Keywords: composites, Reissner beam, geometrical and material non-linearity, strain-based finite element analysis, layered wood columns, interlayer slip.

Composite structures are of increasing interest in building construction, where they are used as floor, wall and roof elements, and in bridge construction. The building up wood columns from various layers connected by means of nailing, bolting or gluing is a common practice. The use of composite structures is often necessary for practical and economical reasons. Composite, or layered structures are built up from two or more subcomponents of like or unlike materials; each of the constituents fulfills the function for which its material characteristics are most suited. The behaviour of composite members depends to a large degree on the type of connection between the subcomponents. Rigid shear connectors usually develop full composite action between the individual components of the member, so that the conventional principles of the analysis can be applied. Flexible shear connectors generally permit the development of only a partial composite action; therefore, the analysis procedure requires the consideration of the interlayer slip between subelements. In this paper, a geometrically and materially non-linear analysis of composite wood beams, where slips between the layers are accounted for, is presented. A special attention is devoted to the buckling behaviour of compressed composite wood columns.

To use wood economically, wood columns are often made from various layers assembled by means of nailing, bolting, or gluing. As already mentioned, the buckling load of layered wooden columns depends on the dimensions and the physical properties of the layers and on the strength and the locations of the connectors. In order to predict this buckling load, a method for analysing the behaviour of such systems is necessary. Let us emphasize that many researchers, e.g. [4,5,8] have developed different procedures for non-linear analysis of composite structures with interlayer slips, where only material non-linearities of layers and contacts between them are taken into account. As it is well known, by using this kind of analysis we can not determine the buckling load of a composite column correctly. The procedures presently used in various codes for designing layered wood columns are based primarily on the results of experiments [2] and the theoretical models available for the analysis of this type of constructions are generally based on the assumption of the rigidity of the connection between the layers [5]. Girhammar and Gopu [3] derived simplified non-linear analysis (so called "second-order theory") of composite beams with interlayer slips, which enables only an approximate buckling load of the composite beam to be calculated.

The paper presents a computational model and a computer program developed for the geometrically exact and materially non-linear analysis of composite structures with interlayer slips. A special attention is devoted to the buckling load of axially compressed layered wood columns. In order to analyse such a composite structure with a sufficient accuracy, new finite element, based on Reissner's theory of beams, is developed. Equation det , where is the tangential stiffness matrix of a composite structure, represents the criterion for determining the critical buckling load of an axially loaded composite beam with interlayer slips. In numerical examples we compare the present results to those obtained by Girhammar and Gopu [3] and the European prenorm for timber structures Eurocode 5 [2]. Our results and the results of Girhammar and Gopu's numerical model fully agree. The results of Eurocode 5 [2] are shown to be rather conservative.

1

B. Cas, " Non-linear analysis of composite beams with interlayer slip", PhD Thesis (in Slovene), University of Ljubljana, Faculty of Civil and Geodetic Engineering, 2004.

2

Eurocode 5, Design of timber structures, Part 1-1: General rules and rules for buildings, ENV 1995-1-1, 1993.

3

U.A. Girhammar, V.K.A. Gopu, " Composite beam-columns with interlayer slip - exact analysis", Journal of Structural Engineering, ASCE, 119(4), 1265-1282, 1993. doi:10.1061/(ASCE)0733-9445(1993)119:4(1265)

4

J.R. Goodman, E.P. Popov, " Layered beam systems with interlayer slip", Journal of the Structural Division, ASCE, 94(11), 2535-2547, 1968.

5

N.M. Newmark, C.P. Siess, C.P. Viest, Test and analysis of composite beams with incomplete interaction", Proceedings of the Society for Experimental Stress Analysis, 9, 75-92, 1951.

6

H.Y. Rassam, J.R. Goodman, " Buckling behaviour of layered wood columns", Wood Science, 2(4), 238-246, 1970.

7

H.Y. Rassam, J.R. Goodman, " Design of layered wood columns with interlayer slip", Wood Science, 3(3), 149-155, 1971.

8

E.G. Thompson, J.R. Goodman, M.D. Vanderbilt, Finite element analysis of layered wood systems", Journal of the Structural Division, ASCE, Vol. 101, No. ST12, 2659-2672, 1975.

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