  5. Bilyap, S. (1979), "An approximate solution for high- rise reinforced concrete panel buildings with combined diaphragms", Int. J. Housing Sci., 3(6), 477-481.
  6. Boutin, C., Hans, S., Ibraim, E. and Roussilon, P. (2005), "In situ experiments and seismic analysis of existing buildings, part II: seismic integrity treshold", Earth. Eng. Struct. Dyn., 34(12), 1531-1546. https://doi.org/10.1002/eqe.503
  7. Bozdogan, K.B. (2009), "An approximate method for static and dynamic analyses of symmetric wall-frame buildings", Struct. Des. Tall Spec. Build., 18(3), 279-290. https://doi.org/10.1002/tal.409
  8. Bozdogan, K.B. and Ozturk, D. (2012), "Vibration analysis of asymmetric shear wall-frame structures using the transfer matrix method", Iranian J. Sci. Tech. Transaction B Engineering, 36(C1), 1-12.
  9. Choi, M.S. (2003), "Free vibration analysis of plate structures using finite element transfer stiffness coefficient method", J. Mech. Sci. Tech., 17(6), 805-815.
  10. Georgoussis, K.G. (2006), "A simple model for assessing and modal response quantities in symmetrical buildings", Struct. Des. Tall Special Build., 15(2), 139-151. https://doi.org/10.1002/tal.286
  11. Heidebrecht, A.C. and Stafford Smith, B. (1973), "Approximate analysis of tall wall-frame buildings", J. Struct. Eng., ASCE, 99 (2), 199-221.
  12. Hoenderkamp, D.C.J. and Snijder, H.H. (2000), "Approximate analysis of high-rise frames with flexible connections", Struct. Des. Tall Build., 9(3), 233-248. https://doi.org/10.1002/1099-1794(200006)9:3<233::AID-TAL156>3.0.CO;2-O
  13. Hoenderkamp, D.C.J. (2001), "Elastic analysis of asymmetric tall buildings", Struct. Des. Tall Build., 10(4), 245-261. https://doi.org/10.1002/tal.183
  14. Hoenderkamp, D.C.J. (2002), "A simplified analysis of high-rise structures with cores", Struct. Des. Tall Build., 11(2), 93-107. https://doi.org/10.1002/tal.192
  15. Jahanshahia, M.R. and Rahgozar, R. (2012), "Free vibration analysis of combined system with variable cross section in tall buildings", Struct. Eng. Mech., 42(5), 715-728. https://doi.org/10.12989/sem.2012.42.5.715
  16. Kazaz, I., Gulkan, P. (2012), "An alternative frame -shear wall model: continuum formulation", Struct. Des. Tall Special Build., DOI:10.1002/tal.626.
  17. Kuang, J.S. and Ng, S.C. (2000), "Coupled lateral vibration of asymmetric shear wall structures", Thin Walled Struct., 38(2), 93-104. https://doi.org/10.1016/S0263-8231(00)00033-1
  18. Kuang, J.S. and Ng, C. (2009), "Lateral shear -st. venant torsion coupled vibration of asymmetric -plan frame structures", Struct. Des. Tall Special Build., 18(6), 647-656. https://doi.org/10.1002/tal.456
  19. Kaviani, P., Rahgozar, R. and Saffari, H. (2008), "Approximate analysis of tall buildings using sandwich beam models with variable cross-section", Struct. Des. Tall Special Build., 17(2), 401-418. https://doi.org/10.1002/tal.360
  20. Laier, J.E. (2008), "An improved continuous medium technique for structural frame analysis", Struct. Des. Tall Special Build., 17(1), 25-38. https://doi.org/10.1002/tal.309
  21. Lee, J., Bang, M. and Kim, J.Y. (2008), "An analytical model for high- rise wall-frame structures with outriggers", Struct. Des. Tall Special Build., 17(4), 839-851. https://doi.org/10.1002/tal.406
  22. Li, G.Q. and Choo, B.S. (1996), "A continous-discrete approach to the free vibration analysis of stiffened pierced walls on flexible foundations", Int. J. Solids Struct., 33(2), 249-263. https://doi.org/10.1016/0020-7683(95)00028-9
  23. Malekinejad, M. and Rahgozar, R. (2011a), "An analytical approach to free vibration analysis of multioutrigger- belt truss-reinforced tall buildings", Struct. Des. Tall Build., 8(2), 155-170.
  24. Malekinejad, M. and Rahgozar, R. (2011b), "Free vibration analysis of tall buildings with outrigger-belt truss system", Earth. Struct., 2(1), 89-107. https://doi.org/10.12989/eas.2011.2.1.089
  25. Mancini, E. and Savassi, W. (1999), "Tall buildings structures unified plane panels behavior", Struct. Des. Tall Build., 8(2), 155-170. https://doi.org/10.1002/(SICI)1099-1794(199906)8:2<155::AID-TAL125>3.0.CO;2-6
  26. Meftah, S.A. and Tounsi, A. (2008), "Vibration characteristics of tall buildings braced by shear walls and thin-walled open-section structures", Struct. Des. Tall Special Build., 17(1), 203-216. https://doi.org/10.1002/tal.346
  27. Michel, C., Hans, S., Guegen, P. and Boutin, C. (2006), "In situ experiment and modeling of rc structure using ambient vibration and timoshenko beam", First European Conference on Earthquake Engineering And Seismology, Geneva-Switzerland.
  28. Miranda, E. (1999), "Approximate lateral drift demands in multi-story buildings subjected to earthquakes", J. Struct. Eng. ASCE, 125(4), 417-425. https://doi.org/10.1061/(ASCE)0733-9445(1999)125:4(417)
  29. Miranda, E. and Reyes, J.C. (2002), "Approximate lateral drift demands in multi-story buildings with nonuniform stiffness", J. Struct. Eng., ASCE, 128(7), 840-849. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:7(840)
  30. Miranda, E. and Taghavi, S. (2005), "Approximate floor acceleration demands in multistorey buildings I formulation", J. Struct. Eng. ASCE, 131(2), 203-211. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:2(203)
  31. Ng, S.C. and Kuang, J.S. (2000), "Triply coupled vibration of asymmetric wall-frame structures", J. Struct. Eng., ASCE, 128(7), 840-849.
  32. Nollet, J.M. and Stafford Smith, B. (1993), "Behavior of curtailed wall-frame structures", J. Struct. Eng., ASCE, 119(10), 2835-2853. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:10(2835)
  33. Ozturk, D., Bozdogan, K. and Nuhoglu, A. (2012), "Modified finite element-transfer matrix method for the static analysis of structures", Struct. Eng. Mech., 43(6), 761-769. https://doi.org/10.12989/sem.2012.43.6.761
  34. Potzta, G. and Kollar, L.P. (2003), "Analysis of building structures by replacement sandwich beams", Int. J. Solids Struct., 40, 535-553. https://doi.org/10.1016/S0020-7683(02)00622-4
  35. Rafezy, B., Zare, A. and Howson, W.P. (2007), "Coupled lateral -torsional frequencies of asymmetric, three dimensional frame structures", Int. J. Solids Struct., 44(1), 128-144. https://doi.org/10.1016/j.ijsolstr.2006.04.019
  36. Rafezy, B. and Howson, W.P. (2008), "Vibration analysis of doubly asymmetric, three dimensional structures comprising wall and frame assemblies with variable cross section", J. Sound Vib., 318(1-2), 247-266. https://doi.org/10.1016/j.jsv.2008.04.018
  37. Rahgozar, R., Ahmadi, A. and Sharifi, Y. (2010), "A simple mathematical model for approximate analysis of tall buildings", J. App. Math. Modelling, 34, 2437-2451. https://doi.org/10.1016/j.apm.2009.11.009
  38. Reinoso, E. and Miranda, E. (2005), "Estimation of floor acceleration demands in high rise buildings during earthquakes", Struct. Des. Tall Special Build., 14(2), 107-130. https://doi.org/10.1002/tal.272
  39. Rong, B., Rui, X.T. and Wang, G.P. (2011), "Modified finite element transfer matrix method for eigenvalue problem of flexible structures", J. App. Mech., 78(2), 021016. https://doi.org/10.1115/1.4002578
  40. Rosman, R. (1964), "Approximate analysis of shear walls subject to lateral loads", Proc. Am. Concr. Inst., 61(6), 717-734.
  41. Savassi, W. and Mancini, E. (2004), "One-dimensional finite element solution for tall building structures unified plane panels formulation", Struct. Des. Tall Special Build., 13(4), 315-333. https://doi.org/10.1002/tal.256
  42. Savassi, W. and Mancini, E. (2009), "One-dimensional finite element solution for non-uniform tall building structures and loading", Struct. Des. Tall Special Build., 18(4), 441-453. https://doi.org/10.1002/tal.445
  43. Stafford Smith, B. and Crowe, E. (1986), "Estimating periods of vibration of tall buildings", J. Struct. Eng., ASCE, 112(5), 1005-1019. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:5(1005)
  44. Swaddiwudhipong, S., Lee, L.S. and Zhou, Q. (2001), "Effect of the axial deformation on vibration of tall buildings", Struct. Des. Tall Buil.,10(2), 79-91. https://doi.org/10.1002/tal.175
  45. Taghavi, S. and Miranda, E. (2005), "Approximate floor acceleration demands in multistorey buildings II: applications", J. Struct. Eng., ASCE, 131(2), 212-220. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:2(212)
  46. Tarjan, G. and Kollar, P.L. (2004), "Approximate analysis of building structures with identical stories subjected to earthquakes", Int. J. Solids Struct., 41(5-6), 1411-1433. https://doi.org/10.1016/j.ijsolstr.2003.10.021
  47. Tekeli, H., Atimtay, E. and Turkmen, M. (2012), "A simplified method for determining sway in reinforced concrete dual buildings and design applications", Struct. Des. Tall Special Build., DOI:10.1002/tal.761.
  48. Toutanji, H. (1997), "The effect of foundation flexibility on the interaction of walls and frames", Eng. Struct., 19(12), 1036-1042. https://doi.org/10.1016/S0141-0296(97)00046-1
  49. Xue, H.Y. (1994), "A combined dynamic finite element-ricatti transfer matrix method for solving non-linear eigenproblems of vibrations", Comp. Struct., 53(6), 1257-1261. https://doi.org/10.1016/0045-7949(94)90393-X
  50. Wang, Y., Arnaouti, C. and Guo, S. (2000), "A simple approximate formulation for the first two frequencies of asymmetric wall-frame multi-storey building structures", J. Sound and Vib., 236 (1), 141-160. https://doi.org/10.1006/jsvi.2000.2984
  51. Wdowicki, J. and Wdowicka, E. (2012), "Analysis of shear wall structures of variable cross section", Struct. Des. Tall Special Build., 21(1),1-15.
  52. Yang, D., Pan, J. and Li, G. (2010), "Interstory drift ratio of building structures subjected to near-fault ground motions based on generalized drift spectral analysis", Soil Dyn. Earthq. Eng., 30, 1182-1197. https://doi.org/10.1016/j.soildyn.2010.04.026
  53. Zalka, K.A. (1994), "Mode coupling in the torsional flexural buckling of regular multistorey buildings", Struct. Des. Tall Build., 3(4), 227-245. https://doi.org/10.1002/tal.4320030403
  54. Zalka, K.A. (2001), "A simplified method for calculation of natural frequencies of wall-frame Buildings", Eng. Struct., 23(12),1544-1555. https://doi.org/10.1016/S0141-0296(01)00053-0
  55. Zalka, K.A. (2002), "Buckling analysis of buildings braced by frameworks, shear walls and cores", Struct. Des. Tall Build., 11(3), 197-219. https://doi.org/10.1002/tal.194
  56. Zalka, K.A. (2003), "Hand method for predicting the stability of regular buildings, using frequency measurements", Struct. Des. Tall Special Build., 12( 4), 273-281. https://doi.org/10.1002/tal.221
  57. Zalka, K.A. (2009), "A simple method for the deflection analysis of tall-wall-frame building structures under horizontal load", Struct. Des. Tall Special Build., 18(3), 291-311. https://doi.org/10.1002/tal.410

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