# Theoretical and Numerical Simulation Research on Fire of Large-Span Spatial Structures
[PERSON]  
1 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; [EMAIL_ADDRESS] (S.X.) [PERSON]  
1 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; [EMAIL_ADDRESS] (S.X.) [PERSON]  
1 College of Architecture and Civil Engineering, Beijing University of Technology, Beijing 100124, China; xxi122@mails. Due to the expansive construction areas, increasing power requirements, substantial personnel movement, and variable on-site conditions of large-space buildings, fire incidents are prevalent, often leading to significant loss of life and property, as depicted in Figure 2. Consequently, the study of fire protection performance in such structures is a perennial research priority [2]. Moreover, contemporary spherical dome structures, including gym-nasiums, predominantly employ natural ventilation for smoke exhaust, incorporating metal or mixed-material roofs, as well as localized open-roofing systems. These practices underscore the importance of fire prevention analysis and the design of natural smoke exhaust systems in spherical dome space structures [3]. The fire phenomenon, despite its inherent complexity, adheres to natural laws and can be encapsulated within empirical formulas, experimental data, or control equations that describe the combustion process [4]. Pioneering work by [PERSON] et al. [5] in 1956 introduced the virtual point source concept, positing that the plume originates from such a point. Subsequent researchers, including [PERSON] [6], [PERSON] [7; 8], [PERSON] [9; 10], and [PERSON] [11; 12], expanded upon this foundation, advancing the understanding of smoke behavior in building fires. [PERSON] and [PERSON] [13] built upon [PERSON]'s entrainment formula to conduct theoretical analyses of smoke control in large spaces, deriving simplified formulas for calculating smoke layer heights under various ventilation scenarios, including natural filling, side wall exhaust, and mechanical smoke extraction, complemented by full-scale experimental validation. The NFPA 92B [14] standard elucidates the physical model underpinning fire smoke movement in large spaces, detailing smoke exhaust calculations and control requirements, and provides the mass entrainment formula for the plume model, further enhancing the comprehension of smoke management in such settings. The ISO834 curve [15] is a standard formula used to measure the fire resistance of a structure. It is suitable for small rooms and is suitable for scientific research and engineering design. For the large space building structure, the building height and internal area are  
Figure 1: Large-span spherical dome structure at home and abroad. (Reproduced from Baidu Images (2024), as permitted under the Creative Commons Attribution License Agreement). (**a**) Millennium dome; (**b**) Fukuoka Open and Closed Dome Gymnasium; (**c**) Ejin Horo Sports Center; (**d**) China Coal Trading Center. Figure 2: Fire incidents in large-span structures both domestically and internationally. (Reproduced from Baidu Images (2024), as permitted under the Creative Commons Attribution License Agreement). (**a**) Shanghai Hongkou Sports Stadium Fire; (**b**) Jinan Olympic Sports Center Fire; (**c**) Linyi Olympic Sports Center Fire; (**d**) Denmark Copenhagen Stadium Fire. large, and the fire development is quite different from that of the general small indoor structure. The ventilation conditions of large space buildings are not the same as those of small rooms, and the location of fire source is also discrete, so when there is no suitable heating curve to describe the fire development, the regional model and the field model are the two commonly used fire simulation models. Therefore, the fire heating curve is obtained, which is of great significance for the fire protection structure design of large-span space buildings.