CC BY
25SUBSTANTIATION OF THE SIMPLIFIED METHOD OF EVALUATION OF FIRE RESISTANCE OF
PROTECTED STEEL STRUCTURES
Dobrostan O.
PhD, the Head of Scientific Testing Center Ukrainian Civil Protection Research Institute
Drizhd V.
PhD, Vice Head of the Science of Research and Production Enterprise "Spetsmaterialy"
Shkarabura I.
Postgraduate student, Chair of Fire Tactics and Emergency Rescue Works Cherkasy Institute of Fire Safety named after Chornobyl Heroes of National University of Civil Defence of Ukraine
Maladyka I.
PhD, Docent, The Head Faculty of Operational and Rescue Forces Cherkasy Institute of Fire Safety named after Chornobyl Heroes of National University of Civil Defence of Ukraine
Abstract
For the assessment of fire resistance of protected steel structures, European methods are used, which are given in standards EN 13381-4: 2013 and EN 13381-8: 2013. The practical implementation of these methods requires considerable material costs, in particular, the need for the use of special fire furnaces with equipment for loading steel structure specimens and the creation of a large number of standardized specimens. Therefore, it is important to develop a simplified method, and why this research is dedicated. The substantiation of the test procedures, the parameters of the test specimens (their number, shape, cross-section coefficient, thickness of the fire protection system) and the critical values of the critical temperature of steel for a simplified method of evaluating the fire resistance of protected steel structures are given in the article. It is shown that it is expedient to use steel columns with a height of 2.0 m of the I-section of profile No. 20 according to DSTU 8768, which have the highest value of the cross-section coefficient. The critical temperature range of steel is set from 350 °C to 500 °C, for which the simplified method should calculate the minimum thickness of the fire protection system. The choice of such a range is justified by the acceptable difference between the results of the fire resistance rating of the protected steel structures, obtained taking into account and without taking into account the performance of the fire retardant system and (or) its ability to remain intact during fire exposure. The values of the minimum thickness of the coating layer (plaster) made of flame retardant material "Endotherm 210104", which provide normalized classes of fire resistance of steel structures obtained by a simplified method. It is shown that for steel structures with a cross-sectional ratio of significantly less than 294 m-1 are presented, the values of the minimum thickness of the fire protection system will be substantially smaller (by tens of percent) than those obtained by the simplified method.
Keywords: fire resistance, critical steel temperature, fire rating, fire protection system, simplified method, steel structure, standard
1. Introduction
European standards EN 13381-4 [1] and EN 13381-8 [2] establish test methods for determining the effect of passive and reactive fire protection systems on the fire resistance of protected steel structures that can be used as beams or columns. These methods make it possible to determine values of the minimum thickness of the fire protection system for a wide range of cross section coefficient of steel profile and critical (design) steel temperature, under which the normalized fire resistance classes of these steel structures are provided. However, the practical implementation of these methods requires significant material costs associated, in particular, with the need to use special furnaces with equipment for loading specimens of steel structures and to create a large number of standardized specimens (steel columns and beams lined with flame retardant materials). more than 200 thermocouples should be installed.
When assessing the fire resistance of steel structures at the stage of designing a fire protection system, as well as the operation of buildings, the use of such European methods is not always acceptable. At
this stage, it is advisable to apply a method that requires significantly less material costs than the above methods and provides acceptable reliability of the results of the evaluation of the fire resistance of steel structures. Considering this, it is important to consider the research aimed at further improvement and development of methods of assessment of fire resistance of steel structures, in particular, to the development of a simplified method, acceptable for structures with passive and reactive fire protection systems.
2. Literature Data Analysis and Problem Statement
When tested by European methods [1, 2], a certain number of steel structures of the I-profile (I or H) and (or) voids protected by the fire protection system are subjected to fire exposure under the standard temperature regime. Short unloaded columns and beams (1.0 m in size) and loaded columns (3.0 m high) and beams (4.0 m long), and an extra high column (2.0 m in size) are applied for reactive fire protection systems. The number of steel structures to be tested and their parameters depend on the scope of evaluation. In particular, when evaluating the fire resistance of steel
structures with reactive fire protection systems, the number of these samples can be from 15 to 43. During the tests, the temperature values of the steel structure samples for different duration of fire exposure according to the standard temperature regime are measured. The results of comparing the values of the temperature on the loaded and unloaded samples determine the correction factor. This factor determines the difference in the ability of the fire retardant system to clutch and (or) the ability to remain intact during fire exposure when applied to laden and unladen steel structures. Using this coefficient, experimental data on the temperature of short structures is corrected. According to these corrected data, one of the estimation methods given in the above European standards determines the values of the minimum thickness of the fire protection system at which the temperature of the steel structures does not exceed the value of the critical temperature of the steel for the normalized duration of the fire action (fire resistance class).
Studies of the limits of application and accuracy of these methods of assessment, carried out using the method of computational experiment, found that all these methods allow to determine the values of the minimum thickness of the fire protection system, which provide normalized classes of fire resistance of steel structures [3]. At the same time, these thickness values are significantly overestimated relative to the true (exact) values determined by the method of computational experiment, in the case of their calculation by the method of numerical regression. The standard deviation of the calculated values from the exact thickness values for the numerical regression method reaches 190%. For the other two estimation methods given in the European standards [1, 2], which are based on the solution of the non-stationary thermal conductivity equation, this standard deviation does not exceed 43 %.
In [4, 5], the results of studies of the convergence of data on the minimum thickness of the fire protection system obtained by different methods of estimation are presented. In addition to the assessment methods given in European Standards [1, 2], these studies used a method based on the solution of the inverse heat conduction problem, which is implemented in the national standard of Ukraine DSTU B B.1.1-17 [6]. Experimental data on the temperature of specimens of steel structures obtained with the use of passive and reactive fire protection systems were used in the studies. The results of these studies show that the greatest deviations in the thickness of the flame retardant occur when comparing the calculated data obtained by the numerical regression method with the values determined by the method based on the solution of the inverse heat conduction problem. The standard deviation of this data reaches 94%. At the same time, for the estimation methods based on the solution of the non-stationary thermal conductivity equation [1, 2], the standard deviation does not exceed 80%. The values of this deviation for the reactive flame retardant system are much greater (two or more times) than for the passive flame retardant system used in the studies.
The standard deviation of this data reaches 94%.
At the same time, for the estimation methods based on the solution of the non-stationary thermal conductivity equation [1, 2], the standard deviation does not exceed 80%. The values of this deviation for the reactive flame retardant system are much greater (two or more times) than for the passive flame retardant system used in the studies. In some methods, such as [7-9], such a procedure is not used, tests are carried out without mechanical loading of the samples and without taking into account the ability of the fire retardant system to clutch and (or) its ability to remain intact during fire exposure.
In works [10, 11], the data on the difference between the results of fire resistance assessment of protected steel structures, obtained by the methods [1, 2, 6], taking into account the indicators of the ability of the fire protection system to grip and (or) its ability to remain intact during fire exposure and without taking them into account. It is shown that the difference between the values of the minimum thickness of the fire protection system, determined taking into account and without taking into account these indicators, depends on the value of the cross section coefficient of the steel profile, the critical temperature of the steel and the normalized limit of fire resistance of the steel structure. The dependence of this difference on the cross section coefficient of the steel profile for the passive and reactive flame retardant system investigated is largely monotonic. The difference for most of these dependencies decreases significantly with the increase of the cross section coefficient of the steel profile. The maximum value of this difference for the passive and reactive fire protection systems is 38.7% and 28.0%, respectively. The average difference value for a reactive flame retardant system is insignificantly dependent on the critical temperature of the steel and has a maximum value of 5.5%. For a passive fire protection system with an increase in the critical temperature of the steel, the mean difference increases monotonically and reaches 18.8% at 750 ° C.
In addition to the above test methods [1, 2, 6], in which specimens of steel structures of the I-profile (I or H) and (or) rectangular profile are subjected to heat, methods are used in which samples having a different shape and size are used. [7, 12-15]. In the method [7], square steel plates with a side of 500 mm with a thickness of 5 mm are used. In the method of [12, 13], in addition to these steel plates, 10 mm thick plates are used. In the methods [14, 15], in addition to steel plates with a side of 500 mm and a thickness of 5 mm, square steel plates with a side of 200 mm and a thickness of 5 mm are used. According to the results of studies reported in [16, 17], it is found that the values of the minimum thickness of the reactive fire protection system obtained from the test data of the samples in the form of a plate, are preferably larger than when using samples from the I-T profile. For the passive fire protection system, on the contrary, mostly larger values have the minimum thickness data obtained using two-T-shaped specimens. The difference between the minimum thickness values of the reactive flame retardant system obtained on samples of various shapes reaches 79.0%, and for the passive flame retardant
system - 62.5%. The results of these studies conclude that it is not possible to use plate-shaped specimens to evaluate the fire resistance of protected steel structures of the I-profile for all ranges of the cross-section coefficient of the steel profile and the critical temperature of steel given in [1, 2, 6].
The following conclusions can be drawn from the analysis of methods for evaluating the fire resistance of protected steel structures. The application of European methods [1, 2] requires considerable costs, in particular the cost of designing steel structures and preparing them for testing. These costs can be reduced by reducing the number of test specimens, including by removing specimens of loaded beams and columns. However, to substantiate the possibility of using a method with a reduced number of samples to evaluate the fire resistance of protected steel structures, the results reported in [10, 11] are not enough. Therefore, there is reason to believe that the lack of certainty of the influence of the number of samples for testing and their other parameters on the results of the evaluation of the fire resistance of protected steel structures necessitates research in this direction.
2. The purpose and objectives of the study
The purpose of the study is to substantiate the test
procedures, the parameters of the test specimens (their number, shape, cross-section coefficient, thickness of the fire protection system) and the critical steel temperature limits for a simplified method for evaluating the fire resistance of protected steel structures.
To achieve this, the following tasks have been set:
- to determine the components and procedures of a simplified method for evaluating the fire resistance of protected steel structures using a reduced number of samples (relative to European methods [1, 2]) and not using loaded samples for testing;
- determine the coefficient of cross-sectional samples for testing, and other options, as well as the limit values of the critical temperature of steel in which an acceptable convergence assessment results of fire resistance obtained with and without taking into account the performance ability of the system of fire protection to grip and (or) its ability to remain intact during the fire exposure is achieved;
- to conduct fire resistance assessment of protected steel structures using simplified method (with reduced number of samples and without application of loaded samples).
3. Research Methods and Results and Their Discussion
Analytical and experimental methods have been applied to solve these tasks. Determination of the components and procedures of the simplified method of assessment of fire resistance of protected steel structures was performed on the basis of provisions of European
standards [1, 2] and national standards of Ukraine [79, 18]. The proposed simplified method has two components - experimental and design ones. In the experimental part, the temperature measurements of steel structures samples under fire conditions according to the standard temperature regime are carried out. In the calculation part, according to the obtained experimental data on the temperature of these samples, the values of the minimum thickness of the fire protection system, which provide the normalized classes of fire resistance of steel structures are determined.
In the experimental part, procedures for the manufacture of specimens for testing, the installation of thermocouples on them, the installation and mounting of specimens in the furnace, the measurement of temperature in the furnace and the specimens are used. For the production of samples steel columns with a height of 2.0 m I-section of profile No. 20 according to DSTU 8768 [19] are used. The use of specimens in the form of a plate is impractical because of the significant errors in the results of evaluating the fire resistance of protected steel structures from the I-profile [16, 17]. The choice of such a height of the specimens is justified by the provisions given in DSTU B V.1.1-14 [9] i EN 13381-8 [2]. According to 7.1.2 DSTU B.V.1.1-14 [9] the height of the sample to be tested without loading must be not less than 1,0 m. According to 6.2.4 i 6.2.5 EN 13381-8 [2] unloaded short and tall columns should have a height of 1.0 m and 2.0 m, respectively. The choice of profile № 20 is justified as follows. According to the results of studies presented in [10, 11], it is found that the difference between the values of the minimum thickness of the fire protection system, determined taking into account and without taking into account the indicators of its ability to grip and (or) the ability to remain intact during fire exposure, significantly decreases with increasing the cross section coefficient of the steel profile Am/V, the value of which is determined by the ratio of the surface area Am, that is affected, and the amount of steel V. In particular, in Fig. 1 dependencies of this difference are given dd,mod from the combined thickness of the steel profile V/Am, which is the inverse of the cross-section coefficient and the critical temperature of the steel defined for the passive fire protection system [11]. From this figure it follows that the difference 3d,mod has much smaller values for the small magnitude of the reduced thickness V/Am than for the large size of this thickness. Therefore, the steel structure of the I-section of profile No. 20, which has the least value of the reduced thickness, which is V/Am = 3,4 mm, and the largest value of the cross-section coefficient AJV = 294 m-1 than other structures commonly used in construction are used in test specimens.
Figure 1 Dependences of the difference dd,mod on the combined thickness of the steel profile V/Am and the critical temperature of the steel 0cr, defined for the passive fire protection system and the normalized limit of
fire resistance 240 min 240 min [11]
The set of samples for testing by the simplified method contains four columns of the I-section of profile № 20. Two samples use a system of fire protection that has a minimum thickness, and in other samples - a system of fire protection that has the maximum thickness. The use of identical samples is conditioned by the requirement 7.1.4 DSTU B V.1.1-14 [9].
To measure the temperature of the samples on the metal surface of each sample set three thermocouples. They are located in the middle of the height of the column in the center of the wall and the centers of the inner surfaces of the shelves. Such number and location of thermocouples correspond 8.1.2 DSTU B V.1.1-14 [9]. The temperature measurements are carried out until all critical steel temperatures are reached.
In the calculation part of the simplified method, the obtained experimental data on the average temperature of these samples determine the thickness of the fire protection system, which provides normalized classes of fire resistance of steel structures. The following procedures are applied.
According to the formula (1) [18] the values of the duration of fire exposure (hereinafter - the time tCT) are determined according to the standard temperature regime, by which the critical temperature of steel is achieved on the samples.
tcr = tmes - At, (1)
where tcr - time to reach critical steel temperature,
min;
tmes - the minimum value of the time interval from the start of the test to the critical temperature of the steel, as determined by the average sample temperature, min;
At - error, min.
The error value is determined by the formula [18]:
At = (0,015tmes + 3)(As - Af)/(As - A mm), (2)
where As, Amin - integral values (areas under curves) of standard temperature and minimum allowable temperature in the furnace, according to [18], ° C. min;
Af - the integral value (the area under the curve) average temperature in the furnace during the test, ° C. min.
If Af > As , then it is considered, that At = 0.
Approximation of the data on the time tcr is, is conducted by applying the numerical linear regression equation (3), which establishes the relationship between the time to reach the critical steel temperature and the thickness of the fire protection system, and determine the values of the four constants a0 - a3 of this equation.
tcr = a0 + a dp + a2#cr + a3 dp Ocr , (3)
where dp - thickness of the fire protection system,
mm;
8cr - critical temperature of steel, mm;
ao, ah a2, a3 - constants (regression coefficients).
The acceptability of the obtained values of the constants a0 - a3 is determined by the following procedure. By equation (3), using the obtained values of constants ao - a3, the estimated time values tCT,cul are determined and compared with the time (1). The values of the regression coefficients are considered acceptable by the following criteria:
- for each sample the estimated time tCT,cul should not exceed more than 30 % of experimental time tcr;
- the average value of the difference between the calculated time tcr,cul and the experimental time tcr for each sample should be less than zero;
- a maximum of 20% of all values of the difference between the estimated time tcr,cul and experimental time tcr should be greater than zero.
If the above eligibility criteria are not met, then modification of regression coefficients (value adjustments a0 - a3) is conducted. To do this, a linear modification factor (less than 1.0) is determined, which, when applied to all regression constants, leads to the fact that the estimated time tcr,cul satisfies the eligibility criteria. According to this procedure, which corresponds to G.3.1 of DSTU B V.1.1-17 [6], we
determine the modified regression coefficients, which are used in further calculations.
By the formula (4) the values of the minimum thickness of the fire protection system are determined, which provide normalized classes of fire resistance of steel structures having a cross-sectional ratio of not more than the test specimens.
dP =
tfi,requ a0 a2@ci
(4)
a + a3ecr
where tfi,requ - limit of fire resistance, which corresponds to the normalized fire resistance class of steel structure, min.
Calculations of the minimum thickness of the fire protection system are carried out for the critical steel temperature range from 350 ° C to 500 ° C. The choice of this range was made based on the analysis of the data on the difference 3d mod between the results of the fire
resistance assessment of the protected steel structures, obtained taking into account and without taking into account the indicators of the ability of the fire protection system to grip and (or) its ability to remain intact during fire action. [10, 11]. According to the results of this analysis, it is established that in the range of critical temperature of steel from 350 °C go 500 °C the differencedd,mod has insignificant values, which, in particular, for the passive fire protection system do not exceed 10 % (fig. 2 [11]). In addition, the critical temperature of steel, which is 500 °C, is used in national standards DSTU B B.1.1-4 [18], DSTU B B.1.1-13 [8], DSTU B B.1.1-14 [9] for evaluation of fire resistance of protected steel structures, which is carried out using only unloaded test specimens. The lower limit value of the critical steel temperature range of 350 ° C corresponds to the value given in European and national standards [1, 2, 6, 20, 21].
Figure 2 Dependencies of the minimum value dd,mod,min (1), of maximum value dd,mod,max (2) and average value Sd,mod,avg (3) the difference dd,modfrom the critical temperature of the steel, obtained for the passive fire protection
system [11]
Determination of the minimum thickness of the fire protection system according to the formula (4) is carried out for the critical temperature of steel 350 °C, 400 °C, 450 °C, 500 °C. If the purpose of the evaluation is to determine the minimum thickness of the flame retardant system only for the specific value of the critical steel temperature, e.g., 500 °C [8, 9, 18] or estimated value set according to Eurocode 3 [20, 21], then instead of equation (3) we use an equation in which there are no components a^cr, a3dpda, and instead of formula (4), a formula without components a2&cr, a3dcr. The results of the assessment are applicable to fire protection systems throughout the thickness range of the fire retardant material tested (from minimum to maximum thickness values on test specimens).
According to the simplified method discussed above, the fire resistance of steel structures of an I-
profile with a profiled passive flame retardant system was used, in which a fire-retardant plaster of "Endotherm 210104" fire-retardant material was used [22]. The purpose of this evaluation was to determine the minimum thickness values of the specified flame retardant material for which normalized fire resistance classes of steel structures are provided for a critical steel temperature of 500 °C.
The surface of the test specimens (four steel columns with a height of 2.0 m of the I-section of profile No. 20) was pre-applied with a thickness of 0.05 mm. The thickness of the coating layer (in the dry state) of flame retardant material "Endotherm 210104" [22] was: 28.20 mm for sample No. 1, 28.08 mm for sample No. 2, 39.25 mm for sample No. 3, 38.35 mm for sample No. 4. The experimental data on the average temperature of these samples are shown in Fig. 3.
Figure 3 - Dependences of the average temperature of the samples on the duration offire exposure according to
the standard temperature regime
The results of the approximation of the time data tcr and the modification of the regression coefficients ao, ai, an equation was determined (5), which establishes the relationship between the time of reaching the critical temperature of steel, which is 5oo °C, and the thickness of the coating layer of flame retardant material "Endotherm 210104".
tcr = -47,628 + 5,868^, (5)
where dp - thickness of the coating layer of flame retardant material, mm;
The results of determining the values of the minimum thickness of the coating layer of flame retardant material "Endotherm 210104", which provide the normalized classes of fire resistance of steel structures obtained using equation (5), are given in table i. The data in this table applies to columns and beams, having a cross-sectional ratio of no more than 294 m-1.
Table i
Values of the minimum thickness of the coating layer of flame retardant material "Endotherm 210104",
Fire resistance class of steel structures The minimum thickness of the coating layer dp, mm
R 120 28,56
R 150 33,68
R 180 38,79
Table 2 shows the minimum thickness of the boxlike fire protection system using endotherm 210104 fire-retardant flame retardants [22], defined for the R 120, R 150, R 180 fire resistance classes and the critical
steel temperature of 500 ° C. These data were obtained by the European method by testing ten short columns and four I-beam beams using numerical regression analysis [1].
Table 2
Data on the minimum thickness of the box-shaped fire protection system using endotherm 210104 flame retardant material
Fire resistance class of steel structures R 120 R 50 R 180
The cross-section coefficient AJV, m-1 Minimum thickness of flame retardant dp, mm
50 18,1 22,8 27,4
60 20,8 25,9 31,1
70 23,0 28,6 34,2
80 25,0 30,9 36,9
90 26,7 33,0 39,2
100 28,2 34,7 41,3
110 29,5 36,3 43,1
120 30,7 37,8 44,8
130 31,8 39,0 46,3
140 32,8 40,2 47,6
150 33,7 41,3 48,8
160 34,5 42,2 49,9
170 35,2 43,1 51,0
180 35,9 43,9 51,9
190 36,5 44,6 52,8
200 37,1 45,3 53,6
210 37,6 46,0 54,3
220 38,1 46,6 55,0
230 38,6 47,1 55,7
240 39,1 47,7 56,3
250 39,5 48,1 56,8
Although comparisons of the data in Tables 1, 2 are not entirely acceptable due to the difference in properties (in particular in density) of the flame retardant made from Endotherm 210104 [22] and the flame retardant of the same material, they can be used for such analysis. From table 2 it follows that for the box system, the values of the minimum thickness of fire protection significantly depend on the cross-section coefficient. As it rises from 50 m-1 to 250 m-1 the minimum thickness of the fire protection increases 2.2 times. From this it can be assumed that the values of the minimum thickness of the coating layer (plaster) of the flame retardant material for cross-section coefficients significantly less than 294 m-1 will be significantly smaller (by tens of percent) than those given in Table 1. It means that tests using the simplified method result in obtaining data on the minimum thickness of the fire protection system, which can be inflated by several tens of percent relative to the values obtained by European methods [1, 2]. Such a difference between the results of the tests obtained by the simplified method and the European methods can be considered permissible for determining the data on fire resistance at the stage of development of fire protection systems, as well as the operation of buildings.
However, it should be noted that the study was subjected only to a passive fire protection system using material "Endotherm 210104" [22]. For fire retardant materials of other trademarks, it is possible to exclude the possibility of obtaining results different from those given. Such uncertainty imposes restrictions on the use of the results obtained, which may be interpreted as disadvantages of this study. The inability to remove these limitations in the framework of this study justifies the direction of further research, which, in particular,
can be aimed at assessing the convergence between the values of the minimum thickness of the fire protection system, which provide normalized fire resistance classes of steel structures obtained by the simplified method and European methods [1, 2].
6. Conclusions
A simplified method for evaluating the fire resistance of protected steel structures has been developed, which uses four unloaded steel columns for testing, which is much less than required by European methods [1, 2]. The components and procedures of this simplified method are defined. The values of the sample cross-section coefficient for the tests and their other parameters are substantiated. It is shown that it is advisable to use steel columns with a height of 2.0 m of double-section section of profile No. 20 according to DSTU 8768 [19], which have the highest value of the cross-section coefficient.
The critical temperature range of steel is set from 350 °C to 500 °C, for which the simplified method should calculate the minimum thickness of the fire protection system. The choice of such a range is justified by the acceptable difference between the results of the fire resistance rating of the protected steel structures, obtained taking into account and without taking into account the performance of the fire retardant system and (or) its ability to remain intact during fire exposure.
The minimum thickness of the coating layer (plaster) of the flame retardant material "Endotherm 210104" was established [22], under which the normalized fire resistance classes of steel structures obtained by the simplified method are provided. It is shown that for steel structures with a cross-sectional ratio of significantly less than 294 m-1, the values of the
minimum thickness of the fire protection system will be substantially smaller (by tens of percent) than those obtained by the simplified method.
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