PSI - Issue 64

Amir Mofidi et al. / Procedia Structural Integrity 64 (2024) 999– 1008 Mofidi et al./ Structural Integrity Procedia 00 (2019) 000 – 000 5 full height of the RC beams and is the effective depth of longitudinal steel reinforcement. In addition, is the FRP effective strain which is taken as =min( − , − ), where in the modified Mofidi et al. (2016), − , the debonding FRP strain is now calculated using the Eq. 11 which is slightly revised from that in Mofidi et al. (2016). 0.25 '0.33 0.85 ef f c per fe b f f k f L E A   − = (11) where is the ratio of the length of the failure plane perpendicular to the concrete surface, i.e., the depth into the concrete cover, and the length of the failure plane parallel to the concrete surface, ′ is the concrete compressive strength, is the debonding failure length in cross-section, and is the modification factor calculated as Eq. 12. g total ef eff k L k L = (12) where is an experimental coefficient to consider the group effect for all active NSM FRP rods and laminates. This parameter is taken equal to revised values of 0.8 and 0.5 for rods and laminates, respectively. Meanwhile, is the total length of the NSM FRP rods or laminates that actively contribute to the shear strength and is the NSM FRP effective length. A slightly modified equation is used here to calculate the effective strain in NSM FRP corresponding to concrete cover splitting ( − ) than that used in Mofidi et al. (2016) as shown in Eq. 13. ' 0.4 c cf f fe c f f v f A S A E d  − = (13) In the modified Mofidi et al. (2016), unlike that in the original Mofidi et al. (2016), the concrete surface area of splitting failure ( ) does not include term as presented in Eqs. 14. (2 0.3 ) cf mb f mb f A L w L t = + + for FRP plates (14) where the embedment length ( ) can be taken equal to the minimum of ( and 2 ) , and , and stand for the width, thickness and diameter of NSM FRP. It should be noted that the original Mofidi et al. (2016) is missing the geometrical terms, i.e., [ + ) ] , in the equations to calculate the in the published journal article. In the modified Mofidi et al. (2016) considered in this article, Eq. 10 is used for all major shear crack angels and Eq. 15 is used when is assumed to be equal 45  . ( ) sin cos f fe f v f f A E d V S    + = (15) 2.7. Mofidi et al. (2023) A new theoretical model with accurate, transparent, and practical design equations was developed by Mofidi et al. (2023) for RC beams strengthened in shear using NSM FRP bars and laminates. The proposed new design equations benefit from the state-of-the-art NSM bond model proposed by Zhang et al. (2014) for greater accuracy in the predicted 1003 (3 0.3 ) f mb A L D L = + cf mb for FRP rods