Keywords: fire, interlayer slip, wood, charring, finite element method, finite difference method.

The purpose of this paper is to examine the mechanical response of composite wooden beams with interlayer slip, when one or more faces are exposed to fire. When analysing numerically the behaviour of load bearing wooden beams in fires, the contributions of shrinkage-swelling, temperature, viscous creep and mechano-sorptive strains are of major importance. The developments of all mentioned strains is strongly affected by the actual temperature and moisture content field of the beams. In this sense the determination of the spatial and temporal distribution of temperature and moisture content over the element according to ambient conditions is the first key phase of the analysis. Since experimental observations of behaviour of wooden beams exposed to fire prove the mutual effect of the temperature and moisture content gradients in wood, the non-stationary coupled heat and moisture transfer over the composite wooden beams is considered. This process in rather complicated mechanism, and is, in the case of porous media, like wood, described with a coupled system of non-linear partial differential equations presented by Luikov [1]. Assuming the homogeneity of the humidity and temperature field along the beam, the 2-D Luikov equations are solved for the cross-section of the composite wooden beam. Due to rectangular cross-section the finite difference method using an equidistant mesh of difference points is chosen for the solution. For the spatial integration the symmetric formulae based on quadratic shape functions are introduced, whereas for the time-integration linear shape functions are employed.

When the distribution of temperature and moisture content and the formation of char over the cross-section is known for each time step of the analysis, it can be used in the second key phase of the analysis, the mechanical response analysis of wooden composite beams exposed simultaneously to static loading and fire. The each layer of the composite wooden beam is modelled by linearized Reissner [2] kinematic equations. The mathematical model of the composite wooden beam is described by a set of algebraic-differential equations and boundary conditions. the principle of virtual work has been employed as a basis for the finite element discretization. Thus, we have proposed a modified form of the principle of virtual work by including the linear kinematic equations as constraining equations by the means of a procedure, similar to that of Lagrangian multipliers. In this way we can eliminate the displacement field vector from the principle of virtual work. As a result, the deformation field vector remains the only unknown function to be approximated in the finite element implementation of the principle. Furthermore, the present approach uses the concept of the consistent equilibrium of constitutive and equilibrium-based stress-resultants and the Galerkin type of the finite element formulation is employed.

With the use of the derived model for the analysis of the behaviour of composite wooden beams exposed to static loading and fire, various parametric studies have been performed. The main emphasis has been devoted to the investigation of different material properties on vertical deflections of composite wooden beams when exposed to static loading and standard fire conditions.

1

Luikov A.V. Heat and Mass Transfer in Capillary-porous Bodies. Pergamon Press, Oxford, 1966.

2

E. Reissner, "On one-dimensional finite-strain beam theory: The plane problem", Journal of Applied Mathematics and Physics (ZAMP), 23, 795-804, 1972. doi:10.1007/BF01602645

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £120 +P&P)