Keywords: composite wood beams, interlayer slip, geometrically linear and materially non-linear analysis, strain-based finite element analysis.

Layered composite structural elements are often employed in engineering structures in order to reduce cost and enhance their bearing capacity. They are often used as floor, wall and roof elements, and in bridge construction. Composite structural elements are defined as elements built up from two or more subcomponents of like or unlike materials where each of the constituents fulfills the function for which its material characteristics are most suited. The building up wood beams from various layers connected by means of nailing, bolting or gluing is a common practice. The behaviour of composite members depends to a large degree on the type of connection between the subcomponents. The procedures employed to analyse such systems are often based on the assumption of the rigid connection between layers. But the majority of composite composite structures, however, exhibit a flexible interlayer contact, leading to the relative tangential displacement (slip) between the layers. In this paper, a materially non-linear analysis of composite wood beams, where slips between the layers are accounted for, is presented.

To use wood economically, wood beams are often made from various layers assembled by means of nailing, bolting, or gluing. Extensive results of analytical and experimental investigation of composite wood beams with interlayer slip have been reported [5,6,8]. Researchers have developed various procedures for the analysis of composite wood structures with interlayer slips where, due to simplicity, linear material models of wood and contact between layers are often employed. As it is well known, by using this kind of analysis we cannot determine the load bearing capacity of a composite wood beam correctly. In this paper a materially non-linear analysis of composite wood beams is presented where contact constitutive law used was experimentally determined [1] and non-linear. As it is quite a demanding procedure to measure the material constitutive law of wood [7], we combined our own experimental findings [1] and findings of Steiger [7] to construct a non-linear constitutive law of wood that was used in the calculations.

The paper presents a computational model and a computer program developed for the materially non-linear analysis of composite structures with interlayer slips. A special attention is devoted to the flexural analysis of two-layered wood beams. In order to analyse such a composite structure with a sufficient accuracy, a new finite element is developed. In numerical examples, the results of the present numerical procedure are compared with results of an experimental study of composite wood beams [1]. As already mentioned, the constitutive law of wood and the contact between layers are difficult to be measured exactly. Although it was observed that the chosen constitutive law of wood and the contact between layers significantly influence the behaviour of composite wood beams, great agreement between experimental and numerical results is obtained.

1

B. Cas, "Influence of contact stiffness on the load-bearing capacity of composite beams", Diploma thesis (in Slovene), University of Ljubljana, Faculty of Civil and Geodetic Engineering, 1999.

2

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.

3

"Einfuhrung in die Norm SIA 164", Holzbau, Autographie zum Fortbildungkurs fur Bauingenieure, ETH Zurich, 7-9 Oktober,1981.

4

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

5

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

6

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

7

R. Steiger, E. Gheri, H. Arm, "Einspannvorrichtung für Zugversuche an Holzproben grösseren Querschnitts", Institut für Baustatik und Konstruktion, ETH Zürich, Birhauser Verlag Basel-Boston-Berlin, Bericht 204, 1994.

8

D.L. Wheat, J.M. Calixto, "Non-linear analysis of two layered wood members with interlayer slip", Journal of Structural Engineering, ASCE, 120(6), 1909-1929, 1994. doi:10.1061/(ASCE)0733-9445(1994)120:6(1909)

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