6. Target reliability in case of extreme effects
6.2. Target reliability estimation in case of fire design situation
The appropriate reliability level of structures exposed to fire can be ensured on different ways, using active and/or passive fire safety measures. First of all, as the most obvious case, the structure can be strengthened in order to avoid the failure on high temperature when the strength and stiffness of the material is considered on a reduced value. Passive protection measures, such as intumescent coating, can reduce the temperature of the protected elements. The active protection tools (e.g.
alarm and water extinguish system) result safer solutions by decreasing the possibility of ignition and flashover.
Holickỳ in [64] showed a method for the calculation of optimum reliability on a general example with a few random variables. In [84] a Bayes belief network is presented related to fire design, a simple example and the effectiveness of different safety measures are presented. Within the framework of this research, an investigation defining the target/optimum reliability levels of a tapered steel frame structure is presented where the cost function is formulated similarly to Eq. (6), based on [64]:
( )
f f( )
f ignition fLC x,y C P x,y C C x C y . C P . C
C = ⋅ + 0 + 1⋅ + 2⋅ +001 ⋅ +005 . (41)
Cf, C1 and C2 vary, however reference values are assumed to be as 3 million €, 4,200 € and 27,400
€ (Fig. 6-2, Table 1-2), respectively, for the reference structure. Cf contains direct (e.g. value of stored material or the construction of a new storage hall) and indirect cost components (e.g. missing income or malfunction in production). The typical shape of the function is presented in Fig. 2-2.
The analysed structure is the earlier presented (Fig. 1-1) tapered portal frame structure which is used as a warehouse. The dimensions are selected to be equal to a structure that has been designed by practicing engineers considering 0.2 kN/m2 equipment load. The cost of the superstructure (including the sheeting, purlins and bracing elements) is approximated as C0≈57,000 € (using Table 1-2). The frame is protected by intumescent coating; the appropriate thickness of this passive safety measure is designed on the basis of the section factor and the critical temperature of the element (Fig. 6-2). The intumescent paint of a Hungarian producer [69] is considered in the design process, the thicknesses in Fig. 6-2 are calculated for 30 minutes fire resistance.
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Fig. 6-2 – Calculation details related to prescriptive fire design [BT11]
The considered three fire design cases are the same as the considered design cases within the parametric study (Fig. 7-6): 1) extreme (the combustible material is rubber tire); 2) severe (the combustible material is rubber tire and wood); 3) moderate (the combustible material is wood). With different time demands, namely R30, R45 and R60, altogether 9 cases are investigated. The probability of failure under fire exposure contains the probability of occurrence of two independent events, namely the probability of severe fire and the conditional probability of failure if the severe fire is occurred. Thus the effect of passive and active safety measures can be easily separated in the calculation since the first probability is dependent on the active safety measures (Fig. 6-3), while the second probability depends on the amount of applied passive protection.
Demand\Severity Extreme fire Severe fire Moderate fire
R30 case #1 case #2 case #3
R45 case #4 case #5 case #6
R60 case #7 case #8 case #9
Table 6-3 – Investigated cases
In this investigation the thicknesses of intumescent coating are varied with one amplifier from zero to tenfold value. The conditional probabilities of structural failure have been calculated using developed reliability analysis framework (FORM, Fig. 4-1), a small chance of malfunction of active measures is considered in the network (Fig. 4-4). It has to be noted that in this section, according to Hungarian regulations [71] [72] a minimum active safety measure, namely automatic smoke detection system, is selected.
1
b)
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Fig. 6-3 – Cost and efficiency of different active safety measures including the installation, construction and maintenance for the service life [BT11]
I investigated in an earlier study [BT11] the problem more deeply, regarding to different active safety measures using different assumptions regarding to the consideration of meteorological loads in the reliability analysis, see details in [BT8]. The main conclusions of these studies are the following: a) active safety measures and passive protection have to be applied in order to satisfy the criteria of EC0 (Table 1-1) (Fig. 6-4); b) passive protection without active safety measures is not effective enough when the target reliability is greater than 3.2 – 3.3 (Fig. 6-4); c) the suggested target reliability indices of JCSS seemed to be more appropriate for practically expectable cases.
Fig. 6-4 – Optimal reliability indices for various consequences [BT11]
The resulted target reliability indices of this investigation are presented in Fig. 6-5 for 9 considered cases and for different Cf/Ctot ratios. This ratio for the reference structure is around 30 considering normal design conditions. Because R60 and R45 time demands are more demanding than R30; R60, R45 and R30 demand levels are associated with high, moderate and low relative cost of safety measures, respectively. Using these differentiations, the reliability indices are
0 0.5 1 1.5 2
10−3 10−2 10−1 100
Active safety measures [−]
Conditional probability of flashover [−]
Active safety measure a b c d b+d c+d
Cost [€/m2] 0 25 40 50 75 90
Relative cost of safety
measure 0 0.5 0.8 1.0 1.5 1.8
1 0.25 0.0625 0.02 0.005 0.00125
ignition ignition flashover
ignition flashover
P P
P
⋅
∩ =
ignition flashover P
Scenario:
• a: None of active safety measure is applied
• b: Automatic fire detection and alarm by heat
• c:Automatic fire detection and alarm by smoke
• d: Sprinkler system
• b+d: Sprinkler system + detection by heat
• c+d: Sprinkler system + detection by smoke
( ) . y
I
FL y . e
P =11765 −3755
100 101 102 103 104 105 106
2.5 3 3.5 4 4.5
Cf/(C1+C2)
Target reliability index
EN 0 low consequences
JCSS 0 moderate consequences JCSS 0 minor consequences JCSS 0 large consequences EN 0 high consequences
EN 0 medium consequences
Only passive protection Passive protection + active safety measures
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presented in Table 6-4 (without considering case #3 where the fire is not the leading action) similarly to Table 1-1 using the boundaries of Table 6-2 to differentiate the consequence classes.
However, more accurate values can be read from Fig. 6-5 for a specific design situation. The calculated reliability indices are lower than the suggested values in EC0, they are closer to the recommendations of Joint Committee on Structural Safety [53]. Despite the fact that this conclusion is derived based on analysis of a single storey portal frame structure, the results may be also valid for other type of steel structures because wide range of correlation coefficient and wide range of possible failure consequences are covered. The higher correlation (Fig. 6-5) among the frames may represent the case of a smaller structure with fewer frames or a structure with smaller compartments. In case of higher correlation among the frames the failure probability of the system is lower and higher target indices can be calculated.
Fig. 6-5 – Target reliability indices for various consequences for fire design of example portal frame
The reliability depends on the severity of the fire effect, thus it depends on the function of the building, the quality and the quantity of the combustible material. It has to be noted that β=2.82 reliability index implies that the structure has almost 1.0 conditional failure probability in fire. In these cases the fire effect is too severe and the protection and strengthening of the structure may not be economical. β=2.82 reliability index is a lower bound because the occurrence of flashover is quite rare in the investigated cases [BT11]. For high Cf/Ctot ratios, the curves are flatter than in the case of lower Cf/Ctot ratios because the effectiveness of the intumescent painting is not in linear connection with the layer thickness [BT11]. In Fig. 6-5, from the point where the curves change to horizontal lines, the curves only indicate the values because the optimum thickness amplifiers are out of the investigated range in these cases. The proper target reliability index value should be selected considering the severity of a possible fire event. The application of comparable design
2,8 3 3,2 3,4 3,6
1 10 100 1000
β-target reliability index (ρ=0.4)
Cf/Ctot
1 2 3
4 5 6
7 8 9
2,8 3 3,2 3,4 3,6 3,8
1 10 100 1000
β-target reliability index (ρ=0.9)
Cf/Ctot
1 2 3
4 5 6
7 8 9
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curves (e.g. ISO standard fire curve) may lead inconsistent structural reliability. In case of the investigated example considering both ρ=0.4 and 0.9 correlation coefficients, reliability index β=2.9 – 3.3 may be achieved based on the time demand R45, R30 and R15, respectively, using EC3-1-2 conforming prescriptive design and ISO standard fire curve [BT10]. It means that design based on ISO standard curve is too conservative in case of structures with low failure consequences and it may be unsafe when a possible failure has considerable consequences. The target reliability index may be selected between 2.8 and 3.7 based on the possible failure consequences for industrial steel tapered portal frames with storage function. The presented values are calculated on the basis of Hungarian circumstances, considering the regulations of OTSZ 5.0 and TvMI 5.1.
The presented values may be used later in performance based design, however, further research work is needed in order to extend and validate the suggested numbers and in order to understand better the components of failure costs (Cf). The target reliability indices may be also influenced by the acceptance ability of the society and global economy of the country, so in some cases minimum limits may be used in order to ensure the minimum desired safety.
50 years service life: calculated
Relative cost of safety measure Minor consequences
Moderate consequences
Large consequences High – Severe fire 2.8 (2.8 – 2.9) 2.8 – 3.0 (2.8– 3.1) 2.8 – 3.2 (2.8 – 3.4) Moderate – Medium fire 2.8 (2.8 – 3.0) 2.8 – 3.2 (2.8 – 3.3) 2.8 – 3.5 (3.0 – 3.6) Low – Minor fire 2.8 (2.8 – 3.0) 2.8 – 3.3 (2.8 – 3.4) 3.2 – 3.5 (3.2 – 3.7) Table 6-4 – Calculated target reliability indices for industrial steel tapered portal frame considering ρ=0.4 and
ρ=0.9 correlation among the frames