تجزیه و تحلیل حساسیت از فرمول انتقال حرارت برای قطعات عایق بندی سازه های فولادی

The aim of using fire protection in a building is to reduce the rate of temperature rise of its structural components in case of fire. For protected structural steel, the thermal properties of the insulation materials affect the rate of temperature rise and are crucial in determining the minimum requirements for fire safety for both the steel and the insulation materials. The determination of the required thickness of the insulation materials can be performed by means of test results, analytical solutions or numerical methods. The current Eurocode 3 provides simple analytical solutions for estimating the temperature rise of both protected and unprotected structural steel in a fire. This paper presents a sensitivity analysis to examine the appropriateness of using these analytical solutions for structural steel components protected with insulation materials of contrasting properties including thermal conductivity and density. Results of the analysis show that, for certain types of insulation materials, the temperatures predicted by the Eurocode may differ substantially from those by exact analytical solution. An alternative formulation is presented when these types of insulation materials are used for fire protection of structural steel.

Current building codes in many countries stipulate fire-rating requirements for which the failure temperature profile of a structure needs to be assessed by, for example, elastic or plastic frame analysis [1]. For design purposes, the failure temperature profile has to be checked against the temperatures attained by the structural components with or without fire protection in a fire. In most cases, particularly in multi-storey steel-framed buildings, fire protection is needed for steel members of reasonable size. The choice of the insulation materials, such as gypsum boards and sprayed mineral fibre, is often up to the design engineer. The insulation material usually has low density and low thermal conductivity so that the resulting thickness of the insulation can be minimised. However, for aesthetic and practical reasons, the use of fire protection for steel members as insulation materials with high density and high thermal conductivity, such as brick and concrete, is not uncommon. A form of fire protection for steel column by concrete encasement has been a subject of investigation [2] and semi-empirical formula for the calculation of its fire resistance has been developed. The current practice for determining the thickness of a chosen fire protection material is by means of standard test results, analytical solutions or numerical analysis. When using the method by test results, design charts and material properties are usually provided by the manufacturers. This information is established by standard fire tests. While the method by numerical analysis is often tedious and prone to human error, the method by analytical solutions is commonly used in many design codes [3] and [4]. In practice, analytical solution is preferred because it enables the design to be carried out using a flexible approach to a wide variety of problems which may include realistic fire scenarios, various types of structural member sections and different insulation materials. The analytical solutions provided in EC3 [3], to be formally adopted as a full European standard in the near future, for temperature prediction of both protected and unprotected steelwork are based on the most recent research findings. The formulations are dependent on a number of parameters including heat transfer coefficients, insulation thickness and thermal properties of insulation materials. The purpose of this study here is to examine these parameters in the EC3 formulations for temperature prediction of structural steel members protected with insulation materials of various thermal properties. A sensitivity analysis is presented and the results of the analysis show that, for certain insulation materials, the temperatures predicted by the Eurocode may differ substantially from those by exact analytical solution. An alternative formulation is presented for cases where these types of insulation materials are used for fire protection of structural steel.

The Eurocode 3 (EC3) provides formulation for temperature calculation of protected structural steel. For insulation with low density and low conductivity, the formulation gives reasonable results comparable to the exact solution which is based on the solution of the differential equations for heat transfer through Laplace Transformation. However, from the sensitivity analysis carried out here, it has been found that for insulation with relatively high density and high conductivity, such as concrete, EC3 formulation may give results which differ significantly from the exact solution. In those circumstances, the use of the exact solution is recommended. It should be noted that the results presented here are applicable to particular cases where thick steel tubes and thin concrete layers may be used, as exemplified in the analysis. In most cases, EC3 formulations are applicable. The difficulty in using the exact solution is the complexity in evaluating the parameters related to the thermal resistance of the insulation. A simplified form for each of these parameters is proposed when the exact solution is used. Finally, the discussion given in this paper is based on ENV1993-1-2 which may have been revised when the full EN version of the code is published. However, to the authors’ knowledge at the time of writing this paper, the revision will not affect significantly the subject matter of the discussion. Details of the issues in relation to the conversion of ENV to EN are given by Twilt [17].