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A numerical model for evaluating fire performance of composite box bridge girders
Journal of Constructional Steel Research 165 (2020) 105823
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A numerical model for evaluating fire performance of composite box bridge girders Gang Zhang a, *, Venkatesh Kodur b, Chaojie Song a, Shuanhai He a, Qiao Huang c a
School of Highway, Chang'an University, Xi'an, Shaanxi, 710064, China Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, 48864, USA c School of Transportation, Southeast University, Nanjing, 210096, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 June 2019 Received in revised form 8 October 2019 Accepted 21 October 2019 Available online xxx
This paper presents an approach for evaluating fire performance of composite box bridge girders exposed to fire. The model takes into account critical parameters, namely, fire scenario, fire exposure length, load level, numbers of longitudinal stiffeners in web and bottom flange and web pattern, that influence fire performance of bridges. A three dimensional finite element model, developed in the computer program ANSYS, is applied to model the fire response of composite box bridge girders. The finite element model is validated by comparing predicted sectional temperatures and deflections from the model with fire test data generated from a test on box bridge girder. The applicability of the numerical model in practical application is illustrated through numerical analysis on a composite box bridge girder subjected to simultaneous structural loading and fire exposure. Results from the numerical study clearly show that fire severity, fire exposure length, load level, number of longitudinal stiffeners and web slenderness have significant influence on the fire resistance of composite bridge girders. Provision of longitudinal stiffeners can result in lower deflections; thus enhancing fire resistance. Further, inclined web (configuration) incorporated into sectional shape can enhance fire resistance of composite box bridge girders. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Bridge fires Fire resistance Composite box bridge girders Finite element analysis Thermo-structural analysis
1. Introduction Steel-concrete composite box bridge girders, comprising of a Ushaped steel girder (vertical or inclined web) supporting a reinforced concrete slab, are widely used in medium- and long-span bridge construction (See Fig. 1) due to number of advantages such girders offer over other traditional steel girders [1e7]. These advantages include rapid fabrication of steel shapes, ease of installation, light weight, strong crossing ability, conducive to environment protection, cost effectiveness, and high wind resistance and seismic performance [8e12]. However, a major drawback of composite box bridge girders is that steel shapes (girders) exhibit much lower fire resistance than similar concrete structural members due to low specific heat, high thermal conductivity and rapid degradation of strength and modulus of steel at elevated temperatures. As a result, steel shapes, in composite box bridge girders loose their capacity at a faster pace under fire exposure conditions. While structural members in building are required to have sufficient fire resistance in the event of a fire, there is no specific fire resistance
* Corresponding author. E-mail address: [email protected] (G. Zhang). https://doi.org/10.1016/j.jcsr.2019.105823 0143-974X/© 2019 Elsevier Ltd. All rights reserved.
requirements for bridge structures as per current codes and standards [13,14]. In the last three decades, there has been an increase in the number of fires on bridges. This is due to rapid raise in transportation of fuels, chemicals and highly combustible products that contain deflagrated and flammable materials. These fuels combust rapidly and burn at high intensity reaching temperature of 1000 C with the first few minutes of fire exposure. Such high intense fire can pose a severe threat to stability of structural members in a bridge and, in some instances, even can produce large deflections or even collapse of the bridges [15e17]. Damage or collapse, specially in case of critical bridges, can lead to high property losses, and lengthy repair process. Further any delays resulting from traffic detouring to nearby routes can add to significant indirect costs, as well as hardships to commuters and general public (i.e. congestion and traffic pressure). There are a number of instances of fire-damage in bridges and these are reported in the literature [8e18]. Fire induced collapse in bridges such as the MacArthur Maze I-80/880 interchange in Okland, California in 2007, and the I-75 expressway near Hazel Park, Michigan in 2009, are clear examples of damage from high intensity fires [8e18]. Recent fire incident, caused by an overturned oil tanker when passing through the Mathilde Bridge in Rouen,
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2. Selection of composite box bridge girder for analysis A typical highway steel-concrete composite bridge girder, fabricated with box-shaped steel section and a concrete slab, is selected for fire resistance analysis. The box shaped girder, with vertical web, spans a length of 30 m, and has width of 3.1 m, and height of 1.6 m, and has simply supported ends. The slab on the top of composite box bridge girder is made of concrete of compressive strength (cube strength) of 50 MPa. The yield strength of steel used in box girder is 345 MPa. To increase bending capacity of composite box bridge girder, transverse diaphragms were provided every 3 m along span length. Two transverse stiffeners were placed evenly between two transverse diaphragms. Concrete slab is reinforced with rebars of 12 mm and yield strength of 420 MPa. The sectional details of the box-shaped steel girder and reinforced concrete slab are shown in Fig. 2, and also in Table 1. 3. Numerical model A three dimensional numerical model, is developed in ANSYS [24] to evaluate response of composite box bridge girders under fire exposure conditions. The above discussed composite box bridge girder comprising of U-shaped steel girder, RC slab, intermediate diaphragms and transverse and longitudinal stiffeners, is analyzed under the effects of fire exposure and structural loading to trace the response during the entire range of behavior, from start of fire exposure till failure of the girder. 3.1. Analysis details Fig. 1. Bridge construction using composite box girder.
France, in 2012, is an example of devastation of fire on a bridge. This fire-damaged bridge was so severe that could be opened after two years. The economic loss caused by this fire event was estimated at about £18 million [18], which clearly shows how bridge fires can lead to significant economic losses. Much of the fire research [19e24] in the past four decades concentrated on structural members, typically used in buildings. Although fire insulation are required to mitigate fire damage to critical structural members in case of buildings, application of such measure is not realistic or practical in structural members in bridges due to major cost implications and application complexities. However, limited research has been performed to improve the fire resistance of bridge structural members. Currently, there are very few fire experiments that have been performed on composite bridge with I-shaped steel girder under fire exposure conditions [8e22]. In these limited tests, the influence of web buckling, composite action, prestressing tendon on Ishaped steel girders are investigated [8e22]. These test specimens have small spans and simplified structural configuration, and are only enforced with concentrated loading under a low intense fire exposure (ISO 834). However, these studies and experimental work do not reflect the response of realistic bridge fires encountered in practice. This can be attributed to the difference of fire severity, geometric configuration, material characteristics, structural shapes, dimensions of girders as well as load patterns. Therefore, there is limited information on the behavior of composite box bridge girders under realistic fire exposure conditions. To overcome these gaps, an investigation in to fire performance of composite box bridge girder under different fire exposure conditions is undertaken as part of this study.
A coupled thermo-mechanical analysis is applied to trace the behavior of girder under localized fire exposure and simultaneous structural loading. In the first step, the temperature rise in the girder resulting from fire exposure is computed and a heat transfer analysis is carried out to determine temperature progression with in the girder section. In the second step, the structural response of the composite box bridge girder, due to the combined effects of fire exposure and structural loading, is evaluated. The fire resistance analysis on composite box bridge girder is carried out under an applied loading consisting of 100％ dead load plus 30％ live load (vehicle load). The self-weight of the box bridge girder and the pavement (12 kN/m) constitute the dead load. The live load is comprised of a concentrated load (96 kN) enforced on midspan and a uniform load (3.15 kN/m) distributed over the bridge girder span. These load distribution pattern is in line with recommended design values of practical vehicle lane loads as per China code [25]. Based on the preliminary analysis, a concentrated load enforced on midspan of simply supported composite box bridge girders is regarded to be the worst-case loading scenario. 3.2. Discretization of girder For the thermal analysis, the box-shaped steel girder together with diaphragm and stiffeners, was discretized with a 3-D “SHELL57” element, that is applicable to steady-state or transient thermal analysis, as shown in Fig. 3. The concrete slab was discretized using “SOLID70” element which has a 3-D thermal conduction capability. This element having eight nodes with a single degree of freedom, i.e. temperature, at each node, is suitable to model steady-state or transient thermal analysis problem. The rebars with in concrete slab was discretized with LINK33 element, and these are uniaxial elements with the ability to conduct heat between two nodes.
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Fig. 2. Details of composite box bridge girder (Unit: mm).
Table 1 Parameters related to sectional geometry. Portions
Height (mm)
Width (mm)
Thickness (mm)
box-shaped steel girder Bottom flange Web Top flange Diaphgram Stiffener
1446 e 1400 e e e
1500 1582 e 400 e 150
e 24 18 22 18 18
Both convection and radiation heat transfer effect was applied at the fire exposed surface areas of the shell and solid elements. In addition, radiation loads were also applied at the surface of the concrete slab inside box-shaped steel girder. Convection heat transfer coefficients of ac ¼ 50 W/(m2 C) and ac ¼ 25 W/(m2 C)
were used for the thermal analysis under hydrocarbon and ISO 834 fire exposure conditions [26,27] respectively as per Eurocode 1 [28]. Different values of effective emissivity factor associated with the exposure boundaries were applied in the thermal analysis as per specific provisions. Effective emissivity coefficients of 0.7 and 0.5 were applied for the bottom flange and the web outside box section respectively, and an effective emissivity of 0.4 was applied for the fire exposed surface of the top flange and bottom of the concrete slab. To simulate heat emissivity inside box steel girder at elevated temperature, an emissivity factor of 0.2 was used for the concrete slab inside box girder to account for radiation generated from steel girder under high temperature effects. A Stefan-Botzmann radiation constant of 5.67 108 W/(m2 C4) was applied to simulate radiative heat transfer. For structural analysis, the composite box bridge girder was modeled with three elements, namely, SHELL181 element for the
Fig. 3. 3-D discretization of composite box bridge girder.
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box steel girder, SOLID65 element for the concrete slab, and LINK8 element for the rebar [24], as shown in Fig. 3. SHELL181, a 4-node element with three translations and rotations degree of freedom at each node, is well-suited for analyzing thin to moderately-thick shell structures and also suitable for linear, large rotation and large strain nonlinear problems. SOLID65 elements used for modeling concrete with and without reinforcing steel are capable of accounting for cracking in tension and crushing in compression, which links well with LINK8 elements used to model rebar. 3.3. Material properties Temperature dependent thermal properties of steel and concrete, namely thermal conductivity, specific heat and thermal expansion were provided as input data into ANSYS, and these property relations are taken from Eurocodes 2 and 3 relations [29,30] and other sources [31]. Mechanical properties of concrete and steel, varying as a function of temperature, were applied as per the specified relations taken from literature [29,30]. Stress-strain relations of concrete and steel have predominant influence on fire-resistance, and these relations vary significantly with temperature rise, as shown in Fig. 4.
200 mm respectively, and the width of concrete slab and box steel girder is 700 mm and 320 mm respectively. The thickness of bottom flange, web and top flange is equal to 5 mm. The diameter and height of shear studs are designed to be 20 mm and 80 mm, respectively. The steel reinforcement used to reinforce the concrete slab has diameter of 12 mm. The validation was performed by comparing thermal and structural response predictions from the analysis with that measured in fire test. Fig. 6(a) shows a comparison of predicted temperature at different depths in the section by the FEM model with temperature data measured during fire tests. It can be seen that the predicted temperatures agree well with those measured in fire tests. The slight difference in temperature can be attributed to variation in actual fire test conditions and adopted temperature-dependent thermal parameters, such as convection coefficient and emissivity for the thermal analysis. Fig. 6(b) shows a comparison of midspan deflection of the girder predicted using the FEM model with that reported in the fire test. It can be seen that predictions from ANSYS match well with test data. Slight variation in deflections can be attributed to idealization of fire and variations in mechanical properties, adopted in the analysis from that present in tests (such as actual fire exposure length and stressestrain relations of concrete and steel).
3.4. Failure criterion 4. Parametric study Fire resistance analysis on the girder is carried out at incrementing time steps, till failure occurred through one of the limiting states; through deflection or strength limit state. According to deflection and rate of deflection limit state, when maximum deflection in a girder surpasses L2/400d (1360 mm) limit or rate of deflection reaches L2/9000d (60.5 mm/min) [32], the girder is said to fail. As per strength limit state, if moment capacity drops below bending moment arising from applied structural loading, then failure of the girder is said to occur. 3.5. Model validation The above finite element model is validated by selecting a scaled composite box bridge girder tested under localized fire exposure condition whose temperature rise follow that of ISO834 fire [4,27,33]. The fire exposure length symmetric about the mid-span is 1.4 m. The U-shaped steel girder supporting a reinforced concrete slab, has a span length of 3.4 m with simply support conditions (See Fig. 5). The height of total section and that of web are 300 mm and
To evaluate fire behavior of a typical composite box bridge girder under localized fire exposure conditions, a simply supported composite box bridge girder was analyzed with the above model by subjecting the composite girder to varying parameters, including fire severity, load level, stiffness and web configuration. 4.1. Thermal gradients Fig. 7 shows the thermal gradients developed across the depth of the section of composite box bridge girder with fire exposure time. It can be seen that temperature distribution along the girder depth is quite similar and temperature increases gradually with fire exposure time, however hydrocarbon fire exposure produces larger temperature rise, as expected. At 15 min and 50 min of hydrocarbon fire and ISO 834 fire exposure respectively, the temperature in bottom flange and web surpass 600 C. This temperature rise leads to rapid deterioration of mechanical properties in steel leading to significant degradation in flexural capacity of the girder.
Fig. 4. Stress - strain relations for concrete and steel.
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Fig. 5. Dimensions of the test girder.
Fig. 6. Comparison of predicted and measured data.
Fig. 7. Thermal gradient along the depth of a bridge girder section.
The peak temperature attained in concrete slab and steel girder under two different fire scenarios are shown in Table 2. The concrete temperatures are on the unexposed side of the slabs. In Case 1, these sectional temperatures are captured prior to failure of the girder, while in “Case 2” the sectional temperatures are shown at different fire exposure time. It can be seen in Table 2 that the peak temperature in concrete slab (rebar) and steel girder are much higher under hydrocarbon fire exposure than that under ISO 834 fire exposure. The higher sectional temperatures result in earlier failure time.
4.2. Structural response The structural response of a typical box composite bridge girder is illustrated in Fig. 8, where midspan deflection of the girder is plotted as a function of fire exposure time, for varying scenarios, namely fire severity (Case 1), fire exposure length (Case 2), load level (Case 3), longitudinal stiffeners in compression portion of web and bottom flange (Cases 4 and 5) and transverse stiffeners in web (Case 6), and web configuration (Case 7). From previous literature, fire exposure around midspan of a simply supported bridge girder,
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Table 2 Peak temperature in concrete slab and steel girder. Case
Parameter
Case 1
Fire severity
Case 2
Fire exposure length
Time
Prior to failure Prior to failure 40 min 35 min 33 min
Peak temperature ( C)
Fire scenarios
Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire
is the worst-condition of fire scenario, therefore, fire exposure length is assumed to be 10 m, 20 m and 30 m symmetric about the midspan respectively. The live load present during fire exposure is varied as 30％, 65％ and 100％. The number of longitudinal stiffeners, evenly distributed in compression portion of web, is designed to be two and three, respectively. The number of longitudinal stiffeners, evenly distributed in bottom flange, is varied as three, four and five. The number of transvers stiffeners, uniformly provided between two neighboring transverse diaphragms, is assumed to be one and two, respectively. Web configuration, including vertical and inclined web incorporated into sectional shape, is varied to evaluate its effect on fire response of composite box bridge girder. The general trend of the deflection progression in all cases, shown in Fig. 8, can be grouped into four stages namely, Stage I, Stage II, Stage III and Stage Ⅳ. At early stage of fire exposure (Stage I), the midspan deflection increases slightly and the deflection is mainly dependent on thermal bowing resulting from temperature gradient developed across the box-shaped girder section. In second stage (Stage II) of fire exposure, the midspan deflection increases at a faster pace and this deflection is mainly due to temperature induced deterioration in mechanical properties of steel in bottom flange and web, and also, that of concrete in slab outside boxshaped steel girder. At the third stage of fire exposure (Stage III), the progression of midspan deflection enters a steady pace and this is attributed to two main reasons. I.e., degradation of sectional stiffness, resulting from lower rise in temperature in steel at this stage of fire exposure, begins to slow down. This is due to the fact that specific heat in steel, experiencing peak value between 700 C and 800 C, is much higher than that in other temperature, as per specified provision in Eurocodes [29,30]. Further, presence of this stage is closely related to fire exposed surface (double- or single-surface fire exposure) in steel because the composite box bridge girder is exposed to fire only on surface in steel outside box-shaped girder. When the fire exposed surface in steel is small (single-surface fire exposure), time through steel temperature between 700 C and 800 C will be extended. Therefore, this stage is unique and remarkable in boxshaped steel girders as compared to I-shaped steel girders reported in literature [8e11]. Towards the final stage of fire exposure (Stage Ⅳ), the midspan deflection, in all cases except the case of increased (three) longitudinal stiffeners in web (Case 4) and increased (five) longitudinal stiffeners in bottom flange (Case 5), increases rapidly. This can be mainly attributed to the rapid spread of plasticity in steel when temperature in steel surpasses 800 C; thus leading to formation of a plastic hinge at midspan. At this stage, concrete in the slab at midspan of the girder experienced severe crushing. With increased longitudinal stiffeners in web and bottom flange, the rate of deflection increases slowly toward the final stage of fire exposure. This is due to the fact that the flexural rigidity in girder
fire fire fire fire
Concrete slab
Rebar
Steel girder
22 21 24 21 22 21 22 21
78 47 88 53 78 47 73 44
975 540 1030 601 975 540 945 514
section is highly improved. In case 7, inclined web incorporated into web configuration can slow down the progression of midspan deflection. This can be attributed to the fact that the area of concrete slab inside box-shaped section using inclined web is larger than that with vertical web. Therefore, towards the final stage of fire exposure, larger area of concrete slab, inside box-shaped section with inclined web, can effectively prevent rapid degradation of sectional rigidity. The degradation of moment capacity in the composite box bridge girder is evaluated and plotted in Fig. 9. Also shown in Fig. 9 is the bending moment acting on the girder during fire exposure. The progression of moment capacity can be grouped into three stages, namely, stage 1, stage 2 and stage 3. In stage 1, at early stage of fire exposure, the moment capacity does not decrease and this is due to the fact that there is no loss in strength of steel till steel temperatures are about 400 C. In stage 2, the moment capacity degrades at a rapid pace. This can be attributed to significant degradation of strength in steel with increased steel temperatures. In this stage, the neutral axis shifts rapidly upwards towards the concrete slab. At last stage of fire exposure, the moment capacity decreases slowly. This is due to the fact that concrete slab, which governs the progression of moment capacity when the neutral axis shifts into the concrete slab, is still at lower level of temperature (See Fig. 7). In case of fire severity (Case 1), the moment capacity in composite box bridge girder suffered from hydrocarbon fire exposure decreases more rapidly than that from ISO 834 fire exposure condition. This is due to the fact that rate of heating generated from hydrocarbon fire is much more rapid than that from ISO834 fire. The degrading trend in moment capacity in Cases 2 to 6 is similar. This degradation is mainly dependent on temperature rise in the box-shaped girder and the associated loss of strength of steel, which in turn is a function of temperature in the steel. In Case 7, moment capacity, in composite box bridge girder with inclined web and vertical web, is easily designed to be identical; thus two moment capacity curves coincide as can be seen in Fig. 9(g). A summary of fire resistance analysis results, including failure time based on different failure criteria, for different cases is presented in Table 3. It is concluded that the time to failure is governed by rate of deflection failure criterion, in all cases except in Case 4 and Case 5, where three and five longitudinal stiffeners are present. No failure occurred as per rate of deflection failure criterion; when the longitudinal stiffeners increased to four and five. Therefore, increase of longitudinal stiffeners in web and bottom flange can slow down progression of deflection in fire exposed girders. This in turn can prevent sudden collapse of bridge girders in a fire. The increased transverse stiffeners in web cannot improve fire resistance of composite box bridge girders. Inclined web incorporated into web configuration can enhance fire resistance of composite box bridge girders, as can be seen in Case 7 results.
G. Zhang et al. / Journal of Constructional Steel Research 165 (2020) 105823
Fig. 8. Effect of the different parameters on the fire resistance of a simply supported composite box bridge girder.
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G. Zhang et al. / Journal of Constructional Steel Research 165 (2020) 105823
Fig. 9. Degradation in flexural capacity.
G. Zhang et al. / Journal of Constructional Steel Research 165 (2020) 105823
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Table 3 Summary of parameters studies. Case
Case 1
Parameter
Fire severity
Case 2
Fire exposure length
Case 3
Load level
Case 4
Number of longitudinal stiffeners in web
Case 5
Number of longitudinal stiffeners in bottom flange
Case 6
Number of transverse stiffeners in web
Case 7
Web pattern
Value
e e 10 m 20 m 30 m 30％ 65％ 100％ 1 2 3 3 4 5 1 2 Vertical Inclined
5. Design implications As per current codes and standards, there are no requirements for provision of fire resistance to structural members in a bridge [13,14]. Recent studies have shown that fire can be significant hazard in bridges and in structures. Fire risk control measures, such as restriction of trucks with explosives, chemical etc., and guidance cars arranged for trucks transporting gasoline and oil and chemicals (through fire severity and fire exposure length) when passing bridges, can be applied to some extent to mitigate fire hazard in critical bridges. Alternatively passive fire-protective measures, such as enhanced sectional stiffness (through longitudinal stiffeners) and modified web configuration (through inclined web) can be incorporated into a bridge girder so as to enhance inherent fire resistance. The proposed approach of enhancing fire resistance, through passive fire-protective measure, can be applied to any composite bridge girders with different structural configuration, fire scenarios etc. For developing alternative passive fire protection so as to enhance fire resistance, numerical model such as the one presented in this paper lays out a detailed procedure for undertaking fire resistance analysis of a typical composite box bridge girder (representative of that used in bridges) under different fire exposure conditions, including localized fire scenario. This procedure can be applied to evaluate fire resistance of any given composite box bridge girders. However, due consideration should be given to relevant conditions (support conditions, sectional details) present in a specific girder. This can be done through proper discretization of the girder and relevant input parameters, such as boundary conditions.
6. Conclusions Based on the analysis results presented herein, the following conclusions can be drawn: Transient finite-element analysis procedure can be applied to evaluate fire behavior of composite box bridge girders under any specified fire exposure and structural loading conditions. Fire resistance of composite box bridge girder is highly influenced by the fire severity, extent of fire exposure, peak fire temperature reached, as well as load level present on the girder.
Fire scenarios
Fire resistance (min)
Hydrocarbon fire ISO 834 fire Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon
fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire
Deflection based failure criterion
Rate of deflection based failure criterion
Moment capacity based failure criterion
38 85
35 82
48 No failure
43 38 36 38 34 30 38 40 44 38 No failure No failure 38 38 38 43
40 35 33 35 32 27 35 40 No failure 35 43 No failure 35 35 35 42
48 48 48 48 43 38 48 52 No failure 48 52 55 48 48 48 48
Increase of longitudinal stiffeners at bottom flange and web can significantly slow down the deflection levels towards the final stages of fire exposure; thus preventing sudden collapse of a bridge girder. In contrast, lack of longitudinal stiffeners in bottom flange and web can accelerate the progression of midspan deflections, leading to crushing of concrete and then formation of plastic hinge at critical section of the girder. Web configuration has significant influence on the progression of deflection, where vertical web can accelerate the raise in midspan deflection in a bridge girder, leading to early failure. Thus, inclined web incorporated into steel sectional shape can enhance fire resistance of composite box bridge girders. The rate of deflection criterion governs failure of a fire exposed composite box bridge girder in most cases.
Conflicts of interest There is no conflicts of interest. Acknowledgments The authors wish to acknowledge the support from Ministry of Transport of the People's Republic of China (Grant No. 2011318812970) and the support from Natural Science Foundation of China (Grant No. 51878057 and No. 51308056), National Science Basic Research Plan in Shaanxi Province of China (Gran No. 2018JM5018), Research fund for Central Universities of China (Grant No. 310821172003), Michigan State University and Southeast University. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors. References [1] M.N.H. Nahid, E.D. Sotelino, B.Y. Lattimer, Thermo-structural response of highway bridge structures with tub girders and plate girders, J. Bridge Eng. 22 (10) (2017), 04017069. [2] V.K.R. Kodur, M.Z. Naser, Designing steel bridges for fire safety, J. Constr. Steel Res. 156 (2019) 46e53. [3] G. Zhang, M.C. Zhu, V.K.R. Kodur, G.Q. Li, Behavior of welded connections after exposure to elevated temperature, J. Constr. Steel Res. 130 (2017) 88e95. [4] G. Zhang, V.K.R. Kodur, W.F. Yao, Q. Huang, Behavior of composite box bridge girders under localized fire exposure, Struct. Eng. Mech. 69 (2) (2019) 193e204.
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A numerical model for evaluating fire performance of composite box bridge girders Gang Zhang a, *, Venkatesh Kodur b, Chaojie Song a, Shuanhai He a, Qiao Huang c a
School of Highway, Chang'an University, Xi'an, Shaanxi, 710064, China Department of Civil and Environmental Engineering, Michigan State University, East Lansing, MI, 48864, USA c School of Transportation, Southeast University, Nanjing, 210096, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 June 2019 Received in revised form 8 October 2019 Accepted 21 October 2019 Available online xxx
This paper presents an approach for evaluating fire performance of composite box bridge girders exposed to fire. The model takes into account critical parameters, namely, fire scenario, fire exposure length, load level, numbers of longitudinal stiffeners in web and bottom flange and web pattern, that influence fire performance of bridges. A three dimensional finite element model, developed in the computer program ANSYS, is applied to model the fire response of composite box bridge girders. The finite element model is validated by comparing predicted sectional temperatures and deflections from the model with fire test data generated from a test on box bridge girder. The applicability of the numerical model in practical application is illustrated through numerical analysis on a composite box bridge girder subjected to simultaneous structural loading and fire exposure. Results from the numerical study clearly show that fire severity, fire exposure length, load level, number of longitudinal stiffeners and web slenderness have significant influence on the fire resistance of composite bridge girders. Provision of longitudinal stiffeners can result in lower deflections; thus enhancing fire resistance. Further, inclined web (configuration) incorporated into sectional shape can enhance fire resistance of composite box bridge girders. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Bridge fires Fire resistance Composite box bridge girders Finite element analysis Thermo-structural analysis
1. Introduction Steel-concrete composite box bridge girders, comprising of a Ushaped steel girder (vertical or inclined web) supporting a reinforced concrete slab, are widely used in medium- and long-span bridge construction (See Fig. 1) due to number of advantages such girders offer over other traditional steel girders [1e7]. These advantages include rapid fabrication of steel shapes, ease of installation, light weight, strong crossing ability, conducive to environment protection, cost effectiveness, and high wind resistance and seismic performance [8e12]. However, a major drawback of composite box bridge girders is that steel shapes (girders) exhibit much lower fire resistance than similar concrete structural members due to low specific heat, high thermal conductivity and rapid degradation of strength and modulus of steel at elevated temperatures. As a result, steel shapes, in composite box bridge girders loose their capacity at a faster pace under fire exposure conditions. While structural members in building are required to have sufficient fire resistance in the event of a fire, there is no specific fire resistance
* Corresponding author. E-mail address: [email protected] (G. Zhang). https://doi.org/10.1016/j.jcsr.2019.105823 0143-974X/© 2019 Elsevier Ltd. All rights reserved.
requirements for bridge structures as per current codes and standards [13,14]. In the last three decades, there has been an increase in the number of fires on bridges. This is due to rapid raise in transportation of fuels, chemicals and highly combustible products that contain deflagrated and flammable materials. These fuels combust rapidly and burn at high intensity reaching temperature of 1000 C with the first few minutes of fire exposure. Such high intense fire can pose a severe threat to stability of structural members in a bridge and, in some instances, even can produce large deflections or even collapse of the bridges [15e17]. Damage or collapse, specially in case of critical bridges, can lead to high property losses, and lengthy repair process. Further any delays resulting from traffic detouring to nearby routes can add to significant indirect costs, as well as hardships to commuters and general public (i.e. congestion and traffic pressure). There are a number of instances of fire-damage in bridges and these are reported in the literature [8e18]. Fire induced collapse in bridges such as the MacArthur Maze I-80/880 interchange in Okland, California in 2007, and the I-75 expressway near Hazel Park, Michigan in 2009, are clear examples of damage from high intensity fires [8e18]. Recent fire incident, caused by an overturned oil tanker when passing through the Mathilde Bridge in Rouen,
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2. Selection of composite box bridge girder for analysis A typical highway steel-concrete composite bridge girder, fabricated with box-shaped steel section and a concrete slab, is selected for fire resistance analysis. The box shaped girder, with vertical web, spans a length of 30 m, and has width of 3.1 m, and height of 1.6 m, and has simply supported ends. The slab on the top of composite box bridge girder is made of concrete of compressive strength (cube strength) of 50 MPa. The yield strength of steel used in box girder is 345 MPa. To increase bending capacity of composite box bridge girder, transverse diaphragms were provided every 3 m along span length. Two transverse stiffeners were placed evenly between two transverse diaphragms. Concrete slab is reinforced with rebars of 12 mm and yield strength of 420 MPa. The sectional details of the box-shaped steel girder and reinforced concrete slab are shown in Fig. 2, and also in Table 1. 3. Numerical model A three dimensional numerical model, is developed in ANSYS [24] to evaluate response of composite box bridge girders under fire exposure conditions. The above discussed composite box bridge girder comprising of U-shaped steel girder, RC slab, intermediate diaphragms and transverse and longitudinal stiffeners, is analyzed under the effects of fire exposure and structural loading to trace the response during the entire range of behavior, from start of fire exposure till failure of the girder. 3.1. Analysis details Fig. 1. Bridge construction using composite box girder.
France, in 2012, is an example of devastation of fire on a bridge. This fire-damaged bridge was so severe that could be opened after two years. The economic loss caused by this fire event was estimated at about £18 million [18], which clearly shows how bridge fires can lead to significant economic losses. Much of the fire research [19e24] in the past four decades concentrated on structural members, typically used in buildings. Although fire insulation are required to mitigate fire damage to critical structural members in case of buildings, application of such measure is not realistic or practical in structural members in bridges due to major cost implications and application complexities. However, limited research has been performed to improve the fire resistance of bridge structural members. Currently, there are very few fire experiments that have been performed on composite bridge with I-shaped steel girder under fire exposure conditions [8e22]. In these limited tests, the influence of web buckling, composite action, prestressing tendon on Ishaped steel girders are investigated [8e22]. These test specimens have small spans and simplified structural configuration, and are only enforced with concentrated loading under a low intense fire exposure (ISO 834). However, these studies and experimental work do not reflect the response of realistic bridge fires encountered in practice. This can be attributed to the difference of fire severity, geometric configuration, material characteristics, structural shapes, dimensions of girders as well as load patterns. Therefore, there is limited information on the behavior of composite box bridge girders under realistic fire exposure conditions. To overcome these gaps, an investigation in to fire performance of composite box bridge girder under different fire exposure conditions is undertaken as part of this study.
A coupled thermo-mechanical analysis is applied to trace the behavior of girder under localized fire exposure and simultaneous structural loading. In the first step, the temperature rise in the girder resulting from fire exposure is computed and a heat transfer analysis is carried out to determine temperature progression with in the girder section. In the second step, the structural response of the composite box bridge girder, due to the combined effects of fire exposure and structural loading, is evaluated. The fire resistance analysis on composite box bridge girder is carried out under an applied loading consisting of 100％ dead load plus 30％ live load (vehicle load). The self-weight of the box bridge girder and the pavement (12 kN/m) constitute the dead load. The live load is comprised of a concentrated load (96 kN) enforced on midspan and a uniform load (3.15 kN/m) distributed over the bridge girder span. These load distribution pattern is in line with recommended design values of practical vehicle lane loads as per China code [25]. Based on the preliminary analysis, a concentrated load enforced on midspan of simply supported composite box bridge girders is regarded to be the worst-case loading scenario. 3.2. Discretization of girder For the thermal analysis, the box-shaped steel girder together with diaphragm and stiffeners, was discretized with a 3-D “SHELL57” element, that is applicable to steady-state or transient thermal analysis, as shown in Fig. 3. The concrete slab was discretized using “SOLID70” element which has a 3-D thermal conduction capability. This element having eight nodes with a single degree of freedom, i.e. temperature, at each node, is suitable to model steady-state or transient thermal analysis problem. The rebars with in concrete slab was discretized with LINK33 element, and these are uniaxial elements with the ability to conduct heat between two nodes.
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Fig. 2. Details of composite box bridge girder (Unit: mm).
Table 1 Parameters related to sectional geometry. Portions
Height (mm)
Width (mm)
Thickness (mm)
box-shaped steel girder Bottom flange Web Top flange Diaphgram Stiffener
1446 e 1400 e e e
1500 1582 e 400 e 150
e 24 18 22 18 18
Both convection and radiation heat transfer effect was applied at the fire exposed surface areas of the shell and solid elements. In addition, radiation loads were also applied at the surface of the concrete slab inside box-shaped steel girder. Convection heat transfer coefficients of ac ¼ 50 W/(m2 C) and ac ¼ 25 W/(m2 C)
were used for the thermal analysis under hydrocarbon and ISO 834 fire exposure conditions [26,27] respectively as per Eurocode 1 [28]. Different values of effective emissivity factor associated with the exposure boundaries were applied in the thermal analysis as per specific provisions. Effective emissivity coefficients of 0.7 and 0.5 were applied for the bottom flange and the web outside box section respectively, and an effective emissivity of 0.4 was applied for the fire exposed surface of the top flange and bottom of the concrete slab. To simulate heat emissivity inside box steel girder at elevated temperature, an emissivity factor of 0.2 was used for the concrete slab inside box girder to account for radiation generated from steel girder under high temperature effects. A Stefan-Botzmann radiation constant of 5.67 108 W/(m2 C4) was applied to simulate radiative heat transfer. For structural analysis, the composite box bridge girder was modeled with three elements, namely, SHELL181 element for the
Fig. 3. 3-D discretization of composite box bridge girder.
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box steel girder, SOLID65 element for the concrete slab, and LINK8 element for the rebar [24], as shown in Fig. 3. SHELL181, a 4-node element with three translations and rotations degree of freedom at each node, is well-suited for analyzing thin to moderately-thick shell structures and also suitable for linear, large rotation and large strain nonlinear problems. SOLID65 elements used for modeling concrete with and without reinforcing steel are capable of accounting for cracking in tension and crushing in compression, which links well with LINK8 elements used to model rebar. 3.3. Material properties Temperature dependent thermal properties of steel and concrete, namely thermal conductivity, specific heat and thermal expansion were provided as input data into ANSYS, and these property relations are taken from Eurocodes 2 and 3 relations [29,30] and other sources [31]. Mechanical properties of concrete and steel, varying as a function of temperature, were applied as per the specified relations taken from literature [29,30]. Stress-strain relations of concrete and steel have predominant influence on fire-resistance, and these relations vary significantly with temperature rise, as shown in Fig. 4.
200 mm respectively, and the width of concrete slab and box steel girder is 700 mm and 320 mm respectively. The thickness of bottom flange, web and top flange is equal to 5 mm. The diameter and height of shear studs are designed to be 20 mm and 80 mm, respectively. The steel reinforcement used to reinforce the concrete slab has diameter of 12 mm. The validation was performed by comparing thermal and structural response predictions from the analysis with that measured in fire test. Fig. 6(a) shows a comparison of predicted temperature at different depths in the section by the FEM model with temperature data measured during fire tests. It can be seen that the predicted temperatures agree well with those measured in fire tests. The slight difference in temperature can be attributed to variation in actual fire test conditions and adopted temperature-dependent thermal parameters, such as convection coefficient and emissivity for the thermal analysis. Fig. 6(b) shows a comparison of midspan deflection of the girder predicted using the FEM model with that reported in the fire test. It can be seen that predictions from ANSYS match well with test data. Slight variation in deflections can be attributed to idealization of fire and variations in mechanical properties, adopted in the analysis from that present in tests (such as actual fire exposure length and stressestrain relations of concrete and steel).
3.4. Failure criterion 4. Parametric study Fire resistance analysis on the girder is carried out at incrementing time steps, till failure occurred through one of the limiting states; through deflection or strength limit state. According to deflection and rate of deflection limit state, when maximum deflection in a girder surpasses L2/400d (1360 mm) limit or rate of deflection reaches L2/9000d (60.5 mm/min) [32], the girder is said to fail. As per strength limit state, if moment capacity drops below bending moment arising from applied structural loading, then failure of the girder is said to occur. 3.5. Model validation The above finite element model is validated by selecting a scaled composite box bridge girder tested under localized fire exposure condition whose temperature rise follow that of ISO834 fire [4,27,33]. The fire exposure length symmetric about the mid-span is 1.4 m. The U-shaped steel girder supporting a reinforced concrete slab, has a span length of 3.4 m with simply support conditions (See Fig. 5). The height of total section and that of web are 300 mm and
To evaluate fire behavior of a typical composite box bridge girder under localized fire exposure conditions, a simply supported composite box bridge girder was analyzed with the above model by subjecting the composite girder to varying parameters, including fire severity, load level, stiffness and web configuration. 4.1. Thermal gradients Fig. 7 shows the thermal gradients developed across the depth of the section of composite box bridge girder with fire exposure time. It can be seen that temperature distribution along the girder depth is quite similar and temperature increases gradually with fire exposure time, however hydrocarbon fire exposure produces larger temperature rise, as expected. At 15 min and 50 min of hydrocarbon fire and ISO 834 fire exposure respectively, the temperature in bottom flange and web surpass 600 C. This temperature rise leads to rapid deterioration of mechanical properties in steel leading to significant degradation in flexural capacity of the girder.
Fig. 4. Stress - strain relations for concrete and steel.
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Fig. 5. Dimensions of the test girder.
Fig. 6. Comparison of predicted and measured data.
Fig. 7. Thermal gradient along the depth of a bridge girder section.
The peak temperature attained in concrete slab and steel girder under two different fire scenarios are shown in Table 2. The concrete temperatures are on the unexposed side of the slabs. In Case 1, these sectional temperatures are captured prior to failure of the girder, while in “Case 2” the sectional temperatures are shown at different fire exposure time. It can be seen in Table 2 that the peak temperature in concrete slab (rebar) and steel girder are much higher under hydrocarbon fire exposure than that under ISO 834 fire exposure. The higher sectional temperatures result in earlier failure time.
4.2. Structural response The structural response of a typical box composite bridge girder is illustrated in Fig. 8, where midspan deflection of the girder is plotted as a function of fire exposure time, for varying scenarios, namely fire severity (Case 1), fire exposure length (Case 2), load level (Case 3), longitudinal stiffeners in compression portion of web and bottom flange (Cases 4 and 5) and transverse stiffeners in web (Case 6), and web configuration (Case 7). From previous literature, fire exposure around midspan of a simply supported bridge girder,
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Table 2 Peak temperature in concrete slab and steel girder. Case
Parameter
Case 1
Fire severity
Case 2
Fire exposure length
Time
Prior to failure Prior to failure 40 min 35 min 33 min
Peak temperature ( C)
Fire scenarios
Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire Hydrocarbon ISO 834 fire
is the worst-condition of fire scenario, therefore, fire exposure length is assumed to be 10 m, 20 m and 30 m symmetric about the midspan respectively. The live load present during fire exposure is varied as 30％, 65％ and 100％. The number of longitudinal stiffeners, evenly distributed in compression portion of web, is designed to be two and three, respectively. The number of longitudinal stiffeners, evenly distributed in bottom flange, is varied as three, four and five. The number of transvers stiffeners, uniformly provided between two neighboring transverse diaphragms, is assumed to be one and two, respectively. Web configuration, including vertical and inclined web incorporated into sectional shape, is varied to evaluate its effect on fire response of composite box bridge girder. The general trend of the deflection progression in all cases, shown in Fig. 8, can be grouped into four stages namely, Stage I, Stage II, Stage III and Stage Ⅳ. At early stage of fire exposure (Stage I), the midspan deflection increases slightly and the deflection is mainly dependent on thermal bowing resulting from temperature gradient developed across the box-shaped girder section. In second stage (Stage II) of fire exposure, the midspan deflection increases at a faster pace and this deflection is mainly due to temperature induced deterioration in mechanical properties of steel in bottom flange and web, and also, that of concrete in slab outside boxshaped steel girder. At the third stage of fire exposure (Stage III), the progression of midspan deflection enters a steady pace and this is attributed to two main reasons. I.e., degradation of sectional stiffness, resulting from lower rise in temperature in steel at this stage of fire exposure, begins to slow down. This is due to the fact that specific heat in steel, experiencing peak value between 700 C and 800 C, is much higher than that in other temperature, as per specified provision in Eurocodes [29,30]. Further, presence of this stage is closely related to fire exposed surface (double- or single-surface fire exposure) in steel because the composite box bridge girder is exposed to fire only on surface in steel outside box-shaped girder. When the fire exposed surface in steel is small (single-surface fire exposure), time through steel temperature between 700 C and 800 C will be extended. Therefore, this stage is unique and remarkable in boxshaped steel girders as compared to I-shaped steel girders reported in literature [8e11]. Towards the final stage of fire exposure (Stage Ⅳ), the midspan deflection, in all cases except the case of increased (three) longitudinal stiffeners in web (Case 4) and increased (five) longitudinal stiffeners in bottom flange (Case 5), increases rapidly. This can be mainly attributed to the rapid spread of plasticity in steel when temperature in steel surpasses 800 C; thus leading to formation of a plastic hinge at midspan. At this stage, concrete in the slab at midspan of the girder experienced severe crushing. With increased longitudinal stiffeners in web and bottom flange, the rate of deflection increases slowly toward the final stage of fire exposure. This is due to the fact that the flexural rigidity in girder
fire fire fire fire
Concrete slab
Rebar
Steel girder
22 21 24 21 22 21 22 21
78 47 88 53 78 47 73 44
975 540 1030 601 975 540 945 514
section is highly improved. In case 7, inclined web incorporated into web configuration can slow down the progression of midspan deflection. This can be attributed to the fact that the area of concrete slab inside box-shaped section using inclined web is larger than that with vertical web. Therefore, towards the final stage of fire exposure, larger area of concrete slab, inside box-shaped section with inclined web, can effectively prevent rapid degradation of sectional rigidity. The degradation of moment capacity in the composite box bridge girder is evaluated and plotted in Fig. 9. Also shown in Fig. 9 is the bending moment acting on the girder during fire exposure. The progression of moment capacity can be grouped into three stages, namely, stage 1, stage 2 and stage 3. In stage 1, at early stage of fire exposure, the moment capacity does not decrease and this is due to the fact that there is no loss in strength of steel till steel temperatures are about 400 C. In stage 2, the moment capacity degrades at a rapid pace. This can be attributed to significant degradation of strength in steel with increased steel temperatures. In this stage, the neutral axis shifts rapidly upwards towards the concrete slab. At last stage of fire exposure, the moment capacity decreases slowly. This is due to the fact that concrete slab, which governs the progression of moment capacity when the neutral axis shifts into the concrete slab, is still at lower level of temperature (See Fig. 7). In case of fire severity (Case 1), the moment capacity in composite box bridge girder suffered from hydrocarbon fire exposure decreases more rapidly than that from ISO 834 fire exposure condition. This is due to the fact that rate of heating generated from hydrocarbon fire is much more rapid than that from ISO834 fire. The degrading trend in moment capacity in Cases 2 to 6 is similar. This degradation is mainly dependent on temperature rise in the box-shaped girder and the associated loss of strength of steel, which in turn is a function of temperature in the steel. In Case 7, moment capacity, in composite box bridge girder with inclined web and vertical web, is easily designed to be identical; thus two moment capacity curves coincide as can be seen in Fig. 9(g). A summary of fire resistance analysis results, including failure time based on different failure criteria, for different cases is presented in Table 3. It is concluded that the time to failure is governed by rate of deflection failure criterion, in all cases except in Case 4 and Case 5, where three and five longitudinal stiffeners are present. No failure occurred as per rate of deflection failure criterion; when the longitudinal stiffeners increased to four and five. Therefore, increase of longitudinal stiffeners in web and bottom flange can slow down progression of deflection in fire exposed girders. This in turn can prevent sudden collapse of bridge girders in a fire. The increased transverse stiffeners in web cannot improve fire resistance of composite box bridge girders. Inclined web incorporated into web configuration can enhance fire resistance of composite box bridge girders, as can be seen in Case 7 results.
G. Zhang et al. / Journal of Constructional Steel Research 165 (2020) 105823
Fig. 8. Effect of the different parameters on the fire resistance of a simply supported composite box bridge girder.
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Fig. 9. Degradation in flexural capacity.
G. Zhang et al. / Journal of Constructional Steel Research 165 (2020) 105823
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Table 3 Summary of parameters studies. Case
Case 1
Parameter
Fire severity
Case 2
Fire exposure length
Case 3
Load level
Case 4
Number of longitudinal stiffeners in web
Case 5
Number of longitudinal stiffeners in bottom flange
Case 6
Number of transverse stiffeners in web
Case 7
Web pattern
Value
e e 10 m 20 m 30 m 30％ 65％ 100％ 1 2 3 3 4 5 1 2 Vertical Inclined
5. Design implications As per current codes and standards, there are no requirements for provision of fire resistance to structural members in a bridge [13,14]. Recent studies have shown that fire can be significant hazard in bridges and in structures. Fire risk control measures, such as restriction of trucks with explosives, chemical etc., and guidance cars arranged for trucks transporting gasoline and oil and chemicals (through fire severity and fire exposure length) when passing bridges, can be applied to some extent to mitigate fire hazard in critical bridges. Alternatively passive fire-protective measures, such as enhanced sectional stiffness (through longitudinal stiffeners) and modified web configuration (through inclined web) can be incorporated into a bridge girder so as to enhance inherent fire resistance. The proposed approach of enhancing fire resistance, through passive fire-protective measure, can be applied to any composite bridge girders with different structural configuration, fire scenarios etc. For developing alternative passive fire protection so as to enhance fire resistance, numerical model such as the one presented in this paper lays out a detailed procedure for undertaking fire resistance analysis of a typical composite box bridge girder (representative of that used in bridges) under different fire exposure conditions, including localized fire scenario. This procedure can be applied to evaluate fire resistance of any given composite box bridge girders. However, due consideration should be given to relevant conditions (support conditions, sectional details) present in a specific girder. This can be done through proper discretization of the girder and relevant input parameters, such as boundary conditions.
6. Conclusions Based on the analysis results presented herein, the following conclusions can be drawn: Transient finite-element analysis procedure can be applied to evaluate fire behavior of composite box bridge girders under any specified fire exposure and structural loading conditions. Fire resistance of composite box bridge girder is highly influenced by the fire severity, extent of fire exposure, peak fire temperature reached, as well as load level present on the girder.
Fire scenarios
Fire resistance (min)
Hydrocarbon fire ISO 834 fire Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon Hydrocarbon
fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire fire
Deflection based failure criterion
Rate of deflection based failure criterion
Moment capacity based failure criterion
38 85
35 82
48 No failure
43 38 36 38 34 30 38 40 44 38 No failure No failure 38 38 38 43
40 35 33 35 32 27 35 40 No failure 35 43 No failure 35 35 35 42
48 48 48 48 43 38 48 52 No failure 48 52 55 48 48 48 48
Increase of longitudinal stiffeners at bottom flange and web can significantly slow down the deflection levels towards the final stages of fire exposure; thus preventing sudden collapse of a bridge girder. In contrast, lack of longitudinal stiffeners in bottom flange and web can accelerate the progression of midspan deflections, leading to crushing of concrete and then formation of plastic hinge at critical section of the girder. Web configuration has significant influence on the progression of deflection, where vertical web can accelerate the raise in midspan deflection in a bridge girder, leading to early failure. Thus, inclined web incorporated into steel sectional shape can enhance fire resistance of composite box bridge girders. The rate of deflection criterion governs failure of a fire exposed composite box bridge girder in most cases.
Conflicts of interest There is no conflicts of interest. Acknowledgments The authors wish to acknowledge the support from Ministry of Transport of the People's Republic of China (Grant No. 2011318812970) and the support from Natural Science Foundation of China (Grant No. 51878057 and No. 51308056), National Science Basic Research Plan in Shaanxi Province of China (Gran No. 2018JM5018), Research fund for Central Universities of China (Grant No. 310821172003), Michigan State University and Southeast University. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors. References [1] M.N.H. Nahid, E.D. Sotelino, B.Y. Lattimer, Thermo-structural response of highway bridge structures with tub girders and plate girders, J. Bridge Eng. 22 (10) (2017), 04017069. [2] V.K.R. Kodur, M.Z. Naser, Designing steel bridges for fire safety, J. Constr. Steel Res. 156 (2019) 46e53. [3] G. Zhang, M.C. Zhu, V.K.R. Kodur, G.Q. Li, Behavior of welded connections after exposure to elevated temperature, J. Constr. Steel Res. 130 (2017) 88e95. [4] G. Zhang, V.K.R. Kodur, W.F. Yao, Q. Huang, Behavior of composite box bridge girders under localized fire exposure, Struct. Eng. Mech. 69 (2) (2019) 193e204.
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