Parametric analysis related to dimensioning of tubular steel columns filled with concrete in a fire situation

Rodrigues, Fábio Masini; Moreno Júnior, Armando Lopes; Munaiar Neto, Jorge

doi:10.1590/S1983-41952022000200010

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ORIGINAL ARTICLE • Rev. IBRACON Estrut. Mater. 15 (2) • 2022 • https://doi.org/10.1590/S1983-41952022000200010 copy

Parametric analysis related to dimensioning of tubular steel columns filled with concrete in a fire situation

Análise paramétrica do dimensionamento de pilares tubulares de aço preenchidos com concreto em situação de incêndio.

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

For the dimensioning of structural elements in fire situation, simplified equations and parameters are commonly used in analytical equations or numerical models. More complex equations or simplified values can be chosen by the designer for determine materials properties in high temperature in numerical models, however, numerical modeling can be quite sensitive to the variation of some of the physical and mechanical properties. In this paper, the sensitivity of the numerical model in relation to the values according to the level of simplification chosen was evaluated, presenting an analysis in relation to the results found to contribute to the choice of these parameters and presenting the indications found in the literature. In this sense, this work presents a study of sensitivity to the variation of the values of steel and concrete properties, presented in the Eurocode and Brazilian standards, in addition to the moisture content and emissivity of the surface exposed to fire, for the dimensioning, in a fire situation, of steel tube columns, of circular and square section, filled with concrete. The studies were carried out via numerical modeling developed in the software ABAQUS. It was verified that the resulting emissivity values equal to 0.7 or 0.8, recommended in the literature, are conservative, and the choice of either does not bring significant changes in the temperature field obtained for the structural elements under analysis. It was also verified that the concrete moisture content is a relevant aspect for the formation of its temperature field, also affecting, but to a lesser extent, the steel temperature. Regarding the physical and mechanical properties of the materials, this sensitivity study suggests the adoption of the values from the equations presented in Eurocodes, without simplifications, and with the specific heat and thermal conductivity of the concrete, adopted in accordance with the Eurocode 4.

Keywords:
fire situation; column; steel; concrete; numerical models

Steel temperature θ_a (°C)	Steel yielding strength reduction factor (Ky_a,_θ)	Steel elastic modulus reduction factor (KE_a,θ)
	*1 / 2 / 3	^* * 1- EN 1994-1-2 [3]; 2- ABNT NBR14323:2013 [4] (steel not subject to local buckling); 3-EN 1993-1-2 [6] 1 / /2 / 3
20	1.000	1.000
100	1.000	1.000
200	1.000	0.900
300	1.000	0.800
400	1.000	0.700
500	0.780	0.600
600	0.470	0.310
700	0.230	0.130
800	0.110	0.090
900	0.060	0.0675
1000	0.040	0.045
1100	0.020	0.0225
1200	0.000	0.000

Reference	Recommended emissivity values
Reference	Fire (e_m,f)	Steel (e_m,s)	Concrete (e_m,c)
EN1991-1-2 [¹⁰10 European Commitee for Standardization, Eurocode 1: Actions on Structures – Part 1.2: General Actions - Actions on Structures Exposed to Fire, EN 1991-1-2, 2002.]	1	-	-
EN1992-1-2 [⁵5 European Commitee for Standardization, Eurocode 2: Design of Concrete Structures – Part 1.2: General Rules – Structural Fire Design, EN 1992-1-2, 2004.]	1	-	0.7
EN1993-1-2 [⁶6 European Commitee for Standardization, Eurocode 3: Design of Steel Structures – Part 1.2: General Rules – Structural Fire Design, EN 1993-1-2, 2005.]	1	0.7	-
EN1994-1-2 [³3 European Commitee for Standardization, Eurocode 4: Design of Composite Steel and Concrete Structures – Part 1.2: Structural Fire Design, EN 1994-1-2, 2005.]	1	0.7	0.7
Lie and Irwin [¹¹11 T. T. Lie and R. J. Irwin, "Fire resistance of retangular steel columns filled with bar-reforced concrete," J. Struct. Eng., vol. 121, pp. 797–805, 1995.]	0.75	0.7	-
Irwin and Lie [¹²12 R. J. Irwin and T. T. Lie, Fire Resistance of Rectangular Hollow Steel Sections Filled with Bar-Reinforced Concrete (Internal Report 631). Ottawa, Canada: Natl. Res. Counc. Canada, 1992.]	-	0.8	-
Rush [¹³13 D. Rush, “Fire performance of unprotected and protected concrete filled steel hollow structural sections,” Ph.D. dissertation, Univ. Edinburgh, Edinburgh, 2013.]	0.75	0.7	-
Drysdale [¹⁴14 D. Drysdale, An Introduction to Fire Dynamics, 3rd ed. Wiley, 2011, 551 p.]	1	0.2	-
Chaoming et al. [¹⁵15 Y. Chaoming, Z. Huang, W. Burgess, and R. J. Plank, “3D modelling of bi-steel structures subject to fire,” in Proc. Struct. Fire Workshop, 2006.]	-	0.8	-	Temperature
Paloposki and Liedquist ^[16]16 T. Paloposki and L. Liedquist, Steel Emissivity at High Temperatures: Research Notes. Tampere, Finland: Tech. Res. Cent. Finland, 2005.	-	0.2	-	20 to 385 °C
	-	0.65	-	550 to 1200 °C
NIST ^[17]17 D. P. Bentz, L. M. Hanssen, and B. Wilthan, Thermal Performance of Fire Resistive Materials III. Fire Test on a Bare Steel Column (NIST Interagency/Internal Report (NISTIR) 7576). Massachusetts, USA: National Institute of Standards and Technology, 2009, pp. 13.	1	0.32	-	20 °C
		0.32	-	200 °C
		0.85	-	400 °C
		0.95	-	800 °C
		0.95	-	1200 °C
Sadiq et al. ^[18]18 H. Sadiq, M. B. Wong, J. Tashan, R. Al-Mahaidi, and X. L. Zhao, "Determination of steel emissivity for the temperature prediction of structural steel members in fire," J. Mater. Civ. Eng., vol. 25, no. 2, pp. 167–173, 2013.	-	0.28	-	θ< 380 °C
		0.00304θ - 0.888		380 ≤θ< 520 °C
		0.69		θ≥ 520 °C

Reference	Emissivity
1	Concrete (ε_m,c)	Steel (ε_m,s)
Han and Gillie [²¹21 Z. G. Han and M. Gillie, “Temperature modeling for concrete-filled steel tube’s cross section in fire,” in Proc. Int. Conf. Mech. Civ. Eng., 2014.]	0.92	0.23
O’Loughlin et al.[²²22 E. O’Loughlin, D. Rush, and L. Bisby, “Concrete-filled structural hollow sections in fire: accounting for heat transfer across a gap,” in Proc. 15th Int. Conf. Exp. Mech., Porto, Portugal, 2012, pp. 1-17.]	0.97	0.32

Reference	Section	L or D	t	Fc	Fya	l
1	Cross-section	(mm)	(mm)	(MPa)	(MPa)	(mm)
1- PQ-100-5	Square	100	5	30	350	500
2- PQ-140-5	Square	140	5	30	350	500
3- PQ-200-5	Square	200	5	30	350	500
4- PQ-250-8	Square	250	8	30	350	500
5- PC-114-5	Circular	114.3	5	30	350	500
6- PC-150-5	Circular	150	5	30	350	500
7- PC-195-5	Circular	195	5	30	350	500
8- PC-250-8	Circular	250	8	30	350	500

	Thermal expansion of concrete	Type of aggregate	Thermal expansion of steel	Concrete moisture content	Concrete density
1	1	1	1	1	1
M1	EN1994-1-2 [³3 European Commitee for Standardization, Eurocode 4: Design of Composite Steel and Concrete Structures – Part 1.2: Structural Fire Design, EN 1994-1-2, 2005.]: 20 °C< θc ≤ 805 °C: Δl/l,c= -1.2 ⋅10-4+6 ⋅10-6 ⋅θc+1.4 ⋅10-11⋅θc3 805 °C< θc ≤ 1200 °C: Δl/l,c = 12⋅10-3	Calcareous	EN1994-1-2 [³3 European Commitee for Standardization, Eurocode 4: Design of Composite Steel and Concrete Structures – Part 1.2: Structural Fire Design, EN 1994-1-2, 2005.]: 20 °C < θa ≤ 750 °C: Δl/l,a = -2.416 ⋅10-4 +1.2⋅10-5 ⋅θa+0.4⋅10-8 ⋅θa2 750 °C < θa ≤ 860 °C: Δl/l,a = 11⋅10-3 860 °C < θa ≤ 1200 °C: Δl/l,a = -6.2⋅10-3 + 2⋅10-5 ⋅ θa	3%	EN1994-1-2 [³3 European Commitee for Standardization, Eurocode 4: Design of Composite Steel and Concrete Structures – Part 1.2: Structural Fire Design, EN 1994-1-2, 2005.]: 20 °C ≤ θc ≤ 115 °C: ρ(θc) = ρ(20 °C) = 2300 kg/m3 115 °C < θc ≤ 200 °C: ρ(θc)=ρ(20 °C) ⋅ (1-0.02 ⋅ (θc-115)/85) 200 °C < θc ≤ 400 °C: ρ(θc) = ρ(20 °C) ⋅ (0.98-0.03 ⋅ (θc-200)/200) 400 °C < θc ≤ 1200 °C: ρ(θc) = ρ(20 °C) ⋅ (0.95-0.07(θc-400)/800)
M2	EN1994-1-2 [³3 European Commitee for Standardization, Eurocode 4: Design of Composite Steel and Concrete Structures – Part 1.2: Structural Fire Design, EN 1994-1-2, 2005.]: 20 °C< θc ≤ 700 °C: Δl/l,c= -1.8 ⋅10-4+9 ⋅10-6 ⋅θc+2.3⋅10-11 ⋅θc3 700 °C< θc ≤ 1200 °C: Δl/l,c = 14⋅10-3	Siliceous		3%
M3				10%
M4				3%	2300 kg/m3
M5					2400 kg/m3
M6	simplified: Δl/l,c = 6 ⋅ 10-6		simplified: Δl/l,a = 12 ⋅ 10-6		same density of the M1, M2 and M3 models

Reference	Cross	L or D	t	fc	Fya	l
Reference	section	(mm)	(mm)	(MPa)	(MPa)	(mm)
1- PC-168-6	Circular	168.3	6.4	-	-	-
2- PC-168-10	Circular	168.3	10	-	-	-
3- PC-300-10	Circular	300	10	-	-	-

Specimen (Table 5)	Model M	Fire resistance time (minutes)	Temperature (°C)
1	1	1	1
1	1	1	1	2	3	4	5
3-PQ-200-5	1	59.0	905.2	629.8	357.1	219.8	140.9
1	2	50.2	835.5	516.9	243.1	119.6	75.1
1	3	57.0	844.4	471.1	154.3	61.5	43.1
1	4	51.4	833.6	511.5	239.4	118.2	74.7
1	5	52.7	831.1	502.9	229.7	111.3	70.7
1	6	60.9	893.8	612.3	337.8	199.7	123.3
7-PC-195-5	1	45.9	815.1	505.8	250.2	124.4	73.8
1	2	43.2	785.6	458.0	209.7	98.7	61.3
1	3	47.5	804.5	423.3	116.6	55.4	39.4
1	4	43.4	777.0	442.4	198.2	93.7	58.8
1	5	45.9	787.2	451.5	204.1	96.2	60.1
1	6	51.7	852.9	570.0	309.7	174.9	97.2
2-PQ-140-5	1	43.4	815.1	567.7	374.4	254.1	198.0
1	2	36.7	791.3	527.4	332.7	210.4	151.8
1	3	43.7	784.1	453.8	214.9	89.2	62.7
1	4	38.4	789.0	521.1	327.0	206.0	149.0
1	5	38.9	785.9	511.1	315.0	193.2	137.1
1	6	40.7	791.5	529.4	335.1	212.4	153.4
5-PC-114-5	1	31.2	736.3	541.6	344.9	243.2	186.0
1	2	30.0	726.9	524.8	328.1	225.7	164.8
1	3	33.4	725.7	471.4	216.9	89.1	66.3
1	4	30.0	725.0	518.6	322.6	221.5	161.4
1	5	30.0	721.9	508.7	310.5	208.0	146.6
1	6	32.0	753.6	571.5	375.6	275.8	225.4

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[1] Corresponding author: Fábio Rodrigues. E-mail: fabiosecfmr@gmail.com