Impact of variability in thermal properties of SFRM on steel temperatures in fire

https://doi.org/10.1016/j.firesaf.2021.103361Get rights and content

Abstract

For structural steel components protected by spray-applied fire-resistive materials (SFRMs), variations in the thermal properties and thickness of SFRM may influence steel temperatures during fires. This paper presents a sensitivity analysis of the influence of assumed thermal properties and thickness of SFRM on predicted steel temperatures in fire. For this purpose, material test data in the literature on the thermal properties of SFRMs were used to determine reasonable bounds for three variables: thermal conductivity, volumetric heat capacity, and insulation thickness. Fifteen material models were developed assuming temperature-independent values for these variables based on a face-centered central composite experiment design. Finite element models were developed for three structural fire experiments. In addition, a fourth model of a composite beam was developed with localized hole in the SFRM representing an ID tag, which in practice is affixed to beam webs. Each model was analyzed using the fifteen material models. The choice of SFRM thermal properties had a significant influence on steel temperatures, and statistical analysis of the experimental design showed that steel temperatures increased with increasing thermal conductivity, and decreased with increasing thickness and volumetric heat capacity. The influence of volumetric heat capacity was smaller than that of thermal conductivity and thickness.

Introduction

In the United States, spray-applied fire-resistive materials (SFRMs) are commonly used to protect steel structures against the effects of fire. SFRMs are typically composed of mineral wool, quartz, perlite, vermiculite, or bauxite, along with a binding agent such as cement or gypsum [1]. SFRMs provide passive protection to structural steel components by serving as an insulative layer during a fire. They are currently qualified and certified based on fire resistance tests such as ASTM E119 [2]. While these tests provide fire ratings, expressed by the duration, in hours, that SFRMs provide protection to the test specimen in the standard fire, the severities of actual or design fires may be substantially different from those specified by the prescriptive codes. To evaluate steel temperatures under fire conditions that differ from the standard fire, thermal analysis can be performed, but such analysis requires knowledge of the thermal material properties of SFRMs.

Although the thermal properties of SFRMs are known to vary with temperature, depending on their composition, temperature-independent or effective constant thermal properties are often assumed in practice when calculating the temperature response of steel members protected by SFRMs [3,4]. There are several reasons that temperature-independent thermal properties are commonly used. First, a lack of test data available in the literature on the properties of SFRMs at high temperatures prevents development of more sophisticated models. For example, reliable data on thermal properties of SFRMs at temperatures over 800 °C are not available in the literature due to the limitations of testing techniques. However, the temperature of SFRMs in actual fires regularly approaches gas temperature and can exceed 800 °C. Second, simple calculation models for predicting the temperature of protected steel members in fire (e.g., the Eurocode 3 [5]) are based on temperature-independent thermal properties [6]. Third, product literature published by the manufacturers of SFRMs (e.g. Ref. [7]) usually only specifies their thermal properties at ambient temperature. Currently, there is little consensus for how to determine the effective constant thermal properties of SFRMs, and studies have shown that using improper thermal properties can lead to inaccurate evaluation of the fire resistance of protected steel structures [8]. Therefore, it is important to study the influence of uncertainty in assumed thermal properties of SFRMs in predicting the temperatures of the protected steel in fire.

In addition to the thermal properties of the SFRM, its thickness strongly influences the rate of temperature rise of the protected steel during a fire. The thickness of SFRM applied to the steel may be different from the designed thickness, as was found in the NIST World Trade Center (WTC) investigation [9]. Further, SFRM may be locally debonded from the steel [10] during its service life, resulting in further uncertainties in the SFRM layer thickness along with potential loss of SFRM.

This paper presents a sensitivity analysis of the influence of assumed thermal properties and thickness of SFRMs on the predicted steel temperatures in fire. The analysis determined the predominant SFRM parameters that impact the steel temperatures, including cases with holes in the SFRM. For the purpose of these analyses, material test data on the thermal properties of SFRMs reported in the literature were used to determine the reasonable bounds of three variables: the thermal conductivity, volumetric heat capacity, and insulation thickness. Fifteen material models were developed assuming temperature-independent values for the thermal conductivity, volumetric heat capacity, and insulation thickness, the combinations of which were determined by a face-centered central composite experimental design [11]. Finite element (FE) models were developed and analyzed for three structural fire experiments including (1) a furnace test on an insulated column, (2) a compartment fire test on an insulated composite beam, and (3) furnace tests on insulated steel columns with local loss of SFRM. The computational FE modeling approach used in this study has been validated against experimental data in a number of earlier studies, see e.g., Ref. [12]. In addition to these models of structural fire experiments, a fourth FE model was developed for thermal analysis of an insulated composite beam with a localized hole in the SFRM. The motivation for considering this scenario is the use of ID tags on steel beams, which, in practice, may be affixed to the web of the beams using an adhesive. If left in place, these ID tags could prevent adhesion of SRFM at this location, resulting in a hole in the SFRM at the location of the ID tag. This fourth model allowed for examination of the influence of such a hole in the SFRM on the thermal response of a composite beam. Each of the FE models was analyzed using the fifteen different material models from the experimental design, and the influence of the varying properties in those material models was discussed.

Section snippets

Heat conduction equation

The governing equation of heat conduction in a homogeneous solid, with no internal heating source, is given by∇2T=1α∂T∂twhere T is the temperature, t is time, and α=k/(ρc) is the thermal diffusivity, in which k is the thermal conductivity, and ρc is the volumetric heat capacity (ρ is the density and c is the specific heat). Equation (1) shows that heat conduction in solids is influenced by two material properties: the thermal conductivity, k, and the volumetric heat capacity, ρc.

Simple formulae

Material models with temperature-independent thermal properties

Table 2 lists 15 combinations of assumed thermal material properties and corresponding thicknesses of SFRMs (with each combination termed a “Material Model”), determined based on a face-centered central composite experimental design [11]. Dashed lines in Fig. 1, Fig. 4 show the lower and upper bounds of thermal conductivity and volumetric heat capacity, respectively considered in the computational study. In both plots, data below 800 °C predominantly fall within the bounds; the data falling

Statistical analysis of the influence of the thermal properties of SFRM

The values of volumetric heat capacity, thermal conductivity, and thickness factor used in the FE modeling were arranged in a face-centered central composite experimental design to allow assessing the relative importance of those variables on steel temperatures. This was achieved through the development of response surfaces for three response variables:

  • 1.

    Maximum average temperature in the furnace test on insulated steel column [19], Section 3.2

  • 2.

    Maximum lower flange temperature in the compartment

Summary and conclusions

SFRMs are common fire protection materials for structural steels, whose temperature-dependent thermal properties are normally unknown. SFRM material models with equivalent constant thermal properties are widely used in practice. This paper presents a sensitivity analysis of the influence of assumed thermal properties and thickness of SFRMs on the predicted steel temperatures in fire. The analysis determined the predominant SFRM parameters that impact the steel temperatures, including cases with

Disclaimer

Certain commercial entities, equipment, software, or materials may be identified in this document in order to describe an experimental procedure or concept adequately. Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the entities, materials, or equipment are necessarily the best available for the purpose.

CRediT authorship contribution statement

Chao Zhang: Methodology, Software, Validation, Formal analysis, Writing – original draft. Adam Pintar: Formal analysis, Writing – original draft. Jonathan M. Weigand: Methodology, Visualization, Writing – review & editing. Joseph A. Main: Methodology, Writing – review & editing. Fahim Sadek: Conceptualization, Writing – review & editing, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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    • Cited by (1)

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      Citation Excerpt :

      It should be noted that the modeling of bond between SFRM and steel at ambient and fire conditions plays an important role in results. However, due to the limitations of modeling in the current version of the software, it is not possible to consider the debonding, which is why in the technical literature [5,33–39], modeling has been done in the same way and with simplification. Besides, this study is related to two-dimensional models in which modeling of the deboding behavior is not easily done.

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