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Fire resistance of composite slim floor beams
Journal of Constructional Steel Research 54 (2000) 345–363 www.elsevier.com/locate/jcsr
Fire resistance of composite slim floor beams Pentti Ma¨kela¨inen *, Zhongcheng Ma Laboratory of Steel Structures, Helsinki University of Technology, P.O. Box 2100, FIN-02015 Hut, Finland Received 1 March 1999; received in revised form 5 August 1999; accepted 7 September 1999
Abstract There is an increasing interest in the steel-concrete composite slim floor construction in the Nordic Countries and the UK. The slim floor beams, which are partly contained within the floor slab, have inherent good performance under fire. At the moment, a new type of slim floor beam is under development in Finland. In this paper, the thermal and structural performance of this new slim floor beam is investigated under fire by using numerical analysis programs. The temperature analysis and calculations of the load-bearing capacity are carried out under fire conditions (both ISO standard fire and natural fire) according to Eurocode 1 Part 2.2. The structural fire resistance behaviour of this new slim floor beam is investigated and the relationship between the fire resistance time and load ratio under ISO standard fire is discussed. Moreover, the minimum load ratio of the beam under a natural fire is analyzed. The critical relationship between the minimum load ratio and the fire parameters (opening factor and fire load density) is also established, provided that the structural failure is caused by a reduction in the flexural capacity of the fire-exposed beam. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Temperature analysis; Fire resistance; Slim floor beam
1. Introduction In recent years, an increasing interest has been shown in the Nordic countries and the UK in developing and designing shallow floor systems in steel-framed buildings. In the shallow floor system, the steel beam is contained within the depth of the precast concrete floor or composite slab with profiled steel decks. This form of construc* Corresponding author. Tel.: +358-9451-3780; fax: +358-9451-5019. E-mail address: [email protected] (P. Ma¨kela¨inen) 0143-974X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 9 7 4 X ( 9 9 ) 0 0 0 5 9 - 0
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Nomenclature Af At c di e h Kint K0 Ki Mu Ms Mh Ml O q qf R Rcr Ri T Tg Ts √rlc a e j f l r s
floor area of enclosure (m2) total surface area of enclosure (m2) specific heat (J/kgK) centroid distance (mm) specific volumetric enthalpy (J/m3) distance of plastic neutral axis to the top side of floor slab (mm) interface thermal resistance coefficient (W/m2K) thermal conduction term (W/m2K) thermal conduction term (W/m2K) plastic bending moment capacity of composite cross-section (kNm) sagging bending moment capacity of composite beam (kNm) hogging bending moment capacity of composite beam (kNm) applied bending moment of simply supported beam (kNm) opening factor (m1/2) heat input rate per unit area (W/m2) fire load density per unit floor area (MJ/m2) load ratio critical load ratio thermal resistance term (m2K/W) temperature (°C) fire temperature (°C) surface temperature of structural component (°C) thermal property of enclosure boundary (J/m2s1/2K) convection coefficient (W/m2K) resultant emissivity coefficient volume ratio of moisture content in concrete diameter of reinforcement bar (mm) thermal conductivity (W/mK) material density (kg/m3) Stephan-Boltzmann constant, s=5.67×10⫺8 W/m2K 4
tion achieves a minimum depth of building and the flat floor is beneficial because the building services can be run in any direction. Structurally, the shallow floor system has inherent good fire resistance by virtue of the partial encasement of the steel section. The shallow floor can be designed using various forms of steel beams comprising either of rolled or welded sections. The word “slim floor” is used in the Nordic countries and the UK for this type of construction. Some examples of shallow floor beam sections are shown in Fig. 1. One of the original slim floor concepts developed in Scandinavia was the “Thorbeam” (Fig. 1a), which consists of two channel sections welded to a flat plate.
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Fig. 1.
347
Different types of slim floor beams.
Additional angles are welded to the top flanges to provide the shear connection. British Steel plc and the Steel Construction Institute (SCI) have developed a Slimflor beam (Fig. 1c), which consists of a universal column section welded to a steel plate. Recently, interest has been concentrated on the asymmetric hot-rolled steel beam (Fig. 1d) in the UK, and on the asymmetric welded steel beam in Finland. In Finland, a new asymmetric slim floor beam is under development. The objective is to develop a new section shape for the slim floor beam, which is suitable to apply to the present Finnish composite deck. In this paper, the fire resistance of the new slim floor beam is investigated both in ISO standard fire and natural fire situations.
2. Section shape of the new slim floor beam The section shape of the slim floor beam is illustrated in Fig. 2. The depth of the floor slab is 300 mm and the height of the profiled steel deck is 117 mm (Rannila 120). The steel beam consists of three plates welded together. The web plate is welded to the bottom and top flange by using the submerged arc welding method. The new asymmetric steel beam has a relatively thin top flange with a thickness of 10 mm and a web with a thickness of 20 mm. The bottom steel flange is 18 mm thick and 400 mm wide. The height of the steel beam is 258 mm. The new floor system has a concrete slab depth of 183 mm over the steel deck, which is demanded by the sound insulation requirements. The section gives an efficient fire resistance to the floor system. This is presented in Section 4.
3. Temperature analysis The thermal response of the new slim floor beam in fire is analyzed using the computer program, TACS-FIR (Temperature Analysis of Composite Structures Exposed to FIRe), which is a two-dimensional finite difference program developed
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Fig. 2.
Section shape of the new slim floor beams.
in the Laboratory of Steel Structures at Helsinki University of Technology [1]. The moisture content of concrete can be analyzed and the interface resistance of heat transfer between concrete and steel can be modelled with this program. The material properties of concrete and steel (thermal and mechanical) are temperature dependent. The fire temperature-time curves can be chosen according to the ISO standard fire or any kind of natural fire. There are several collections of fire temperature-time models and temperature-dependent material properties in this program. In this paper, the thermal and mechanical properties of the steel and concrete are given in accordance with Eurocode 3 Part 1.2 and Eurocode 4 Part 1.2 [2,3], and the fire temperature-time curve for natural fire is according to the Annex B of Eurocode 1 Part 2.2 [4]. 3.1. Heat transfer model The transient heat transfer equation based on Fourier Law is given as ⫺ⵜT(lⵜT)⫹e˙⫽0
(1)
where T is the temperature (°C), l is the thermal conductivity matrix (W/mK), e˙ =de/dt is the rate of specific volumetric enthalpy change. The gradient operator ⵜ is defined as ⵜ⫽
冋
∂ ∂ ∂ ∂x ∂y ∂z
册
T
(2)
where x, y and z are Cartesian co-ordinates. Superscript T is the transfer operator of the vector.
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By some intermediate transformations, the above equations can be derived as follows (rc⫹rwcwj)·
dT T1−T0 T2−T0 T3−T0 T4−T0 ⫽ ⫹ ⫹ ⫹ dt R1⌬x R2⌬y R3⌬x R4⌬y
(3)
where rc is the volumetric specific heat (J/m3K), rwcw is the volumetric specific heat of water, j is the volume ratio of moisture content. Ti is the temperature of the ith element in the local system (Fig. 3). Ri is the thermal resistance term, which can be given by 1 1 1 Ri⫽ ⫹ ⫹ Ki K0 Kint
(4)
where Ki and K0 are the thermal conduction terms. Kint is the interface resistance coefficient. In [5] the value Kint=50 W/m2K is proposed for the interface coefficient between steel and concrete. This value is also taken for this study. In the case of perfect contact, Kint=⬁ can be presumed. It is assumed in the program that the interface resistance is caused by the water evaporation of water [1]. The heat input rate q is expressed as q⫽es[(Tg⫹273)4⫺(Ts⫹273)4]⫹a(Tg⫺Ts)
(5)
where s is the Stephan-Boltzmann constant, s=5.67×10⫺8 W/m2K 4; e is the resultant emissivity coefficient. Following the work in [6,7], e=0.6 is adopted for the bottom steel flange and e=0.3 for the composite floor. a is the convection factor, which is assumed as 25 W/m2K for the exposed side and as 8 W/m2K for the unexposed side [8].
Fig. 3.
Local system of an internal element.
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3.2. Temperature-time curves of fires The Eurocodes allow the structures to be calculated either under the ISO standard fire or under specified parametric fires. In this paper, the temperature distributions of the new slim floor beam are analyzed both under the ISO standard fire and under the parametric natural fires as defined by Eurocode 1 Part 2.2. The ISO standard fire curve is an idealiszed temperature-time curve, which has only the ascending phase shown by the solid line in Fig. 4. In reality, the temperaturetime curves of fires can vary widely. The two most important factors that determine the fire temperature-time curves are the fire load and the size of openings through which the air can enter. Usually, the fire load is characterized by the fire load density per unit floor area, and the size of opening by the opening factor. Fig. 4 shows how the fire load and the opening factor affect the temperature-time curves, primarily in relation to the intensity and the duration of fire. 3.3. Temperature distribution The analysis program is validated extensively by the two Slimflor test results of the SCI, some composite columns and other types of composite beams [1]. The cross-section of the beam is modelled using a rectangular grid. The division of the slim floor section into cells is shown in Fig. 5. The temperature distribution of the new slim floor beam at 60 minutes under ISO standard fire is illustrated in Fig. 6. It shows that the bottom steel flange has a high temperature (about 750°C on average) and there exists a large temperature difference, around 200°C, between the end and the central point. This phenomenon is caused by the two-way heat input at the end of the bottom steel flange. Within the web, an extremely non-uniform temperature distribution exists due to the encasement of the concrete. The temperature of the steel beam above one quarter of the web depth from the bottom flange is lower than 400°C and the full strength can be expected.
Fig. 4.
Fire temperature-time curves.
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Fig. 5.
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Division of section into cells for temperature analysis.
Fig. 6. Temperature distribution in the new slim floor beam under ISO fire (at 60 minutes). Figures in bold and black shade are for the steel parts. The others are for the concrete parts of the section.
On the top side of the floor, the temperature is less than 50°C and the insulation criterion is certainly satisfied. The temperature development of the steel section is shown in Fig. 7. The curve of point 1 represents the average temperature rise of the bottom steel flange. Within the first 40 minutes, the rate of temperature rise is in the range of 12 to 18°C/min. From 40 to 60 minutes, the average rate of temperature rise is about 8°C/min. The curve of point 2 represents the temperature rise at one quarter of the web depth. Within the 60 minutes duration of ISO fire, the heating rate is in the range of 3 to 8°C/min, which is much lower than that of the bottom steel flange. Fig. 8 illustrates the temperature rise of the steel section under natural fire. The natural fire curve is calculated according to Annex B of Eurocode 1 Part 2.2 (Fig.
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Fig. 7.
Temperature rise in the steel section under the ISO fire.
Fig. 8.
Temperature rise in the steel section under a natural fire.
4). The opening factor O is 0.02 m1/2 and the fire load density qf is 1100 MJ/m2. In practical cases, this curve defines a severe fire scenario. It shows that the average heating rate at the bottom steel flange reaches a value of 20°C/min in the ascending phase and a value of 6°C/min in the cooling phase. At point 2, the average heating rate is 8°C/min and the cooling rate is 2°C/min, respectively.
4. Resistance analysis for the ISO standard fire case The plastic moment capacity of the slim floor beam at elevated temperatures was analyszed by using the moment capacity method. In this method, a full shear connection between steel and concrete is assumed. The division of elements was the same as that in the temperature analysis case. The mechanical properties of steel and concrete under high temperatures are given according to Eurocode 3 and Eurocode 4. The moment capacity Mu can be calculated by
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冘冘 m
353
n
M u⫽
fij⌬xij⌬yijdi
(6)
i⫽1j⫽1
where m and n are the numbers of divisions in the x and y directions, respectively; fij is the concrete or steel strength of the element (i,j); ⌬xij and ⌬yij are the element dimensions; di is the centroid distance of the elements (i,j) from the plastic neutral axis. The Pposition of the plastic neutral axis (p.n.a.) can be obtained by
冘冘 m
n
fij ⌬xij ⌬yij ⫽0
(7)
i⫽1j⫽1
where fij has a positive value in the tensile zone and a negative value in the compressive zone. The tensile strength of the concrete is ignored. The reduced moment capacity of the composite section under fire is described using the concept of load ratio, which is defined as R⫽
Moment capacity in fire Ultimate moment capacity at 20°C
(8)
Fire is regarded in the design philosophy of the Eurocodes as an accidental situation or an accidental action. Therefore, the characteristic values of relevant material properties are adopted in fire design, and the partial safety factors are accordingly assumed as unity (1.0) when the moment capacity under fire conditions is analyzed. The ultimate moment capacity at 20°C is calculated using the partial safety factors presented in Eurocode 4 Part 1.1 [10]. The following factors affecting the fire resistance of the slim floor beam are investigated in this section: 앫 앫 앫 앫
Type of concrete: normal-weight and light-weight Enhanced reinforcement Fire protection of the bottom steel flange Fire resistance of continuous beam using the plastic hinge analysis method
There are two important factors that affect the plastic moment capacity of a slim floor beam: the resistant force of each part of the beam section and the position of the plastic neutral axis. The calculations were also carried out to analyze the contributions of the section parts to the plastic moment capacity in fire. Changing of the plastic neutral axis position in the cross-section under fire with heating time is investigated further. In all the analyses, the effective width of the concrete floor slab is defined as one quarter of the beam span in the sagging region and as triple the width of the upper steel flange in the hogging region. In the hogging moment calculation, the reinforcement bars are taken as f16 c/c 150. Analyses show that the change of hogging reinforcement bars does not have any significant influence on the load ratio in the hogging region. For instance, if the reinforcement bars f16 c/c 50 are used instead of f16 c/c 150, the load ratio is slightly lower, i.e. about 0.05. In this context, the
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“sagging region” means the beam region where the cross-section is subjected to a sagging (positive) bending moment, and the “hogging region” means the region where the cross-section is subjected to a hogging (negative) bending moment. 4.1. Influence of concrete types Fig. 9 represents the relationship between load ratio R and heating time under the ISO fire for normal-weight and light-weight concrete. It shows that the load ratio for lightweight concrete is slightly lower than that for normal-weight concrete. In the sagging region, the load ratio for lightweight concrete and normal-weight concrete at 60 minutes is 0.44 and 0.47, respectively. This small difference is due to the fact that the slim floor beam with a lightweight concrete slab has a higher temperature in the bottom flange of the steel section. This is caused by the bad heat-sinking effect of the lightweight concrete. Fig. 9 also shows the variation of load ratio against heating time both in the sagging and in the hogging region. It shows that the load ratio in the sagging region is much lower than that in hogging region. At 60 minutes, the load ratio in the sagging region and in the hogging region (normal-weight concrete) is 0.47 and 0.73, respectively. 4.2. Influences of enhanced reinforcement and fire protection In the practical cases, the applied load ratio of the beam under fire rarely exceeds 0.6 and values in the range of 0.5 to 0.55 are most common [6]. Analysis of the previous section indicates that the applied load ratio should be lower than 0.47 if a 60-minute fire resistance is desired. Therefore, for the new slim floor beam, some other measures have to be found to obtain a 60-minute fire resistance. Applications of an enhanced reinforcement and fire protection of the bottom steel flange are the efficient measures (Fig. 10) commonly used in practice. Fig. 11 illustrates the influence of enhanced reinforcement on the load ratio (for details of reinforcement see Fig. 10a). At 60 minutes, the load ratio is 0.57 when a reinforcement 2f32 is added.
Fig. 9.
Influence of concrete types on load ratio in the sagging and hogging region.
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Fig. 10.
Fig. 11.
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Enhanced reinforcement and fire protection in the composite section.
Influence of enhanced reinforcement and fire painting on load ratio in the sagging region.
Fig. 11 also illustrates the effect of fire protection in the bottom flange of the steel section. The intumescent fire painting, Nullifire S607 [9], with an allowed minimum thickness of 250 µm was used in the analysis. The details of the fire painting are illustrated in Fig. 10b. As indicated in Fig. 11, the full strength can be obtained at 60 minutes with a load ratio of 0.98, if the fire painting is used, and a load ratio of 0.67 at 90 minutes. 4.3. Plastic hinge analysis of continuous slim floor beam In the common practice, there is interest in designing a moment-resistant connection between the slim floor beam and the column. In this case, the bending resistance of the slim floor beam under fire depends on both the sagging and the hogging moment resistances of the sections. It is assumed that the plastic resistance can be developed in the section and the bending moment capacity can be determined from the following expressions: Internal span: Ms⫹MhⱖMl
(9)
End span: Ms⫹0.45MhⱖMl
(10)
In Eqs. (9) and (10), Ms is the sagging moment resistance, Mh is the hogging moment resistance and Ml is the applied bending moment in a simply supported beam.
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The plastic moment resistance of the continuous slim floor beam is illustrated in Fig. 12. It can be seen that a load ratio value of 0.52 for the end span and that of 0.58 for the internal span can be reached at 60 minutes under an ISO fire. Therefore, a 60-minute fire resistance can be achieved in most cases if the continuity of the slim floor beam is taken into consideration. 4.4. Resistance analysis: contributions of the composite cross-section parts To investigate the contributions of the beam section parts to the fire resistance, the beam cross-section is divided into five parts: bottom steel flange, top steel flange, lower part of web, upper part of web and compression part of the concrete slab cross-section. Here the lower part of the web means the part of web below the plastic neutral axis and the upper part of web is that above the plastic neutral axis. The yield strength of both structural steel and reinforcement steel is 355 N/mm2 and the cube strength of concrete is 30 N/mm2. For the calculations of moment capacity at ambient temperatures, partial safety factors of the material strength of 1.1 for structural steel, 1.15 for reinforcement steel and 1.5 for concrete [10] are used. For the moment capacity calculations under fire, the partial safety factor of the material strength is taken as unity (1.0) for both steel and concrete. In Table 1, the contributions of the beam section parts to the total sagging moment capacity at 60 minutes are compared with those at ambient temperatures. Due to the elevated temperature, the moment capacity contribution of the bottom flange is reduced to 26% from the original value of 59% at ambient temperature. The lower part of web contributes 55% of the total moment capacity under fire while this value is 14% at ambient temperature. It can be seen that the web contributes a major part to the total moment capacity in fire while the bottom flange has a major contribution at ambient temperature. The top flange makes a slight contribution to the moment capacity both at ambient and at elevated temperatures because of its position close to the plastic neutral axis. At 60 minutes under the ISO fire, the concrete above the top steel flange still has a very low temperature (ⱕ60°C) (Fig. 6) and the full strength
Fig. 12. Influence of the slim floor beam continuity on load ratio.
(Numbers in brackets are those for ambient temperature).
650苲870 85苲580 – 50苲80 ⱕ100
Bottom flange Lower part of web Upper part of web Top flange Concrete slab Total moment capacity (kNm)
a
Temperature (°C)
Section parts
227 (189) 121 (90) – (25) 0.6 (55) 32 (60)
Centroid distance from p.n.a. (mm) 399 1555 – 710 2034
(2324) (1162) (323) (646) (2550)
90 (439) 188 (105) – (8) 0.4 (36) 66 (153) 344 (741)
Axial resistance (kN) Moment resistance (kNm)
Table 1 Sagging moment capacity contributions for the section parts under ISO fire (60 minutes)a
26 55 – 0 19
(59) (14) (1) (5) (21)
Percentage of total moment capacity (%)
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can be expected. The contribution by this part to the total moment capacity is approximately 20%. In Table 2, the contributions of the composite section parts to the total moment capacity in the hogging region is analyzed in a similar way to that in the sagging region. In the hogging region, the hogging reinforcement, top steel flange and upper part of the web are in tension. The bottom steel flange, lower part of the web and the concrete near the bottom flange are in compression. At ambient temperature, the compressive parts contribute only 8% to the total moment capacity and the contribution by tensile parts is 92%. However, in fire, the compressive parts contribute 42% and the tensile parts 58% to the total moment capacity, respectively. This is caused by the significant change of the plastic neutral axis position in fire even if the full strength in the tensile parts is remaineds after 60 minutes heating. Fig. 13 illustrates the changing of the plastic neutral axis position during fire. The position of plastic neutral axis (p.n.a.) is referred to as the distance h from the p.n.a. to the top side of the floor slab. In the sagging region, the p.n.a. distance h has a stable value of 100 mm atfor the first 25 minutes, and then it declines rapidly to 65 mm at 40 minutes. After that, the p.n.a. distance h varies slightly with the heating time. This can be interpreted clearly by referring both to Fig. 7 and to the strength reduction of steel at elevated temperatures. After 25 minutes heating, the average temperature of the bottom flange rises uprose to 400°C, where the strength reduction begins. From 25 to 40 minutes, the average temperature of the bottom flange rises up to 600°C at a heating rate of 18°C/min while the material strength of the steel sharply drops to 45% of its original value. Therefore, a rapid decline in the p.n.a. position occurs between 25 and 40 minutes. After 40 minutes heating, the average heating rate of the bottom steel flange is less than 8°C/min. In the hogging region, changing of the p.n.a. distance h is changing similarly to that in the sagging region. The original p.n.a. distance h is about 290 mm, i.e. very close to the upper side of the bottom flange. A rapid change ofin the p.n.a. distance h occurs between 25 and 40 minutes and after that the change becomes more slowlyer. Generally, the p.n.a. distance h in the hogging region varies more significantly than that in the sagging region. One important reason for thatis is the significant reduction in the compression part resistance of the concrete and bottom steel flange at elevated temperature.
5. Resistance analysis for the natural fire cases The Eurocodes give an alternative way of analyzing the fire resistance of structures under specified natural fires. In this section, the structural fire resistance of the new slim floor beam will be investigated under the parametric natural fires defined by Annex B of Eurocode 1 Part 2.2. The major controlling parameters of the natural fires in Euorocde 1 are the opening factor O, fire load density qf and the thermal property of enclosure boundary √rlc. Generally, the effect of the thermal property of the enclosure boundary on the fire temperature is in the range of 10苲20% [11]. Here the thermal property of the
(Numbers in brackets are those for ambient temperature).
30苲40 50苲80 85苲250 250苲580 650苲870 100苲800
Re-bars Upper flange Upper part of web Lower part of web Bottom flange Concrete Total moment capacity (kNm)
a
Temperature (°C)
Section parts
150 115 55 49 129 63
(260) (225) (113) (5) (14) (5)
Centroid distance from p.n.a. (mm) 428 710 781 775 399 795
(372) (646) (1452) (32) (2324) (33)
64 82 43 38 51 50 328
(97) (145) (163) (0.2) (33) (0.2) (438)
Axial resistance (kN) Moment resistance (kNm)
Table 2 Hogging moment capacity contributions for the section parts under ISO fire (60 minutes)a
20 25 13 12 15 15
(22) (33) (37) (0) (8) (0)
Percentage of total moment capacity (%)
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Fig. 13.
Changing of plastic neutral axis position with heating time.
enclosure boundary is taken as 1160 (J/m2s1/2K), which represents a standard compartment. Another factor is the ratio of the floor area Af to the total surface area At. Calculations show that the effect of this factor on the fire temperature according to Annex B of Eurocode 1 Part 2.2 is within the range of 10%, if the ratio Af/At varies between 1:3苲1:8. Here the ratio Af/At is taken as 1:4, which represents a relatively severe situation in the fire compartment. A parametric study iswas performed to investigate the minimum load ratio R with the major controlling parameters of natural fires. These parameters were as follows: 앫 앫 앫 앫
Opening factor O (m1/2): 0.02, 0.06, 0.10, 0.15, 0.20 Fire load density per unit floor area qf (MJ/m2): 275, 550, 825, 1100, 1375 Thermal property √rlc of the enclosure boundary (J/m2s1/2K): 1160 Ratio of floor area to total surface area of enclosure (Af:At): 1:4
Due to the fact that a natural fire curve has both an ascending and a cooling phase, the irreversibility of the material properties of the concrete in the cooling phase has to be taken into account. The strength of the concrete parts depends on the maximum temperature ever attained, and it cannot be recovered during or after the cooling phase. For the steel parts, the strength is dependent on the temperature at the current time. In the cooling phase, the strength of steel can be recovered. Fig. 14 illustrates the variation in load ratio both during the natural fires and an ISO fire in the sagging region. It shows that the load ratio curve has a recovering part in a natural fire while that curve always declines in an ISO fire. There is a minimum load ratio for each parametric natural fire (Fig. 14). The relationship between the minimum load ratio and the fire parameters can be obtained when the moment capacity analyses under different parametric fire curves are carried out. Table 3 illustrates the analysis results of the minimum load ratio and the fire parameters. The minimum load ratio in Table 3 is called “critical load ratio” (Rcr) because the slim floor beam is unsafe during fire if the applied load ratio is higher than the corresponding value in Table 3.
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Fig. 14. Load ratio vs. heating time under two natural fires. Table 3 Critical load ratio of the slim floor beam in the sagging region under natural fires given by opening factor and fire load density Opening factor O (m1/2)
Load ratio
Fire load density qf (MJ/m2)
275 550 825 1100 1375
0.02
0.06
0.10
0.15
0.20
1.16 0.94 0.70 0.56 0.48
1.17 0.99 0.66 0.51 0.43
1.17 1.06 0.70 0.52 0.44
1.17 1.12 0.75 0.57 0.47
1.17 1.13 0.87 0.63 0.50
In practical cases, the opening factor has more significant uncertainty and the fire load density is taken as the major fire parameter in ranking the fire severity in buildings. From Table 3 it can be seen that for a specified fire load density there exists a lowest load ratio corresponding to the most severe fire for all opening factors. Fig. 15 illustrates the relationship between the lowest critical load ratio and the
Fig. 15.
Lowest critical load ratio vs. fire load density.
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fire load density. Generally, the slim floor beam can be used without applied fire protection if the fire load density is lower than 1100 MJ/m2. When the fire load density is 1375 MJ/m2, the lowest critical load ratio is 0.43 for the sagging region.
6. Conclusions There is increasing interest in slim floor construction in the Nordic countries and the UK. At the moment, a new asymmetric slim floor beam is under development in Finland. In this paper, the fire resistance behaviour of the new slim floor beam is investigated. The following conclusions can be drawn on the basis of this study: 앫 A 60 minute fire resistance can be achieved if the applied load ratio for a simply supported beam is lower than 0.47. Otherwise, some additional measures such as an enhanced reinforcement and/or fire protection of the bottom steel flange are required. 앫 Generally, the new slim floor beam can achieve a 60 minute fire resistance without any additional measures, if the moment-resistant beam-to-column connection is reliably designed. 앫 The fire resistance of the slim floor beam is provided mainly by the lower part of the steel web, while the bottom flange loses its resistance under fire. 앫 The fire resistance behaviour of the slim floor beam is also investigated under natural fires defined by Eurocode 1. The results show that the new slim floor beam can be used without any additional measures if the fire load density is less than 1100 MJ/m2, which is rarely exceeded in office and residential buildings [11,12].
Acknowledgements The financial support provided for this research project by the Technology Development Centre of Finland (TEKES), the Finnish Constructional Steelwork Association Ltd (FCSA) and the Finnish companies, Rautaruuki Oyj, PPTH Tera¨s Oy and Deltatek Oy is gratefully acknowledged by the authors.
References [1] Ma Z, Ma¨kela¨inen P. Temperature analysis of composite structures exposed to fires — TACS-FIR. Helsinki University of Technology, Espoo: Laboratory of Steel Structures Publications 10, 1999. [2] ENV 1993-1-2, Eurocode 3, Design of Steel Structures, Part 1.2: General Rules — Structural Fire Design. CEN/TC250/SC3, Brussels, September 1995. [3] ENV 1994-1-2, Eurocode 4, Design of Composite Steel and Concrete Structures, Part 1.2: Structural Fire Design. Final edited version/CEN/TC250/SC4, Brussels, November 1993. [4] ENV 1991-2-2, Eurocode 1, Basis of Design and Actions on Structures, Part 2.2, Actions on Structures Exposed to Fire. Final edited version/CET/TC250/SC1, Brussels, November 1994.
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[5] Newman GM. Fire resistance of slim floor beams. Journal of Constructional Steel Research 1995;33(1-2):87–100. [6] Lawson RM, Mullett DL, Rackham JW. Design of asymmetric slimflor beams using deep composite decking. The Steel Construction Institute, Publication P175, 1997. [7] Schleich JB. Fire safety, design of composite columns. Presented at the International Conference on Fire Safe Steel Construction: Practical Design, Luxembourg, April 1984. [8] Both C, Fellinger JHH, Twilt L. Shallow floor construction with deep composite deck: from fire tests to simple calculation rules. Heron 1997;42(3):145–58. [9] Nullifire S607 — fire painting, Certified directions for use (in Finnish), TRY-18-1996, Helsinki, 1996. [10] ENV 1994-1-1, Eurocode 4, Design of Composite Steel and Concrete Structures, Part 1.1: General Rules and Rules for Buildings. Final edited version/CEN/TC250/SC4, Brussels, November 1993. [11] CIB W14, Design Guide — Structural Fire Safety. Fire Safety Journal 1986;9:77-136. [12] Schleich J-B. Global fire safety concept for buildings: connection to ECSC research, ECCS developments and CEN standardization. In: Proceedings of International Conference on Steel and Composite Structures, Delft, The Netherlands, 1999:8.1–8.26.
Fire resistance of composite slim floor beams Pentti Ma¨kela¨inen *, Zhongcheng Ma Laboratory of Steel Structures, Helsinki University of Technology, P.O. Box 2100, FIN-02015 Hut, Finland Received 1 March 1999; received in revised form 5 August 1999; accepted 7 September 1999
Abstract There is an increasing interest in the steel-concrete composite slim floor construction in the Nordic Countries and the UK. The slim floor beams, which are partly contained within the floor slab, have inherent good performance under fire. At the moment, a new type of slim floor beam is under development in Finland. In this paper, the thermal and structural performance of this new slim floor beam is investigated under fire by using numerical analysis programs. The temperature analysis and calculations of the load-bearing capacity are carried out under fire conditions (both ISO standard fire and natural fire) according to Eurocode 1 Part 2.2. The structural fire resistance behaviour of this new slim floor beam is investigated and the relationship between the fire resistance time and load ratio under ISO standard fire is discussed. Moreover, the minimum load ratio of the beam under a natural fire is analyzed. The critical relationship between the minimum load ratio and the fire parameters (opening factor and fire load density) is also established, provided that the structural failure is caused by a reduction in the flexural capacity of the fire-exposed beam. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Temperature analysis; Fire resistance; Slim floor beam
1. Introduction In recent years, an increasing interest has been shown in the Nordic countries and the UK in developing and designing shallow floor systems in steel-framed buildings. In the shallow floor system, the steel beam is contained within the depth of the precast concrete floor or composite slab with profiled steel decks. This form of construc* Corresponding author. Tel.: +358-9451-3780; fax: +358-9451-5019. E-mail address: [email protected] (P. Ma¨kela¨inen) 0143-974X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 9 7 4 X ( 9 9 ) 0 0 0 5 9 - 0
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Nomenclature Af At c di e h Kint K0 Ki Mu Ms Mh Ml O q qf R Rcr Ri T Tg Ts √rlc a e j f l r s
floor area of enclosure (m2) total surface area of enclosure (m2) specific heat (J/kgK) centroid distance (mm) specific volumetric enthalpy (J/m3) distance of plastic neutral axis to the top side of floor slab (mm) interface thermal resistance coefficient (W/m2K) thermal conduction term (W/m2K) thermal conduction term (W/m2K) plastic bending moment capacity of composite cross-section (kNm) sagging bending moment capacity of composite beam (kNm) hogging bending moment capacity of composite beam (kNm) applied bending moment of simply supported beam (kNm) opening factor (m1/2) heat input rate per unit area (W/m2) fire load density per unit floor area (MJ/m2) load ratio critical load ratio thermal resistance term (m2K/W) temperature (°C) fire temperature (°C) surface temperature of structural component (°C) thermal property of enclosure boundary (J/m2s1/2K) convection coefficient (W/m2K) resultant emissivity coefficient volume ratio of moisture content in concrete diameter of reinforcement bar (mm) thermal conductivity (W/mK) material density (kg/m3) Stephan-Boltzmann constant, s=5.67×10⫺8 W/m2K 4
tion achieves a minimum depth of building and the flat floor is beneficial because the building services can be run in any direction. Structurally, the shallow floor system has inherent good fire resistance by virtue of the partial encasement of the steel section. The shallow floor can be designed using various forms of steel beams comprising either of rolled or welded sections. The word “slim floor” is used in the Nordic countries and the UK for this type of construction. Some examples of shallow floor beam sections are shown in Fig. 1. One of the original slim floor concepts developed in Scandinavia was the “Thorbeam” (Fig. 1a), which consists of two channel sections welded to a flat plate.
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Fig. 1.
347
Different types of slim floor beams.
Additional angles are welded to the top flanges to provide the shear connection. British Steel plc and the Steel Construction Institute (SCI) have developed a Slimflor beam (Fig. 1c), which consists of a universal column section welded to a steel plate. Recently, interest has been concentrated on the asymmetric hot-rolled steel beam (Fig. 1d) in the UK, and on the asymmetric welded steel beam in Finland. In Finland, a new asymmetric slim floor beam is under development. The objective is to develop a new section shape for the slim floor beam, which is suitable to apply to the present Finnish composite deck. In this paper, the fire resistance of the new slim floor beam is investigated both in ISO standard fire and natural fire situations.
2. Section shape of the new slim floor beam The section shape of the slim floor beam is illustrated in Fig. 2. The depth of the floor slab is 300 mm and the height of the profiled steel deck is 117 mm (Rannila 120). The steel beam consists of three plates welded together. The web plate is welded to the bottom and top flange by using the submerged arc welding method. The new asymmetric steel beam has a relatively thin top flange with a thickness of 10 mm and a web with a thickness of 20 mm. The bottom steel flange is 18 mm thick and 400 mm wide. The height of the steel beam is 258 mm. The new floor system has a concrete slab depth of 183 mm over the steel deck, which is demanded by the sound insulation requirements. The section gives an efficient fire resistance to the floor system. This is presented in Section 4.
3. Temperature analysis The thermal response of the new slim floor beam in fire is analyzed using the computer program, TACS-FIR (Temperature Analysis of Composite Structures Exposed to FIRe), which is a two-dimensional finite difference program developed
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Fig. 2.
Section shape of the new slim floor beams.
in the Laboratory of Steel Structures at Helsinki University of Technology [1]. The moisture content of concrete can be analyzed and the interface resistance of heat transfer between concrete and steel can be modelled with this program. The material properties of concrete and steel (thermal and mechanical) are temperature dependent. The fire temperature-time curves can be chosen according to the ISO standard fire or any kind of natural fire. There are several collections of fire temperature-time models and temperature-dependent material properties in this program. In this paper, the thermal and mechanical properties of the steel and concrete are given in accordance with Eurocode 3 Part 1.2 and Eurocode 4 Part 1.2 [2,3], and the fire temperature-time curve for natural fire is according to the Annex B of Eurocode 1 Part 2.2 [4]. 3.1. Heat transfer model The transient heat transfer equation based on Fourier Law is given as ⫺ⵜT(lⵜT)⫹e˙⫽0
(1)
where T is the temperature (°C), l is the thermal conductivity matrix (W/mK), e˙ =de/dt is the rate of specific volumetric enthalpy change. The gradient operator ⵜ is defined as ⵜ⫽
冋
∂ ∂ ∂ ∂x ∂y ∂z
册
T
(2)
where x, y and z are Cartesian co-ordinates. Superscript T is the transfer operator of the vector.
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By some intermediate transformations, the above equations can be derived as follows (rc⫹rwcwj)·
dT T1−T0 T2−T0 T3−T0 T4−T0 ⫽ ⫹ ⫹ ⫹ dt R1⌬x R2⌬y R3⌬x R4⌬y
(3)
where rc is the volumetric specific heat (J/m3K), rwcw is the volumetric specific heat of water, j is the volume ratio of moisture content. Ti is the temperature of the ith element in the local system (Fig. 3). Ri is the thermal resistance term, which can be given by 1 1 1 Ri⫽ ⫹ ⫹ Ki K0 Kint
(4)
where Ki and K0 are the thermal conduction terms. Kint is the interface resistance coefficient. In [5] the value Kint=50 W/m2K is proposed for the interface coefficient between steel and concrete. This value is also taken for this study. In the case of perfect contact, Kint=⬁ can be presumed. It is assumed in the program that the interface resistance is caused by the water evaporation of water [1]. The heat input rate q is expressed as q⫽es[(Tg⫹273)4⫺(Ts⫹273)4]⫹a(Tg⫺Ts)
(5)
where s is the Stephan-Boltzmann constant, s=5.67×10⫺8 W/m2K 4; e is the resultant emissivity coefficient. Following the work in [6,7], e=0.6 is adopted for the bottom steel flange and e=0.3 for the composite floor. a is the convection factor, which is assumed as 25 W/m2K for the exposed side and as 8 W/m2K for the unexposed side [8].
Fig. 3.
Local system of an internal element.
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3.2. Temperature-time curves of fires The Eurocodes allow the structures to be calculated either under the ISO standard fire or under specified parametric fires. In this paper, the temperature distributions of the new slim floor beam are analyzed both under the ISO standard fire and under the parametric natural fires as defined by Eurocode 1 Part 2.2. The ISO standard fire curve is an idealiszed temperature-time curve, which has only the ascending phase shown by the solid line in Fig. 4. In reality, the temperaturetime curves of fires can vary widely. The two most important factors that determine the fire temperature-time curves are the fire load and the size of openings through which the air can enter. Usually, the fire load is characterized by the fire load density per unit floor area, and the size of opening by the opening factor. Fig. 4 shows how the fire load and the opening factor affect the temperature-time curves, primarily in relation to the intensity and the duration of fire. 3.3. Temperature distribution The analysis program is validated extensively by the two Slimflor test results of the SCI, some composite columns and other types of composite beams [1]. The cross-section of the beam is modelled using a rectangular grid. The division of the slim floor section into cells is shown in Fig. 5. The temperature distribution of the new slim floor beam at 60 minutes under ISO standard fire is illustrated in Fig. 6. It shows that the bottom steel flange has a high temperature (about 750°C on average) and there exists a large temperature difference, around 200°C, between the end and the central point. This phenomenon is caused by the two-way heat input at the end of the bottom steel flange. Within the web, an extremely non-uniform temperature distribution exists due to the encasement of the concrete. The temperature of the steel beam above one quarter of the web depth from the bottom flange is lower than 400°C and the full strength can be expected.
Fig. 4.
Fire temperature-time curves.
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Fig. 5.
351
Division of section into cells for temperature analysis.
Fig. 6. Temperature distribution in the new slim floor beam under ISO fire (at 60 minutes). Figures in bold and black shade are for the steel parts. The others are for the concrete parts of the section.
On the top side of the floor, the temperature is less than 50°C and the insulation criterion is certainly satisfied. The temperature development of the steel section is shown in Fig. 7. The curve of point 1 represents the average temperature rise of the bottom steel flange. Within the first 40 minutes, the rate of temperature rise is in the range of 12 to 18°C/min. From 40 to 60 minutes, the average rate of temperature rise is about 8°C/min. The curve of point 2 represents the temperature rise at one quarter of the web depth. Within the 60 minutes duration of ISO fire, the heating rate is in the range of 3 to 8°C/min, which is much lower than that of the bottom steel flange. Fig. 8 illustrates the temperature rise of the steel section under natural fire. The natural fire curve is calculated according to Annex B of Eurocode 1 Part 2.2 (Fig.
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Fig. 7.
Temperature rise in the steel section under the ISO fire.
Fig. 8.
Temperature rise in the steel section under a natural fire.
4). The opening factor O is 0.02 m1/2 and the fire load density qf is 1100 MJ/m2. In practical cases, this curve defines a severe fire scenario. It shows that the average heating rate at the bottom steel flange reaches a value of 20°C/min in the ascending phase and a value of 6°C/min in the cooling phase. At point 2, the average heating rate is 8°C/min and the cooling rate is 2°C/min, respectively.
4. Resistance analysis for the ISO standard fire case The plastic moment capacity of the slim floor beam at elevated temperatures was analyszed by using the moment capacity method. In this method, a full shear connection between steel and concrete is assumed. The division of elements was the same as that in the temperature analysis case. The mechanical properties of steel and concrete under high temperatures are given according to Eurocode 3 and Eurocode 4. The moment capacity Mu can be calculated by
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冘冘 m
353
n
M u⫽
fij⌬xij⌬yijdi
(6)
i⫽1j⫽1
where m and n are the numbers of divisions in the x and y directions, respectively; fij is the concrete or steel strength of the element (i,j); ⌬xij and ⌬yij are the element dimensions; di is the centroid distance of the elements (i,j) from the plastic neutral axis. The Pposition of the plastic neutral axis (p.n.a.) can be obtained by
冘冘 m
n
fij ⌬xij ⌬yij ⫽0
(7)
i⫽1j⫽1
where fij has a positive value in the tensile zone and a negative value in the compressive zone. The tensile strength of the concrete is ignored. The reduced moment capacity of the composite section under fire is described using the concept of load ratio, which is defined as R⫽
Moment capacity in fire Ultimate moment capacity at 20°C
(8)
Fire is regarded in the design philosophy of the Eurocodes as an accidental situation or an accidental action. Therefore, the characteristic values of relevant material properties are adopted in fire design, and the partial safety factors are accordingly assumed as unity (1.0) when the moment capacity under fire conditions is analyzed. The ultimate moment capacity at 20°C is calculated using the partial safety factors presented in Eurocode 4 Part 1.1 [10]. The following factors affecting the fire resistance of the slim floor beam are investigated in this section: 앫 앫 앫 앫
Type of concrete: normal-weight and light-weight Enhanced reinforcement Fire protection of the bottom steel flange Fire resistance of continuous beam using the plastic hinge analysis method
There are two important factors that affect the plastic moment capacity of a slim floor beam: the resistant force of each part of the beam section and the position of the plastic neutral axis. The calculations were also carried out to analyze the contributions of the section parts to the plastic moment capacity in fire. Changing of the plastic neutral axis position in the cross-section under fire with heating time is investigated further. In all the analyses, the effective width of the concrete floor slab is defined as one quarter of the beam span in the sagging region and as triple the width of the upper steel flange in the hogging region. In the hogging moment calculation, the reinforcement bars are taken as f16 c/c 150. Analyses show that the change of hogging reinforcement bars does not have any significant influence on the load ratio in the hogging region. For instance, if the reinforcement bars f16 c/c 50 are used instead of f16 c/c 150, the load ratio is slightly lower, i.e. about 0.05. In this context, the
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“sagging region” means the beam region where the cross-section is subjected to a sagging (positive) bending moment, and the “hogging region” means the region where the cross-section is subjected to a hogging (negative) bending moment. 4.1. Influence of concrete types Fig. 9 represents the relationship between load ratio R and heating time under the ISO fire for normal-weight and light-weight concrete. It shows that the load ratio for lightweight concrete is slightly lower than that for normal-weight concrete. In the sagging region, the load ratio for lightweight concrete and normal-weight concrete at 60 minutes is 0.44 and 0.47, respectively. This small difference is due to the fact that the slim floor beam with a lightweight concrete slab has a higher temperature in the bottom flange of the steel section. This is caused by the bad heat-sinking effect of the lightweight concrete. Fig. 9 also shows the variation of load ratio against heating time both in the sagging and in the hogging region. It shows that the load ratio in the sagging region is much lower than that in hogging region. At 60 minutes, the load ratio in the sagging region and in the hogging region (normal-weight concrete) is 0.47 and 0.73, respectively. 4.2. Influences of enhanced reinforcement and fire protection In the practical cases, the applied load ratio of the beam under fire rarely exceeds 0.6 and values in the range of 0.5 to 0.55 are most common [6]. Analysis of the previous section indicates that the applied load ratio should be lower than 0.47 if a 60-minute fire resistance is desired. Therefore, for the new slim floor beam, some other measures have to be found to obtain a 60-minute fire resistance. Applications of an enhanced reinforcement and fire protection of the bottom steel flange are the efficient measures (Fig. 10) commonly used in practice. Fig. 11 illustrates the influence of enhanced reinforcement on the load ratio (for details of reinforcement see Fig. 10a). At 60 minutes, the load ratio is 0.57 when a reinforcement 2f32 is added.
Fig. 9.
Influence of concrete types on load ratio in the sagging and hogging region.
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Fig. 10.
Fig. 11.
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Enhanced reinforcement and fire protection in the composite section.
Influence of enhanced reinforcement and fire painting on load ratio in the sagging region.
Fig. 11 also illustrates the effect of fire protection in the bottom flange of the steel section. The intumescent fire painting, Nullifire S607 [9], with an allowed minimum thickness of 250 µm was used in the analysis. The details of the fire painting are illustrated in Fig. 10b. As indicated in Fig. 11, the full strength can be obtained at 60 minutes with a load ratio of 0.98, if the fire painting is used, and a load ratio of 0.67 at 90 minutes. 4.3. Plastic hinge analysis of continuous slim floor beam In the common practice, there is interest in designing a moment-resistant connection between the slim floor beam and the column. In this case, the bending resistance of the slim floor beam under fire depends on both the sagging and the hogging moment resistances of the sections. It is assumed that the plastic resistance can be developed in the section and the bending moment capacity can be determined from the following expressions: Internal span: Ms⫹MhⱖMl
(9)
End span: Ms⫹0.45MhⱖMl
(10)
In Eqs. (9) and (10), Ms is the sagging moment resistance, Mh is the hogging moment resistance and Ml is the applied bending moment in a simply supported beam.
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The plastic moment resistance of the continuous slim floor beam is illustrated in Fig. 12. It can be seen that a load ratio value of 0.52 for the end span and that of 0.58 for the internal span can be reached at 60 minutes under an ISO fire. Therefore, a 60-minute fire resistance can be achieved in most cases if the continuity of the slim floor beam is taken into consideration. 4.4. Resistance analysis: contributions of the composite cross-section parts To investigate the contributions of the beam section parts to the fire resistance, the beam cross-section is divided into five parts: bottom steel flange, top steel flange, lower part of web, upper part of web and compression part of the concrete slab cross-section. Here the lower part of the web means the part of web below the plastic neutral axis and the upper part of web is that above the plastic neutral axis. The yield strength of both structural steel and reinforcement steel is 355 N/mm2 and the cube strength of concrete is 30 N/mm2. For the calculations of moment capacity at ambient temperatures, partial safety factors of the material strength of 1.1 for structural steel, 1.15 for reinforcement steel and 1.5 for concrete [10] are used. For the moment capacity calculations under fire, the partial safety factor of the material strength is taken as unity (1.0) for both steel and concrete. In Table 1, the contributions of the beam section parts to the total sagging moment capacity at 60 minutes are compared with those at ambient temperatures. Due to the elevated temperature, the moment capacity contribution of the bottom flange is reduced to 26% from the original value of 59% at ambient temperature. The lower part of web contributes 55% of the total moment capacity under fire while this value is 14% at ambient temperature. It can be seen that the web contributes a major part to the total moment capacity in fire while the bottom flange has a major contribution at ambient temperature. The top flange makes a slight contribution to the moment capacity both at ambient and at elevated temperatures because of its position close to the plastic neutral axis. At 60 minutes under the ISO fire, the concrete above the top steel flange still has a very low temperature (ⱕ60°C) (Fig. 6) and the full strength
Fig. 12. Influence of the slim floor beam continuity on load ratio.
(Numbers in brackets are those for ambient temperature).
650苲870 85苲580 – 50苲80 ⱕ100
Bottom flange Lower part of web Upper part of web Top flange Concrete slab Total moment capacity (kNm)
a
Temperature (°C)
Section parts
227 (189) 121 (90) – (25) 0.6 (55) 32 (60)
Centroid distance from p.n.a. (mm) 399 1555 – 710 2034
(2324) (1162) (323) (646) (2550)
90 (439) 188 (105) – (8) 0.4 (36) 66 (153) 344 (741)
Axial resistance (kN) Moment resistance (kNm)
Table 1 Sagging moment capacity contributions for the section parts under ISO fire (60 minutes)a
26 55 – 0 19
(59) (14) (1) (5) (21)
Percentage of total moment capacity (%)
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can be expected. The contribution by this part to the total moment capacity is approximately 20%. In Table 2, the contributions of the composite section parts to the total moment capacity in the hogging region is analyzed in a similar way to that in the sagging region. In the hogging region, the hogging reinforcement, top steel flange and upper part of the web are in tension. The bottom steel flange, lower part of the web and the concrete near the bottom flange are in compression. At ambient temperature, the compressive parts contribute only 8% to the total moment capacity and the contribution by tensile parts is 92%. However, in fire, the compressive parts contribute 42% and the tensile parts 58% to the total moment capacity, respectively. This is caused by the significant change of the plastic neutral axis position in fire even if the full strength in the tensile parts is remaineds after 60 minutes heating. Fig. 13 illustrates the changing of the plastic neutral axis position during fire. The position of plastic neutral axis (p.n.a.) is referred to as the distance h from the p.n.a. to the top side of the floor slab. In the sagging region, the p.n.a. distance h has a stable value of 100 mm atfor the first 25 minutes, and then it declines rapidly to 65 mm at 40 minutes. After that, the p.n.a. distance h varies slightly with the heating time. This can be interpreted clearly by referring both to Fig. 7 and to the strength reduction of steel at elevated temperatures. After 25 minutes heating, the average temperature of the bottom flange rises uprose to 400°C, where the strength reduction begins. From 25 to 40 minutes, the average temperature of the bottom flange rises up to 600°C at a heating rate of 18°C/min while the material strength of the steel sharply drops to 45% of its original value. Therefore, a rapid decline in the p.n.a. position occurs between 25 and 40 minutes. After 40 minutes heating, the average heating rate of the bottom steel flange is less than 8°C/min. In the hogging region, changing of the p.n.a. distance h is changing similarly to that in the sagging region. The original p.n.a. distance h is about 290 mm, i.e. very close to the upper side of the bottom flange. A rapid change ofin the p.n.a. distance h occurs between 25 and 40 minutes and after that the change becomes more slowlyer. Generally, the p.n.a. distance h in the hogging region varies more significantly than that in the sagging region. One important reason for thatis is the significant reduction in the compression part resistance of the concrete and bottom steel flange at elevated temperature.
5. Resistance analysis for the natural fire cases The Eurocodes give an alternative way of analyzing the fire resistance of structures under specified natural fires. In this section, the structural fire resistance of the new slim floor beam will be investigated under the parametric natural fires defined by Annex B of Eurocode 1 Part 2.2. The major controlling parameters of the natural fires in Euorocde 1 are the opening factor O, fire load density qf and the thermal property of enclosure boundary √rlc. Generally, the effect of the thermal property of the enclosure boundary on the fire temperature is in the range of 10苲20% [11]. Here the thermal property of the
(Numbers in brackets are those for ambient temperature).
30苲40 50苲80 85苲250 250苲580 650苲870 100苲800
Re-bars Upper flange Upper part of web Lower part of web Bottom flange Concrete Total moment capacity (kNm)
a
Temperature (°C)
Section parts
150 115 55 49 129 63
(260) (225) (113) (5) (14) (5)
Centroid distance from p.n.a. (mm) 428 710 781 775 399 795
(372) (646) (1452) (32) (2324) (33)
64 82 43 38 51 50 328
(97) (145) (163) (0.2) (33) (0.2) (438)
Axial resistance (kN) Moment resistance (kNm)
Table 2 Hogging moment capacity contributions for the section parts under ISO fire (60 minutes)a
20 25 13 12 15 15
(22) (33) (37) (0) (8) (0)
Percentage of total moment capacity (%)
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Fig. 13.
Changing of plastic neutral axis position with heating time.
enclosure boundary is taken as 1160 (J/m2s1/2K), which represents a standard compartment. Another factor is the ratio of the floor area Af to the total surface area At. Calculations show that the effect of this factor on the fire temperature according to Annex B of Eurocode 1 Part 2.2 is within the range of 10%, if the ratio Af/At varies between 1:3苲1:8. Here the ratio Af/At is taken as 1:4, which represents a relatively severe situation in the fire compartment. A parametric study iswas performed to investigate the minimum load ratio R with the major controlling parameters of natural fires. These parameters were as follows: 앫 앫 앫 앫
Opening factor O (m1/2): 0.02, 0.06, 0.10, 0.15, 0.20 Fire load density per unit floor area qf (MJ/m2): 275, 550, 825, 1100, 1375 Thermal property √rlc of the enclosure boundary (J/m2s1/2K): 1160 Ratio of floor area to total surface area of enclosure (Af:At): 1:4
Due to the fact that a natural fire curve has both an ascending and a cooling phase, the irreversibility of the material properties of the concrete in the cooling phase has to be taken into account. The strength of the concrete parts depends on the maximum temperature ever attained, and it cannot be recovered during or after the cooling phase. For the steel parts, the strength is dependent on the temperature at the current time. In the cooling phase, the strength of steel can be recovered. Fig. 14 illustrates the variation in load ratio both during the natural fires and an ISO fire in the sagging region. It shows that the load ratio curve has a recovering part in a natural fire while that curve always declines in an ISO fire. There is a minimum load ratio for each parametric natural fire (Fig. 14). The relationship between the minimum load ratio and the fire parameters can be obtained when the moment capacity analyses under different parametric fire curves are carried out. Table 3 illustrates the analysis results of the minimum load ratio and the fire parameters. The minimum load ratio in Table 3 is called “critical load ratio” (Rcr) because the slim floor beam is unsafe during fire if the applied load ratio is higher than the corresponding value in Table 3.
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Fig. 14. Load ratio vs. heating time under two natural fires. Table 3 Critical load ratio of the slim floor beam in the sagging region under natural fires given by opening factor and fire load density Opening factor O (m1/2)
Load ratio
Fire load density qf (MJ/m2)
275 550 825 1100 1375
0.02
0.06
0.10
0.15
0.20
1.16 0.94 0.70 0.56 0.48
1.17 0.99 0.66 0.51 0.43
1.17 1.06 0.70 0.52 0.44
1.17 1.12 0.75 0.57 0.47
1.17 1.13 0.87 0.63 0.50
In practical cases, the opening factor has more significant uncertainty and the fire load density is taken as the major fire parameter in ranking the fire severity in buildings. From Table 3 it can be seen that for a specified fire load density there exists a lowest load ratio corresponding to the most severe fire for all opening factors. Fig. 15 illustrates the relationship between the lowest critical load ratio and the
Fig. 15.
Lowest critical load ratio vs. fire load density.
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fire load density. Generally, the slim floor beam can be used without applied fire protection if the fire load density is lower than 1100 MJ/m2. When the fire load density is 1375 MJ/m2, the lowest critical load ratio is 0.43 for the sagging region.
6. Conclusions There is increasing interest in slim floor construction in the Nordic countries and the UK. At the moment, a new asymmetric slim floor beam is under development in Finland. In this paper, the fire resistance behaviour of the new slim floor beam is investigated. The following conclusions can be drawn on the basis of this study: 앫 A 60 minute fire resistance can be achieved if the applied load ratio for a simply supported beam is lower than 0.47. Otherwise, some additional measures such as an enhanced reinforcement and/or fire protection of the bottom steel flange are required. 앫 Generally, the new slim floor beam can achieve a 60 minute fire resistance without any additional measures, if the moment-resistant beam-to-column connection is reliably designed. 앫 The fire resistance of the slim floor beam is provided mainly by the lower part of the steel web, while the bottom flange loses its resistance under fire. 앫 The fire resistance behaviour of the slim floor beam is also investigated under natural fires defined by Eurocode 1. The results show that the new slim floor beam can be used without any additional measures if the fire load density is less than 1100 MJ/m2, which is rarely exceeded in office and residential buildings [11,12].
Acknowledgements The financial support provided for this research project by the Technology Development Centre of Finland (TEKES), the Finnish Constructional Steelwork Association Ltd (FCSA) and the Finnish companies, Rautaruuki Oyj, PPTH Tera¨s Oy and Deltatek Oy is gratefully acknowledged by the authors.
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