Design of FRP Systems for Strengthening Concrete Girders in Shear (2011) / Chapter Skim
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Pages 41-46
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From page 41... ...
Ef, Efrp Elastic modulus of FRP (Ef ρf) lim Limiting value of FRP rigidity separating debonding and FRP rupture failure modes Es Elastic modulus of steel reinforcement fc, f ′c Concrete compressive strength fck Concrete characteristic cubic strength fcm Mean cylindrical compressive strength of concrete fctm Concrete mean tensile strength ffd Design ultimate strength of FRP ffdd Debonding FRP strength Notations
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From page 42... ...
ka Coefficient describing anchorage considerations [Deniaud and Cheng, 2001, 2004] kb Covering/scale coefficient ke Integer describing number of debonding ends L Girder span length lb Available bond length of FRP Le, Leff, Lfe, le Effective bond length leq Bonded length projected vertically that would be necessary if the fabric strain was uniform Lmax Maximum bond length n Number of FRP plies n Ratio of elastic modulus of FRP to elastic modulus of transverse steel (Ef/Es)
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From page 43... ...
TFRP Tension force in FRP tp Nominal thickness of FRP sheet or bonded plate ts Width of each FRP strip Tv Tension force in stirrups V Shear force Vc Shear contribution of concrete Vcy Concrete contribution to shear resistance corresponding with yielding of the stirrups along the primary shear crack Vcu Concrete contribution to shear resistance corresponding with the ultimate (maximum) load carried by the girder Vexp Experimentally measured ultimate shear strength Vf, Vfd, Vf,max, Vf,max, Vfrp Shear contribution of FRP VFE Analytically (Finite Element)
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From page 44... ...
load carried by the girder wf, wfrp Width of FRP strip wfe Effective width of FRP strip Z Limit state function z Length of a vertical tension tie zb Co-ordinate of lower edge of effective FRP bonded to the sides of a beam zrid,eq Vertically projected length of the FRP strip, minus the effective bond length where bond is building up, plus a bonded length that would be necessary if the FRP stress was uniform under the debonding slip zt Co-ordinate of upper edge of effective FRP bonded to the sides of a beam α Angle of inclination of transverse steel reinforcement to longitudinal axis of beam α Reduction factor [Triantafillou and Antonopoulos, 2000] α Crack inclination angle [Carolin and Taljsten, 2005]
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From page 45... ...
ε _ z,max Maximum normalized strain in FRP [Chen and Teng, 2003 b] φf Shear strength reduction factor for FRP φR Coefficient accounting for the effects of sheets wrapped around a corner γf, γfrp, γRd Partial safety factor for FRP γfs The ratio of the vertical component of average strain in the FRP sheets to the average strain in the steel stirrups γf,d Partial safety factor depending on the FRP application accuracy ΓFk Specific fracture energy of the FRP-concrete bond interface η Average fiber utilization (effectiveness)
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From page 46... ...
τ Shear stress τave Average shear stress τmax Ultimate direct bond shear strength between FRP and concrete τult Interface shear strength between concrete and fiberglass plates [Al-Sulaimani et al., 1994] ζ Coordinate ratio of the upper edge to the lower edge of the effective FRP = zt/zb ζDC Random variable for component dead load ζLL+IM Random variable for highway live load including impact loads ζWS Random variable for wearing surface dead load = A b s v v 46
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