Simplified Analytical Approach for Calculating the Transverse Load Distribution of Precast Slab Bridges with and without Concrete Overlays
Publication: Journal of Bridge Engineering
Volume 29, Issue 7
Abstract
Precast slab bridges are an attractive option for short- to medium-span bridges; however, the presence of longitudinal joints and concrete overlays adds great complexity to the transverse load distribution (TLD) analysis. Currently, one of the most commonly used methods for simplified analysis relies on the semiempirical formulas provided in AASHTO LRFD Bridge Design Specifications; yet, these formulas have certain limitations in their applicability. This study presents an algorithm based on the transfer matrix method (TMM) to determine the TLD of precast slab bridges. A connection model utilizing shear-and-torsion spring hinges (STSHs) is proposed to simulate the structural behavior of shear keys and the overlay of precast slab bridges in TLD calculations. The transfer matrices and transfer equations between slabs and between joints are established. The TLD for slabs is then computed by introducing boundary conditions and solving transfer equations. In addition, the finite-element method (FEM), along with the existing field tests of two different bridges, is used to verify the accuracy and validity of the proposed method. The study concludes that the TMM shows high algorithmic efficiency compared to the FEM modeling procedure and better precision and applicability than the semiempirical equations provided in AASHTO LRFD. Moreover, extended parametric studies are conducted on the effects of the thickness of concrete overlay and the relative flexibility coefficients of slabs on the TLD of bridges.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The financial support provided by the National Key R&D Program of China (No. 2019YFE0119800) is gratefully acknowledged. The second author acknowledges the support of the research projects TED2021-130272B-C21 funded by MCIN/AEI/10.13039/501100011033 “European Union Next Generation EU/PRTR” and PID2021-123701OB-C21 funded by MCIN/AEI/10.13039/501100011033 and the European Regional Development Fund (ERDF) “A way to make Europe.” The author also thank Dr. Weizhuo Shi for his linguistic assistance during the preparation of this manuscript.
References
AASHTO. 1973. Standard specifications for highway bridges. 11th ed. Washington, DC: AASHTO.
AASHTO. 2020. LRFD bridge design specification. 9th ed. Washington, DC: AASHTO.
ABAQUS. 2019. ABAQUS/standard user’s manual. Ver. 2019. Providence, RI: Dassault Systemes.
ACI (American Concrete Institute). 2016. Report on flexural live load distribution methods for evaluating existing bridges. ACI 342R-16. Farmington Hills, MI: ACI.
ACI (American Concrete Institute). 2022. Live load distribution on concrete bridges: Design, evaluation, construction, innovation. ACI SP-352. Farmington Hills, MI: ACI.
Barbieri, D. M., Y. Chen, E. Mazzarolo, B. Briseghella, and A. M. Tarantino. 2018. “Longitudinal joint performance of a concrete hollow core slab bridge.” Transp. Res. Rec. 2672 (41): 196–206. https://doi.org/10.1177/0361198118781653.
BridgeTech. 2007. Simplified live load distribution factor equations. NCHRP Rep. No. 592. Washington, DC: National Cooperativel Highway Research Program, Transportation Research Board, National Research Council.
Cai, C. S. 2005. “Discussion on AASHTO LRFD load distribution factors for slab-on-girder bridges.” Pract. Period. Struct. Des. Constr. 10 (3): 171–176. https://doi.org/10.1061/(ASCE)1084-0680(2005)10:3(171).
CEN (European Committee for Standardization). 2003. Actions on structures part 2: Traffic loads on bridges. Eurocode 1. Brussels, Belgium: CEN.
Chang, S. T. 1998. “Computation of the influence lines for lateral load distribution in straight, skew and horizontally curved bridges.” Adv. Struct. Eng. 2: 1–16. https://doi.org/10.1177/136943329800200102.
Cheng, Z., Z. Shi, A. Palermo, H. Xiang, W. Guo, and A. Marzani. 2020. “Seismic vibrations attenuation via damped layered periodic foundations.” Eng. Struct. 211: 110427. https://doi.org/10.1016/j.engstruct.2020.110427.
Cheung, M. S., B. Bakht, and L. G. Jaeger. 1982. “Analysis of box-girder bridges by grillage and orthotropic plate methods.” Can. J. Civ. Eng. 9: 595–601. https://doi.org/10.1139/l82-069.
Crabtree, B., B. E. Ross, T. E. Cousins, and P. Ziehl. 2021. “Live-load testing of flat precast slab bridge to determine joint efficiency and distribution factors for moment.” J. Perform. Constr. Facil 35 (1): 04020134. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001543.
CSA (Canadian Standards Association). 2019. Canadian highway bridge design code. CSA-S6. Mississauga, ON, Canada: CSA.
Fu, C. 2015. “The effect of switching cracks on the vibration of a continuous beam bridge subjected to moving vehicles.” J. Sound Vib. 339: 157–175. https://doi.org/10.1016/j.jsv.2014.11.009.
Fu, C. C., M. Elhelbawey, M. A. Sahin, and D. R. Schelling. 1996. “Lateral distribution factor from bridge field testing.” J. Struct. Eng. 122 (9): 1106–1109. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:9(1106).
Grace, N. F., K. D. Patki, E. M. Soliman, and J. Q. Hanson. 2011. “Flexural behavior of side-by-side box-beam bridges: A comparative study.” PCI J. 56 (3): 94–112. https://doi.org/10.15554/pcij.06012011.94.112.
Guo, K., Z. Liu, and J.-M. Bairán. 2022. “Transfer matrix method for calculating the transverse load distribution of articulated slab bridges.” Buildings 12 (10): 1610. https://doi.org/10.3390/buildings12101610.
Hambly, E. C. 1991. Bridge deck behaviour. 2nd ed. London, UK: Chapman and Hall.
Harris, D. K., and A. Gheitasi. 2013. “Implementation of an energy-based stiffened plate formulation for lateral load distribution characteristics of girder-type bridges.” Eng. Struct. 54: 168–179. https://doi.org/10.1016/j.engstruct.2013.04.002.
Harris, D. K. 2010. “Assessment of flexural lateral load distribution methodologies for stringer bridges.” Eng. Struct. 32 (11): 3443–3451. https://doi.org/10.1016/j.engstruct.2010.06.008.
He, B., Y. Zhang, W.-Y. Ge, Y. An, and D. Liu. 2018. “Buckling analysis of thin-walled members with open-branched cross section via semi-analytical finite strip transfer matrix method.” Thin-Walled Structures 124: 20–31. https://doi.org/10.1016/j.tws.2017.11.039.
Hussein, H. H., K. K. Walsh, S. M. Sargand, F. T. Al Rikabi, and E. P. Steinberg. 2017. “Modeling the shear connection in adjacent box-beam bridges with ultrahigh-performance concrete joints. I: Model calibration and validation.” J. Bridge Eng. 22 (8): 04017043. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001070.
JARA (Japan Road Association). 2012. Specifications for highway bridges, part I: Common specifications. Tokyo: JARA.
Kong, S. Y., L. D. Zhuang, M. X. Tao, and J. S. Fan. 2020. “Load distribution factor for moment of composite bridges with multi-box girders.” Eng. Struct. 215: 19.
Li, G., and D. Shi. 1987. Calculation of load transverse distribution for highway bridges. [In Chinese.] Beijing: China Communications Press.
Liu, H., X. He, and Y. Jiao. 2018. “Damage identification algorithm of hinged joints for simply supported slab bridges based on modified hinge plate method and artificial bee colony algorithms.” Algorithms 11: 198. https://doi.org/10.3390/a11120198.
Mu, Y. J. 2012. “The load transverse distribution of research on the simply-supported hollow slab bridge.” [In Chinese.] Master’s thesis, College of Transportation, Jilin Univ.
Newmark, N. M. 1949. “Design of I-beam bridges.” Trans. Am. Soc. Civ. Eng. 114 (1): 997–1022. https://doi.org/10.1061/TACEAT.0006257.
Ottosen, N. S., M. Ristinmaa, and A. G. Davis. 2004. “Theoretical interpretation of impulse response tests of embedded concrete structures.” J. Eng. Mech. 130 (9): 1062–1071. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:9(1062).
Restrepo, E., T. Cousins, and J. Lesko. 2005. “Determination of bridge design parameters through field evaluation of the route 601 bridge utilizing fiber-reinforced polymer girders.” J. Perform. Constr. Facil 19 (1): 17–27. https://doi.org/10.1061/(ASCE)0887-3828(2005)19:1(17).
Rong, B., X. Rui, G. Wang, and F. Yang. 2010. “New efficient method for dynamic modeling and simulation of flexible multibody systems moving in plane.” Multibody Sys. Dyn. 24 (2): 181–200. https://doi.org/10.1007/s11044-010-9196-9.
Semendary, A. A. 2018. “Behavior of adjacent prestressed concrete box beam bridges containing ultra high performance concrete (UHPC) longitudinal joints.” Ph.D. thesis, Faculty of the Russ College of Engineering and Technology, Ohio Univ.
Semendary, A. A., E. P. Steinberg, K. K. Walsh, and E. Barnard. 2017. “Live-load moment-distribution factors for an adjacent precast prestressed concrete box beam bridge with reinforced UHPC shear key connections.” J. Bridge Eng. 22 (11): 04017088. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001127.
Shi, W., B. Shafei, Z. Liu, and B. Phares. 2020. “Longitudinal box-beam bridge joints under monotonic and cyclic loads.” Eng. Struct. 220: 110976. https://doi.org/10.1016/j.engstruct.2020.110976.
Sun, J., K. Liu, G. Liu, and H. Li. 2021. “A developed transfer matrix method for analysis of elastic–plastic behavior of structures.” Int. J. Steel Struct. 21 (5): 1620–1629. https://doi.org/10.1007/s13296-021-00524-8.
Terzioglu, T., M. B. D. Hueste, and J. B. Mander. 2017. “Live load distribution factors for spread slab beam bridges.” J. Bridge Eng. 22 (10): 04017067. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001100.
Wang, Z., D. Duan, H. Yu, Y. Xin, and F. Li. 2021. “Local bending deformation monitoring of bi-dimensional bridge deck based on the displacement–strain transfer matrix.” J. Civ. Struct. Health Monit. 11 (3): 809–832. https://doi.org/10.1007/s13349-021-00485-w.
Westergaard, H. M. 1930. “Computation of stresses in bridge slabs due to wheel loads.” Public Roads 11 (1): 1–23.
Yousif, Z., and R. Hindi. 2007. “AASHTO-LRFD live load distribution for beam-and-slab bridges: Limitations and applicability.” J. Bridge Eng. 12 (6): 765–773. https://doi.org/10.1061/(ASCE)1084-0702(2007)12:6(765).
Zhao, Y., X. Cao, Y. Zhou, G. Wang, and R. Tian. 2020. “Lateral load distribution for hollow slab bridge: Field test investigation.” Int. J. Concr. Struct. Mater. 22: 8.
Zhou, H., X. Yang, L. Sun, and F. Xing. 2015. “Free vibrations of a two-cable network with near-support dampers and a cross-link.” Struct. Control Health Monit. 22 (9): 1173–1192. https://doi.org/10.1002/stc.1738.
Zokaie, T., T. A. Osterkamp, and R. A. Imbsen. 1991. Distribution of wheel loads on highway bridges. Washington, DC: Transportation Research Board, National Research Council.
Zou, B., J. F. Davalos, A. Chen, and I. Ray. 2011. “Evaluation of load distribution factor by series solution for orthotropic bridge decks.” J. Aerosp. Eng. 24: 240–248. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000007.
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Published In
Journal of Bridge Engineering
Volume 29 • Issue 7 • July 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Jul 4, 2023
Accepted: Feb 23, 2024
Published online: May 6, 2024
Published in print: Jul 1, 2024
Discussion open until: Oct 6, 2024
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