Lateral stability analysis of multistory buildings using the differential transform method

다국어 초록 (Multilingual 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).

참고문헌 (Reference)

1 Zhifeng Liu, "Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam" 국제구조공학회 48 (48): 697-709, 2013

2 Zalka, K.A., "Structural analysis of regular multi-storey buildings" Taylor & Francis Group 2013

3 Aristizabal-Ochoa, J.D., "Story stability of braced, partially braced and unbraced frames; classical approach" ASCE 123 (123): 799-807, 1997

4 Wang, S.K., "Stiffness, stability and fundamental period of coupled shear walls of variable thickness" 122 (122): 334-338, 1997

5 Li. Q.S., "Stability of tall buildings with shear wall structures" 23 : 1177-1185, 2001

6 Gustafsson, D., "Stability of tall buildings" Chalmers University of Technolog 2005

7 Rutenberg, A., "Stability of shear-wall structures" ASCE 114 (114): 707-716, 1988

8 Xu, L., "Stability of multi-storey unbraced steel frames subjected to variable loading" 63 (63): 1506-1514, 2007

9 Wang, C.M., "Stability formulae for shear-wall frame structures" 26 (26): 217-222, 1991

10 Rosman, R., "Stability and dynamics of shear-wall frame structures" 9 : 55-63, 1974

11 Chen, C., "Solution of two point boundary value problems using the differential transformation method" 99 (99): 23-35, 1998

12 Girgin, K., "Simplified procedure for determining buckling loads of threedimensional framed structures" 29 (29): 2344-2352, 2007

13 Kollar, L., "Second order effects on building structures-an approximate evaluation" 2008

14 Chai, Y.H., "Reexamination of the vibrational period of coupled shear walls by differential transformation" ASCE 135 (135): 1330-1339, 2009

15 Kaveh, A., "Optimal Analysis of Structures by Concepts of Symmetry and Regularity" Springer Verlag, GmbH 2013

16 Gantes, C.J., "Improved stiffness distribution factors for evaluation of effective buckling lengths in multi-story sway frames" 27 (27): 1113-1124, 2005

17 Zalka, K.A., "Global stability analysis and structural performance of buildings braced by infilled frames" 152 (152): 213-224, 2002

18 Zalka, K.A., "Global Structural Analysis of Buildings" Taylor & Francis Group 2000

19 Zalka, K.A., "Full-height buckling of frameworks with cross-bracing" 134 (134): 181-191, 1999

20 Ellwanger, R.J., "Floors number influence on the instability parameter of reinforced concrete wall-or core-braced buildings" 6 (6): 783-810, 2013

21 Ozgumus, O.O., "Flapwise bending vibration analysis of double tapered rotating Euler-Bernoulli beam by using the differential transform method" 41 (41): 661-670, 2006

22 Pukhov, G.E., "Expanison formulas for differential transforms" 17 (17): 460-464, 1981

23 Aristizabal-Ochoa, J.D., "Elastic stability and second-order analysis of three dimensional frames: effects of column orientation" ASCE 129 (129): 1254-1267, 2003

24 Syngellakis, S., "Elastic critical loads for plane frames by transfer matrix method" ASCE 120 (120): 1140-1157, 1994

25 Nadjai, A., "Elastic and elasto-plastic analysis of planar coupled shear walls with flexible bases" 68 : 213-229, 1998

26 Wood, R.H., "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" 52 (52): 341-346, 1974

27 Wood, RH., "Effective lengths of columns in multi-story buildings. part 2 effective lengths of multiple columns in tall buildings with sidesway" 52 (52): 295-302, 1974

28 Wood, R.H., "Effective lengths of columns in multi-story buildings. part 1 Effective lengths of Single columns and allowances for continuity" 52 (52): 235-244, 1974

29 Rajasekaran, S., "Dynamics of Earthquake Engineering: Theory and Application using Mathematica and Matlab" Woodhead Publishing in Materials, CRC Press 2009

30 Hoenderkamp, J.C.D., "Critical loads of lateral load resisting structures for tall buildings" 11 (11): 221-232, 2002

31 Xenidis, H., "Critical buckling load of multi-story r/c buildings" 2004

32 Aristizabal-Ochoa, J.D., "Classic buckling of three-dimensional multi-column systems under gravity loads" ASCE 128 (128): 613-624, 2002

33 Mageirou, G.E., "Buckling strength of multi-story sway, non-sway and partially sway frames with semi rigid connections" 62 : 893-905, 2006

34 S. Rajasekaran, "Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods" 국제구조공학회 28 (28): 221-238, 2008

35 Tong, G.S., "Buckling of frames braced by flexural bracing" 63 : 229-236, 2007

36 Zhang, L., "Buckling of flexural-shear bracing system and its braced steel frames" 18 (18): 1831-1844, 2015

37 Kaveh, A., "Buckling load of symmetric plane frames using canonical forms" 85 : 1420-1430, 2006

38 Günay Özmen, "Buckling lengths of unbraced multi-storey frame columns" 국제구조공학회 19 (19): 55-71, 2005

39 Girgin, K., "Buckling lengths of irregular frame columns" 62 : 605-613, 2006

40 Gomes, F.C., "Buckling length of a steel column for fire design" 29 (29): 2497-2502, 2007

41 Rosman, R., "Buckling and vibrations of spatial building structures" 3 : 194-202, 1981

42 Gengshu, T., "Buckling and second order effects in dual shear-flexural Systems" ASCE 134 (134): 1726-1732, 2008

43 Zalka, K.A., "Buckling analysis of buildings braced by frameworks, shear walls and cores" 11 (11): 197-219, 2002

44 Lal, R., "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method" 52 : 85-94, 2015

45 Colunga, T.C., "Assessment of the lateral stiffness of walls with openings" 2015

46 Keskin, Y., "Approximate solutions of generalized pantograph equations by the differential transform method" 8 : 159-164, 2007

47 Orumu, S.T., "Approximate elastic model for determination of critical loads and effective lengths for simple sway frames" 2 (2): 113-120, 2013

48 Potzta, G., "Analysis of building structures by replacement sandwich beams" 40 : 535-553, 2003

49 Bozdogan, K.B., "An approximate method for lateral stability analysis of wall-frame buildings including shear deformations of walls" 35 (35): 241-253, 2010

50 Gengshu, T., "A simplified method for the buckling of outrigger-shear wall braced Structures" 11 (11): 1-15, 2008

51 Zalka, K.A., "A hand method for predicting the stability of regular buildings, using frequency measurements" 12 (12): 273-281, 2003