Title:
Deflection Calculation for Reinforced Ultra-High- Performance Concrete Beams Based on Effective Moment of Inertia
Author(s):
Fei Peng, Zhi Fang, and Song Cui
Publication:
Structural Journal
Volume:
119
Issue:
4
Appears on pages(s):
263-275
Keywords:
beam; deflection; effective moment of inertia; tension stiffening; ultra-high-performance concrete (UHPC)
DOI:
10.14359/51734523
Date:
7/1/2022
Abstract:
Due to the bridging effect of steel fibers in ultra-high-performance concrete (UHPC), reinforced UHPC beams exhibit much higher post-cracking stiffness and smaller deflection compared with conventional reinforced concrete beams. This paper attempts to develop a mechanics-based yet simplified method for determining the instantaneous deflection of reinforced UHPC beams at serviceability limit state. First, a validated numerical procedure is developed to predict the moment-curvature behavior of reinforced UHPC sections under serviceability conditions. Then, the tension stiffening in the beam is evaluated. It is found that the moment-curvature response of the UHPC section at the stabilized microcracking stage is almost parallel to that of the fully cracked section, with a nearly full tension-stiffening response. On this basis, a design equation for the effective moment of inertia is derived for calculating the deflection of reinforced UHPC beams. It is found that the proposed approach can provide reasonably conservative deflection predictions, with a mean value of the predicted-to-measured deflection ratio of 1.21 and a standard deviation of 0.309,
by comparing its predictions with available experimental results of 82 flexural tests.
Related References:
Aaleti, S.; Petersen, B.; and Sritharan, S., 2013, “Design Guide for Precast UHPC Waffle Deck Panel System, including Connections,” FHWA-HIF-13-032, U. S. Department of Transportation, Federal Highway Administration, Washington, DC, 127 pp.
AASHTO, 2017, “LRFD Bridge Design Specifications,” eighth edition, American Association of State Highway and Transportation Officials, Washington, DC, 1781 pp
ACI Committee 239, 2018, “Ultra-High-Performance Concrete: An Emerging Technology Report (ACI 239R-18),” American Concrete Institute, Farmington Hills, MI, 21 pp.
ACI Committee 318, 2019, “Building Code Requirements for Structural Concrete (ACI 318-19) and Commentary (ACI 318R-19),” American Concrete Institute, Farmington Hills, MI, 623 pp.
ACI Committee 544, 2018, “Guide to Design with Fiber-Reinforced Concrete (ACI 544.4R-18),” American Concrete Institute, Farmington Hills, MI, 39 pp.
AFGC, 2013, “Bétons Fibrés Á Ultra-Hautes Performances: Recommendations,” Association Française de Génie Civil, Paris, France, 357 pp.
Bischoff, P. H., 2005, “Reevaluation of Deflection Prediction for Concrete Beams Reinforced with Steel and Fiber Reinforced Polymer Bars,” Journal of Structural Engineering, ASCE, V. 131, No. 5, May, pp. 752-767. doi: 10.1061/(ASCE)0733-9445(2005)131:5(752)
Bischoff, P. H., and Gross, S. P., 2011a, “Equivalent Moment of Inertia Based on Integration of Curvature,” Journal of Composites for Construction, ASCE, V. 15, No. 3, pp. 263-273. doi: 10.1061/(ASCE)CC.1943-5614.0000164
Bischoff, P. H., and Gross, S. P., 2011b, “Design Approach for Calculating Deflection of FRP Reinforced Concrete,” Journal of Composites for Construction, ASCE, V. 15, No. 4, pp. 490-499. doi: 10.1061/(ASCE)CC.1943-5614.0000195
Branson, D. E., 1963, “Instantaneous and Time-Dependent Deflections of Simple and Continuous Reinforced Concrete Beams,” Report No. 7, Alabama Highway Research Report, Bureau of Public Roads, Montgomery, AL, 78 pp.
CSA S6-19, 2019, “Canadian Highway Bridge Design Code,” CSA Group, Toronto, ON, Canada, 1179 pp.
Chao, S.-H.; Shamshiri, M.; Liu, X.; Palacios, G.; Schultz, A. E.; and Nojavan, A., 2021, “Seismically Robust Ultra-High-Performance Fiber-Reinforced Concrete Columns,” ACI Structural Journal, V. 118, No. 2, Mar., pp. 17-32. doi: 10.14359/51730391
Chen, S.; Zhang, R.; Jia, L. J.; and Wang, J. Y., 2018, “Flexural Behaviour of Rebar-Reinforced Ultra-High-Performance Concrete Beams,” Magazine of Concrete Research, V. 70, No. 19, pp. 997-1015. doi: 10.1680/jmacr.17.00283
Deng, Z.; Wang, Y.; Xiao, R.; Lan, M.; and Chen, X., 2015, “Flexural Test and Theoretical Analysis of UHPC Beams with High Strength Rebars,” Journal of Basic Science and Engineering, V. 23, No. 1, pp. 68-78. (in Chinese) doi: 10.16058/j.issn.1005-0930.2015.01.006
Graybeal, B. A., 2008, “Flexural Behavior of an Ultrahigh-Performance Concrete I-Girder,” Journal of Bridge Engineering, ASCE, V. 13, No. 6, pp. 602-610. doi: 10.1061/(ASCE)1084-0702(2008)13:6(602)
Hung, C. C.; Lee, H. S.; and Chan, S. N., 2019, “Tension-Stiffening Effect in Steel-Reinforced UHPC Composites: Constitutive Model and Effects of Steel Fibers, Loading Patterns, and Rebar Sizes,” Composites. Part B, Engineering, V. 158, pp. 269-278. doi: 10.1016/j.compositesb.2018.09.091
JSCE, 2008, “Recommendations for Design and Construction of High-Performance Fibre Reinforced Cement Composites with Multiple Fine Cracks (HPFRCC),” Concrete Engineering Series 82, Japanese Society of Civil Engineers, Tokyo, Japan, 113 pp.
JTG 3362, 2018, “Specifications for Design of Highway Reinforced Concrete and Prestressed Concrete Bridges and Culverts,” China Communications Press, Beijing, China, 261 pp.
Khorami, M.; Navarro-Gregori, J.; and Serna, P., 2021, “Tensile Behaviour of Reinforced UHPFRC Elements under Serviceability Conditions,” Materials and Structures, V. 54, No. 1, pp. 1-17. doi: 10.1617/s11527-021-01630-z
Kodur, V.; Solhmirzaei, R.; Agrawal, A.; Aziz, E. M.; and Soroushian, P., 2018, “Analysis of Flexural and Shear Resistance of Ultra High-Performance Fiber Reinforced Concrete Beams without Stirrups,” Engineering Structures, V. 174, pp. 873-884. doi: 10.1016/j.engstruct.2018.08.010
Liang, X.; Wang, P.; Xu, M.; Wang Z.; Yu, J.; and Li, L., 2019, “Investigation on Flexural Capacity of Reinforced Ultra High-Performance Concrete Beams,” Engineering Mechanics, V. 36, No. 5, pp. 113-122. (in Chinese) doi: 10.6052/j.issn.1000-4750.2018.03.0164
Liu, C.; Zhang, Y.; Yao, Y.; and Huang, Y., 2019, “2019, “Calculation Method for Flexural Capacity of High Strain-Hardening Ultra-High Performance Concrete T-Beams,” Structural Concrete, V. 20, No. 1, pp. 405-419. doi: 10.1002/suco.201800151
MCS-EPFL, 2016, “Recommendation: Ultra-High Performance Fibre Reinforced Cement-Based Composites (UHPFRC),” Maintenance, Construction and Safety of Structures (MCS)- École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, 37 pp.
Mota, C.; Alminar, S.; and Svecova, D., 2006, “Critical Review of Deflection Formulas for FRP-RC Members,” Journal of Composites for Construction, ASCE, V. 3, No. 10, pp. 183-194. doi: 10.1061/(ASCE)1090-0268(2006)10:3(183)
NF P18-710, 2016, “National Addition to Eurocode 2 – Design of Concrete Structures: Specific Rules for Ultra-High-Performance Fibre-Reinforced Concrete (UHPFRC),” Association Francaise de Normalisation, Paris, France, 136 pp.
Peng, F.; Xue, W.; and Xue, W., 2020, “Database Evaluation of Shear Strength of Slender Fiber-Reinforced Polymer-Reinforced Concrete Members,” ACI Structural Journal, V. 117, No. 3, May, pp. 273-281. doi: 10.14359/51723504
Peng, F.; Yi, W.; and Fang, Z., 2022, “Design Approach for Flexural Strength of Reinforced UHPC Members Considering Size Effect,” ACI Structural Journal, V. 119, No. 1, Jan., pp. 281-294. doi: 10.14359/51734140
Qiu, M.; Shao, X.; Zhu, Y.; Zhan, J.; Yan, B.; and Wang, Y., 2020, “Experimental Investigation on Flexural Cracking Behavior of Ultrahigh Performance Concrete Beams,” Structural Concrete, V. 21, No. 5, pp. 2134-2153. doi: 10.1002/suco.201900339
Randl, N.; Simon, C.; and Sciences, A., 2013, “Experimental Investigations on UHP(FR)C Beams with High Strength Reinforcement,” RILEM-fib-AFGC International Symposium on Ultra-High-Performance Fibre-Reinforced Concrete, Marseille, France, Oct., pp. 557-566.
Russell, H. G., and Graybeal, B. A., 2013, “Ultra-High-Performance Concrete: A State-of-the-Art Report for the Bridge Community,” Rep. No. FHWA-HRT-13-060, Federal Highway Administration, McLean, VA.
Sim, C.; Tadros, M.; Gee, D.; and Asaad, M., 2020, “Flexural Design of Precast, Prestressed Ultra-High-Performance Concrete Members,” PCI Journal, V. 65, No. 6, pp. 35-61. doi: 10.15554/pcij65.6-02
Singh, M.; Sheikh, A. H.; Mohamed Ali, M. S.; Visintin, P.; and Griffith, M. C., 2017, “Experimental and Numerical Study of the Flexural Behaviour of Ultra-High-Performance Fibre Reinforced Concrete Beams,” Construction and Building Materials, V. 138, pp. 12-25. doi: 10.1016/j.conbuildmat.2017.02.002
Steinberg, E., 2010, “Structural Reliability of Prestressed UHPC Flexure Models for Bridge Girders,” Journal of Bridge Engineering, ASCE, V. 15, No. 1, pp. 65-72. doi: 10.1061/(ASCE)BE.1943-5592.0000039
Sturm, A. B.; Visintin, P.; and Oehlers, D. J., 2019, “Rational Design Approach for the Instantaneous and Time-Dependent Serviceability Deflections and Crack Widths of FRC and UHPFRC Continuous and Simply Supported Beams,” Journal of Structural Engineering, ASCE, V. 145, No. 11, p. 04019138. doi: 10.1061/(ASCE)ST.1943-541X.0002423
Sturm, A. B.; Visintin, P.; and Oehlers, D. J., 2020, “Blending Fibres to Enhance the Flexural Properties of UHPFRC Beams,” Construction and Building Materials, ASCE, V. 244, p. 118328. doi: 10.1016/j.conbuildmat.2020.118328
Sturm, A. B.; Visintin, P.; Oehlers, D. J.; and Seracino, R., 2018, “Time-Dependent Tension-Stiffening Mechanics of Fiber-Reinforced and Ultra-High-Performance Fiber-Reinforced Concrete,” Journal of Structural Engineering, ASCE, V. 144, No. 8, p. 04018122. doi: 10.1061/(ASCE)ST.1943-541X.0002107
Su, J.; Fu, Y.; Huang, Q.; Chen, B.; and Wei, J., 2017, “Flexural Test and Finite Element Analysis of Reinforced UHPC Beams,” Journal of China & Foreign Highway, V. 37, No. 6, pp. 99-105. (in Chinese) doi: 10.14048/j.issn.1671-2579.2017.06.022
Wahba, K., 2012, “Mechanical and Structural Properties of Ultra High Performance Fiber Reinforced Concrete,” master’s dissertation, Ryerson University, Toronto, ON, Canada, 79 pp.
Wang, Y.; Shao, X.; Cao J.; Deng, S.; and Li, Y., 2020, “Research on Flexural Performance of UHPPC Deck Panel Containing Small Coarse Aggregates,” China Civil Engineering Journal, V. 53, No. 3, pp. 67-79. (in Chinese) doi: 10.15951/j.tmgcxb.2020.03.009
Wang, Y.; Shao, X.; Cao, J.; Zhao, X.; and Qiu, M., 2021, “Static and Fatigue Flexural Performance of Ultra-High-Performance Fiber Reinforced Concrete Slabs,” Engineering Structures, V. 231, p. 111728. doi: 10.1016/j.engstruct.2020.111728
Xue, W.; Peng, F.; and Xue, W., 2020, “Calibration of Strength Reduction Factor for Reinforced Ultra-High-Performance Concrete Bridge Girders in Flexure,” Journal of Bridge Engineering, ASCE, V. 25, No. 10, p. 04020086. doi: 10.1061/(ASCE)BE.1943-5592.0001621
Yang, I. H.; Joh, C.; and Bui, T. Q., 2019, “Estimating the Tensile Strength of Ultra-High-Performance Fiber-Reinforced Concrete Beams,” Advances in Materials Science and Engineering, V. 2019, pp. 1-16. doi: 10.1155/2019/5128029
Yang, I. H.; Joh, C.; and Kim, B. S., 2010, “Structural Behavior of Ultra High Performance Concrete Beams Subjected to Bending,” Engineering Structures, V. 32, No. 11, pp. 3478-3487. doi: 10.1016/j.engstruct.2010.07.017
Yang, I. H.; Park, J.; Bui, T. Q.; Kim, K. C.; Joh, C.; and Lee, H., 2020, “An Experimental Study on the Ductility and Flexural Toughness of Ultrahigh-Performance Concrete Beams Subjected to Bending,” Materials (Basel), V. 13, No. 10, p. 2225. doi: 10.3390/ma13102225
Yoo, D. Y., and Yoon, Y. S., 2015, “Structural Performance of Ultra-High-Performance Concrete Beams with Different Steel Fibers,” Engineering Structures, V. 102, pp. 409-423. doi: 10.1016/j.engstruct.2015.08.029
Yuan, J., and Graybeal, B., 2015, “Bond of Reinforcement in Ultra-High-Performance-Concrete,” ACI Structural Journal, V. 112, No. 6, Nov.-Dec., pp. 851-860. doi: 10.14359/5168791