Dynamic Proportionality of Inertia and Reaction Forces in CFRP-Strengthened L-Shaped RC Beams under Impact Loading
Downloads
This study computationally investigates to examine the impacts of repeated loading on L-shaped spandrel beams made of reinforced concrete, which were strengthened by externally bonded carbon fiber reinforced plastic sheets. The object of the research is to evaluate the following three aspects of structural behavior: degradation of reaction forces, evolution of inertia forces, and residual performance. Ayad and Oukaili's experimental impact-loading program, which featured midspan drop-weight loading on RC spandrel beams before and after strengthening, was used to validate a comprehensive three-dimensional finite element model created in ABAQUS. A sequence of 25 impacts before and 25 impacts after CFRP application was simulated to trace impact force, reaction force, inertia force, midspan deflection, and damage progression. Because of cumulative stiffness deterioration, the peak impact force in the unstrengthened beams reduced by 45%, the reaction force decreased by 54.7–57.3%, and the inertia force increased by 237.5–1090%. The peak impact force decline was limited to 31.8% with CFRP strengthening, whereas the reaction force reduction varied from 36.9% to 39%. In comparison to the much greater amplification seen prior to strengthening, the rise in inertia forces was also much reduced, staying between 114.6 and 122.2%. Additionally, there was a 19.2–23.2% decrease in the midspan deflection at the 25th impact. After 25 impacts, CFRP-strengthened beams maintained 68.3–70% of their initial capacity, but unstrengthened beams only maintained 56.2–60.1%, according to the residual performance index (RPI), which showed a notable improvement. Concrete had saturated tensile cracking prior to strengthening, according to damage analysis, but matrix microcracking (HSNMTCRT) without fiber tensile damage (DAMAGEFT) dominated post-retrofit behavior, indicating the efficient confinement and energy-dissipating function of CFRP. These results extend the previous experimental interpretation by quantifying repeated-impact trends in reaction and inertia forces, and show that externally bonded CFRP sheets improve the service-life performance of reinforced concrete ledged beams by enhancing stiffness retention, energy dissipation, inertial stability, and damage control.
Downloads
[1] Raths, C. H. (1984). Spandrel Beam Behavior and Design. PCI Journal, 29(2), 62–131. doi:10.15554/pcij.03011984.62.131.
[2] Cleland, N. M., & Baber, T. T. (1986). Behavior of Precast Reinforced Concrete Ledger Beams. PCI Journal, 31(2), 96–117. doi:10.15554/pcij.03011986.96.117.
[3] Logan, D. R. (2007). L-spandrels: Can torsional distress be induced by eccentric vertical loading? PCI Journal, 52(2), 46–60. doi:10.15554/pcij.03012007.46.61.
[4] Ali, A. A. M. (1983). Strength and behaviour of reinforced concrete spandrel beams. Ph.D. Thesis, University of Edinburgh, Edinburgh, Scotland.
[5] Lucier, G., Rizkalla, S., Zia, P., & Klein, G. (2007). Precast concrete, L-shaped spandrels revisited: Full-scale tests. PCI Journal, 52(2), 62–76. doi:10.15554/pcij.03012007.62.76.
[6] Hassan, T., Lucier, G., Rizkalla, S., & Zia, P. (2007). Modeling of L-shaped, precast, prestressed concrete spandrels. PCI Journal, 52(2), 78–92. doi:10.15554/pcij.03012007.78.92.
[7] Mercan, B., Schultz, A. E., & Stolarski, H. K. (2010). Finite element modeling of prestressed concrete spandrel beams. Engineering Structures, 32(9), 2804–2813. doi:10.1016/j.engstruct.2010.04.049.
[8] Salman, R., & Ali, A. (2015). Reinforced Concrete Spandrel -Floor Beams Interaction. International Journal of Innovative Research in Science, Engineering and Technology, 4(6), 3793–3800.
[9] Hussein, P. A., Nabil, M., & El-Deen, E. (2017). Contribution of Inner Stirrups With the. Al-Azhar University Civil Engineering Research Magazine (CERM, 39(39), 245–262.
[10] Wilden, H. (2010). PCI Design Handbook: Precast and Prestressed Concrete. Precast/Prestressed Concrete Institute, Chicago, United States.
[11] ACI 318-14. (2014). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Farmington Hills, United States.
[12] Hariharan, V., Lucier, G., Rizkalla, S., Zia, P., Klein, G., & Gleich, H. (2019). Behavior Of Compact L-Shaped Spandrel Beams with Alternative Web Reinforcement. PCI Journal, 64(2), 39–54. doi:10.15554/pcij64.2-04.
[13] Pham, T. M., & Hao, H. (2016). Review of Concrete Structures Strengthened with FRP Against Impact Loading. Structures, 7, 59–70. doi:10.1016/j.istruc.2016.05.003.
[14] Salom, P. R., Gergely, J., & Young, D. T. (2004). Torsional retrofit of spandrel beams with composite laminates. Proceedings of the Institution of Civil Engineers: Structures and Buildings, 157(1), 69–76. doi:10.1680/stbu.2004.157.1.69.
[15] Salom, P. R., Gergely, J., & Young, D. T. (2004). Torsional Strengthening of Spandrel Beams with Fiber-Reinforced Polymer Laminates. Journal of Composites for Construction, 8(2), 157–162. doi:10.1061/(asce)1090-0268(2004)8:2(157).
[16] Al-Rousan, R., & Abo-Msamh, I. (2019). Bending and torsion behaviour of CFRP strengthened RC beams. Magazine of Civil Engineering, 92(8), 48–62. doi:10.18720/MCE.92.4.
[17] Al-Rousan, R., & Abo-Msamh, I. (2020). Impact of anchored CFRP on the torsional and bending behaviour of RC beams. Magazine of Civil Engineering, 96(4), 79–93. doi:10.18720/MCE.96.7.
[18] Askandar, N. H., & Mahmood, A. D. (2020). Torsional Strengthening of RC Beams with Continuous Spiral Near-Surface Mounted Steel Wire Rope. International Journal of Concrete Structures and Materials, 14(1), 7. doi:10.1186/s40069-019-0386-4.
[19] Alzabidi, S. M., Diaa, G., Abadel, A. A., Sennah, K., & Abdalla, H. (2023). Rehabilitation of reinforced concrete beams subjected to torsional load using ferrocement. Case Studies in Construction Materials, 19, 2433. doi:10.1016/j.cscm.2023.e02433.
[20] Ayaad, N., & Oukaili, N. (2023). Efficiency of CFRP torsional strengthening technique for L-shaped spandrel reinforced concrete beams. Journal of the Mechanical Behavior of Materials, 32(1), 20220243. doi:10.1515/jmbm-2022-0243.
[21] Ayaad, N., & Oukaili, N. (2023). Effectiveness of embedded through-section technique in strengthening reinforced concrete spandrel beams. Results in Engineering, 18, 101062. doi:10.1016/j.rineng.2023.101062.
[22] Ayaad, N., & Oukaili, N. (2023). Impact torsional behavior and strengthening of reinforced concrete spandrel beams. Case Studies in Construction Materials, 19, 2591. doi:10.1016/j.cscm.2023.e02591.
[23] Kawarai, T., Komuro, M., & Kishi, N. (2025). Low-Velocity Impact-Load-Carrying Behavior of Reinforced Concrete Beams Strengthened in Flexure by Bonding a Carbon Fiber-Reinforced Polymer Sheet to the Tension-Side Surface. Buildings, 15(10), 1713. doi:10.3390/buildings15101713.
[24] Saad, A. G., Sakr, M. A., Khalifa, T. M., & Darwish, E. A. (2025). CFRP Strengthening of RC Beams with Openings Under Impact Loads. International Journal of Concrete Structures and Materials, 19(1), 95. doi:10.1186/s40069-025-00837-6.
[25] Homayoonifar, A., Momeni, M., Hadianfard, M. A., & Bedon, C. (2026). Investigating Different Patterns of CFRP Sheets in Strengthening RC Panels Under Repeated Drop-Weight Impact Loads: An Experimental Study. Iranian Journal of Science and Technology, Transactions of Civil Engineering. doi:10.1007/s40996-025-02117-5.
[26] Duan, L., Zhang, Y., Yan, L., Bao, S., Liu, H., & Lu, J. (2025). Investigation on the crack development behaviour of CFRP strengthened RC beams under static and impact loading. Engineering Failure Analysis, 171, 109369. doi:10.1016/j.engfailanal.2025.109369.
[27] Luo, J., Zhang, J., Mao, B., Zhang, X., Ma, J., & Wu, J. (2026). Impact and post-impact performance of RC beams strengthened with near-surface mounted CFRP strips: Experimental and numerical evaluation. Structures, 86, 111452. doi:10.1016/j.istruc.2026.111452.
[28] Schaeffer, D. M. (1966). The effect of combined torsional and bending loads on a channel beam with one end restrained from warping. Master Thesis, Missouri University of Science and Technology, Rolla, United States.
[29] Mogbo, N. C. (1968). Torsional behavior of spandrel beams. Master Thesis, Rice University, Houston, United States.
[30] Klein, G. J. (1986). Design of Spandrel Beams. PCI Journal, 31(5), 76–124. doi:10.15554/pcij.09011986.76.124.
[31] Lucier, G., Walter, C., Rizkalla, S., Zia, P., & Klein, G. (2011). Development of a rational design methodology for precast concrete slender spandrel beams: Part 1, experimental results. PCI Journal, 56(2), 88–112. doi:10.15554/pcij.03012011.88.112.
[32] Lucier, G., Walter, C., Rizkalla, S., Zia, P., & Klein, G. (2011). Development of a rational design methodology for precast concrete slender spandrel beams: Part 2, analysis and design guidelines. PCI Journal, 56(4), 106–133. doi:10.15554/pcij.09012011.106.133.
[33] Zia, P., & Hsu, T. T. C. (2004). Design for torsion and shear in prestressed concrete flexural members. PCI Journal, 49(3), 34–42. doi:10.15554/pcij.05012004.34.42.
[34] ACI 318-11. (2011). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Farmington Hills, United States.
[35] ACI 318-19. (2014). Building Code Requirements for Structural Concrete and Commentary. American Concrete Institute (ACI), Farmington Hills, United States.
[36] ABAQUS (2022). ABAQUS Version 2022, Dassault Systèmes Simula Corp, Waltham, United States.
[37] Dassault Systèmes. (2022). Abaqus Analysis User's Manual Version 2022. Dassault Systèmes Simula Corp, Waltham, United States.
[38] Lubliner, J., Oliver, J., Oller, S., & Oñate, E. (1989). A plastic-damage model for concrete. International Journal of Solids and Structures, 25(3), 299–326. doi:10.1016/0020-7683(89)90050-4.
[39] Lee, J., & Fenves, G. L. (1998). Plastic-Damage Model for Cyclic Loading of Concrete Structures. Journal of Engineering Mechanics, 124(8), 892–900. doi:10.1061/(asce)0733-9399(1998)124:8(892).
[40] Fedoroff, A., & Calonius, K. (2020). Using the Abaqus CDP model in impact simulations. Rakenteiden Mekaniikka, 53(3), 180–207. doi:10.23998/rm.79723.
[41] Jiang, H., Wang, X., & He, S. (2012). Numerical simulation of impact tests on reinforced concrete beams. Materials & Design, 39, 111–120. doi:10.1016/j.matdes.2012.02.018.
[42] Lin, S. C., Li, D., & Yang, B. (2019). Experimental study and numerical simulation on damage assessment of reinforced concrete beams. International Journal of Impact Engineering, 132, 103323. doi:10.1016/j.ijimpeng.2019.103323.
[43] Silva, L. M. E., Christoforo, A. L., & Carvalho, R. C. (2021). Calibration of concrete damaged plasticity model parameters for shear walls. Revista Materia, 26(1), 12944. doi:10.1590/s1517-707620210001.1244.
[44] Rainone, L. S., Tateo, V., Casolo, S., & Uva, G. (2023). About the Use of Concrete Damage Plasticity for Modeling Masonry Post-Elastic Behavior. Buildings, 13(8), 1915. doi:10.3390/buildings13081915.
[45] Hordijk, D. A. (1992). Tensile and tensile fatigue behaviour of concrete; experiments, modelling and analyses. Heron, 37(1), 1–79.
[46] Saenz, L. P. (1964). Equation for the Stress-Strain Curve of Concrete. ACI Journal Proceedings, 61(3), 1229–1235. doi:10.14359/7785.
[47] Johnson, G. R. & Cook, W. H. (1983). A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates, and High Temperatures. Proceedings 7th International Symposium on Ballistics, 19-21 April 1983, The Hague, Netherlands.
[48] Dassault Systèmes. (2022). Using the Johnson–Cook hardening model to define classical metal plasticity, Abaqus Documentation, SIMULIA User Assistance, Dassault Systèmes Simula Corp, Waltham, United States.
[49] Hano, M. M., Hano, S. M. A., & Al-Rawe, H. S. (2025). Examining the Compressive Behavior of SFRC and SCC Using Finite Element and Experimental Methods. Civil Engineering Journal, 11(3), 1132–1144. doi:10.28991/CEJ-2025-011-03-017.
[50] Li, J., Wu, C., & Hao, H. (2015). An experimental and numerical study of reinforced ultra-high performance concrete slabs under blast loads. Materials and Design, 82, 64–76. doi:10.1016/j.matdes.2015.05.045.
[51] ACI PRC 440.2:2023. (2023). Design and construction of externally bonded fiber-reinforced polymer (FRP) systems for strengthening concrete structures—Guide. American Concrete Institute (ACI), Farmington Hills, United States.
[52] Zhang, J., Wu, J., Du, W., Tong, C., Zhu, Z., & Jing, Y. (2023). Residual load-carrying performance of CFRP strengthened RC beam after drop hammer impact. International Journal of Impact Engineering, 175, 104547. doi:10.1016/j.ijimpeng.2023.104547.
[53] Youbi, M. El, Tbatou, T., Kadiri, I., & Fertahi, S. E. D. (2022). Numerical Investigation of HSC Columns Retrofitted by CFRP Materials under Combined Load. Civil Engineering Journal, 8(4), 765–779. doi:10.28991/CEJ-2022-08-04-011.
[54] Alobaidi, H. E., & Al-Zuhairi, A. H. (2023). Structural Strengthening of Insufficiently Designed Reinforced Concrete T-Beams using CFRP Composites. Civil Engineering Journal, 9(8), 1880–1896. doi:10.28991/CEJ-2023-09-08-05.
- Authors retain all copyrights. It is noticeable that authors will not be forced to sign any copyright transfer agreements.
- This work (including HTML and PDF Files) is licensed under a Creative Commons Attribution 4.0 International License.
