Figure 8 - uploaded by Yong C Wang
Content may be subject to copyright.
![FE model of a test given by Li and Harmathy [17].](profile/Yong-Wang-115/publication/225669636/figure/fig6/AS:393713864986629@1470880108385/FE-model-of-a-test-given-by-Li-and-Harmathy-17.png)
Source publication
The applicability of using different formulae for calculating the temperature of insulated steel members exposed to natural
fires which include heating and cooling phases has been investigated. The widely referenced ‘Swedish’ fire curves and measured
temperature time curves in real fire tests are adopted to represent different natural fire environm...
Citations
... In the field of fire safety, the historical development of research on structural fire resistance also reflects the development trend from "single physical field analysis" to "multi-physical field coupling analysis". In the past, traditional fire resistance research in civil engineering relied on standard time-temperature curves, and the fire resistance rating of a building component is determined by a standard fire resistance test conducted on an isolated member subjected to the specified time temperature curve [1]. With the development of the last decade, significant progress has been made in structural fire research, and the basis for conducting research based on performance-based analysis in this field has been initially established. ...
A research idea of multi-physics field coupling can be used to solve the structural fire resistance problem. Most of the previous CFD-FEM numerical simulations in structural fire resistance studies apply adiabatic surface temperature (AST) to accurately describe the complex fire analysis boundary conditions, and this methodology belongs to the use of iterative coupling methods to achieve fluid-solid heat transfer coupling. However, there is less application for another direct two-way coupling method. In this paper, a 2.5-meter-high square steel tube column is selected to investigate the thermodynamic phenomena when surrounding by fire plume. Based on CFD code, the thermal-mechanical coupling in fluid domain is firstly realized, and then the fluid-solid thermal coupling is realized by using iterative coupling method (AST method) and direct coupling method (Conjugate heat transfer method, CHT method) respectively, and the accuracy of this two coupling methodology is verified by comparing with experimental data. The heat flux received at the column surface is analyzed in the CHT method while the characteristics of the AST parameters are analyzed in the AST method. Finally, the mechanical analysis is completed with the solid temperature as the boundary condition and the thermal-mechanical coupling in solid domain is realized.
... 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. ...
... Simple formulae are provided in structural fire design codes for predicting the steel temperatures of uniformly insulated steel members in fire [12]. These formulae are derived from a condensed 1-dimensional (1-D) heat transfer model based on the lumped heat capacity method assuming a uniform temperature within the steel section [13]. ...
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.
... Based on experimental investigations, analytical (Usmani et al. 2001;Huang and Tan 2003) and numerical (Choi 2008;Zhang et al. 2012Zhang et al. , 2013) studies were carried out, and various computational models were proposed to predict the thermal and mechanical responses of steel beams and columns in fire, including the spatial and temporal temperature distributions and structural deflections. ...
This paper presents high temperature measurements using a Brillouin scattering-based fiber optic sensor and the application of the measured temperatures and building code recommended material parameters into enhanced thermomechanical analysis of simply supported steel beams subjected to combined thermal and mechanical loading. The distributed temperature sensor captures detailed, nonuniform temperature distributions that are compared locally with thermocouple measurements with less than 4.7% average difference at 95% confidence level. The simulated strains and deflections are validated using measurements from a second distributed fiber optic (strain) sensor and two linear potentiometers, respectively. The results demonstrate that the temperature-dependent material properties specified in the four investigated building codes lead to strain predictions with less than 13% average error at 95% confidence level and that the Europe building code provided the best predictions. However, the implicit consideration of creep in Europe is insufficient when the beam temperature exceeds 800°C.
... Fig. 5 compares the Eq. 8 prediction against the finite element method (FEM) calculated average temperatures of bare steel I sections when all sides are exposed to the standard ISO 834 fire. In previous work [9], the FEM was successfully used to predict the temperature of steel members in a fire test. Table 1 lists the investigated sections and their section factors. ...
... Consider Fig. 3, by interpreting T 1 as the fire temperature (Dirichlet boundary condition), R 1 as the thermal resistance of the insulation (R in ) and R 2 as the thermal resistance of the steel, from Eq. 7 we get the requirement for applying the lumped heat capacity method for uniformly insulated steel members, (9) 3.2.5. Temperature of uniformly insulated steel members-In the Eurocode [8], the average steel temperature of uniformly insulated steel sections is calculated from (10) with (11) where c i , ρ i are the specific heat and density of the insulation, respectively; and d i is the thickness of the insulation. ...
... As a result, the temperature of a component depends on the heating mechanism of the compartment (and also on the location of the component). However, as shown in Fig. 13, in the current approach to calculate the temperature of a component in a fire compartment, a fire curve is first derived from the one zone model, and then the curve is used to calculate the temperature of the component [9]. Since the heat sink effect of the component is not considered in the one zone model, the current approach over-predicts the temperature of the component [13]. ...
Structural fire engineering (SFE) is a relatively new interdisciplinary subject, which requires a comprehensive knowledge of heat transfer, fire dynamics and structural analysis. It is predominantly the community of structural engineers who currently carry out most of the structural fire engineering research and design work. The structural engineering curriculum in universities and colleges do not usually include courses in heat transfer and fire dynamics. In some institutions of higher education, there are graduate courses for fire resistant design which focus on the design approaches in codes. As a result, structural engineers who are responsible for structural fire safety and are competent to do their jobs by following the rules specified in prescriptive codes may find it difficult to move toward performance-based fire safety design which requires a deep understanding of both fire and heat. Fire safety engineers, on the other hand, are usually focused on fire development and smoke control, and may not be familiar with the heat transfer principles used in structural fire analysis, or structural failure analysis. This paper discusses the fundamental heat transfer principles in thermal calculation of structures in fire, which might serve as an educational guide for students, engineers and researchers. Insights on problems which are commonly ignored in performance based fire safety design are also presented.
... Many researchers have conducted substantial research on the development of simple formulas for predicting temperatures in insulated steel members exposed to fire. Detailed descriptions and assessments of these formulas can be found elsewhere, such as Wong and Ghojel (2003), Zhang et al. (2012) and Banerjee (2013). 1 However, such formulas were mostly obtained by solving a simplified 1D heat transfer problem based on the "lumped heat capacity method." That is, the temperatures inside the steel section are assumed to be uniform and the temperature difference between the fire and the insulation surface is ignored (Carslaw and Jaeger 1995;Wang et al. 2005;Zhang et al. 2012;Banerjee 2013). ...
... Detailed descriptions and assessments of these formulas can be found elsewhere, such as Wong and Ghojel (2003), Zhang et al. (2012) and Banerjee (2013). 1 However, such formulas were mostly obtained by solving a simplified 1D heat transfer problem based on the "lumped heat capacity method." That is, the temperatures inside the steel section are assumed to be uniform and the temperature difference between the fire and the insulation surface is ignored (Carslaw and Jaeger 1995;Wang et al. 2005;Zhang et al. 2012;Banerjee 2013). The lumped heat capacity method is appropriate for steel because of its high thermal conductivity but is inappropriate for insulated RC members primarily for two reasons: (1) the temperature gradient in a concrete section is often significant (i.e., the temperature is significantly nonuniform over the section), and (2) the temperature difference between the fire and the insulation surface is significant and cannot be ignored. ...
Fire safety is a significant concern for fiber-reinforced-polymer (FRP)–strengthened RC structures, particularly for indoor applications. To satisfy fire resistance requirements, fire insulation layers may be provided to protect FRP-strengthened RC members. This paper presents a simple, design-oriented method for predicting temperatures in insulated FRP-strengthened RC members under standard fire exposure. The proposed method consists of two sets of formulas: one set for predicting temperatures in unprotected FRP-strengthened
RC members exposed to a standard fire; and another set to convert a fire insulation layer into an equivalent concrete layer. As a result, an insulated FRP-strengthened RC member can be analyzed as an unprotected RC member with an enlarged section for which a similar simple method has previously been established by these authors. In the present study, a finite element (FE) approach for the temperature analysis of insulated FRP-strengthened RC members was first developed and then verified using existing test data. Then the verified FE approach was employed in a parametric study to generate extensive numerical data, on which the second set of formulas were established. The proposed temperature prediction method is shown to provide accurate predictions of both FE results and test data of insulated FRP-strengthened RC members.
... Not only are prone to various types of buckling (local, distortional and global), they also have non-uniform temperature distributions in the cross-section due to fire exposure from one side (Fig. 2) and the presence of the gypsum plasterboards and interior insulation. Whilst fire resistant design methods for hot-rolled members [1,4], including allowing for natural (parametric) fire conditions, are well established, the development for design methods for thinwalled members in fire is still at a relatively early stage. ...
... Not only are prone to various types of buckling (local, distortional and global), they also have nonuniform temperature distributions in the cross-section due to fire exposure from one side ( Figure 2) and the presence of the gypsum plasterboards and interior insulation. Whilst fire resistant design methods for hotrolled members [1,4], including allowing for natural (parametric) fire conditions, are well established, the development for design methods for thin-walled members in fire is still at a relatively early stage. Evaluating fire resistance of a structural member includes obtaining temperature distributions in the crosssection first and then calculating the structural load-bearing capacity at elevated temperatures. ...
... Many researchers have conducted substantial research on the development of simple formulas for predicting temperatures in insulated steel members exposed to fire. Detailed descriptions and assessments of these formulas can be found elsewhere, such as Wong and Ghojel (2003), Zhang et al. (2012) and Banerjee (2013). 1 However, such formulas were mostly obtained by solving a simplified 1D heat transfer problem based on the "lumped heat capacity method." That is, the temperatures inside the steel section are assumed to be uniform and the temperature difference between the fire and the insulation surface is ignored (Carslaw and Jaeger 1995;Wang et al. 2005;Zhang et al. 2012;Banerjee 2013). ...
... Detailed descriptions and assessments of these formulas can be found elsewhere, such as Wong and Ghojel (2003), Zhang et al. (2012) and Banerjee (2013). 1 However, such formulas were mostly obtained by solving a simplified 1D heat transfer problem based on the "lumped heat capacity method." That is, the temperatures inside the steel section are assumed to be uniform and the temperature difference between the fire and the insulation surface is ignored (Carslaw and Jaeger 1995;Wang et al. 2005;Zhang et al. 2012;Banerjee 2013). The lumped heat capacity method is appropriate for steel because of its high thermal conductivity but is inappropriate for insulated RC members primarily for two reasons: (1) the temperature gradient in a concrete section is often significant (i.e., the temperature is significantly nonuniform over the section), and (2) the temperature difference between the fire and the insulation surface is significant and cannot be ignored. ...
Fire insulation layers are often provided to protect fiber-reinforced polymer (FRP)-strengthened RC members. For the fire resistance evaluation of these insulated members, accurate prediction of temperatures in the member under fire is a pre-requisite. Although for a given fire insulation scheme, the temperature analysis can be conducted using a finite-difference (FD) or finite element (FE) procedure, a much simpler, approximate method is highly attractive for practical design purposes. This paper presents such an approximate design-oriented method for predicting temperatures in insulated FRP-strengthened RC members under a standard fire exposure. The proposed method consists of two sets of formulae: (1) a set of formulae for predicting temperatures in un-protected RC members exposed to a standard fire; and (2) a set of formulae through which the fire insulation layer is converted into an equivalent concrete layer; the latter is expressed as a function of the thickness and the thermal properties of the insulation layer. As a result, the temperature analysis of insulated FRP-strengthened RC members becomes that of un-protected RC members with enlarged sectional dimensions. The accuracy of the proposed method is demonstrated through comparisons with results of existing standard fire tests.
... ECCS [19], CECS [20]. Those simple formulae are, however, only applicable to situations where the properties of the insulation materials are or can be treated as constant or temperatureindependent [21]. This paper intends to develop a simple procedure to determine the equivalent constant thermal resistance of intumescent coatings for calculating the limiting temperatures by simple formulae. ...
... 3. Equivalent Thermal Resistance of Intumescent Coatings Figure 2 shows the one-dimensional (1D) heat transfer model used for calculating the temperature of steel members insulated by coatings [21,22]. Due to its high conductivity, the temperature gradient within the steel section has been ignored in the model. ...
... Ignoring the heat absorbed by the insulation materials, by energy balance the steel temperature can be calculated by [21] 534 Fire Technology 2012 ...
Intumescent coatings are now the dominant passive fire protection materials used for steel construction. Intumescent coatings
will react at high temperatures and the thermal properties of intumescent coatings can not be measured directly by the current
standard test methods which are originally designed for the traditional inert fireproofing materials. This paper proposed
a simple procedure to assess the fire resistance of intumescent coatings by using the concept of equivalent constant thermal
resistance. The procedure is based on the approximate formula for predicting the limiting temperatures of protected steel
members subjected to the standard fire. Test data from investigations on both small-scale samples and full-scale steel members
are used to calculate the equivalent constant thermal resistance. Using the equivalent constant thermal resistance of intumescent
coatings, the calculated steel temperatures agree well with the test data in the range of the limiting temperatures from 400°C
to 600°C. The procedure needs no complex computation and is recommended for practical usage. The equivalent constant thermal
resistance could be used to quantify the insulation capacity of intumescent coatings.
KeywordsIntumescent coatings–Fire resistance–Equivalent constant thermal resistance–Simple method–Limiting temperatures–Steel members
