NUMERICAL STUDY AND EVALUATION OF FIRE DAMAGE ON SLOPED STEEL BRIDGES AND ANALYSIS OF THE PROTECTIVE EF-
FECT OF SPRINKLER SYSTEMS ON BRIDGE COLUMNS
Cherng-Shing Lin Min Ma* Jui-Pei Hsu Chao-Hsing Chang
Department of Mechanical Engineering Yuan Ze University Taoyuan, Taiwan 330, R.O.C.
Key Words: bridge, CFD, numerical simulation, smoke.
ABSTRACT
This paper proposes a numerical simulation analysis of the problems in a bridge after a fire. The problems were discussed to provide safety for the bridgework domain. The article used a fire dynamic simulation (FDS) software for analysis. The investigation on the scene of a bridge fire and the detection of bridge damage caused by fire were described to discuss the effects on concrete and steel girder components. The effects of fire temperature and smoke at the scene of a fire were estimated to provide criteria for bridge fire prevention and in enhancing bridge safety. This paper proposes using a sprinkler system to protect bridges against fire hazards and found out the reasonable flow rate to implement protection with a minimum water quantity. For the characteristics of concrete fire damage, a fire-damaged reinforced concrete bridge inspection and evaluation method was introduced using an engineering example, and a bridge fire handling scheme was proposed. The method and idea could provide beneficial references for handling similarly inclined bridge fires. A risk management evaluation method was planned and a numerical simulation model of a bridge fire was built to provide criteria for improving bridge management safety.
I. INTRODUCTION
With continuous development of economic and traffic construction, the number of bridges has grown greatly. In recent years, bridges that have been affected by fire inci- dents have heavily influenced traffic. Bridges have been damaged and even become unusable, causing road transport interruptions. The physical and chemical properties of the bridge structural materials change at high temperatures, leading to structural damage and influencing bridge safety.
At present, research on structural damage detection and evaluation after a fire has concentrated on the architecture,
and the study and practice of numerical simulations of in- spection and evaluation after bridge structure fires have only gradually increased. This paper discusses the numer- ical simulation analysis of a bridge after a fire and discusses the examples, in the hopes of rationally evaluating bridge damage after a fire. Fire Dynamics Simulator (FDS) soft- ware was used for validation and simulation, as it is the most widely used model for complex fire modeling. FDS has been extensively used in the fire research area [1-5], includ- ing architecture fires, vehicle fires, tunnel fires, etc. Ac- tual cases were collected for reconstruction and simulation of the fire scenes to find out the fire scenario, based on which
*Corresponding author: Min Ma, e-mail: [email protected]
Fig. 1 Violent fire under the bridge at the bridge column
the fire scene environment was studied in depth. How to control suburban burning events was analyzed [6]. The fire hazard to the human body is extensive and the most se- rious level is death, because the temperature at the fire scene causes burning and scalding universally. Especially in de- veloping countries, emergency evacuations in public traffic station fires should be paid close attention to. Yang et al.
[7] studied an integrated fire-human model, FDS + Evac, which has been extensively used to numerically solve sim- ultaneous fire and evaluation processes. A method of ap- plication was proposed to reduce the simulation time and cost of fire emergency evacuations. The grid resolution was analyzed to determine the appropriate cell size to opti- mize the accuracy and time of the solution. A fire is a dis- aster that all humans may face. A large-scale fire can cause considerable life and property losses, and the subse- quent investigation work is very complicated and can in- clude full-scale or large-scale fire scene simulations [8].
Such simulation results are relatively accurate, but the cost and time consumption are considerable. Peris-Sayol et al.
[9] used a numerical model to study bridge fires and ana- lyzed the response of a tank truck fire to a typical girder bridge. This paper provided a new idea on modeling tech- nology that could save considerable modeling and analysis time. Kolaitis et al. and Bezas et al. [10-11] discussed the sub-cycle algorithm between a CFD fire simulation and a conduction heat transfer model. The sub-cycle algorithm implements evaluation based on precision and the conver- gence rate. Sprinklers have also been studied extensively in recent years, as they are helpful for fire prevention [12- 16].
II. CASE STUDY
Due to the instant development of cities and road trans- portation, the number of unsafe factors in highway bridges
has increased. However, people’s bridge fire safety con- sciousness is weak and bridges are exposed to increasing fire risks. This study investigated a bridge fire that oc- curred next to the Taoyuan interchange in Taiwan. The fire occurred in a warehouse under the land bridge at 1:30PM on August 6, 2017 and involved a number of oil storage tanks. The fire behavior was out of control, and black smoke covered the sky and obscured the driving sight, as shown in Fig. 1 [17]. There were 16 fire engines sent to control the fire; however, the bridge column concrete broke and the reinforcing bars were deformed by high temperature, forcing the bridge to be fully closed.
III. COMPUTATIONAL FLUID DYNAMICS MODEL
The bridge structure was analyzed and the original sce- nario was reconstructed in order to reflect the real effect of the fire on the structure. In order to make the bridge resist fire invasion more effectively, an improvement system was proposed to enhance bridge safety more quickly and effec- tively.
Fire Dynamics Simulator (FDS) is a computational fluid dynamics (CFD) model of a fire-driven fluid flow.
The software numerically solves a form of the Navier- Stokes equations for thermally-driven flow at a low-speed, with an emphasis on heat transport and smoke from fires.
FDS is a software tool provided by the National Institute of Standards and Technology (NIST) of the United States De- partment of Commerce [18-19]. The equations can be found in the FDS manual.
1. Choosing the Mesh Dimensions
Theoretically, the finer the mesh is, the more precise the results will be; however, the equipment, time and accu- racy must match each other because it is important to deter- mine an appropriate grid size that will optimize the solution accuracy. For simulations involving buoyant plumes, a measure of how well the flow field is resolved can be given by the non-dimensional expression כΤ [20-21]: Ɂ
2 5
D
• p• • Q
C T g
U
f f
§ ·
¨¨© ¸¸¹
(1)
where, Dכ is a characteristic fire diameter and x is the nom- inal size of a mesh cell, Q is the heat release rate,Uf is the density, CU is the specific heat, ܶஶ is the ambient tem- perature, and g is gravity.
Table 1 The moving speed of people with various body types
Body types Rd (m) R1 / Rd (-) Rs / Rd (-) dsRd (-) Speed
Adult 0.255 ± 0.035 0.5882 0.3725 0.6275 1.25 ± 0.30
Female 0.240 ± 0.020 0.5833 0.3750 0.6250 1.15 ± 0.20
Male 0.270 ± 0.020 0.5926 0.3704 0.6296 1.35 ± 0.20
Child 0.210 ± 0.015 0.5714 0.3333 0.6667 0.90 ± 0.30
Elderly 0.250 ± 0.020 0.6000 0.3600 0.6400 0.80 ± 0.30
Fig. 2 Human evacuation the approximate body types
Fig. 3 Sloped bridge scene of the fire.
It was concluded in the mesh density sensitivity study of NUREG 1824 [22] that when the D*Τ ratio is the rec-x ommended 4-16, the grid will have preferable computa- tional accuracy and equilibrium of computer resource allo- cation. The environmental parameters were
1.204kgm3
U f ,CU=1.005kj KJ kg-k
and the atmos- pheric temperature was 25 , i.e. T=298°K and g=9.81 m sΤ . According to the feature fire diameter 2 equation, the Heat Release Rate of different fire sources uses different grid size values.
For example, for an intense fire under a single-span beam bridge, the large-scale fire heat release rate is 75MW [23], then D* = 5.4, i.e. the unit grid size can be 0.4-1.5m.
It was set as 0.4m for the simulation.
2. Passenger evacuation motion equation
2
2
( ) ( )
i
i i i
d x t
m f t t
dt [ (2)
Where ݉ is the mass of passenger i, ݔሺݐሻ is the
Fig. 4. A schematic drawing of the bridge.
Fig. 5 Computational setup with the sloped bridge at angle.
position of passenger i at time point t, ݒሺݐሻ ൌ ݀ݔ ݀ݐΤ is the moving speed of passenger i, ݂ሺݐሻ is the influence of the surrounding environment on passenger i, and ߦሺݐሻ is the influence of unexpected events on passenger i. As shown in Fig. 2, a person’s body type is represented by three circles arranged in an oval shape. The shape and size of passengers and their unobstructed moving speed is shown in Table 1.
3. The General Differential Equation
The review of the relevant differential equations indicated that all the dependent variables of interest seem to obey a generalized conservation principle. If the depend- ent variable is denoted by , the general equation is:
div u div
t
grad S U
w UI I * I
w (3)
where, is the diffusion coefficient and S is the source term.
The quantities and S are specific to a particular meaning of .
Rd
Rt
Rs 5.0
6.0 8.0
4.0 2.0 0.0
10.0 0.0 10.0
20.015.0 5.0 15.0 20.0
25.0 25.0 30.0 35.0 40.0
Bridge column Girder
Fence Unit:meter
= 2
3.5
28
4.5
Fig. 6 FDS model sprinkler locations in a Z = 4.5m cross section.
Fig. 7 Temperature distribution slices at the plane of y = 15m: (a) at 100 sec / (b) at 200 sec / (c) at 300 sec when the bridge was inclined at 2 to the horizon- tal.
4. Description and Establishment of the Physical Model
The fire was simulated in a bridge with a 3D space, and the scene of the fire is shown in Fig. 3. The test compart- ment dimensions were 44m (length) by 30m (width) by 10m (height). The bridge construction structure contained con- crete and steel. The dimensional coordinates are shown in Fig. 4. The distance between bridge beam columns was 28m; the first beam column was 4.5m high, the second beam column was 3.5 m high, and the angle of slope was 2°, as shown in Fig. 5.
5. Sprinkler Spray Characteristics
In order to predict the protective effect of sprinklers on the bridge column, once the sprinkler is activated, the drop- let size, temperature and trajectory of a representative sam- ple of water droplets will be calculated in FDS. Therefore, the sprinkler was actuated forcibly in the current FDS cal- culation. The water flow was directly determined by the spray nozzle characteristic and working pressure. In this
Fig. 8 Temperature curve at locations a, b, and c.
study, the spray model for simulation was water spray using a ‘K-11’ type sprinkler [14]. The flow rate of the sprinkler was 189 l / min and the latitude angles for measuring the water droplet diffusion zone were 30 and 80. The activa- tion temperature was 74. Different flow rates were compared under the K-11 type sprinkler condition, and the flow rates were 100 l / m, 50 l / m, and 25 l / m, as shown in Fig. 6.
IV. RESULTS AND DISCUSSION
The damage simulation after bridge fire was aimed at the damage to the bridge column and bridge, in which judg- ment of the temperature field was an important index of damage.
1. Temperature Characteristic of the Sloped Bridge
Fig. 7 shows the slope of the fire source. The heat source moved upward, and three thermocouples were set up to capture the temperature change. The time-temperature curve was shown when the bridge was inclined at 2 to the horizontal. The temperatures on both sides of the fire source were symmetrical; however, the left temperature was higher than the right temperature, as shown in Fig. 8. The temperature in the upper position of the slope was higher, which is a characteristic of inclined bridges. The left pro- tection should have been enhanced in this case. The fire source at the initial stage of the fire (within 300 seconds) was in the lower part of location b. It was observed that the temperature at location a was higher than that at loca- tion c by about 200 at 300 sec, while the temperature at (13.0, 7.0, 4.5)
(17.0, 23.0, 4.5)
Location a =(12.4, 15, 4) a
(a)
(b)
(c) b
Slice temp
C 670 605 540 475 410 345 280 215 150 85.0 20.0
c Location b =(14.0, 15, 4)
Location c =(15.6, 15, 4)
Location a Location b Location c
300
200
100
50 100 150 200 250 300 350
0 0 400
500 600 700 800
Temperature ( C )
Time (s)
Fig. 9 Temperature vector graph of the velocity slices at the plane of y = 15m: (a) at 200 sec / (b) at 400 sec.
Fig. 10 Calculation results contrasted with post-disaster photo: (a) steel girder deformation / (b) tempera- ture distribution at steel girder.
location a was almost higher than the temperature at loca- tion c within 300 sec. Fig. 9 shows the temperature vector graph. In Fig. 9(a), the vectorial angle above the fire source was approximately 130° at 200 seconds. In Fig. 9(b), the vectorial angles above the fire source was dispersed be- tween 110° and 140° at 400 seconds. This zone shows that the fire spread towards the upper left instead of in a positive direction, and the vectorial angles dispersed with the fire behavior.
2. Damage Investigation and Analysis
According to the fire condition field survey after the fire under the bridge, the physical characteristics of the ma- terial, and the fire spread characteristics, the CFD simula- tion calculation was implemented. Fig. 10 shows the re- sults and a post-disaster photo. The post-disaster condi- tion of the steel girder (located at approximately X = 20m,
Fig. 11 Calculation results contrasted with post-disaster photo: (a) melted convex traffic mirror / (b) tem- perature distribution at the convex traffic mirror.
Fig. 12 Calculation results contrasted with post-disaster photo: (a) polyvinyl chloride (PVC) pipe / (b)tem- perature distribution at PVC pipe.
Y = 6m) was compared with the simulation and the temper- ature was found to be about 520, so that the steel was sig- nificantly deformed [24]. The post-disaster photo of the convex traffic mirror and the calculated temperature distri- bution are illustrated in Fig. 11. It was seen that the out- side reflective mirror (made of plastic material) was se- verely melted due to the temperature reached about 190.
However, the surrounding structure made of steel remained intact.
The temperature outside the bridge was estimated at over 200, which caused the polyvinyl chloride (PVC) pipe to nearly catch fire, and the paint peeled off due to the high temperature, as shown in Fig. 12. A great deal of smoke resulted in low visibility under the bridge; fortu- nately, nobody was under the bridge, as shown in Fig. 13.
Therefore, the steel girder and concrete surface were black- ened.
When a fire occurs, the loss of concrete strength de- pends mainly on the fire temperature of the concrete com- ponent. When the fire temperature exceeds 300, the concrete begins to crack due to C-S-H decomposition, and the concrete strength begins to decrease. When the tem- perature exceeds 400, as the C-S-H colloid in the concrete becomes severely damaged, the concrete strength declines
(a)
(b)
Slice temp
670 605 540 475 410 345 280 215 150 85.0 20.0
C
temp
C 560
500 440 380 320 260
(a) (b)
Slice temp
C 270 245 220 195 170 145
120 95.0
70.0
(a) (b)
520 470 420 370 320 270 Slice temp
C
(a) (b)
Fig. 13 Diffusion of a large quantity of smoke.
Fig. 14 (a) Bridge column and bridge pier after fire hazard / (b)temperature distribution slices at the plane of x = 13m at 400 sec.
sharply. Fig. 14(a) shows the concrete breakaway after the fire, in which the temperature in the position presents a high-temperature bridge column, as shown in Fig. 14(b).
The inspection result showed that the concrete in the se- verely damaged position was partially destroyed; there was extensive spalling, the surface concrete was loose and the adhesive force between the reinforcing bar and concrete may have been partially damaged. The concrete surface in the moderately damaged position exhibited check cracks and peeling. The concrete strength was influenced to some extent, but the effect on the adhesive force between the reinforcing bar and concrete was slight. The concrete surface in the slightly damaged position was covered with black smoke, which was the product of incomplete combus- tion. The concrete surface heating temperature in this area was lower than 300, and the effect on the structural state was slight.
3. Enhanced Sprinkler System Fire Protection
Concrete and steel girder fires can cause a bridge to collapse; therefore, it is necessary to take effective fire pro- tection measures for concrete and steel girder structures.
Relevant scholars and experts realized the importance of protecting concrete and steel structures after a series of in- vestigations on steel structure fires. At present, common fire protection measures include spraying fire-retardant coatings, sprinklers and screen methods. In terms of an
Fig. 15 The sprinkler system activated at (a) 60 sec / (b) 120 sec.
Fig. 16 Temperature cure of the original scenario com- pared to the sprinkler system.
automatic sprinkler system, when a fire occurs, the auto- matic sprinkler system detects the temperature rise and smoke spread and sprays water automatically; it can con- trol the overall fire scene temperature and even extinguish the flame. This method has a high cost but is an effective method. As shown in Fig. 15, the bridge was protected after the sprinkler system activated. As shown in Fig. 16, when the sprinkler equipment was mounted, the temper- ature near the bridge column dropped considerably.
Generally speaking, the higher the flow rate was, the better the effect would be. When the flow rate was 190 L / min and 100 L / min, the temperature remained lower than 300 and the damage to the concrete was slight; how- ever, a flow rate of 25L / min damaged the concrete con- siderably. The other flow rate schemes were approxi- mately acceptable. As shown in Fig. 16(c), the original maximum temperature of 680 was reduced by 210,
Slice temp
C 670 605 540 475 410 345 280 215 150 85.0 20.0
(a) (b)
(a) (b)
Location (12.4, 8.0, 4.0) Location (12.4, 10.0, 4.0)
Location (12.4, 12.0, 4.0) Location (12.4, 14.0, 4.0) Time (s)
Temperature ( C )
(a) (b)
400 300 200 100
200 400 600 800 1000
00 500 600
400 300 200 100 0 500 600 700
Temperature ( C )
200 400 600 800 1000
0
Temperature ( C )
Temperature ( C )
400 300 200 100 0 500 600 700
400 300 200 100 0 500 600 700 800
No sprinkler Flow Rate: 190 L/min Flow Rate: 100 L/min Flow Rate: 50 L/min Flow Rate: 25 L/min
No sprinkler Flow Rate: 190 L/min Flow Rate: 100 L/min Flow Rate: 50 L/min Flow Rate: 25 L/min No sprinkler Flow Rate: 190 L/min Flow Rate: 100 L/min Flow Rate: 50 L/min Flow Rate: 25 L/min No sprinkler
Flow Rate: 190 L/min Flow Rate: 100 L/min Flow Rate: 50 L/min Flow Rate: 25 L/min
Time (s)
Time (s)
(c) (d)
200 400 600 800 1000
0 0 200 400 600 800 1000
Time (s)
which greatly lessened the damage to the concrete.
V. CONCLUSIONS
FDS has been extensively used in fire simulations and the reproduction and prediction of fire scenes. The simu- lation result in this study matched the actual fire scene.
The numerical simulation was extended into research on bridge fire incidents. The evaluation and prevention of bridge structure fire damage are complicated work. The use of CFD software for reasonable detection and preven- tion is important for the normal use of bridges after a fire.
The research conclusions of this study are as follows:
1. In the basic scenario of a fire incident with onsite burn- ing, the high amount of dense smoke creates toxic gases that spread with the wind, therefore people nearby must be evacuated from the fire source to protect them against hazardous gas exposure.
2. The structure of a beam may be affected by a fire, there- fore bridge usage must be stopped immediately until its safety is validated. The large temperature differences in an inclined bridge result in a strong horizontal acting force. These forces may lead to flexural deformation of the road surface. The scenario where the fire loca- tion is near a bridge column is worse than one in the intermediate zone, as the Coanda effect results in a higher temperature.
3. A bridge must be evaluated in detail after a fire, and fea- sible and reliable prevention schemes must be planned.
An automatic sprinkler system is one of the most effec- tive schemes, as it can implement effective protection when the flow rate is 100 L / min, thereby saving water resources.
The use of numerical simulations to reconstruct the course of a fire has been implemented by fire researchers for years. This paper used different bridge inspection means comprehensively and obtained a good effect, and the results could be used as a reference for bridge safety after a fire.
REFERENCES
1. Su, S., and L. Wang. 2013. “Three Dimensional Recon- struction of The Fire in A Ship Engine Room with Multi- layer Structures.” Ocean Engineering 70 (2013): 201-207.
doi: 10.1016/j.oceaneng.2013.05.032.
2. Wagner, N., and V. Agrawal. 2014. “An Agent-Based Sim- ulation System for Concert Venue Crowd Evacuation
Modeling in The Presence of A Fire Disaster.” Expert Sys- tems with Applications 41 (6): 2807-2815. doi:
10.1016/j.eswa.2013.10.013.
3. Cuesta, A., and S. M. V. Gwynne. 2016. “The Collection and Compilation of School Evacuation Data for Model Use.” Safety Science 84: 24-36. doi:
10.1016/j.ssci.2015.11.003.
4. Hsu, J. P., and C. S. Lin. 2019. “Numerical Analysis of Fire Consequences and Effective Solutions in A Corn Starch Explosion Fire Based on Computational Fire Dynamics Simulator.” Cluster Computing 22: 14411-14418. doi:
10.1007/s10586-018-2306-9.
5. Lin, C. S., and M. E. Wu. 2018. “A Study of Evaluating An Evacuation Time.” Advances in Mechanical Engineering 10 (4): 1-11. doi: 10.1177/1687814018772424.
6. Lai, C. C., and C. S. Lin. 2017. “An Analysis of The Design of A Fire-Resistant Elevator Landing Door.” Journal of the Chinese Institute of Engineers 40 (5): 428-440. doi:
10.1080/02533839.2017.1336116.
7. Yang, P., C. Li, and D. Chen. 2013. “Fire Emergency Evac- uation Simulation Based on Integrated Fire-Evacuation Model with Discrete Design Method.” Advances in Engi- neering Software 65: 101-111. doi: 10.1016/j.adveng- soft.2013.06.007.
8. Horváth, I., J. van Beeck, and B. Merci. 2013. “Full-Scale and Reduced-Scale Tests on Smoke Movement in Case of Car Park Fire.” Fire Safety Journal 57: 35-43. doi:
10.1016/j.firesaf.2012.10.009.
9. Peris-Sayol, G., I. Paya-Zaforteza, J. Alos-Moya, and A.
Hospitaler. 2015. “Analysis of The Influence of Geometric, Modeling and Environmental Parameters on The Fire Re- sponse of Steel Bridges Subjected to Realistic Fire Scenar- ios.” Computers & Structures 158: 333-345. doi:
10.1016/j.compstruc.2015.06.003.
10. Kolaitis, D. I., E. K. Asimakopoulou, and M. A. Founti.
2017. “Fire Behaviour of Gypsum Plasterboard Wall Assemblies: CFD Simulation of A Full-Scale Residen- tial Building.” Case Studies in Fire Safety 7: 23-35. doi:
10.1016/j.csfs.2016.11.001.
11. Bezas, M. Z., T. N. Nikolaidis, and C. C. Baniotopoulos.
2017. “Fire Protection and Sustainability of Structural Steel Buildings with Double-Shell Brickwork Cladding.”
Procedia Environmental Sciences 38: 298-305. doi:
10.1016/j.proenv.2017.03.082.
12. Floyd, J., and R. McDermott. 2017. “Development and Evaluation of Two New Droplet Evaporation Schemes for Fire Dynamics Simulations.” Fire Safety Journal 91:
643-652. doi: 10.1016/j.firesaf.2017.04.036.
13. Frank, K., M. Spearpoint, G. Baker, C. Wade, P. Collier, and C. Fleischmann. 2017. “Measuring Modified Glass
Bulb Sprinkler Thermal Response in Plunge and Com- partment Fire Experiments.”, Fire Safety Journal 91:
662-670. doi: 10.1016/j.firesaf.2017.03.017.
14. Link, E., T. Myers, A. Trouvé, and A. Marshall. 2017.
“Measurements of Spray-Plume Interactions for Model Validation.” Fire Safety Journal 91: 714-722. doi:
10.1016/j.firesaf.2017.04.024.
15.Parent, G., P. Boulet, R. Morlon, and E. Blanchard. 2017.
“Radiation Attenuation and Opacity in Smoke and Wa- ter Sprays.” Journal of Quantitative Spectroscopy and Radiative Transfer 197: 60-67. doi: 10.1016/j.jqsrt.2017.
03.015.
16. Tanklevskiy, L., A. Tsoy, and A. Snegirev. 2017. “Elec- trically Controlled Dynamic Sprinkler Activation: Com- putational Assessment of Potential Efficiency.” Fire Safety Journal 91: 614-623. doi: 10.1016/j.firesaf.2017.
04.019.
17. Shi, M. Q. 2017. “Taoyuan Landing Bridge Has Been Threatened with Closure Duo to Heavy Fire and Bridge Deformation.” Apple Daily. Accessed August 6.
https://tw.apple-
daily.com/new/realtime/20170806/1176736/
18. McGrattan, K., S. Hostikka, R. McDermott, J. Floyd, and C. Weinschenk. 2013. Fire Dynamics Simulator User’s Guide. 6th Ed. Gaithersburg, MD: National Insti- tute of Standards and Technology.
19. McGrattan, K., S. Hostikka, R. McDermott, J. Floyd, R.
McDermott, and M. Vanella. 2013. Fire Dynamics Sim- ulator Technical Reference Guide Volume 3: Validation.
Gaithersburg, MD: National Institute of Standards and
Technology.
20. Cox, G., and S. Kumar. 2002. “Modeling Enclosure Fires Using CFD.” In SFPE Handbook of Fire Protec- tion Engineering, edited by P. J. DiNenn, 132-143. Mas- sachusetts, MA: National Fire Protection Association.
21. Ma, T. G., and J. G. Quintiere. 2003. “Numerical Simu- lation of Axi-Symmetric Fire Plumes: Accuracy and Limitations.” Fire Safety Journal 38 (5): 467-492. doi:
10.1016/S0379-7112(02)00082-6.
22. Peacock, R. D., and P. A. Reneke. 2007. Verification and Validation of Selected Fire Models for Nuclear Power Plant Applications, Volume 5: Consolidated Fire Growth and Smoke Transport Model (CFAST). Report No. NUREG 1824. Palo Alto, CA: Electric Power Re- search Institute.
23. Li, L. J. 2013. “Numerical Simulation of Highway Fire Temperature Field and Analysis of Long-Span Cable Support Bridge Fire.” PhD dissertation, ChangĨan Uni- versity.
24. Fan, X. M. 2013. “Analysis of Displacement and Inter- nal Force of Steel Grid Structure after Fire.” MS disser- tation, Beijing University of Technology.
Manuscript Received: May. 04, 2019 First Revision Received: Jun. 24, 2019 Second Revision Received: Oct. 28, 2019 and Accepted: Nov. 28, 2019
