Technical Papers
Sep 9, 2024

Buckling and Critical Temperature Prediction Formulas of Restrained H-Section Steel Columns in Fire

Publication: Journal of Structural Engineering
Volume 150, Issue 11

Abstract

Buckling and critical temperatures of steel columns are crucial parameters for structural fire safety design. However, the existing simplified design methods for buckling or critical temperature are based on column models with either pin ends or with large rotational restraints. Their applications on steel columns with limited rotational restraint stiffness ratios—the ones smaller than the critical rotational restraint stiffness ratio—is questionable. In this paper, parametric analyses on a validated numerical column model with rotational restraint stiffness ratio varying from 0.0001 to 10.0 were conducted. The effects of slenderness ratio, load ratio, and axial restraint stiffness ratio were also considered. Results show that for steel columns with limited rotational restraint stiffness ratios, prediction errors of existing simplified design methods were significant. Following the parametric analyses, new prediction formulas of buckling temperature and critical temperature are proposed for H-section steel columns. Results of proposed formulas aligned closely with those of parametric analyses in the full range of considered parameters. Furthermore, the proposed formulas were also validated by test results in the literature.

Get full access to this article

View all available purchase options and get full access to this article.

Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Acknowledgments

Financial support from the National Natural Science Foundation of China with Grant Nos. 52378547 and 51908560 is gratefully acknowledged.

References

Agarwal, A., and A. H. Varma. 2014. “Fire induced progressive collapse of steel building structures: The role of interior gravity columns.” Eng. Struct. 58 (Jan): 129–140. https://doi.org/10.1016/j.engstruct.2013.09.020.
Ali, F. A., P. Shepherd, M. Randall, I. W. Simms, D. J. O’Connor, and I. Burgess. 1998. “The effect of axial restraint on the fire resistance of steel columns.” J. Constr. Steel Res. 46 (1–3): 305–306. https://doi.org/10.1016/S0143-974X(98)80036-9.
BSI (British Standards Institution). 2003. Structural use of steelwork in building, Part 8: Code of practical for fire resistance design. BS 5950-8. London: BSI.
Cai, J. G., and J. Feng. 2010. “Thermal buckling of rotationally restrained steel columns.” J. Constr. Steel Res. 66 (6): 835–841. https://doi.org/10.1016/j.jcsr.2010.01.010.
CEN (European Committee for Standardization). 2005. Eurocode 3: Design of steel structures, Part 1.2, General rules—Structural fire design. CEN 1993-1-2. Brussels, Belgium: CEN.
Chen, Y., H. Hao, W. S. Chen, J. Cui, Y. F. Hao, and C. F. Hua. 2021. “Dynamic tensile behaviors of welded steel joint material.” J. Constr. Steel Res. 183 (Aug): 106700. https://doi.org/10.1016/j.jcsr.2021.106700.
Correia, A. J. P. M., and J. P. C. Rodrigues. 2012. “Fire resistance of steel columns with restrained thermal elongation.” Fire Saf. J. 50 (May): 1–11. https://doi.org/10.1016/j.firesaf.2011.12.010.
Correia, A. J. P. M., J. P. C. Rodrigues, and F. C. T. Gomes. 2013. “A simplified calculation method for fire design of steel columns with restrained thermal elongation.” Comput. Struct. 116 (Jan): 20–34. https://doi.org/10.1016/j.compstruc.2012.09.006.
Cowper, G., and P. Symonds. 1957. Strain-hardening and strain-rate effects in the impact loading of cantilever beams. Providence, RI: Division of Applied Mathematics, Brown Univ.
Ding, R. M., S. G. Fan, G. Q. Chen, C. X. Li, E. F. Du, and C. L. Liu. 2019. “Fire resistance design method for restrained stainless steel H-section columns under axial compression.” Fire Saf. J. 108 (Sep): 102837. https://doi.org/10.1016/j.firesaf.2019.102837.
DTU (Document Technique Unifié). 1982. Méthode de prévision par le calcul du comportement au feu des structures an acier. [In French]. Constr. Mét. 3 (1): 39–92.
Fang, C., B. A. Izzuddin, A. Y. Elghazouli, and D. A. Nethercot. 2013. “Simplified energy-based robustness assessment for steel-composite car parks under vehicle fire.” Eng. Struct. 49 (Apr): 719–732. https://doi.org/10.1016/j.engstruct.2012.12.036.
Farmani, M. A., and A. Heidarpour. 2023. “Development of design equations for ultra-high strength steel CHS columns under transient fire conditions considering thermal creep and axial restraint effects.” Fire Saf. J. 136 (Apr): 103756. https://doi.org/10.1016/j.firesaf.2023.103756.
Farmani, M. A., A. Heidarpour, and X. L. Zhao. 2021. “A distinctive approach to testing and modeling thermal creep in ultra-high strength steel.” Int. J. Mech. Sci. 198 (May): 106362. https://doi.org/10.1016/j.ijmecsci.2021.106362.
Franssen, J. M. 2000. “Failure temperature of a system comprising a restrained column submitted to fire.” Fire Saf. J. 34 (2): 191–207. https://doi.org/10.1016/S0379-7112(99)00047-8.
Huang, Z. F., and K. H. Tan. 2003. “Analytical fire resistance of axially restrained steel columns.” J. Struct. Eng. 129 (11): 1531–1537. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:11(1531).
Jiang, B., G.-Q. Li, L. Li, and B. A. Izzuddin. 2018. “Experimental studies on progressive collapse resistance of steel moment frames under localized furnace loading.” J. Struct. Eng. 144 (2): 04017190. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001947.
Jiang, B. H., Z. R. Chen, Z. Y. Yin, and L. Xiao. 2023. “Buckling and critical temperatures of restrained H-section steel columns in fire considering dynamic effect.” Fire Saf. J. 141 (Dec): 104006. https://doi.org/10.1016/j.firesaf.2023.104006.
Jiang, B. H., G. Q. Li, and B. A. Izzuddin. 2016. “Dynamic performance of axially and rotationally restrained steel columns under fire.” J. Constr. Steel Res. 122 (Jul): 308–315. https://doi.org/10.1016/j.jcsr.2016.03.013.
Jiang, B. H., G. Q. Li, L. L. Li, and B. A. Izzuddin. 2017. “Simulations on progressive collapse resistance of steel moment frames under localized fire.” J. Constr. Steel Res. 138 (Nov): 380–388. https://doi.org/10.1016/j.jcsr.2017.05.018.
Jiang, B. H., G. Q. Li, and A. Usmani. 2015. “Progressive collapse mechanisms investigation of planar steel moment frames under localized fire.” J. Constr. Steel Res. 115 (Dec): 160–168. https://doi.org/10.1016/j.jcsr.2015.08.015.
Jiang, B. H., G. Q. Li, and M. C. H. Yam. 2020. “Simplified robustness assessment of steel framed structures under fire-induced column failure.” Steel Compos. Struct. 35 (2): 199–213. https://doi.org/10.12989/scs.2020.35.2.199.
Jiang, B. H., Z. Y. Yin, M. C. H. Yam, J. Z. Zhang, and L. P. Wang. 2022. “Influence of rotational restraints on response of H-section steel columns under fire.” J. Constr. Steel Res. 190 (Mar): 107104. https://doi.org/10.1016/j.jcsr.2021.107104.
Jiang, B. H., Z. Y. Yin, J. Z. Zhang, C. G. Fan, and Y. Z. Li. 2021. “Effect of rotational restraint conditions on performance of steel columns in fire.” Eng. Struct. 238 (Jul): 112237. https://doi.org/10.1016/j.engstruct.2021.112237.
Jiang, J., and G. Q. Li. 2017. “Progressive collapse analysis of 3D steel frames with concrete slabs exposed to localized fire.” Eng. Struct. 149 (Oct): 21–34. https://doi.org/10.1016/j.engstruct.2016.07.041.
Li, G. Q., P. J. Wang, and Y. C. Wang. 2010. “Behaviour and design of restrained steel column in fire, Part 1: Fire test.” J. Constr. Steel Res. 66 (8–9): 1138–1147. https://doi.org/10.1016/j.jcsr.2010.03.017.
Li, Y. Z., M. J. Wang, G. Q. Li, and B. H. Jiang. 2021. “Mechanical properties of hot-rolled structural steels at elevated temperatures: A review.” Fire Saf. J. 119 (Jan): 103237. https://doi.org/10.1016/j.firesaf.2020.103237.
Neves, I. C. 1995. “The critical temperature of steel columns with restrained thermal elongation.” Fire Saf. J. 24 (3): 211–227. https://doi.org/10.1016/0379-7112(95)00026-P.
Neves, I. C., J. C. Valente, and J. P. C. Rodrigues. 2002. “Thermal restraint and fire resistance of columns.” Fire Saf. J. 37 (8): 753–771. https://doi.org/10.1016/S0379-7112(02)00029-2.
Rakshith, B. D., and M. K. Kumar. 2020. “Behaviour of steel columns with realistic boundary restraints under standard fire.” Structures 28 (Dec): 626–637. https://doi.org/10.1016/j.istruc.2020.08.028.
SAC (Standardization Administration of the People’s Republic of China). 2017a. Code for fire safety of steel structures in buildings. [In Chinese.] GB 51249-2017. Beijing: SAC.
SAC (Standardization Administration of the People’s Republic of China). 2017b. Hot rolled H and cut T section steel. [In Chinese.] GB/T 11263-2017. Beijing: SAC.
SAC (Standardization Administration of the People’s Republic of China). 2017c. Standard for design of steel structures. [In Chinese.] GB 50017-2017. Beijing: SAC.
Tan, K. H., W. S. Toh, Z. F. Huang, and G. H. Phng. 2007. “Structural responses of restrained steel columns at elevated temperatures. Part 1: Experiments.” Eng. Struct. 29 (8): 1641–1652. https://doi.org/10.1016/j.engstruct.2006.12.005.
TIDCMHURD-PRC (Technology and Industrialization Development Center of Ministry of Housing and Urban-Rural Development of the People’s Republic of China). 2021. Guide for main component size of steel structure residences. [In Chinese.] Beijing: People’s Republic of China.
Valente, J. C., and I. C. Neves. 1999. “Fire resistance of steel columns with elastically restrained axial elongation and bending.” J. Constr. Steel Res. 52 (3): 319–331. https://doi.org/10.1016/S0143-974X(99)00033-4.
Wang, P. J., G. Q. Li, and Y. C. Wang. 2010a. “Behaviour and design of restrained steel column in fire, Part 3: Practical design method.” J. Constr. Steel Res. 66 (11): 1422–1430. https://doi.org/10.1016/j.jcsr.2010.05.009.
Wang, P. J., Y. C. Wang, and G. Q. Li. 2010b. “A new design method for calculating critical temperatures of restrained steel column in fire.” Fire Saf. J. 45 (6–8): 349–360. https://doi.org/10.1016/j.firesaf.2010.07.002.
Wang, Y. C. 2004. “Postbuckling behavior of axially restrained and axially loaded steel columns under fire conditions.” J. Struct. Eng. 130 (3): 371–380. https://doi.org/10.1061/(ASCE)0733-9445(2004)130:3(371).
Wang, Y. C., and J. M. Davies. 2003. “An experimental study of non-sway loaded and rotationally restrained steel column assemblies under fire conditions: Analysis of test results and design calculations.” J. Constr. Steel Res. 59 (3): 291–313. https://doi.org/10.1016/S0143-974X(02)00040-8.
Wu, Y. W., S. G. Fan, B. B. He, M. J. Liu, and H. Zhou. 2021. “Research on the fire resistance design of high-strength steel hollow columns under axial compression.” Eng. Struct. 234 (May): 111943. https://doi.org/10.1016/j.engstruct.2021.111943.
Xing, Z., O. Zhao, M. Kucukler, and L. Gardner. 2021. “Testing of stainless steel I-section columns in fire.” Eng. Struct. 227 (Jan): 111320. https://doi.org/10.1016/j.engstruct.2020.111320.
Yang, J. J., Y. Xia, W. Y. Wang, and H. Al-azzani. 2021. “Fire resistance of axially restrained Q690 H-shaped welded steel columns: Test, simulation and design.” J. Constr. Steel Res. 177 (Feb): 106413. https://doi.org/10.1016/j.jcsr.2020.106413.
Yin, Z. Y., and B. H. Jiang. 2023. “Predicting equation of quasi-static and dynamic failures of steel columns under fire.” Eng. Struct. 276 (Feb): 115348. https://doi.org/10.1016/j.engstruct.2022.115348.
Zhang, C., G. Q. Li, and Y. C. Wang. 2012. “Predictability of buckling temperature of axially loaded steel columns in fire.” J. Constr. Steel Res. 75 (Aug): 32–37. https://doi.org/10.1016/j.jcsr.2012.03.001.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 150Issue 11November 2024

History

Received: Jan 15, 2024
Accepted: Jun 18, 2024
Published online: Sep 9, 2024
Published in print: Nov 1, 2024
Discussion open until: Feb 9, 2025

Permissions

Request permissions for this article.

Authors

Affiliations

Zhengrong Chen [email protected]
Postgraduate, School of Civil Engineering, Central South Univ., Changsha 410075, China. Email: [email protected]
Binhui Jiang [email protected]
Associate Professor, School of Civil Engineering, Central South Univ., Changsha 410075, China (corresponding author). Email: [email protected]

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share