Predicting Maximum Effective Temperatures and Thermal Gradients for Steel I-Girder in Canadian Climate Regions
Abstract
:1. Introduction
2. Literature Review
2.1. Potential Impacts of Climate Change on Bridge Infrastructure in Canada
2.2. Effects of Time-Dependent Thermal Loads on Steel Bridge Structures
2.3. Experimental and Numerical Thermal Analyses of Temperature Distribution and Gradient and Their Thermally Induced Responses in Steel Structures
3. Methodology
Data Acquisition
4. Heat Transfer Equation and Thermal Boundary Conditions
5. Implementation of Transient Thermal Analysis
- 1.
- The top surface of the top flange and the top surfaces of the bottom flange,
- 2.
- The bottom surface of the bottom flange and the subsurface of the overhangs, and
- 3.
- Vertical webs considering the shadowing effect that changes with time.
6. ANSYS Thermal Model Validation
7. The Parametric Study
7.1. The Canadian Climate Regions
7.2. Ambient Air Temperature and Solar Radiation Data for the Representative Cities of the Climate Regions
8. One-Month FE Thermal Simulations
9. Results and Discussion
9.1. Positive Thermal Gradient Profiles for the Climate Regions
9.2. The Prediction Model of the Daily Maximum Thermal Gradient Variation
9.3. The Proposed Thermal Gradient Variation for the Climate Regions
9.4. The Maximum Effective Temperatures of the Representative Cities of the Climate Regions
9.5. Predicted Maximum Effective Temperature Formula
9.6. Comparison between the Predicted FE Thermal Results and the Corresponding Results Recommended by the CHBDC
10. Conclusions
- The maximum thermal gradient variations and the maximum effective temperatures were found to not occur simultaneously. Extreme heat conditions can lead to the maximum effective temperature. However, the maximum thermal gradient is not necessarily associated with such conditions.
- The developed thermal gradient profiles for each climate region divided the climate regions into two distinct zones, and their maximum thermal gradient variations were determined. A regression analysis was conducted to further analyze the data, and a predicted formula was developed to determine the maximum thermal gradient variation based on geometry and environmental parameters such as flange width, web depth, total solar radiation, daily maximum air temperature and flange thickness. The predicted formula demonstrated a strong correlation between the predicted maximum thermal gradient variations and the FE maximum thermal gradient variations, with a coefficient of determination R2 of 0.98. This indicates that increasing the flange width, web depth and total solar radiation and decreasing the daily maximum air temperature and flange thickness all lead to an increase in the maximum thermal gradient variation. For the determined maximum effective temperature values of standard steel girders in each representative city of the climate regions. A regression analysis model was developed to predict the maximum effective temperature. The predicted formula of the maximum effective temperature was developed. The results of the predicted formula and the comparison of the maximum effective temperature values clearly indicate that the daily air temperature is a major factor to be considered. In addition, it is essential to consider the combined effect of the flange width and the girder’s depth rather than examining them independently to obtain accurate results.
- The comparison between the predicted FE thermal results and their corresponding CHBDC specifications revealed that the FE maximum effective temperatures are higher than their corresponding CHBDC values. In addition, the current study showed that the girder’s depth had a direct impact on the maximum effective temperature and that other parameters should be taken into account. By comparing the thermal gradient profiles and values, it was revealed that a single stationary thermal gradient profile and fixed thermal gradient variations would not satisfy the design requirements of the Canadian climate regions. The CHBDC did not clearly provide an explicit thermal gradient profile or the gradient variation values along the web. However, the current study was able to predict the thermal gradient profile pattern and the maximum thermal gradient variations for two main climate zones.
- The uncertain changes within projected temperature distributions and ranges, heatwaves and extremely high temperatures due to climate change and global warming directly affect the temperature field (thermal gradients and effective temperature) of steel structures, resulting in significant thermally induced responses and effects. A future research direction would be to examine the impact of climate change and global warming on steel structures’ temperature fields. Extreme conditions of future multiyear meteorological and thermal load data can be used as inputs for thermal boundary conditions to simulate the long-term temperature field of steel structures. An extensive thermal analysis can be conducted based on long-term temperature field simulations, and this thermal analysis can be used as a basis for studying and determining extreme temperature events, thermal gradients and temperature variations over time, thus improving structural design methods and specifications.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Groupe Csa. Canadian Highway Bridge Design Code (CHBDC); Csa Group: Toronto, ON, Canada, 2019. [Google Scholar]
- Nasr, A.; Kjellström, E.; Björnsson, I.; Honfi, D.; Ivanov, O.L.; Johansson, J. Bridges in a changing climate: A study of the potential impacts of climate change on bridges and their possible adaptations. Struct. Infrastruct. Eng. 2019, 16, 738–749. [Google Scholar] [CrossRef]
- Khotbehsara, M.M.; Manalo, A.; Aravinthan, T.; Turner, J.; Ferdous, W.; Hota, G. Effects of ultraviolet solar radiation on the properties of particulate-filled epoxy based polymer coating. Polym. Degrad. Stab. 2020, 181, 109352. [Google Scholar] [CrossRef]
- Guest, G.; Zhang, J.; Atadero, R.; Shirkhani, H. Incorporating the Effects of Climate Change into Bridge Deterioration Modeling: The Case of Slab-on-Girder Highway Bridge Deck Designs across Canada. J. Mater. Civ. Eng. 2020, 32, 04020175. [Google Scholar] [CrossRef]
- Nasr, A.; Honfi, D.; Larsson Ivanov, O. Probabilistic analysis of climate change impact on chloride-induced deterioration of reinforced concrete considering Nordic climate. J. Infrastruct. Preserv. Resil. 2022, 3, 8. [Google Scholar] [CrossRef]
- Felio, G.; Canadian Construction Association; Canadian Public Works Association; Canadian Society for Civil Engineering and Federation of Canadian Municipalities. Canadian Infrastructure Report Card 2019; Municipal Roads and Water Systems; Canadian Construction Association: Ottawa, ON, Canada, 2019; Volume 1. [Google Scholar]
- Siddiquee, K.; Alam, M.S. Highway bridge infrastructure in the province of British Columbia (BC), Canada. Infrastructures 2017, 2, 7. [Google Scholar] [CrossRef]
- Gu, B.; Chen, Z.; Chen, X. Temperature gradients in concrete box girder bridge under effect of cold wave. J. Cent. South Univ. 2014, 21, 1227–1241. [Google Scholar] [CrossRef]
- Chen, D.; Qian, H.; Wang, H.; Chen, Y.; Fan, F.; Shen, S. Experimental and numerical investigation on the non-uniform temperature distribution of thin-walled steel members under solar radiation. Thin-Walled Struct. 2018, 122, 242–251. [Google Scholar] [CrossRef]
- Liu, J.; Liu, Y.; Jiang, L.; Zhang, N. Long-term field test of temperature gradients on the composite girder of a long-span cable-stayed bridge. Adv. Struct. Eng. 2019, 22, 2785–2798. [Google Scholar] [CrossRef]
- Zhao, Z.; Liu, H.; Chen, Z. Thermal behavior of large-span reticulated domes covered by ETFE membrane roofs under solar radiation. Thin-Walled Struct. 2017, 115, 1–11. [Google Scholar] [CrossRef]
- Zhu, Q.-X.; Wang, H.; Mao, J.-X.; Wan, H.-; Zheng, W.-Z.; Zhang, Y.-M. Investigation of Temperature Effects on Steel-Truss Bridge Based on Long-Term Monitoring Data: Case Study. J. Bridge Eng. 2020, 25, 05020007. [Google Scholar] [CrossRef]
- Abid, S.R.; Tayşi, N.; Özakça, M. Experimental analysis of temperature gradients in concrete box-girders. Constr. Build. Mater. 2016, 106, 523–532. [Google Scholar] [CrossRef]
- Wu, H.; Lin, X.; Zhou, A. A review of mechanical properties of fibre reinforced concrete at elevated temperatures. Cem. Concr. Res. 2020, 135, 106–117. [Google Scholar] [CrossRef]
- Düğenci, O.; Haktanir, T.; Altun, F. Experimental research for the effect of high temperature on the mechanical properties of steel fiber-reinforced concrete. Constr. Build. Mater. 2015, 75, 82–88. [Google Scholar] [CrossRef]
- Elbadry, M.; Ghali, A. Thermal stresses and cracking of concrete bridges. J. Proc. 1986, 83, 1001–1009. [Google Scholar]
- Wang, H.; Zhang, Y.-M.; Mao, J.-X.; Wan, H.-; Tao, T.-Y.; Zhu, Q.-X. Modeling and forecasting of temperature-induced strain of a long-span bridge using an improved Bayesian dynamic linear model. Eng. Struct. 2019, 192, 220–232. [Google Scholar] [CrossRef]
- Zhou, G.-D.; Yi, T.-H. Thermal Load in Large-Scale Bridges: A State-of-the-Art Review. Int. J. Distrib. Sens. Netw. 2013, 9, 217983. [Google Scholar] [CrossRef]
- Abid, S.R.; Mussa, F.; Tayşi, N.; Özakça, M. Experimental and finite element investigation of temperature distributions in concrete-encased steel girders. Struct. Control. Health Monit. 2018, 25, e2042. [Google Scholar] [CrossRef]
- Lei, X.; Jiang, H.; Wang, J. Temperature effects on horizontally curved concrete box-girder bridges with single-column piers. J. Aerosp. Eng. 2019, 32, 04019008. [Google Scholar] [CrossRef]
- Huang, S.; Cai, C.; Zou, Y.; He, X.; Zhou, T.; Zhu, X. Experimental and numerical investigation on the temperature distribution of composite box-girders with corrugated steel webs. Struct. Control Health Monit. 2022, 29, e3123. [Google Scholar] [CrossRef]
- Lee, J.-H. Investigation of Extreme Environmental Conditions and Design Thermal Gradients during Construction for Prestressed Concrete Bridge Girders. J. Bridge Eng. 2012, 17, 547–556. [Google Scholar] [CrossRef]
- Abid, S.a.l.l.a.l.R.; Tayşi, N.; Özakça, M. Temperature Records in Concrete Box-Girder Segment Subjected to Solar Radiation and Air Temperature Changes. IOP Conf. Ser. Mater. Sci. Eng. 2020, 870, 012074. [Google Scholar] [CrossRef]
- Lu, H.; Hao, J.; Zhong, J.; Wang, Y.; Yang, H. Analysis of Sunshine Temperature Field of Steel Box Girder Based on Monitoring Data. Adv. Civ. Eng. 2020, 2020, 9572602. [Google Scholar] [CrossRef]
- Abid, S.R.; Al-Gasham, T.S.; Xue, J.; Liu, Y.; Liu, J.; Briseghella, B. Geometrical Parametric Study on Steel Beams Exposed to Solar Radiation. Appl. Sci. 2021, 11, 9198. [Google Scholar] [CrossRef]
- Gottsäter, E.; Larsson Ivanov, O. Spatial Temperature Differences in Portal Frame Bridges. Struct. Eng. Int. 2019, 30, 254–261. [Google Scholar] [CrossRef]
- Hagedorn, R.; Martí-Vargas, J.R.; Dang, C.N.; Hale, W.M.; Floyd, R.W. Temperature Gradients in Bridge Concrete I-Girders under Heat Wave. J. Bridge Eng. 2019, 24. [Google Scholar] [CrossRef]
- Liu, H.; Liao, X.; Chen, Z.; Zhang, Q. Thermal behavior of spatial structures under solar irradiation. Appl. Therm. Eng. 2015, 87, 328–335. [Google Scholar] [CrossRef]
- Lee, J.; Jeong, Y.; Kim, W. Buckling behavior of steel girder in integral abutment bridges under thermal loadings in summer season during deck replacement. Int. J. Steel Struct. 2016, 16, 1071–1082. [Google Scholar] [CrossRef]
- Deng, H.-Q.; Li, T.-J.; Xue, B.-J.; Wang, Z.-W. Analysis of thermally induced vibration of cable-beam structures. Struct. Eng. Mech. 2015, 53, 443–453. [Google Scholar] [CrossRef]
- Kim, S.H.; Park, S.J.; Wu, J.; Won, J.H. Temperature variation in steel box girders of cable-stayed bridges during construction. J. Constr. Steel Res. 2015, 112, 80–92. [Google Scholar] [CrossRef]
- Abid, S.R.; Al-Gasham, T.S. Finite element simulation of vertical temperature gradients in a standard W40×235 steel beam. IOP Conf. Ser. Mater. Sci. Eng. 2020, 988, 012035. [Google Scholar] [CrossRef]
- Huang, S.; Cai, C.; Zou, Y.; He, X.; Zhou, T. Investigation of Temperature Variations and Extreme Temperature Differences for the Corrugated Web Steel Beams under Solar Radiation. Sensors 2022, 22, 4557. [Google Scholar] [CrossRef]
- Xu, W.; Chen, D.; Qian, H. Non-Uniform Temperature Fields and Effects of Steel Structures: Review and Outlook. Appl. Sci. 2020, 10, 5255. [Google Scholar] [CrossRef]
- Chen, D.; Xu, W.; Qian, H.; Sun, J.; Li, J. Effects of non-uniform temperature on closure construction of spatial truss structure. J. Build. Eng. 2020, 32, 101532. [Google Scholar] [CrossRef]
- Xu, W.; Chen, D.; Qian, H.; Chen, W. Non-uniform temperature field and effects of large-span spatial truss structure under construction: Field monitoring and numerical analysis. Structures 2021, 29, 416–426. [Google Scholar] [CrossRef]
- Abid, S.R. Temperature variation in steel beams subjected to thermal loads. Steel Compos. Struct. 2020, 34, 819–835. [Google Scholar]
- Ghali, A.; Favre, R.; Elbadry, M. Concrete Structures: Stresses and Deformations: Analysis and Design for Sustainability; CRC Press: Boca Raton, FL, USA, 2019. [Google Scholar]
- Zhang, C.; Liu, Y.; Liu, J.; Yuan, Z.; Zhang, G.; Ma, Z. Validation of long-term temperature simulations in a steel-concrete composite girder. Structures 2020, 27, 1962–1976. [Google Scholar] [CrossRef]
- Kalogirou, S.A. Solar Energy Engineering: Processes and Systems; Academic Press: Cambridge, MA, USA, 2014. [Google Scholar]
- Peng, Y.S. Studies on Theory of Solar Radiation Thermal Effects on Concrete Bridges with Application; Southwest Jiao Tong University: Chengdu, China, 2007. [Google Scholar]
- ANSYS 12 [Computer Software]; ANSYS: Canonsburg, PA, USA, 2009.
- Kehlbeck, F. Einfluss der Sonnenstrahlung bei Brückenbauwerken [Effect of Solar Radiation on Bridge Structure]; Werner: Düsseldorf, Germany, 1975. (In German) [Google Scholar]
- Canada weather stats, Canada Weather Stats. 2022. Available online: https://www.weatherstats.ca/ (accessed on 1 July 2022).
Dimensions (mm) | W36 × 282 | W36 × 232 | W30 × 191 | W30 × 148 | W18 × 86 | W18 × 71 | W10 × 26 | W10 × 19 |
---|---|---|---|---|---|---|---|---|
Depth (d) | 943 | 943 | 779 | 779 | 467 | 469 | 262 | 260 |
Flange width (b) | 422 | 308 | 382 | 266 | 282 | 194 | 147 | 102 |
Flange thickness (t) | 39.9 | 39.9 | 30.1 | 30 | 19.6 | 20.6 | 11.2 | 10 |
Web thickness (w) | 22.5 | 22.1 | 18 | 16.5 | 12.2 | 12.6 | 6.6 | 6.4 |
Climate Region | Representative City | Latitude and Longitude | Altitude (m) |
---|---|---|---|
Region 1 | Toronto | 43°40′00.000″ N | 166 |
Great Lakes and St. Lawrence | 79°24′00.000″ W | ||
Region 2 | Winnipeg | 49°55′00.000″ N | 239 |
Prairies | 97°14′58.000” W | ||
Region 3 | Halifax | 44°50′00.000″ N | 145 |
Atlantic Canada | 55°03′00.000″ N | ||
Region 4 | Victoria | 47°50′00.000″ N | 20 |
Pacific Coast | 77°22′00.000″ W | ||
Region 5 | Whitehorse | 60°43′00.000″ N | 706 |
Yukon and North British Columbia | 135°03′00.000″ W | ||
Region 6 | Yellowknife | 62°27′46.000″ N | 206 |
Mackenzie District | 114°26′25.000″ W | ||
Region 7 | Iqaluit | 63°45′00.000″ N | 34 |
Arctic Mountains and Fiords | 68°33′00.000″ W |
Climate Region | Standard Steel I-Girders | |||||||
---|---|---|---|---|---|---|---|---|
W36 × 282 | W36 × 232 | W30 × 191 | W30 × 148 | W18 × 86 | W18 × 71 | W10 × 26 | W10 × 19 | |
Region 1 | 11.537 | 10.572 | 11.31 | 10.373 | 8.219 | 7.482 | 5.838 | 5.268 |
Region 2 | 11.358 | 10.345 | 11.21 | 9.862 | 7.898 | 7.284 | 5.613 | 5.08 |
Region 3 | 11.572 | 10.666 | 11.382 | 10.473 | 8.634 | 7.479 | 5.936 | 5.363 |
Region 4 | 11.365 | 10.53 | 11.263 | 9.899 | 7.972 | 7.36 | 5.667 | 5.121 |
Region 5 | 9.443 | 8.828 | 9.346 | 8.346 | 6.438 | 6.062 | 4.539 | 4.106 |
Region 6 | 9.891 | 9.249 | 9.718 | 8.761 | 6.801 | 6.381 | 4.799 | 4.167 |
Region 7 | 9.524 | 8.989 | 9.398 | 8.511 | 6.688 | 6.282 | 4.744 | 4.286 |
Representative City | Standard Steel I-Girders | |||||||
---|---|---|---|---|---|---|---|---|
W36 × 282 | W36 × 232 | W30 × 191 | W30 × 148 | W18 × 86 | W18 × 71 | W10 × 26 | W10 × 19 | |
Toronto | 56.28 | 55.21 | 56.42 | 55.11 | 57.81 | 55.94 | 57.64 | 56.63 |
Winnipeg | 55.62 | 54.74 | 55.71 | 55.13 | 56.94 | 55.29 | 56.75 | 55.91 |
Halifax | 51.81 | 50.72 | 51.94 | 50.87 | 52.88 | 51.44 | 52.68 | 51.84 |
Victoria | 57.77 | 56.91 | 57.85 | 57.19 | 59.11 | 57.36 | 58.94 | 57.83 |
Whitehorse | 48.24 | 47.79 | 48.51 | 48.27 | 49.41 | 48.51 | 49.36 | 48.98 |
Yellowknife | 51.28 | 50.84 | 51.46 | 51.11 | 52.52 | 51.49 | 52.52 | 52.16 |
Iqaluit | 44.14 | 43.68 | 44.39 | 44.29 | 45.32 | 44.45 | 45.29 | 45.01 |
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Nassar, M.; Amleh, L. Predicting Maximum Effective Temperatures and Thermal Gradients for Steel I-Girder in Canadian Climate Regions. Appl. Sci. 2023, 13, 5906. https://doi.org/10.3390/app13105906
Nassar M, Amleh L. Predicting Maximum Effective Temperatures and Thermal Gradients for Steel I-Girder in Canadian Climate Regions. Applied Sciences. 2023; 13(10):5906. https://doi.org/10.3390/app13105906
Chicago/Turabian StyleNassar, Musab, and Lamya Amleh. 2023. "Predicting Maximum Effective Temperatures and Thermal Gradients for Steel I-Girder in Canadian Climate Regions" Applied Sciences 13, no. 10: 5906. https://doi.org/10.3390/app13105906