In this paper the potential of the transfer matrix method, which combines both matrix displacement and force method, to provide an efficient as well as accurate analytical tool is explored. The ability of the technique to take advantage of the continuous end-to-end chain topology of a multistory frame structure has already been tested in elastic and inelastic stability analyses of frames with rigid and flexible joints [1,2,3,4,5,6]. The present analysis is based on the simple plane grid element, with the warping effect neglected. For the grillage configurations considered, the effect of this mode of deformation has been shown to be small, further extension of the formulation to account for this deformation would not bring about any significant computational cost. The developed procedure allows for variations of cross sections, spacing and types of supports. It uses matrices of smaller size than the existing conventional methods and is easily programmable on the computer since it does not require complex mathematical operations. Therefore, it combines a considerable degree of versatility and accuracy, both essential in modern practice.

The transfer matrix methodology is adapted to the analysis of orthogonal grillage systems. Partitioning the grillage system along the intersection of the longitudinal elements with each transverse element generates a non branching chain of members. Field and station transfer matrices are derived on the basis of a minimum number of only the essential degrees of freedom per longitudinal spacing. Displacements and internal forces are determined by solving a set of simultaneous equations. The developed formulation accounts for supports flexibility.

The analyses and the computer code are systematically tested for accuracy and efficiency through comparison of their predictions with other methods [7] confirms the validity of the proposed method of solution.

1

Kameshki E.S., and S.S. Syngillakis. "Inelastic Stability of Rectangular Frames by Transfer matrices", J. of Computers and Structures, (7) pp. 373-383, 1999. doi:10.1016/S0045-7949(98)00273-9

2

Kameshki E.S. and Syngellakis S.S. "Stability Analysis of Frames with Flexible Connections by Transfer Matrices", J. Structural Engineering review, Vol. 8, No. 2/3, pp. 177-186, 1996.

3

Kameshki E.S. and Syngillakis S.S. "Inelastic Stability of Rectangular Frames by Transfer matrices", CIVIL-COMP 96, Vol. Advances in Optimization for Structural Engineering, pp. 81-91, Budapest, Hungary, August, 1996.

4

Kameshki E.S. and Syngellakis S.S. "Stability of Unbraced Multistorey Building Frames by Transfer Matrix Method", Proceedings of the Second International Conference in Civil Engineering on Computer Applications Research and Practice. ICCE, Vol. 3, PP: 915-925,University of Bahrain, State of Bahrain, April 1996.

5

Syngellakis S.S and Kameshki E.S. "Elastic Critical Loads for Plane Frames by Transfer Matrix Method", ASCE, Journal of Structural Engineering, Vol. 120, No. 4, pp. 1140-1157, April 1994. doi:10.1061/(ASCE)0733-9445(1994)120:4(1140)

6

Kameshki E.S and Syngillakis S.S. "Stability Analysis of Frames with Flexibile Connections by Transfer matrices", Developments in Structural Engineering Computing, pp. 289-296, Edinburgh, Scotland, August 1993.

7

STAAD III (Structural Analysis And Design), Research Engineers, Inc, Version 20, California, USA, 1994.

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