MATHEMATICAL MODELING FOR THE DESCRIPTION OF THE CONTOUR LINES OF THE CHARRED ZONE OF WOODEN BEAMS WITH FIREPROOF FACING

Abstract

The article provides mathematical modeling of the contours of the
charred zone for various wooden beams without fire protection and with fire protection
facing. The subject of research is influence of design parameters different thicknesses of
wooden beams for fire resistance in conditions of fire exposure according to the
standard temperature regime.
The purpose it’s the use of regression dependencies to construct Bezier lines. nd
reproduction of the contour of the carbonization zone of cross-sections of wooden
beams with different thicknesses with fireproof facing. To fulfill this goal, the following
research tasks: determine the parameters of the regression dependencies of the
distribution of the parameter r/yc
=f(yc/h) for wooden beams, with the help of Bezier
lines approximation of isotherms with a critical temperature of 200 оС; reproduce the
analytical description of the contour lines of the charred zone which will allow to
obtain the geometric characteristics of the cross-sections of the left whole part of the
wooden beams of different geometric configurations, the samples with different
thicknesses of fireproof cladding to calculate the strength of the corresponding wooden
beams. To develop a methodology for calculating temperature distributions inside the
cross-section of a wooden beam with fireproof facing and tabular, thermo physical
methods and mathematical modeling were used to construct contour lines of the
charring zone. The scientific novelty of the study consists in the description of the
geometric charring zone in the cross-section of a wooden beam and the approximation
of its configuration using Bezier lines. The regularity of the position of reference points
for the construction of Bezier lines was revealed. These points approximate the contours
of the carbonization zone, depending on the generalized parameter of the cross-section
geometry in the form of a regression polynomial dependence. After the calculations, the
main result was obtained which make it possible to determine the coefficient of
reduction in the strength of wood during a fire and to estimate the fire resistance of a
wooden beam. This will lead to the development of the methods of calculating the fire
resistance of wooden beams with fireproof facing.