- Email: [email protected]
Behavior of steel columns in a fire with partial damage to fire protection
Journal of Constructional Steel Research 65 (2009) 1392–1400
Contents lists available at ScienceDirect
Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Behavior of steel columns in a fire with partial damage to fire protection Wei-Yong Wang a,∗ , Guo-Qiang Li b,c a
College of Civil Engineering, Chongqing University, Chongqing, 400045, PR China
b
College of Civil Engineering, Tongji University, Shanghai, 200092, PR China
c
State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, PR China
article
info
Article history: Received 8 May 2008 Accepted 23 January 2009 Keywords: Steel column Fire protection Experimental study Critical temperature
a b s t r a c t An experimental study is performed on two specimens in a furnace to investigate the fire behaviour of steel columns with partial loss of fire protection. The steel columns are connected by flush end-plates at two ends and the axial load is kept constant with a load ratio of 0.55 subjected to an elevation of temperature. The specimens are protected with 20 mm thickness of fire protection. The damaged length of fire protection is 7% of the complete length of the column for specimen S-1 and 14% for S-2 at the two ends of the steel columns. The temperature of atmosphere around the specimens in the furnace is assumed to follow the ISO834 standard temperature and the temperatures and displacements are measured in the experiment. The temperature distribution along the steel column is modelled by finite element analysis and compared with the measured results. A continuum model is presented to predict the ultimate load capacity or critical temperature of the columns with fire protection damage. Analyses are carried out on the specimens and compared with the experiment. Experimental and analytical results showed that the fire resistance of steel columns with partial damage to the fire protection is reduced. The damage length of the fire protection has a great effect on the fire resistance of steel columns. The failure of the specimens mainly resulted from the buckling or yielding at the portion where the fire protection is damaged. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction It is known that unprotected steel structures do not have desirable fire-resistance because the temperature of unprotected steel components increases rapidly in fire due to the high thermal conductivity of steel. Spray-on fire protection is widely used to protect steel structures against fire because spray-on protective materials can efficiently slow down heat transfer from the fire to steel components, and hence lower the rate of temperature increase in steel components. However, spray-on materials are often rather fragile, and they may be easily damaged by mechanical action, such as impacts, earthquakes and explosions, resulting in a possible fire resistance reduction for the steel components originally protected. The tragic events in New York on September 11, 2001 have dramatically shown that mechanical accidental actions followed by a fire can cause local structural failure and even progressive collapse of tall buildings. Thus, it is essential to understand the effect of partial protection damage caused by mechanical action on the fire resistance of steel columns. A few numerical studies have been carried out to investigate the effect of partial spray-on protection damage. Wang et al. [1]
∗
Corresponding author. Tel.: +86 23 65121983. E-mail address: [email protected] (W.-Y. Wang).
0143-974X/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2009.01.004
conducted finite element analysis to predict the temperature distribution of steel columns with partial fire protection loss and found that the length and location of fire protection loss has little impact on the model of temperature distribution over the length of steel components. Wang et al. [2] proposed a method to predict the capacity for stability of restrained steel columns based on principle of stationary potential energy. Tomecek and Milke [3] carried out a two-dimensional finite element study to investigate the effect of spray-on protection loss on the fire resistance of steel columns, and showed that a 4% loss of protection resulted in a 15% reduction in the time to reach the critical temperature for a one-hour rated W10X49 column and a 40% reduction in the time for a two-hour rated W10X49 column. Ryder et al. [4] conducted a three-dimensional finite element analysis on a steel column with partial fire protection damage and showed that the fire resistance of the column can be severely diminished if even a small portion of the protection is removed. YU KANG et al. [5] carried out a numerical study to investigate the fire resistance reduction of protected steel beams caused by partial loss of spray-on fire protection and found that partial loss of spray-on fire protection can cause a significant moment capacity reduction for protected steel beams exposed to fire. The results of a heat-transfer analysis of steel columns with partial loss of fire protection using the finite element method were presented by Milke et al. [6]. The results indicated that
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
for a given exposure the area of the missing protection and the size of the column are found to have an appreciable effect upon the thermal response of the column regardless of the protection thickness and the area of the missing protection; this seems to be the primary factor in the temperature rise of the column. Mario Fontana [7] and Markus Knobloch [8] studied the fire behaviour using a three-dimensional finite element heat transfer and structural model, taking into account geometrical nonlinearities, local temperature distributions, thermal strains, and temperature dependent material properties. The results confirmed that local damage of fire protection is a decisive factor for the fire resistance of steel columns and it is important to avoid fire protection damaged by periodical repairs or to use robust fire protection systems. Stephen PESSIKI [9] performed an analysis to examine the behaviour of steel H columns in fires with damaged spray-applied fire resistive material subjected to concentric axial compression. The conclusions declared that the removal of even relatively small amounts of fire resistance material from the column flange causes dramatic decreases in column axial load capacity for fire resistance duration in excess of 30 min. A simplified approach in the temperature domain using the critical temperature criteria for steel columns was used in ASTEM E119 [10] to calculate the fire resistance of steel columns with partially missing fire protection. It seems that the finite element method has been employed by nearly all the previous researchers to study the temperature distribution and fire resistance of steel members with partial loss of fire insulation material. Although the FEM is powerful, it is not straightforward for understanding the failure mechanism of steel members in fires with partial loss of fire protection. In this paper, an experimental study is performed in a furnace to investigate the fire behaviour of steel columns with partial loss of fire protection, the results of which may be used as the database for calibrating the analytical approach including FEM. A continuum model is also presented to predict the ultimate load capacity or critical temperature of the columns with fire protection damage and an analysis is made on the specimens. 2. Material properties In the tests the steel grade of the columns is Q235. At ambient temperature a group of standard tensile test specimens cut from the upper flange and web of the beam section was tested; the Young’s Modulus was found to be 202 kN/mm2 and the yield strength was 272 N/mm2 , the ultimate strength was 413 N/mm2 and the maximum elongation was 18%. At elevated temperatures, the Young’s Modulus and yield strength are adopted as recommended in the Chinese Technical Code for Fire Safety of Steel Buildings [11], which is
ET 7T − 4780 = 20 ◦ C ≤ T ≤ 600 ◦ C E 6T − 4760 ET = 1000 − T 600 ◦ C ≤ T ≤ 1000 ◦ C E 6T − 2800 fyT = 1.0 20 ◦ C ≤ T ≤ 300 ◦ C f y fyT = 1.24 × 10−8 T 3 − 2.096 × 10−5 T 2 fy + 9.228 × 10−3 T − 0.2168 300 ◦ C < T < 800 ◦ C f yT = 0.5 − T 800 ◦ C ≤ T ≤ 1000 ◦ C fy
1393
Fig. 1. Sketch of the test set-up.
3. Experimental study 3.1. Test arrangement and instrumentation Tests were performed in a furnace. The sketch of the experimental set-up is shown in Fig. 1. The temperature–time curve of the furnace follows the ISO834 standard. The instrumentation includes displacement transducers for measuring axial and lateral displacements of the steel columns, load transducers for measuring load and thermocouples for measuring the temperature of the furnace as well as the specimens. Four displacement transducers were employed in the experiments. One of which is used to measure the axial displacement and the others for measuring the lateral displacement of the specimens. Nine thermocouples were utilised to measure the temperature of the specimens, three of which were for measuring the temperature on the portion without fire protection and the others for the portion with fire protection. The axial load, simulating the internal force in the columns, was introduced by a hydraulic jack attached to a reaction frame and powered by a pressure controlled pump, which was kept constant as the specimen expanded and buckled due to increasing temperature. Both fire protection and an aluminium silicate blanket are used to protect the steel portion of the reaction frame in the furnace from the fire. The arrangement of the thermocouples and displacement transducer over the specimen is shown in Fig. 2. The testing procedure comprises three steps. First, the specimen is loaded axially up to a pre-determined load level. Then the fire in the furnace was started and a constant load maintained on the specimen. Finally, the fire in the furnace was stopped when failure occurred in the specimens. Temperatures and displacements were recorded at various times in the constant-load tests. 3.2. Specimen details
(1)
(2)
2000
where ET is modulus of elasticity of steel at a given temperature; E is modulus of elasticity of steel at ambient temperature; fyT is yield strength of steel at a given temperature; fy is yield strength of steel at ambient temperature and T is the temperature of the steel.
The specimens are 2.7 m long columns fabricated with H shaped structural steel and the cross section of which is H140 × 100 × 6 × 6. The steel columns are connected by flush end-plates at the two ends and the axial load is kept constant with a load ratio of 0.55 and subjected to an elevation of temperature in the furnace. The load ratio is defined as a ratio of the load on the steel column to column buckling resistance at the normal temperature. The specimens are protected with a 20 mm depth of fire protection. At the two ends of the steel columns, partial fire protection is damaged artificially through moving it away in order to investigate the behaviour of steel columns with a partial loss of fire protection in a fire. The damaged length of the fire protection is 7% of the column length for one specimen and 14% for another one, which are approximately 190 mm and 380 mm long respectively. The specimen detail is shown in Fig. 3.
1394
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
Fig. 2. Thermocouples and displacement transducer arrangement.
(a) S-1.
(b) S-2.
(c) End-pate joint.
Fig. 3. Specimen details.
Fig. 4. Temperature–time curve of Specimen S-1.
Fig. 5. Temperature–time curve of Specimen S-2.
3.3. Temperature distribution
3.4. Axial displacement and failure temperatures
Figs. 4 and 5 show typical variations against time of the temperatures of the furnace atmosphere, the portion of the steel columns without fire protection, the portion of the steel columns with fire protection during the heating and cooling phases. The temperature of the fire could be controlled to closely follow the ISO834 standard fire temperature curve except in the beginning. Due to the fire protection, in the portion of the column with fire protection, the temperature initially rose much more slowly than the portion of the column without fire protection. The difference between the temperatures of the portion without fire protection and with fire protection increased to almost 500 ◦ C after about 25 min. After the fire was stopped, and the rate of rise in the fire temperature reduced, the rate of rise of temperature in the portion without fire protection also reduced as a result of the lower radiation increase. However, conduction of heat into the portion with fire protection continued.
Fig. 6 shows the time–axial displacement curves for columns with partial fire protection damage. For specimen S-1, after the specimen is exposed to fire for 15 min, the axial displacement increases rapidly and buckling occurs. However, for specimen S-2, the time exposed to the fire can last 40 min due to the length of the column without fire protection being subjected to fire is short. Fig. 7 shows the temperature–axial displacement curves for specimens. The load-bearing capacity of steel columns will be reduced with an elevation of temperature and the steel columns will fail when the load-bearing capacity reaches the ultimate bearing capacity in a fire. When failure occurs, a great displacement along the axis will appear. With the elevation of temperature of steel columns, the loadbearing capacity will decrease and failure occurs when the column buckles or the section yields at some location of the columns, and the axial displacement of the column will increase rapidly. Based on the experiment results, the critical temperature of steel
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
1395
4. Heat transfer analyses The heat transfer mechanisms included in the heat transfer analyses are conduction, convection and radiation. Solid70 elements were used to model both steel columns and fire protection. These elements are three-dimensional-eight-node linear heat transfer elements. Fig. 10 shows the finite element model of S-1 and S-2. The thermal conductivity of the steel as a function of temperature was specified as given in the Eurocode 3 [12]. Similarly, the specific heat of the steel as a function of temperature was specified as given in the Eurocode 3 [12]. Convection and radiation boundary conditions were specified where member surfaces were exposed to fire. The thermal conductivity and specific heat of the fire protection are 0.05 W/(m ◦ C) and 1100 J/(kg ◦ C) respectively, which were given by the coating manufacture company. The density of the coating is 350 kg/m3 . Fig. 11 shows the temperature distribution of the steel along the axial direction of Specimen S-1 and S-2, obtained by using the commercial FEM package ANSYS. As can be seen from Fig. 11, the temperature is high at the portion without fire protection and the temperature is low at the portion with fire protection. There is a temperature transition between the two portions. Figs. 12 and 13 show the comparison of results between analysis and experiment. The results in Figs. 12 and 13 show that the temperature of the steel of both specimens at the portion with fire protection and without fire protection obtained with analytical prediction and experimental measurement agrees with each other well.
Fig. 6. Axial displacement-time curve of the specimens.
5. Continuum model Fig. 7. Axial displacement–temperature curve of the specimens.
columns with partial fire protection damage is defined here as the temperature of the steel in the portion without fire protection at which the axial displacement increases abruptly. As can be seen from Fig. 7, the critical temperatures of the specimen S-1 and S-2 are 500 ◦ C and 750 ◦ C respectively. 3.5. Failure of specimens Figs. 8 and 9 show the failure of the two specimens. For specimen S-1, buckling only occurs around the weak axis on the portion without fire protection near to the applied load. For specimen S-2, section yielding occurs on the two parts of the column without fire protection. The yielding at the portion near the end of the applied load is more serious than the other portion which can be seen clearly from the Fig. 9.
(a) end A.
Fig. 14 shows the mechanical model of a steel column with damaged fire protection at the two ends. The initial flexure of the column may be expressed by y0 = a0 sin (π x/l)
(3)
where l is the length of the column, and a0 is the initial flexure at the mid-span of the column. If the lateral displacements of the column at the location without fire protection and with fire protection are y1 and y2 respectively, according to the differential equation of equilibrium, the following equation can be obtained as
(
ET 1 I (y1 − y0 )00 + P (y1 + e0 ) = 0
0 ≤ y ≤ l0
ET 2 I (y2 − y0 )00 + P (y2 + e0 ) = 0
l0 ≤ y ≤ l/2
(4)
where ET 1 is elastic modulus of steel at temperature T1 ; ET 2 is elastic modulus of steel at temperature T2 ; T1 is the temperature in the portion of the column with damaged fire protection; T2 is
(b) end B. Fig. 8. Failure of Specimen S-1.
1396
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
(a) end A.
(b) end B. Fig. 9. Failure of Specimen S-2.
ratio; hc is height of the cross-section of the column; P is axial force on the column. The general solution to Eq. (4) can be given by
y1 = C1 sin (απ x/l) + C2 cos (απ x/l) a0 sin(π x/l) − e0 + 1 − α2 y = C sin x/l) + C4 cos (βπ x/l) (βπ 2 3 a0 sin(π x/l) − e0 + 1 − β2 Fig. 10. Finite element model of S-1 and S-2.
the temperature in the portion of the column with integrated fire protection; I is inertial moment of column; l0 is the length of the damaged fire protection and e0 is load eccentricity. Due to the displacement at two ends being zero and the rotation of the cross-section of the column continuing through the overall length, the following boundary conditions can be adopted as
y1 (0) = 0, y1 l y01 l0 = −y02 l0 ,
0
0
= y2 l y02 (l/2) = 0.
(5)
For convenience, the following parameters are defined as
µ = l0 /l, ε = a0 /l, η = e 0 / hc 2 2 Pcr1 = π ET 1 I /l , Pcr2 = π 2 ET 2 I /l2 , p p α = P /Pcr1 , β = P /Pcr2
(6)
(7)
where µ is damage length ratio of the fire protection of the column; ε is initial flexure ratio of the column; η is the load eccentricity
(8)
where the parameters C1 C2 C3 C4 are determined by employing the boundary condition (Eq. (5)), given in Box I. If we take the edge fibre yield at the most probable location of the column as the failure criterion, the ultimate load capacity of the column with partial loss of fire protection can be predicted by
P Pa + max 1 = fyT 1 A P
+
W Pamax 2
= fyT 2
(a) (9) (b)
A W where A is area of the cross-section of the column; W is the section flexure modulus of the column; fyT 1 is the yield strength of steel at temperature T1 ; fyT 2 is the yield strength of steel at temperature T2 ; amax 1 = y1 (l1 ), and amax 2 = y2 (l/2). 6. Experiment analysis 6.1. Basic details of the specimens The height of the section is H = 140 mm and the width is B = 100 mm. The thickness of the web and flange is tw = tf = 6 mm.
Fig. 11. Temperature distribution of S-1 and S-2 (60 min).
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
C1 =
a0 1/ 1 − β 2 − 1/ 1 − α 2
1397
sin (µπ ) − e0 cos (µαπ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)]
sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ) [cos (µβπ) + tg (βπ /2) sin (µβπ)] ··· −α cos (µαπ) [cos (µβπ ) + tg (βπ /2) sin (µβπ)]
C2 = e0
C3 =
a0 1/ 1 − β 2 − 1/ 1 − α 2
sin (µπ ) − e0 cos (µαπ) α cos (µαπ )
sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ ) sin (µαπ ) tg (βπ /2) ··· −α cos (µαπ ) [cos (µβπ) + tg (βπ /2) sin (µβπ)] a0 1/ 1 − β 2 − 1/ 1 − α 2 sin (µπ ) − e0 cos (µαπ) α cos (µαπ ) C4 = sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ ) sin (µαπ ) ··· −α cos (µαπ ) [cos (µβπ) + tg (βπ /2) sin (µβπ )] Box I.
Fig. 12. Temperature comparison of S-1 between ANSYS and experiment.
Fig. 14. Mechanical model of steel column.
6.2. Yielding load of specimen at elevated temperature
Fig. 13. Temperature comparison of S-2 between ANSYS and experiment.
The elastic modulus of steel at normal temperatures is E = 2.02 × 105 MPa, and the yield strength is fy = 272 MPa. The cross-section area of the specimens is A = 1968 mm2 , and the moment of inertia is Ix = 6438 976 mm4 and Iy = 1002 304 mm4 . The inertia radius is ix = 57.2 mm and iy = 22.6 mm. The slenderness of the column is λx = 47.2 and λy = 119.6, and the stability factor is φx = 0.87. Therefore, the load capacity of the column is N = ϕy fy A = 0.44 × 272 × 1968 = 234 kN. The load ratio is adopted as 0.55 and therefore the load acting on the steel column is P = 0.55 × 234 = 129 kN. The stress in the section of the column is σ = P /A = 128 848/1968 = 65.5 MPa.
The yielding stress of the steel will reduce with an elevation of temperature. When the strength reduces to the stress induced by the load, the column will fail due to it being unable to support the load. According to the equation fyT A = P, the yielding critical temperature can be obtained as Tycr = 692 ◦ C at which the strength is fyT = P /A = 65.5 MPa. For specimen S-1, the column failed in the experiment at 500 ◦ C and is lower than the critical yield temperature, which may be due to the global stability failure arising. For specimen S-2, the failure temperature is 750 ◦ C which is higher than the critical yield temperature. The reason may be that the steel is hardened at high strain at an elevated temperature. At elevated temperatures, the yielding platform for steel is not obvious and nominal yield strength needs to be defined as shown in Fig. 15. Commonly, the nominal yield strength is the strength at which the plastic residual strain, namely nominal strain is a definite quantity. At normal temperatures, the nominal strain is 0.2%. However, at elevated temperatures, the nominal strain is not globally uniform. In ECCS [13], when the temperature is higher than 400, the nominal strain is 0.5%. In BS5950 [14], for flexure resistance composite members, the nominal strain is 2%; for flexure resistance steel members, the nominal strain is 1.5% and for the other members, the nominal strain is 0.5%. In EC3 [12] and EC4 [15], the nominal strain is 2%. In the analysis on the specimens, the nominal strain is
1398
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400 Table 1 Comparison of results between experiment and analysis. Specimen
Critical temperature (◦ C) Experimental results
S-1 S-2
500 750
Analytical results Yielding strength
Continuum model
Minimum
692 692
665 680
665 680
1%. In the experiment, the mechanical strain on the steel column at the portion of fire protection damage is far more than 1%, as can be seen from Fig. 15. The strength of steel at a high strain is larger than the nominal yield strength.
which may be due to the imperfections of specimen S-1 being serious and leading to failure occurring earlier. Furthermore, at the loaded end of the specimen, some load eccentricity may exist. For specimen S-2, yielding occurred earlier than buckling, since the measured critical temperature is higher than that obtained by analysis. However, the measured temperature is also higher than the temperature at which the whole section yields. This may result from the rotational restrained stiffness and material hardening. To know the influence of rational restrained stiffness and load eccentricity on the critical temperature of the specimens, two parametric studies, namely load eccentricity and rotational restrained stiffness are carried out in the following sections.
6.3. Global stable analysis by continuum model
6.5. Influence of load eccentricity on critical temperature
According to the continuum model proposed in Section 5, the deflections of the columns at the boundary of fire protection damage and mid-span are calculated, under the consideration of 1h initial flexure in the mid-span. Based on the failure criteria of edge-fibre-yielding, the critical temperature can be obtained. For the specimens, yielding may occur at the boundary of the fire protection damage or the mid-span. Figs. 16 and 17 show the critical temperatures for the two specimens. As shown in Fig. 16, the temperature at which the mid-span yields is 865 ◦ C and at which the boundary section of fire protection damage yields is 665 ◦ C. Therefore, the failure temperature of the specimen S-1 is 665 ◦ C. As can be seen in Fig. 17, the temperature at which the yielding of mid-span and the boundary sections of the fire protection damage are 960 ◦ C and 680 ◦ C respectively, so the failure temperature of the specimen S-2 is 680 ◦ C.
A parametric study on load eccentricity was conducted to investigate the influence of load eccentricity on the critical temperature of the specimens by the proposed continuum model. The relationship between the critical temperature of the specimens and load eccentricity ratio is plotted in Fig. 18. As can be seen from the figure, the load eccentricity has great influence on the critical temperature and the critical temperature will decrease with elevation of the load eccentricity ratio. For specimen S-1, the critical temperature will be 500 ◦ C at the load eccentricity ratio of 12%.
Fig. 15. Nominal yield strength of steel at elevated temperatures.
6.4. Comparison of results between experiment and analysis The critical temperatures obtained by experiment and analysis are compared and shown in Table 1. As can be seen from the table, for specimen S-1, buckling occurs before the section yields, for the critical temperature measured in the experiment is less than the temperature at which the whole section yields. However, the measured temperature is also less than that obtained by analysis,
6.6. Influence of rotational stiffness on critical temperature In order to investigate the influence of rotational restrained stiffness at the end of the specimens on the critical temperature, two finite element analyses were carried out by ANSYS software, respectively with simple support and rigid support at the two ends of the specimens. The deflection at the boundary of fire protection damage and mid-span are obtained. In the analysis, the initial flexure ratio is adopted as 1h and the element type is Beam188. The stress–strain relationship used in the analysis is the curved stress–strain relationship recommended in EC3 and presented in Fig. 19. The reduction factor for yield strength and elastic modulus used in the relationship is referred to EC3 [12].
Fig. 16. The critical temperature of specimen S-1.
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
1399
Fig. 17. The critical temperature of specimen S-2.
Fig. 18. The influence of load eccentricity on the critical temperature.
Fig. 20. Deflection–temperature curve of the specimens with simple support.
Fig. 19. The strain–stress relationship of steel at elevated temperatures. Fig. 21. Deflection–temperature curve of the specimens with rigid support.
The deflection of the specimens in the boundary section of fire protection and the mid-span are plotted in Figs. 20 and 21. As can be seen from the Figures, the deflections increase with an elevation of temperature and leaps at a definite temperature at which the specimens fail. For specimens with a simple support, the critical temperature are 620 ◦ C and 680 ◦ C respectively for S-1 and S-2. However, For the specimens with a rigid support, the critical temperatures are 675 ◦ C and 695 ◦ C respectively for S-1 and S-2. In order to seen clearly, a comparison of the results is listed in Table 2. From the results of the analysis, some conclusions may be drawn: (1) The boundary condition at the end of the specimen has little influence on the critical temperature. (2) The rational restrained stiffness has a larger influence on the critical temperature for a larger length of fire protection damage at the end of the columns than a smaller one. This may be due to the deflection of the columns being small for the small fire protection damage at the end of the columns and the strength reduction of the steel becoming the main factor results in failure of the specimens at elevated temperatures.
Table 2 The critical temperatures obtained by ANSYS. Boundary condition
Simply supported Rigidly supported
Critical temperature (◦ C) S-1 (l0 = 380 mm)
S-2 (l0 = 190 mm)
620 680
675 695
7. Concluding remarks Through the experimental and analytical study on the fireresistance of steel columns with partial fire protection damage, the following concluding remarks may be drawn: (1) The failure of the columns with partial damaged fire protection in fire happens at the part of fire protection damage. (2) The damage length of the fire protection has a significant influence on the fire-resistance of the steel columns; the shorter the damage length of the fire protection, the higher the critical temperature of the steel columns, at which the columns fail. (3) The failure mode of the steel columns with damaged fire protection is buckling or yielding at the part of fire protection
1400
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
damage. When the fire protection damage is long, failure of the column is due to buckling and when the fire protection damage is short failure is due to yielding. (4) Load eccentricity has large influence on the critical temperature of the steel column with partial fire protection damage. (5) The rotational restraint stiffness has little influence on the critical temperature when the fire protection damage at the ends of the columns is short. Acknowledgements The support of the Natural Science Foundation of China for Innovative Research Groups (Grant No.50621062) and Key Project (Grant No. 50738005) and Scientific Research Foundation of Chongqing University for Recruited Scholars on the study reported in this paper is gratefully acknowledged. References [1] Wang Jia, Li Guo-qiang. Effect of local damage of fire insulation on temperature distribution of steel members subjected to fire. Structural Engineers 2005; 21(5):30–5 [in Chinese]. [2] Wang Wei-Yong, Li Guo-qiang, Wang Pei-Jun. Stable bearing capacity for restrained steel column after damage of fire protection in fire. Chinese Quarterly of Mechanics 2008;3 [in Chinese]. [3] Tomecek DV, Milke JA. A study of the effect of partial loss of protection on the fire resistance of steel columns. Fire Technology 1993;29(1):4–21.
[4] Ryder NL, Wolin SD, Milke JA. An investigation of the reduction in fire resistance of steel columns caused by loss of spray-applied fire protection. Journal of Fire Protection Engineering 2002;12(1):31–44. [5] Kang Y, Hadjisophocleous GV, Khoo HA. The effect of partial fire protection loss on the fire resistance reduction of steel beams. In: Fourth international workshop Structures in fire. 2006. p. 63–74. [6] Milke JA. Analyses of the impact of loss of spray-applied fire protection on the fire resistance of steel columns. In: Evans Davies D, editor. Fire safety science — Proceedings of the seventh international symposium. 2003. [7] Fontana M, Knobloch M. Fire resistance of steel columns with partial loss of fire protection. In: Proceedings of the IABSE symposium Shanghai 2004. Metropolitan habitats and infrastructure. IABSE report vol. 88. 2004. p. 352f. [8] Knobloch M, Raveglia E, Fontana M. Partial loss of fire protection and structural collapse of high-rise buildings. In: International congress fire safety in tall buildings: Santander (Spain) University of Cantabria; October 2006. [9] Pessiki Stephen, Kwon Kihyon, Lee Byoung-Jun. Fire load behavior of steel building columns with damaged spray-applied fire resistive material. In: Fourth international workshop structures in fire. 2006. p. 235–45. [10] American society of testing and materials. ASTM E-119 00a, Standard test method for fire tests of building constructions and materials. Philadelphia: ASTM; 2000. [11] Chinese technical code for fire safety of steel structure in buildings. CECS200:2006. Beijing; 2006. [12] Eurcode 3: Design of steel structures-part 1.2: General actions-structure fire design. London: British Standards Institution. DD ENV 1993-1-2001; September 2001. [13] ECCS. European recommendations for the fire safety of steel structures. 1983. [14] British Standard Institution. BS 5950: Structure use of steel work in building. Part 8: Code of practice for fire resistant design. BSI 1990. [15] European committee for standardization. ENV 1994-1-2. Eurocode 4. Design of composite and concrete structures, part 1.2: Structural fire design. 1994.
Contents lists available at ScienceDirect
Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/jcsr
Behavior of steel columns in a fire with partial damage to fire protection Wei-Yong Wang a,∗ , Guo-Qiang Li b,c a
College of Civil Engineering, Chongqing University, Chongqing, 400045, PR China
b
College of Civil Engineering, Tongji University, Shanghai, 200092, PR China
c
State Key Laboratory for Disaster Reduction in Civil Engineering, Tongji University, Shanghai, 200092, PR China
article
info
Article history: Received 8 May 2008 Accepted 23 January 2009 Keywords: Steel column Fire protection Experimental study Critical temperature
a b s t r a c t An experimental study is performed on two specimens in a furnace to investigate the fire behaviour of steel columns with partial loss of fire protection. The steel columns are connected by flush end-plates at two ends and the axial load is kept constant with a load ratio of 0.55 subjected to an elevation of temperature. The specimens are protected with 20 mm thickness of fire protection. The damaged length of fire protection is 7% of the complete length of the column for specimen S-1 and 14% for S-2 at the two ends of the steel columns. The temperature of atmosphere around the specimens in the furnace is assumed to follow the ISO834 standard temperature and the temperatures and displacements are measured in the experiment. The temperature distribution along the steel column is modelled by finite element analysis and compared with the measured results. A continuum model is presented to predict the ultimate load capacity or critical temperature of the columns with fire protection damage. Analyses are carried out on the specimens and compared with the experiment. Experimental and analytical results showed that the fire resistance of steel columns with partial damage to the fire protection is reduced. The damage length of the fire protection has a great effect on the fire resistance of steel columns. The failure of the specimens mainly resulted from the buckling or yielding at the portion where the fire protection is damaged. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction It is known that unprotected steel structures do not have desirable fire-resistance because the temperature of unprotected steel components increases rapidly in fire due to the high thermal conductivity of steel. Spray-on fire protection is widely used to protect steel structures against fire because spray-on protective materials can efficiently slow down heat transfer from the fire to steel components, and hence lower the rate of temperature increase in steel components. However, spray-on materials are often rather fragile, and they may be easily damaged by mechanical action, such as impacts, earthquakes and explosions, resulting in a possible fire resistance reduction for the steel components originally protected. The tragic events in New York on September 11, 2001 have dramatically shown that mechanical accidental actions followed by a fire can cause local structural failure and even progressive collapse of tall buildings. Thus, it is essential to understand the effect of partial protection damage caused by mechanical action on the fire resistance of steel columns. A few numerical studies have been carried out to investigate the effect of partial spray-on protection damage. Wang et al. [1]
∗
Corresponding author. Tel.: +86 23 65121983. E-mail address: [email protected] (W.-Y. Wang).
0143-974X/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jcsr.2009.01.004
conducted finite element analysis to predict the temperature distribution of steel columns with partial fire protection loss and found that the length and location of fire protection loss has little impact on the model of temperature distribution over the length of steel components. Wang et al. [2] proposed a method to predict the capacity for stability of restrained steel columns based on principle of stationary potential energy. Tomecek and Milke [3] carried out a two-dimensional finite element study to investigate the effect of spray-on protection loss on the fire resistance of steel columns, and showed that a 4% loss of protection resulted in a 15% reduction in the time to reach the critical temperature for a one-hour rated W10X49 column and a 40% reduction in the time for a two-hour rated W10X49 column. Ryder et al. [4] conducted a three-dimensional finite element analysis on a steel column with partial fire protection damage and showed that the fire resistance of the column can be severely diminished if even a small portion of the protection is removed. YU KANG et al. [5] carried out a numerical study to investigate the fire resistance reduction of protected steel beams caused by partial loss of spray-on fire protection and found that partial loss of spray-on fire protection can cause a significant moment capacity reduction for protected steel beams exposed to fire. The results of a heat-transfer analysis of steel columns with partial loss of fire protection using the finite element method were presented by Milke et al. [6]. The results indicated that
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
for a given exposure the area of the missing protection and the size of the column are found to have an appreciable effect upon the thermal response of the column regardless of the protection thickness and the area of the missing protection; this seems to be the primary factor in the temperature rise of the column. Mario Fontana [7] and Markus Knobloch [8] studied the fire behaviour using a three-dimensional finite element heat transfer and structural model, taking into account geometrical nonlinearities, local temperature distributions, thermal strains, and temperature dependent material properties. The results confirmed that local damage of fire protection is a decisive factor for the fire resistance of steel columns and it is important to avoid fire protection damaged by periodical repairs or to use robust fire protection systems. Stephen PESSIKI [9] performed an analysis to examine the behaviour of steel H columns in fires with damaged spray-applied fire resistive material subjected to concentric axial compression. The conclusions declared that the removal of even relatively small amounts of fire resistance material from the column flange causes dramatic decreases in column axial load capacity for fire resistance duration in excess of 30 min. A simplified approach in the temperature domain using the critical temperature criteria for steel columns was used in ASTEM E119 [10] to calculate the fire resistance of steel columns with partially missing fire protection. It seems that the finite element method has been employed by nearly all the previous researchers to study the temperature distribution and fire resistance of steel members with partial loss of fire insulation material. Although the FEM is powerful, it is not straightforward for understanding the failure mechanism of steel members in fires with partial loss of fire protection. In this paper, an experimental study is performed in a furnace to investigate the fire behaviour of steel columns with partial loss of fire protection, the results of which may be used as the database for calibrating the analytical approach including FEM. A continuum model is also presented to predict the ultimate load capacity or critical temperature of the columns with fire protection damage and an analysis is made on the specimens. 2. Material properties In the tests the steel grade of the columns is Q235. At ambient temperature a group of standard tensile test specimens cut from the upper flange and web of the beam section was tested; the Young’s Modulus was found to be 202 kN/mm2 and the yield strength was 272 N/mm2 , the ultimate strength was 413 N/mm2 and the maximum elongation was 18%. At elevated temperatures, the Young’s Modulus and yield strength are adopted as recommended in the Chinese Technical Code for Fire Safety of Steel Buildings [11], which is
ET 7T − 4780 = 20 ◦ C ≤ T ≤ 600 ◦ C E 6T − 4760 ET = 1000 − T 600 ◦ C ≤ T ≤ 1000 ◦ C E 6T − 2800 fyT = 1.0 20 ◦ C ≤ T ≤ 300 ◦ C f y fyT = 1.24 × 10−8 T 3 − 2.096 × 10−5 T 2 fy + 9.228 × 10−3 T − 0.2168 300 ◦ C < T < 800 ◦ C f yT = 0.5 − T 800 ◦ C ≤ T ≤ 1000 ◦ C fy
1393
Fig. 1. Sketch of the test set-up.
3. Experimental study 3.1. Test arrangement and instrumentation Tests were performed in a furnace. The sketch of the experimental set-up is shown in Fig. 1. The temperature–time curve of the furnace follows the ISO834 standard. The instrumentation includes displacement transducers for measuring axial and lateral displacements of the steel columns, load transducers for measuring load and thermocouples for measuring the temperature of the furnace as well as the specimens. Four displacement transducers were employed in the experiments. One of which is used to measure the axial displacement and the others for measuring the lateral displacement of the specimens. Nine thermocouples were utilised to measure the temperature of the specimens, three of which were for measuring the temperature on the portion without fire protection and the others for the portion with fire protection. The axial load, simulating the internal force in the columns, was introduced by a hydraulic jack attached to a reaction frame and powered by a pressure controlled pump, which was kept constant as the specimen expanded and buckled due to increasing temperature. Both fire protection and an aluminium silicate blanket are used to protect the steel portion of the reaction frame in the furnace from the fire. The arrangement of the thermocouples and displacement transducer over the specimen is shown in Fig. 2. The testing procedure comprises three steps. First, the specimen is loaded axially up to a pre-determined load level. Then the fire in the furnace was started and a constant load maintained on the specimen. Finally, the fire in the furnace was stopped when failure occurred in the specimens. Temperatures and displacements were recorded at various times in the constant-load tests. 3.2. Specimen details
(1)
(2)
2000
where ET is modulus of elasticity of steel at a given temperature; E is modulus of elasticity of steel at ambient temperature; fyT is yield strength of steel at a given temperature; fy is yield strength of steel at ambient temperature and T is the temperature of the steel.
The specimens are 2.7 m long columns fabricated with H shaped structural steel and the cross section of which is H140 × 100 × 6 × 6. The steel columns are connected by flush end-plates at the two ends and the axial load is kept constant with a load ratio of 0.55 and subjected to an elevation of temperature in the furnace. The load ratio is defined as a ratio of the load on the steel column to column buckling resistance at the normal temperature. The specimens are protected with a 20 mm depth of fire protection. At the two ends of the steel columns, partial fire protection is damaged artificially through moving it away in order to investigate the behaviour of steel columns with a partial loss of fire protection in a fire. The damaged length of the fire protection is 7% of the column length for one specimen and 14% for another one, which are approximately 190 mm and 380 mm long respectively. The specimen detail is shown in Fig. 3.
1394
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
Fig. 2. Thermocouples and displacement transducer arrangement.
(a) S-1.
(b) S-2.
(c) End-pate joint.
Fig. 3. Specimen details.
Fig. 4. Temperature–time curve of Specimen S-1.
Fig. 5. Temperature–time curve of Specimen S-2.
3.3. Temperature distribution
3.4. Axial displacement and failure temperatures
Figs. 4 and 5 show typical variations against time of the temperatures of the furnace atmosphere, the portion of the steel columns without fire protection, the portion of the steel columns with fire protection during the heating and cooling phases. The temperature of the fire could be controlled to closely follow the ISO834 standard fire temperature curve except in the beginning. Due to the fire protection, in the portion of the column with fire protection, the temperature initially rose much more slowly than the portion of the column without fire protection. The difference between the temperatures of the portion without fire protection and with fire protection increased to almost 500 ◦ C after about 25 min. After the fire was stopped, and the rate of rise in the fire temperature reduced, the rate of rise of temperature in the portion without fire protection also reduced as a result of the lower radiation increase. However, conduction of heat into the portion with fire protection continued.
Fig. 6 shows the time–axial displacement curves for columns with partial fire protection damage. For specimen S-1, after the specimen is exposed to fire for 15 min, the axial displacement increases rapidly and buckling occurs. However, for specimen S-2, the time exposed to the fire can last 40 min due to the length of the column without fire protection being subjected to fire is short. Fig. 7 shows the temperature–axial displacement curves for specimens. The load-bearing capacity of steel columns will be reduced with an elevation of temperature and the steel columns will fail when the load-bearing capacity reaches the ultimate bearing capacity in a fire. When failure occurs, a great displacement along the axis will appear. With the elevation of temperature of steel columns, the loadbearing capacity will decrease and failure occurs when the column buckles or the section yields at some location of the columns, and the axial displacement of the column will increase rapidly. Based on the experiment results, the critical temperature of steel
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
1395
4. Heat transfer analyses The heat transfer mechanisms included in the heat transfer analyses are conduction, convection and radiation. Solid70 elements were used to model both steel columns and fire protection. These elements are three-dimensional-eight-node linear heat transfer elements. Fig. 10 shows the finite element model of S-1 and S-2. The thermal conductivity of the steel as a function of temperature was specified as given in the Eurocode 3 [12]. Similarly, the specific heat of the steel as a function of temperature was specified as given in the Eurocode 3 [12]. Convection and radiation boundary conditions were specified where member surfaces were exposed to fire. The thermal conductivity and specific heat of the fire protection are 0.05 W/(m ◦ C) and 1100 J/(kg ◦ C) respectively, which were given by the coating manufacture company. The density of the coating is 350 kg/m3 . Fig. 11 shows the temperature distribution of the steel along the axial direction of Specimen S-1 and S-2, obtained by using the commercial FEM package ANSYS. As can be seen from Fig. 11, the temperature is high at the portion without fire protection and the temperature is low at the portion with fire protection. There is a temperature transition between the two portions. Figs. 12 and 13 show the comparison of results between analysis and experiment. The results in Figs. 12 and 13 show that the temperature of the steel of both specimens at the portion with fire protection and without fire protection obtained with analytical prediction and experimental measurement agrees with each other well.
Fig. 6. Axial displacement-time curve of the specimens.
5. Continuum model Fig. 7. Axial displacement–temperature curve of the specimens.
columns with partial fire protection damage is defined here as the temperature of the steel in the portion without fire protection at which the axial displacement increases abruptly. As can be seen from Fig. 7, the critical temperatures of the specimen S-1 and S-2 are 500 ◦ C and 750 ◦ C respectively. 3.5. Failure of specimens Figs. 8 and 9 show the failure of the two specimens. For specimen S-1, buckling only occurs around the weak axis on the portion without fire protection near to the applied load. For specimen S-2, section yielding occurs on the two parts of the column without fire protection. The yielding at the portion near the end of the applied load is more serious than the other portion which can be seen clearly from the Fig. 9.
(a) end A.
Fig. 14 shows the mechanical model of a steel column with damaged fire protection at the two ends. The initial flexure of the column may be expressed by y0 = a0 sin (π x/l)
(3)
where l is the length of the column, and a0 is the initial flexure at the mid-span of the column. If the lateral displacements of the column at the location without fire protection and with fire protection are y1 and y2 respectively, according to the differential equation of equilibrium, the following equation can be obtained as
(
ET 1 I (y1 − y0 )00 + P (y1 + e0 ) = 0
0 ≤ y ≤ l0
ET 2 I (y2 − y0 )00 + P (y2 + e0 ) = 0
l0 ≤ y ≤ l/2
(4)
where ET 1 is elastic modulus of steel at temperature T1 ; ET 2 is elastic modulus of steel at temperature T2 ; T1 is the temperature in the portion of the column with damaged fire protection; T2 is
(b) end B. Fig. 8. Failure of Specimen S-1.
1396
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
(a) end A.
(b) end B. Fig. 9. Failure of Specimen S-2.
ratio; hc is height of the cross-section of the column; P is axial force on the column. The general solution to Eq. (4) can be given by
y1 = C1 sin (απ x/l) + C2 cos (απ x/l) a0 sin(π x/l) − e0 + 1 − α2 y = C sin x/l) + C4 cos (βπ x/l) (βπ 2 3 a0 sin(π x/l) − e0 + 1 − β2 Fig. 10. Finite element model of S-1 and S-2.
the temperature in the portion of the column with integrated fire protection; I is inertial moment of column; l0 is the length of the damaged fire protection and e0 is load eccentricity. Due to the displacement at two ends being zero and the rotation of the cross-section of the column continuing through the overall length, the following boundary conditions can be adopted as
y1 (0) = 0, y1 l y01 l0 = −y02 l0 ,
0
0
= y2 l y02 (l/2) = 0.
(5)
For convenience, the following parameters are defined as
µ = l0 /l, ε = a0 /l, η = e 0 / hc 2 2 Pcr1 = π ET 1 I /l , Pcr2 = π 2 ET 2 I /l2 , p p α = P /Pcr1 , β = P /Pcr2
(6)
(7)
where µ is damage length ratio of the fire protection of the column; ε is initial flexure ratio of the column; η is the load eccentricity
(8)
where the parameters C1 C2 C3 C4 are determined by employing the boundary condition (Eq. (5)), given in Box I. If we take the edge fibre yield at the most probable location of the column as the failure criterion, the ultimate load capacity of the column with partial loss of fire protection can be predicted by
P Pa + max 1 = fyT 1 A P
+
W Pamax 2
= fyT 2
(a) (9) (b)
A W where A is area of the cross-section of the column; W is the section flexure modulus of the column; fyT 1 is the yield strength of steel at temperature T1 ; fyT 2 is the yield strength of steel at temperature T2 ; amax 1 = y1 (l1 ), and amax 2 = y2 (l/2). 6. Experiment analysis 6.1. Basic details of the specimens The height of the section is H = 140 mm and the width is B = 100 mm. The thickness of the web and flange is tw = tf = 6 mm.
Fig. 11. Temperature distribution of S-1 and S-2 (60 min).
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
C1 =
a0 1/ 1 − β 2 − 1/ 1 − α 2
1397
sin (µπ ) − e0 cos (µαπ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)]
sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ) [cos (µβπ) + tg (βπ /2) sin (µβπ)] ··· −α cos (µαπ) [cos (µβπ ) + tg (βπ /2) sin (µβπ)]
C2 = e0
C3 =
a0 1/ 1 − β 2 − 1/ 1 − α 2
sin (µπ ) − e0 cos (µαπ) α cos (µαπ )
sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ ) sin (µαπ ) tg (βπ /2) ··· −α cos (µαπ ) [cos (µβπ) + tg (βπ /2) sin (µβπ)] a0 1/ 1 − β 2 − 1/ 1 − α 2 sin (µπ ) − e0 cos (µαπ) α cos (µαπ ) C4 = sin (µαπ ) [β tg (βπ /2) cos (µβπ) − β sin (µβπ)] − a0 1/ 1 − β 2 − 1/ 1 − α 2 cos (µπ ) − e0 α sin (µαπ ) sin (µαπ ) ··· −α cos (µαπ ) [cos (µβπ) + tg (βπ /2) sin (µβπ )] Box I.
Fig. 12. Temperature comparison of S-1 between ANSYS and experiment.
Fig. 14. Mechanical model of steel column.
6.2. Yielding load of specimen at elevated temperature
Fig. 13. Temperature comparison of S-2 between ANSYS and experiment.
The elastic modulus of steel at normal temperatures is E = 2.02 × 105 MPa, and the yield strength is fy = 272 MPa. The cross-section area of the specimens is A = 1968 mm2 , and the moment of inertia is Ix = 6438 976 mm4 and Iy = 1002 304 mm4 . The inertia radius is ix = 57.2 mm and iy = 22.6 mm. The slenderness of the column is λx = 47.2 and λy = 119.6, and the stability factor is φx = 0.87. Therefore, the load capacity of the column is N = ϕy fy A = 0.44 × 272 × 1968 = 234 kN. The load ratio is adopted as 0.55 and therefore the load acting on the steel column is P = 0.55 × 234 = 129 kN. The stress in the section of the column is σ = P /A = 128 848/1968 = 65.5 MPa.
The yielding stress of the steel will reduce with an elevation of temperature. When the strength reduces to the stress induced by the load, the column will fail due to it being unable to support the load. According to the equation fyT A = P, the yielding critical temperature can be obtained as Tycr = 692 ◦ C at which the strength is fyT = P /A = 65.5 MPa. For specimen S-1, the column failed in the experiment at 500 ◦ C and is lower than the critical yield temperature, which may be due to the global stability failure arising. For specimen S-2, the failure temperature is 750 ◦ C which is higher than the critical yield temperature. The reason may be that the steel is hardened at high strain at an elevated temperature. At elevated temperatures, the yielding platform for steel is not obvious and nominal yield strength needs to be defined as shown in Fig. 15. Commonly, the nominal yield strength is the strength at which the plastic residual strain, namely nominal strain is a definite quantity. At normal temperatures, the nominal strain is 0.2%. However, at elevated temperatures, the nominal strain is not globally uniform. In ECCS [13], when the temperature is higher than 400, the nominal strain is 0.5%. In BS5950 [14], for flexure resistance composite members, the nominal strain is 2%; for flexure resistance steel members, the nominal strain is 1.5% and for the other members, the nominal strain is 0.5%. In EC3 [12] and EC4 [15], the nominal strain is 2%. In the analysis on the specimens, the nominal strain is
1398
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400 Table 1 Comparison of results between experiment and analysis. Specimen
Critical temperature (◦ C) Experimental results
S-1 S-2
500 750
Analytical results Yielding strength
Continuum model
Minimum
692 692
665 680
665 680
1%. In the experiment, the mechanical strain on the steel column at the portion of fire protection damage is far more than 1%, as can be seen from Fig. 15. The strength of steel at a high strain is larger than the nominal yield strength.
which may be due to the imperfections of specimen S-1 being serious and leading to failure occurring earlier. Furthermore, at the loaded end of the specimen, some load eccentricity may exist. For specimen S-2, yielding occurred earlier than buckling, since the measured critical temperature is higher than that obtained by analysis. However, the measured temperature is also higher than the temperature at which the whole section yields. This may result from the rotational restrained stiffness and material hardening. To know the influence of rational restrained stiffness and load eccentricity on the critical temperature of the specimens, two parametric studies, namely load eccentricity and rotational restrained stiffness are carried out in the following sections.
6.3. Global stable analysis by continuum model
6.5. Influence of load eccentricity on critical temperature
According to the continuum model proposed in Section 5, the deflections of the columns at the boundary of fire protection damage and mid-span are calculated, under the consideration of 1h initial flexure in the mid-span. Based on the failure criteria of edge-fibre-yielding, the critical temperature can be obtained. For the specimens, yielding may occur at the boundary of the fire protection damage or the mid-span. Figs. 16 and 17 show the critical temperatures for the two specimens. As shown in Fig. 16, the temperature at which the mid-span yields is 865 ◦ C and at which the boundary section of fire protection damage yields is 665 ◦ C. Therefore, the failure temperature of the specimen S-1 is 665 ◦ C. As can be seen in Fig. 17, the temperature at which the yielding of mid-span and the boundary sections of the fire protection damage are 960 ◦ C and 680 ◦ C respectively, so the failure temperature of the specimen S-2 is 680 ◦ C.
A parametric study on load eccentricity was conducted to investigate the influence of load eccentricity on the critical temperature of the specimens by the proposed continuum model. The relationship between the critical temperature of the specimens and load eccentricity ratio is plotted in Fig. 18. As can be seen from the figure, the load eccentricity has great influence on the critical temperature and the critical temperature will decrease with elevation of the load eccentricity ratio. For specimen S-1, the critical temperature will be 500 ◦ C at the load eccentricity ratio of 12%.
Fig. 15. Nominal yield strength of steel at elevated temperatures.
6.4. Comparison of results between experiment and analysis The critical temperatures obtained by experiment and analysis are compared and shown in Table 1. As can be seen from the table, for specimen S-1, buckling occurs before the section yields, for the critical temperature measured in the experiment is less than the temperature at which the whole section yields. However, the measured temperature is also less than that obtained by analysis,
6.6. Influence of rotational stiffness on critical temperature In order to investigate the influence of rotational restrained stiffness at the end of the specimens on the critical temperature, two finite element analyses were carried out by ANSYS software, respectively with simple support and rigid support at the two ends of the specimens. The deflection at the boundary of fire protection damage and mid-span are obtained. In the analysis, the initial flexure ratio is adopted as 1h and the element type is Beam188. The stress–strain relationship used in the analysis is the curved stress–strain relationship recommended in EC3 and presented in Fig. 19. The reduction factor for yield strength and elastic modulus used in the relationship is referred to EC3 [12].
Fig. 16. The critical temperature of specimen S-1.
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
1399
Fig. 17. The critical temperature of specimen S-2.
Fig. 18. The influence of load eccentricity on the critical temperature.
Fig. 20. Deflection–temperature curve of the specimens with simple support.
Fig. 19. The strain–stress relationship of steel at elevated temperatures. Fig. 21. Deflection–temperature curve of the specimens with rigid support.
The deflection of the specimens in the boundary section of fire protection and the mid-span are plotted in Figs. 20 and 21. As can be seen from the Figures, the deflections increase with an elevation of temperature and leaps at a definite temperature at which the specimens fail. For specimens with a simple support, the critical temperature are 620 ◦ C and 680 ◦ C respectively for S-1 and S-2. However, For the specimens with a rigid support, the critical temperatures are 675 ◦ C and 695 ◦ C respectively for S-1 and S-2. In order to seen clearly, a comparison of the results is listed in Table 2. From the results of the analysis, some conclusions may be drawn: (1) The boundary condition at the end of the specimen has little influence on the critical temperature. (2) The rational restrained stiffness has a larger influence on the critical temperature for a larger length of fire protection damage at the end of the columns than a smaller one. This may be due to the deflection of the columns being small for the small fire protection damage at the end of the columns and the strength reduction of the steel becoming the main factor results in failure of the specimens at elevated temperatures.
Table 2 The critical temperatures obtained by ANSYS. Boundary condition
Simply supported Rigidly supported
Critical temperature (◦ C) S-1 (l0 = 380 mm)
S-2 (l0 = 190 mm)
620 680
675 695
7. Concluding remarks Through the experimental and analytical study on the fireresistance of steel columns with partial fire protection damage, the following concluding remarks may be drawn: (1) The failure of the columns with partial damaged fire protection in fire happens at the part of fire protection damage. (2) The damage length of the fire protection has a significant influence on the fire-resistance of the steel columns; the shorter the damage length of the fire protection, the higher the critical temperature of the steel columns, at which the columns fail. (3) The failure mode of the steel columns with damaged fire protection is buckling or yielding at the part of fire protection
1400
W.-Y. Wang, G.-Q. Li / Journal of Constructional Steel Research 65 (2009) 1392–1400
damage. When the fire protection damage is long, failure of the column is due to buckling and when the fire protection damage is short failure is due to yielding. (4) Load eccentricity has large influence on the critical temperature of the steel column with partial fire protection damage. (5) The rotational restraint stiffness has little influence on the critical temperature when the fire protection damage at the ends of the columns is short. Acknowledgements The support of the Natural Science Foundation of China for Innovative Research Groups (Grant No.50621062) and Key Project (Grant No. 50738005) and Scientific Research Foundation of Chongqing University for Recruited Scholars on the study reported in this paper is gratefully acknowledged. References [1] Wang Jia, Li Guo-qiang. Effect of local damage of fire insulation on temperature distribution of steel members subjected to fire. Structural Engineers 2005; 21(5):30–5 [in Chinese]. [2] Wang Wei-Yong, Li Guo-qiang, Wang Pei-Jun. Stable bearing capacity for restrained steel column after damage of fire protection in fire. Chinese Quarterly of Mechanics 2008;3 [in Chinese]. [3] Tomecek DV, Milke JA. A study of the effect of partial loss of protection on the fire resistance of steel columns. Fire Technology 1993;29(1):4–21.
[4] Ryder NL, Wolin SD, Milke JA. An investigation of the reduction in fire resistance of steel columns caused by loss of spray-applied fire protection. Journal of Fire Protection Engineering 2002;12(1):31–44. [5] Kang Y, Hadjisophocleous GV, Khoo HA. The effect of partial fire protection loss on the fire resistance reduction of steel beams. In: Fourth international workshop Structures in fire. 2006. p. 63–74. [6] Milke JA. Analyses of the impact of loss of spray-applied fire protection on the fire resistance of steel columns. In: Evans Davies D, editor. Fire safety science — Proceedings of the seventh international symposium. 2003. [7] Fontana M, Knobloch M. Fire resistance of steel columns with partial loss of fire protection. In: Proceedings of the IABSE symposium Shanghai 2004. Metropolitan habitats and infrastructure. IABSE report vol. 88. 2004. p. 352f. [8] Knobloch M, Raveglia E, Fontana M. Partial loss of fire protection and structural collapse of high-rise buildings. In: International congress fire safety in tall buildings: Santander (Spain) University of Cantabria; October 2006. [9] Pessiki Stephen, Kwon Kihyon, Lee Byoung-Jun. Fire load behavior of steel building columns with damaged spray-applied fire resistive material. In: Fourth international workshop structures in fire. 2006. p. 235–45. [10] American society of testing and materials. ASTM E-119 00a, Standard test method for fire tests of building constructions and materials. Philadelphia: ASTM; 2000. [11] Chinese technical code for fire safety of steel structure in buildings. CECS200:2006. Beijing; 2006. [12] Eurcode 3: Design of steel structures-part 1.2: General actions-structure fire design. London: British Standards Institution. DD ENV 1993-1-2001; September 2001. [13] ECCS. European recommendations for the fire safety of steel structures. 1983. [14] British Standard Institution. BS 5950: Structure use of steel work in building. Part 8: Code of practice for fire resistant design. BSI 1990. [15] European committee for standardization. ENV 1994-1-2. Eurocode 4. Design of composite and concrete structures, part 1.2: Structural fire design. 1994.