Approximation formula for calculating fire resistance of unprotected steel structures

Introduction. When designing buildings it is necessary to estimate the actual fire resistance limits of unprotected steel structures. Nomograms are a convenient tool for obtaining such an assessment. Practical necessity of integration of “manual” technology and modern means of design automation makes the task of “digitization” of nomo­grams by creating computational data models urgent.

Goals and objectives. The purpose of the work was to obtain a rather simple formula for calculating the fire resistance limits of unprotected steel structures. The following tasks were solved: comparison of the literature data on fire resistance limits with the results of calculations according to the normative document on fire safety “VNPB 73–18”; calculation of a four-digit table of fire resistance limits for the subsequent approximation of functional dependence.

Research methods. The table of fire resistance values is calculated with four correct digits using the Adams multistep method of variable order. The formula for calculation of fire resistance limit of unprotected steel structures was obtained by successive approximation of tabular data first by one variable (thickness, i.e. reciprocal of the section factor) and then by another (critical temperature).

Results and discussion. Calculation according to the methodology VNPB 73–18 gives the fire resistance limits close to the reference values, which were published by A.I. Yakovlev in 1985. The values of convective and radiation heat transfer coefficients adopted in the VNPB 73–18 method correspond to the fire resistance tests according to GOST 30247.0–94 (ISO 834–75).

Conclusions. An approximation formula was obtained, the calculations according to which give the same fire resistance limits as the calculations according to the VNPB 73–18 method. Relative error of approximation does not exceed 0.5 % in the range of parameters change: critical temperature — from 500 to 700 °C; thickness — from 3 to 12 mm.

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