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http://dx.doi.org/10.12989/sem.2016.57.5.861

Lateral stability analysis of multistory buildings using the differential transform method  

Aydin, Suleyman (Vocational School, Kirklareli University)
Bozdogan, Kanat Burak (Department of Civil Engineering, Kirklareli University)
Publication Information
Structural Engineering and Mechanics / v.57, no.5, 2016 , pp. 861-876 More about this Journal
Abstract
The determination of the critical buckling load of multistory structures is important since this load is used in second order analysis. It is more realistic to determine the critical buckling load of multistory structures using the whole system instead of independent elements. In this study, a method is proposed for designating the system critical buckling load of torsion-free structures of which the load-bearing system consists of frames and shear walls. In the method presented, the multistory structure is modeled in accordance with the continuous system calculation model and the differential equation governing the stability case is solved using the differential transform method (DTM). At the end of the study, an example problem is solved to show the conformity of the presented method with the finite elements method (FEM).
Keywords
stability; differential transform method; continuous system; multistory structure; wall-frame;
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Times Cited By KSCI : 3  (Citation Analysis)
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1 Gengshu, T., Pi, Y.L., Bradford, M.A. and Tin-Loi, F. (2008), "Buckling and second order effects in dual shear-flexural Systems", J. Struct. Eng., ASCE, 134(11), 1726-1732.   DOI
2 Gengshu, T. and Yun, W. (2008), "A simplified method for the buckling of outrigger-shear wall braced Structures", Adv. Struct. Eng., 11(1), 1-15.   DOI
3 Girgin, K., Ozmen, G. and Orakdogen, E. (2006), "Buckling lengths of irregular frame columns", J. Const. Steel Res., 62, 605-613.   DOI
4 Girgin, K. and Ozmen, G. (2007), "Simplified procedure for determining buckling loads of threedimensional framed structures", Eng. Struct., 29(9), 2344-2352.   DOI
5 Gomes, F.C., e Costa, P.M.P., Rodrigues, J.P.C. and Neves, I.C. (2007), "Buckling length of a steel column for fire design", Eng. Struct., 29(10), 2497-2502.   DOI
6 Gustafsson, D. and Hehir J. (2005), "Stability of tall buildings", MSc. Dissertation, Chalmers University of Technolog, Goteborg.
7 Hoenderkamp, J.C.D. (2002), "Critical loads of lateral load resisting structures for tall buildings", Struct. Des. Tall Build., 11(3), 221-232.   DOI
8 Kaveh, A. and Salimbahrami, B. (2006), "Buckling load of symmetric plane frames using canonical forms", Comput. Struct., 85, 1420-1430.
9 Kaveh, A. (2013), Optimal Analysis of Structures by Concepts of Symmetry and Regularity, Springer Verlag, GmbH, Wien-NewYork.
10 Keskin, Y., Kurnaz, A., Kiris, M. and Oturanc, G. (2007), "Approximate solutions of generalized pantograph equations by the differential transform method", Int. J. Nonlin. Sci., 8, 159-164.
11 Kollar, L. (2008), "Second order effects on building structures-an approximate evaluation", 17th Congress of IABSE, Chicago, September.
12 Lal, R. and Ahlawat, N. (2015), "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method", Eur. J. Mech. A Solid., 52, 85-94.   DOI
13 Li. Q.S. (2001), "Stability of tall buildings with shear wall structures", Eng. Struct., 23, 1177-1185.   DOI
14 Liu, Z., Yin, Y., Wang, F., Zhao, Y. and Cai, L. (2013), "Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam", Struct. Eng. Mech., 48(5), 697-709.   DOI
15 Mageirou, G.E. and Gantes, C.J. (2006), "Buckling strength of multi-story sway, non-sway and partially sway frames with semi rigid connections", J. Const. Steel Res., 62, 893-905.   DOI
16 Nadjai, A. and Johnson, D. (1998), "Elastic and elasto-plastic analysis of planar coupled shear walls with flexible bases", Comput. Struct., 68, 213-229.   DOI
17 Orumu, S.T. (2013), "Approximate elastic model for determination of critical loads and effective lengths for simple sway frames", IJES, 2(8), 113-120.
18 Ozgumus, O.O. and Kaya, M.O. (2006), "Flapwise bending vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method", Meccanica, 41(6), 661-670.   DOI
19 Ozmen, G. and Girgin, K. (2005), "Buckling lengths of unbraced multi-storey frame columns", Struct. Eng. Mech., 19(1), 55-71.   DOI
20 Potzta, G. and Kollar, L.P. (2003), "Analysis of building structures by replacement sandwich beams", Int. J. Solid. Struct., 40, 535-553.   DOI
21 Wood, RH. (1974b), "Effective lengths of columns in multi-story buildings. part 2 effective lengths of multiple columns in tall buildings with sidesway", Struct. Eng., 52(7), 295-302.
22 Wood, R.H. (1974c), "Effective lengths of columns in multi-story buildings.part 3 features which increase the stiffness of tall frames against sway collapse, and recommendations for designers", Struct. Eng., 52(7), 341-346.
23 Xenidis, H. and Makarios, T. (2004), "Critical buckling load of multi-story r/c buildings", 13th World Conference on Earthquake Engineering, Vancouver, Canada, August.
24 Xu, L. and Wang, X.H. (2007), "Stability of multi-storey unbraced steel frames subjected to variable loading", J. Const. Steel Res., 63(10), 1506-1514.   DOI
25 Zalka, K.A. (1999), "Full-height buckling of frameworks with cross-bracing", Proc. Instn. Civ. Eng. Struct. Build., 134(2), 181-191.   DOI
26 Zalka, K.A. (2000), Global Structural Analysis of Buildings, Taylor & Francis Group, Boca Raton, FL, USA.
27 Zalka, K.A. (2002a), "Global stability analysis and structural performance of buildings braced by infilled frames", Proc. Instn. Civ. Eng. Struct. Build., 152(3), 213-224.   DOI
28 Zalka, K.A. (2002b), "Buckling analysis of buildings braced by frameworks, shear walls and cores", Struct. Des. Tall Build., 11(3), 197-219.   DOI
29 Zalka, K.A. (2003), "A hand method for predicting the stability of regular buildings, using frequency measurements", Struct. Des. Tall Build., 12(4), 273-281.   DOI
30 Zalka, K.A. (2013), Structural analysis of regular multi-storey buildings, Taylor & Francis Group, Boca Raton, FL, USA.
31 Aristizabal-Ochoa, J.D. (1997), "Story stability of braced, partially braced and unbraced frames; classical approach", J. Struct. Eng., ASCE, 123(6), 799-807.   DOI
32 Aristizabal-Ochoa, J.D. (2002), "Classic buckling of three-dimensional multi-column systems under gravity loads", J. Struct. Eng., ASCE, 128(6), 613-624.
33 Aristizabal-Ochoa, J.D. (2003), "Elastic stability and second-order analysis of three dimensional frames: effects of column orientation", J. Struct. Eng., ASCE, 129(11), 1254-1267.
34 Bozdogan, K.B. and Ozturk, D. (2010), "An approximate method for lateral stability analysis of wall-frame buildings including shear deformations of walls", Sadhana, 35(3), 241-253.   DOI
35 Chai, Y.H. and Chen, Yanfei. (2009), "Reexamination of the vibrational period of coupled shear walls by differential transformation", J. Struct. Eng., ASCE, 135(11), 1330-1339   DOI
36 Chen, C. and Liu, Y. (1998), "Solution of two point boundary value problems using the differential transformation method", J. Opt. Theor. Appl., 99(1), 23-35.   DOI
37 Colunga, T.C. and Hernandez, G.R. (2015), "Assessment of the lateral stiffness of walls with openings", COMPYDY, Crete island, Greece, May.
38 Ellwanger, R.J. (2013), "Floors number influence on the instability parameter of reinforced concrete wall-or core-braced buildings", IBRACON Estrut. Mater., 6(5), 783-810.   DOI
39 Gantes, C.J. and Mageirou, G.E. (2005), "Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames", Eng. Struct., 27(7), 1113-1124.   DOI
40 Pukhov, G.E. (1981), "Expanison formulas for differential transforms", Cybern. Syst. Anal., 17(4), 460-464.
41 Rajasekaran, S. (2009), Structural Dynamics of Earthquake Engineering: Theory and Application using Mathematica and Matlab, Woodhead Publishing in Materials, CRC Press India.
42 Rajasekaran, S. (2008), "Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods", Struct. Eng. Mech., 28(2), 221-238.   DOI
43 Rosman, R. (1974), "Stability and dynamics of shear-wall frame structures", Build. Sci., 9, 55-63.   DOI
44 Rosman, R. (1981), "Buckling and vibrations of spatial building structures", Eng. Struct., 3, 194-202.   DOI
45 Rutenberg, A., Levithian, I. and Decalo, M. (1988), "Stability of shear-wall structures", J. Struct. Eng., ASCE, 114(3), 707-716.   DOI
46 Syngellakis, S. and Kameshki, E.S. (1994), "Elastic critical loads for plane frames by transfer matrix method" J. Struct. Eng., ASCE, 120(4), 1140-1157.   DOI
47 Tong, G.S. and Ji, Y. (2007), "Buckling of frames braced by flexural bracing", J. Const. Steel Res., 63, 229-236.   DOI
48 Wang, C.M., Ang, K.K. and Quek, S.T. (1991), "Stability formulae for shear-wall frame structures", Build. Env., 26(2), 217-222.   DOI
49 Wang, S.K. (1997), "Stiffness, stability and fundamental period of coupled shear walls of variable thickness", Proc. Instn Civ. Eng. Struct. Build., 122(3), 334-338.   DOI
50 Wood, R.H. (1974a), "Effective lengths of columns in multi-story buildings. part 1 Effective lengths of Single columns and allowances for continuity", Struct. Eng., 52(7), 235-244.
51 Zhang, L., Tong, G.S. and Ji, Y. (2015), "Buckling of flexural-shear bracing system and its braced steel frames", Adv. Struct. Eng., 18(11), 1831-1844.   DOI