A new model for deflections of FRP-reinforced concrete beams



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Kansas State University


Fiber reinforced polymer has recently become a popular replacement for steel rebar, used to reinforce concrete. Therefore much research is taking place to help develop and propose methods for best approximating the response of FRP reinforced members, to make them comparable to steel reinforced members. With this popularity comes multiple approaches to FRP deflection calculations. However, this study is significant, because it investigates the cracking moment equation adopted by ACI 318, in conjunction with state of the art deflection calculation methods. Specifically this research compares four deflection calculation methods. The first approach is proposed by Bischoff and implemented by ACI 440 in its latest revision. The second deflection calculation method is proposed by Rasheed et al. The third calculation is also suggested by Bischoff, as it is specific to four point bending. The fourth calculation method is proposed by this specific research and seeks to find a median between both the Bischoff and Rasheed equations. This fourth technique will be referred to as the Rasheed-Jacobs method, proposed to create a more conservative and relevant method for investigating the effect of cracking moment on the deflection calculations. This research was done with the help of Dr. Shawn Gross, and the database he had previously built through his investigation on FRP reinforced beams. Gross’s database shows results for 106 samples tested using the actual experimental cracking moment as well as the ultimate moment capacity values. Of these 106 samples, 56 independent samples were used to investigate three different moment levels of 0.333Mn, 0.400Mn, and 0.467Mn. From this research, Gross’s database was used to calculate the cracking moment of FRP reinforced beams based on ACI 318-08. A program was developed that uses the Gross database samples to calculate the cracking moment and deflection with the Rasheed, Bischoff, and Bischoff2 models as well as the new Rasheed-Jacobs model. This program calculates the Rasheed-Jacobs results, and then graphs the findings against the deflection values from the Rasheed, Bischoff, Bischoff2 models. These graphs showed very similar patterns amongst all four models, with the Rasheed-Jacobs results mainly falling on the more conservative side. However, when looking at the predicted deflection verse the Gross experimental deflection, the best results came from the 0.467Mn moment level, which shows consistent correlation while the lower moment levels are being less predictable using the cracking moment based on the ACI equation. It can reasonably be said that the 0.467Mn shows the best correlation between the four methods and the experimental results, because it is farther away from the actual nominal cracking moment of the FRP reinforced concrete beams.



FRP, Deflection, Reinforced concrete

Graduation Month



Master of Science


Department of Civil Engineering

Major Professor

Hayder A. Rasheed