Free vibration analysis of tall buildings with outrigger-belt truss system

• Accepted : 2010.10.22
• Published : 2011.03.25

Abstract

In this paper a simple mathematical model is presented for estimating the natural frequencies and corresponding mode shapes of a tall building with outrigger-belt truss system. For this purposes an equivalent continuum system is analyzed in which a tall building structure is replaced by an idealized cantilever continuum beam representing the structural characteristics. The equivalent system is comprised of a cantilever shear beam in parallel to a cantilever flexural beam that is constrained by a rotational spring at outrigger-belt truss location. The mathematical modeling and the derivation of the equation of motion are given for the cantilevers with identically paralleled and rotational spring. The equation of motion and the associated boundary conditions are analytically obtained by using Hamilton's variational principle. After obtaining non-trivial solution of the eigensystem, the resulting is used to determine the natural frequencies and associated mode shapes of free vibration analysis. A numerical example for a 40 story tall building has been solved with proposed method and finite element method. The results of the proposed mathematical model have good adaptation with those obtained from finite element analysis. Proposed model is practically suitable for quick evaluations during the preliminary design stages.

References

1. Ali, M.M. and Moon, K.S. (2007), "Structural developments in tall buildings: current trends and future prospects", Architect. Sci. Rev., 50(3), 205-223. https://doi.org/10.3763/asre.2007.5027
2. Bozdogan, K.B. (2006), "A method for free vibration analysis of stiffened multi-bay coupled shear walls", Asian J. Civil Eng. (Build. Housing), 7(6), 639-649.
3. Bozdogan, K.B. (2009), "An approximate method for static and dynamic analysis of symmetric wall-frame buildings", Struct. Des. Tall Spec., 18, 279-290. https://doi.org/10.1002/tal.409
4. Campbell, S., Kwok, K.C.S, Hitchcock, P.A, Tse, K.T. and Leung, H.Y. (2007), "Field measurements of natural periods of vibration and structural damping of wind-excited tall residential buildings", Wind Struct., 10(5), 401-420. https://doi.org/10.12989/was.2007.10.5.401
5. Connor, J.J. and Pouangare, C.C. (1991), "Simple model for design of framed tube structures", J. Struct. Eng. - ASCE, 117(12), 3623-3644. https://doi.org/10.1061/(ASCE)0733-9445(1991)117:12(3623)
6. Coull, A. and Bose, B. (1975), "Simplified analysis of framed-tube structures", J. Struct. Division - ASCE, 101(11), 2223-2240.
7. Coull, A. and Bose, B. (1976), "Torsion of frame-tube structures", J. Struct. Division - ASCE, 102(12), 2366-2370.
8. Coull, A. and Bose, B. (1977), "Discussion of simplified analysis of frame-tube structures", J. Struct. Division - ASCE, 103(1), 297-299.
9. Coull, A. and Ahmed, K. (1978), "Deflection of framed-tube structures", J. Struct. Division - ASCE, 104(5), 857- 862.
10. Dym, C.L. and Williams, H.E. (2007), "Estimating fundamental frequencies of tall buildings", J. Struct. Eng. - ASCE, 133(10), 1-5. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:1(1)
11. Eisenberger, M. (1994), "Vibration frequencies for beams on variable one and two parameter elastic foundations", J. Sound Vib., 175(5), 577-584. https://doi.org/10.1006/jsvi.1994.1347
12. Gerasimidis, S., Efthymiou, E. and Baniotopoulos C.C. (2009), "Optimum outrigger locations of high-rise steel buildings for wind loading", EACWE 5, Florence, Italy.
13. Geourgoussis, K.G. (2006), "A simple model for assessing and modal response quantities in symmetrical buildings", Struct. Des. Tall Spec., 15, 139-151. https://doi.org/10.1002/tal.286
14. Halis Gunel, M. and Emer Ilgin, H. (2007), "A proposal for the classification of structural systems of tall buildings", J. Build. Environ., 42, 2667-2675. https://doi.org/10.1016/j.buildenv.2006.07.007
15. Hoenderkamp, J.C.D. and Bakker, M.C.M. (2003), "Analysis of high-rise braced frames with outriggers", Struct. Des. Tall Spec., 12, 335-350. https://doi.org/10.1002/tal.226
16. Hoenderkamp, J.C.D. (2004), "Shear wall with outrigger trusses on wall and column foundations", Struct. Des. Tall Spec., 12, 73-87.
17. Kaviani, P., Rahgozar, R. and Saffari, H. (2008), "Approximate analysis of tall buildings using sandwich beam models with variable cross-section", Struct. Des. Tall Spec., 17, 401-418. https://doi.org/10.1002/tal.360
18. Kian, P.S. and Siahaan, T.S. (2001), "The use of outrigger and belt truss system for high-rise concrete buildings", Dimensi Teknik Sipil, 3(1), 36-41.
19. Kuang, J.S. and Ng, S.C. (2004), "Coupled vibration of tall buildings structures", Struct. Des. Tall Spec., 13, 291-303. https://doi.org/10.1002/tal.253
20. Kuang, J.S. and Ng, S.C. (2009), "Lateral shear St. Venant torsion coupled vibration of asymmetric-plan frame structures", Struct. Des. Tall Spec., 18(6), 647-656. https://doi.org/10.1002/tal.456
21. Kwan, A.K.H. (1994), "Simple method for approximate analysis of framed tube structures", J. Struct. Eng. - ASCE, 120(4), 1221-1239. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:4(1221)
22. Lau, J.H. (1984), "Vibration frequencies and mode shapes for a constrained cantilever", J. Appl. Mech. - ASME, 51, 182-187. https://doi.org/10.1115/1.3167565
23. Lavan, O. and Levy, R. (2010), "Performance based optimal seismic retrofitting of yielding plane frames using added viscous damping", J. Earthq. Struct., 1(3), 307-326. https://doi.org/10.12989/eas.2010.1.3.307
24. Lee, K. and Loo, Y. (2001), "Simple analysis of framed-tube structures with multiple internal tubes", J. Struct. Eng. - ASCE, 127, 450-460. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:4(450)
25. Lee, J., Bang, M. and Kim, J.Y. (2008), "An analytical model for high-rise wall-frame structures with outriggers", Struct. Des. Tall Spec., 17, 839-851. https://doi.org/10.1002/tal.406
26. Maurizi, M.J., Rossi, R.E. and Reyes, J.A. (1976), "Vibration frequencies for a uniform beam with one end spring-hinged and subjected to a translational restraint at the other end", J. Sound Vib., 48(4), 565-568. https://doi.org/10.1016/0022-460X(76)90559-9
27. Mathematica, 7.0.0, Wolfram Research Inc.
28. Matsuda, H., Morita, C. and Sakiyama, T. (1992), "A method for vibration analysis of a tapered Timoshenko beam with constraint at any points and carrying a heavy tip body", J. Sound Vib., 158(2), 331-339. https://doi.org/10.1016/0022-460X(92)90055-3
29. Meirovitch, L. (1980), Computational methods in structural dynamics, The Netherland Rockville, Maryland, U. S. A.
30. Moudarres, F.R. (1984), "Outrigger-braced coupled shear walls", J. Struct. Eng. - ASCE, 10(12), 2876-2890.
31. Piersol, A.G. and Paez, T.L. (2010), Harri's shock and vibration handbook, McGraw-Hill, New York.
32. Poon, D.C.K., Shieh, S. and Joseph, L.M. (2004), "Structural design of Taipei 101, the world's tallest building", Proceedings of the CTBUH 2004, Seoul Conference, Seoul, Korea, 271-278.
33. Rahgozar, R. and Sharifi, Y. (2009), "An approximate analysis of combined system of framed tube, shear core and belt truss in high-rise buildings", Struct. Des. Tall Spec., 18(6), 607-624. https://doi.org/10.1002/tal.503
34. Rahgozar, R., Ahmadi, A. and Sharifi, Y. (2010), "A simple mathematical model for approximate analysis of tall buildings", J. Appl. Math. Model., 34, 2437-2451. https://doi.org/10.1016/j.apm.2009.11.009
35. Rutenberg, A. (1978), "Vibration frequencies for a uniform cantilever with a rotational constraint at a point", J. Appl. Mech. - ASME, 45, 422-423. https://doi.org/10.1115/1.3424312
36. Rutenberg, A. and Tal, D. (1987), "Lateral load response of belted tall building structures", J. Eng. Struct., 9, 53-67. https://doi.org/10.1016/0141-0296(87)90041-1
37. Rutenberg, A. (1979), "Earthquake analysis of belted high-rise building structures", J. Eng. Struct., 1, 191-196. https://doi.org/10.1016/0141-0296(79)90046-4
38. SAP2000 Advanced 12.0.0, Computers and structures, Berkeley, California, USA.
39. Stafford Smith, B. and Coull, A. (1991), Tall building structures: analysis and design, Wiley, New York.
40. Stafford Smith, B. and Salim, I. (1983), "Formulae for optimum drift resistance of outrigger braced tall building structures", Comput. Struct., 17(1), 45-50. https://doi.org/10.1016/0045-7949(83)90027-5
41. Swaddiwudhipong, S., Zhou, Q. and Lee, SL. (2001), "Effect of axial deformation on vibration of tall buildings", Struct. Des. Tall Spec., 10, 79-91.
42. Swaddiwudhipong, S., Soelarno, Sidji, S. and Lee, S.L. (2002), "The effects of axial deformation and axial force on vibration characteristics of tall buildings", Struct. Des. Tall Spec., 11, 309-328.
43. Takabatake, H., Mukai, H. and Hirano, T. (1993), "Doubly symmetric tube structures. I: static analysis", J. Struct. Eng. - ASCE, 119(7), 1981-2001. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:7(1981)
44. Takahashi, K. (1980), "Eigenvalue problem of a beam with a mass and spring at the end subjected to an axial force", J. Sound Vib., 71(3), 453-457. https://doi.org/10.1016/0022-460X(80)90427-7
45. Taranath, B.S. (1988), Structural analysis and design of tall buildings, McGraw-Hill, New York.
46. Tarjan, G. and Kollar, L.P. (2004), "Approximate analysis of building structures with identical stories subjected to earthquakes", Int. J. Solids Struct., 41, 1411-1433. https://doi.org/10.1016/j.ijsolstr.2003.10.021
47. Tso, W.K. and Biswas, J.K. (1972), "An approximate seismic analysis of coupled shear walls", Build. Sci., 7(4), 249-256. https://doi.org/10.1016/0007-3628(72)90006-0
48. Wang, Q. (1996), "Sturm-Liouville equation for free vibration of a tube-in-tube tall building", J. Sound Vib., 191(3), 349-355. https://doi.org/10.1006/jsvi.1996.0126
49. Wang, Q. (1996), "Modified ODE-solver for vibration of tube-in-tube structures", Comput. Method. Appl. M., 129, 151-156. https://doi.org/10.1016/0045-7825(95)00895-0
50. Wu, J.R., Li, Q.S. and Tuan Alex, Y. (2008), "Wind-induced lateral-torsional coupled responses of tall buildings", Wind Struct., 11(2), 153-178. https://doi.org/10.12989/was.2008.11.2.153

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