Keywords: charring, fire, wood, beam, coupled heat and mass transfer.

This paper describes a mathematical model developed to solve a coupled heat and moisture transfer and the charring behavior of timber beams when exposed to fire. The model consists of two coupled non-linear partial differential equations for heat and moisture transfer with the corresponding boundary conditions. The model also predicts the char formation in the wood beam as a function of its temperature, moisture content, density, etc. Since the analytical solution is seldom obtainable, the problem is solved numerically by the finite difference method.

The results are tested on the one dimensional case in standard fire conditions [1,2], for which comparison is made with the results of a one-dimensional charring rate models for wood presented in the literature [3,4,5,6] and experimental results published by Fredlund [7,8] A comparison of different charring models shows that the charring rates obtained by the proposed mathematical model are shown to be in excellent agreement with the results obtained experimentally by Fredlund [7,8]. The model is also shown to be in good agreement with the Eurocode 5 [9] model and model proposed by White and Nordheim [4], when compared with other charring models it differs considerably.

The proposed mathematical model is also used to perform the parametric studies to investigate the influence of initial moisture content and density of wood on the charring behaviour of timber beams. The comparison reveals that the influence is considerable.

The same model is used to analyze the two-dimensional behavior of a wood beam exposed to fire from three sides. Faster charring at the corners and typical rounding effects are observed. Since the comparison showed a good agreement with the proposed mathematical model and models presented in the literature, we can conclude that a relatively simple mathematical model is generally appropriate for the accurate prediction of the thermomechanical behaviour of timber beams exposed to fire.

1

ISO 834,Fire-resistance test - Elements of building construction-Part 1. General requirements. ISO 834-1, International organization for standardization, Geneva, Switzerland, 1999.

2

ASTM, Standard test methods for fire tests of building construction and materials , Standard designation E 119-00, West Conshohocken, PA:ASTM, 2000.

3

R. H. White, Charring rates of different wood species , Dissertation, University of Wisconsin, Madison, WI, USA, 1988.

4

R. H. White and E. V.Nordheim,Charring rate of wood for ASTM E 119 exposure , Fire Technology, 28 (1), 5-30, 1992 doi:10.1007/BF01858049

5

E.L. Schaffer, Charring rate of selected woods-transverse to grain, Research paper FPL-69, USDA Forest Product Laboratory, Madison, Wisconsin, USA, 1967

6

D. I. Lawson, C. T. Webster and L. A. Ashton, Fire endurance of timber beams and floors , Journal of Structural Engineering, 30 (2), 27-34, 1952.

7

B. Fredlund, A model for heat and mass transfer in timber structures during fire. A theoretical, numerical and experimental study , Report LUTVDG/(TVBB-1033), Department of fire safety engineering, Lund institute of science and Technology, Sweden, 1988.

8

B. Fredlund, Modelling of heat and mass transfer in wood structures during fire, Fire Safety Journal, 20, 39-69, 1993. doi:10.1016/0379-7112(93)90011-E

9

EN 1995-1-2, Eurocode 5, Design of timber structures Part 1-2: General-Structural fire design , 2004.

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