PSI - Issue 64

Amir Mofidi et al. / Procedia Structural Integrity 64 (2024) 999– 1008 Mofidi et al./ Structural Integrity Procedia 00 (2019) 000 – 000

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2.1. Parreti and Nanni (2004) In this model, a similar approach used in ACI 440.2R-02 (2002) for EB FRP laminates was adopted. A reduction factor of equal to 0.85 was applied only to the contribution of NSM FRP reinforcement to the shear strength of the member. The slope of the shear crack was assumed 45 degrees and bond stresses were assumed constant along the effective length of the FRP bar at ultimate. Eqs. 2 and 3 show V f for circular bars and rectangular bars, respectively. 2 f b b tot V d L   = (2) 4( ) f b tot V a b L  = + (3) where, , , and are the nominal FRP bar diameter, average bond stress of the bars crossed by a shear crack and the sum of the length of each single NSM bar crossed by a 45-degree shear crack, respectively. Meanwhile, and are cross-sectional dimensions for rectangular bars. 2.2. Rizzo and De Lorenzis (2009) In 2009, Rizzo and De Lorenzis (2009b) generalized a simple approach proposed by De Lorenzis and Nanni (2001) for different values of FRP spacing and shear crack angle. A constant shear stress at failure, , at the bar-epoxy interface was assumed in all FRP bars intersected by the shear crack at ultimate. Eq. 4 represents the model. (4) where, ′ , , and account for total embedment length, the perimeter along which the bond stress acts, and the angle of the FRP bars to the horizontal axis, respectively. It is worth noting that the value of computed for the most unfavourable position of the crack with respect to the strengthening system introduced as , and the upper limit of the FRP contribution to the shear capacity is noted as ̅ , were proposed as Eqs. 5 and 6. min , min 2 sin f emb tot f V l p   = (5) where, , is a reduction of tangential stress. Rizzo and De Lorenzis (2009b) concluded that using the simplified model with a properly reduced value of design bond strength can offer reasonable accuracy. 2.3. Dias and Barros (2013) In this model, the contribution of the laminates to the shear resistance of the beam ( ) was proposed as Eq. 7. The effective strain in the laminates ( ), which corresponds to the level of mobilization of the CFRP when the strengthened RC beam reaches its shear capacity, was used as an indicator of the NSM strengthening effectiveness. (cot cot )sin fv f w fe f f f f A V h E S     = + (7) where ℎ is the web depth of the beam (equal to the length of vertical laminates), is the cross-sectional area of CFRP stirrup that is formed by two lateral laminates, is the spacing of laminates, is the elastic modulus of the , emb tot 2 V l = sin p   f f , min , f red 2 V l = sin f emb tot p   (6)