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51 These proposed changes to AASHTO LRFD Bridge Design Specifications are the recommendations of the NCHRP Project 12-75 Research Team at the Missouri University of Science and Technology. These changes have not been approved by NCHRP or any AASHTO committee nor formally accepted for the AASHTO specifications. A T T A C H M E N T A Recommended Changes to AASHTO LRFD Bridge Design Specifications
52 5.2 Definitions â (only additions are shown in this section) FRP â fiber-reinforced polymer laminate consisting of fibers (carbon, aramid, or glass) and an epoxy matrix. 5.3 Notation â (only additions and particularly relevant notations are shown) dv = effective shear depth as determined in Article 5.8.2.9 (in.) df = effective depth of FRP shear reinforcement in Article 5.8.3.3 (in.) ffe = effective stress of FRP shear reinforcement as determined in Article 5.8.3.3 (ksi) s = spacing of stirrups (in.) sf = center-to-center spacing of FRP shear reinforcement in Article 5.8.3.3 (in.) hf = flange thickness in Article 5.8.3.3 (in.) = angle of inclination of transverse steel reinforcement to longitudinal axis (°) f = angle of inclination of transverse FRP reinforcement to longitudinal axis in Article 5.8.3.3 (°) Af = sum of area of FRP reinforcement on both faces of the web within a distance sf in Article 5.8.3.3 (in.2) Vf = shear resistance provided by externally bonded FRP shear reinforcement in Article 5.8.3.3 (kip ) fE = modulus of elasticity of FRP reinforcement in Article 5.8.3.3 (ksi) fe = effective strain of FRP reinforcement in Article 5.8.3.3 fu = failure tensile strain of FRP reinforcement in Article 5.8.3.3 Rf = strain reduction factor to account for the effectiveness of FRP strengthening in Article 5.8.3.3 f = FRP shear reinforcement ratio in Article 5.8.3.3 fn = number of plies of FRP reinforcement in Article 5.8.3.3 ft = thickness of one ply of FRP reinforcement in Article 5.8.3.3 (in.) fw = width of FRP shear reinforcement in Article 5.8.3.3 (in.)
53 SPECIFICATIONS COMMENTARY 5.8.2.6 Types of Transverse Reinforcement Transverse reinforcement may consist of Steel reinforcement in the form of: o Stirrups making an angle not less than 45° with the longitudinal tension reinforcement; o Welded wire fabric reinforcement, with wires located perpendicular to the axis of the member, provided that the transverse wires are certified to undergo a minimum elongation of 4 percent, measured over a gage length of at least 4.0 in. including at least one cross wire; o Anchored prestressed tendons, detailed and constructed to minimize seating and time- dependent losses, which make an angle not less than 45° with the longitudinal tension reinforcement; o Longitudinal bars bent to provide an inclined portion making an angle of 30° or more with the longitudinal tension reinforcement and inclined to intercept potential diagonal cracks; o Combinations of stirrups, tendons, and bent longitudinal bars; or o Spirals. Externally bonded FRP shear reinforcement making an angle not less than 45° with the longitudinal flexural tensile reinforcement in accordance with Article 5.8.3.5 and 5.8.3.6.3 as applicable. Transverse reinforcement shall be detailed such that the shear force between different elements or zones of a member are effectively transferred. Torsional reinforcement shall consist of both transverse and longitudinal steel reinforcement. Longitudinal steel reinforcement shall consist of bars and/or tendons. Transverse steel reinforcement shall consist of: Closed stirrups perpendicular to the longitudinal axis of the member, A closed cage of welded wire fabric with transverse wires perpendicular to the axis of the member, or Spirals. Transverse torsion reinforcement shall be made fully continuous and shall be anchored by 135° standard hooks around longitudinal reinforcement.
54 SPECIFICATIONS COMMENTARY 5.8.2.7 Maximum Spacing of Transverse Reinforcement The center-to-center spacing of the transverse steel reinforcement and the center-to-center spacing between externally bonded FRP shear reinforcement shall not exceed the maximum permitted spacing, maxs , determined as: If '0.125 thenu cv f max 0.8 24.0 in.vs d If '0.125 thenu cv f max 0.4 12.0 in.vs d where: uv = the shear stress calculated in accordance with 5.8.2.9 (ksi) vd = effective shear depth as defined in Article 5.8.2.9 (in.) For segmental post-tensioned concrete box girder bridges, spacing of closed stirrups or closed ties required to resist shear effects due to torsional moments shall not exceed one- half of the shortest dimension of the cross section, or 12.0 in. 5.8.2.8 Design and Detailing Requirements Transverse steel reinforcement shall be anchored at both ends in accordance with the provisions of Article 5.11.2.6. For composite flexural members, extension of beam shear reinforcement into the deck slab may be considered when determining if the development and anchorage provisions of Article 5.11.2.6 are satisfied. The design yield strength of nonprestressed transverse steel reinforcement shall be taken equal to the specified yield strength when the latter does not exceed 60.0 ksi. For nonprestressed transverse steel reinforcement with yield strength in excess of 60.0 ksi, the design yield strength shall be taken as the stress corresponding to a strain of 0.0035, but not to exceed 75.0 ksi. The design yield strength of prestressed transverse steel reinforcement shall be taken as the effective stress, after allowance for all prestress losses, plus 60.0 ksi, but not greater than fpy. When welded wire reinforcement is used as transverse reinforcement, it shall be anchored at both ends in accordance with Article 5.11.2.6.3. No welded joints other than those required for anchorage shall be permitted. Components of inclined flexural compression and/or flexural tension in variable depth members shall be considered when calculating shear resistance. Externally bonded FRP shear reinforcement shall be installed to a beam using: Side bonding, in which the FRP is only bonded C5.8.2.7 Maximum Spacing of Transverse Reinforcement Sections that are highly stressed in shear require more closely spaced reinforcement to provide crack control. C5.8.2.8 Figure C5.8.2.8-1 shows different possible configurations of the FRP when applied to a beam. (a) (b) (c) Figure C5.8.2.8-1 - Configuration of FRP Application: (a) Two-side bonding, (b) U-wrap, and (c) Complete wrap
55 SPECIFICATIONS COMMENTARY to the sides of the component; U-wrap, in which FRP U-jackets are bonded on both the sides and the soffit of the component; or Complete wrapping, in which the FRP is wrapped around the entire cross section. The fibers in the FRP in its final position on the concrete component shall be oriented to provide the required resistance. The orientation of the fibers shall be shown on the contract documents. Externally bonded FRP shear reinforcement may be anchored to the concrete. Mechanical anchorage systems consisting of FRP composite plates and concrete anchor bolts shall be proportioned such that the factored bearing resistance of the concrete anchor bolts used to anchor one end of a FRP strip is not less than the tensile force exerted from the FRP strip calculated on the basis of the failure tensile strain of the FRP. The use of additional horizontal strips of FRP as anchorage for FRP shear reinforcement shall not be permitted. 5.8.3.3 Nominal Shear Resistance The nominal shear resistance, nV , shall be determined as the lesser of: n c s f pV V V V V (5.8.3.3-1) and 0.25 n c v v pV f b d V (5.8.3.3-2) in which: 0.0316c v vc = f V b d , if the procedures of Articles 5.8.3.4.1 or 5.8.3.4.2 are used (5.8.3.3-3) Vc = the lesser of Vci and Vcw, if the procedure of Article 5.8.3.4.3 are used (cot cot ) sinv y v s A f d + V s (5.8.3.3-4) (sin cos )f fe ff f f f A f d V + s (5.8.3.3-5) where: Af = area of FRP shear reinforcement within a distance sf (in.2) Av = area of steel shear reinforcement (stirrups) within a distance sv (in.2) bv = effective web width taken as the minimum web width within the depth dv as determined in Article 5.8.2.9 (in.) The direction of the fibers relative to the direction of the stresses the FRP reinforcement is meant to resist will effect the effectiveness of the FRP reinforcement. The fibers should be oriented in the direction that maximizes the effectiveness of the FRP reinforcement. Anchoring externally bonded FRP shear reinforcement helps reduce the potential for premature failure due to debonding. There are various types of anchorage systems available in the literature [NCHRP Report 12-75]. Examples of mechanical anchorage systems consisting of FRP composite plates and concrete anchor bolts are available in the literature [NCHRP Report 12-75]. C5.8.3.3 Center-to-Center Spacing of FRP Strip (s Width of FRP Strips (w )f Width of FRP Strips (w )f Center-to-Center Spacing of FRP Strip (s )f )f Figure C5.8.3.3-1 Illustration of the Terms sf and wf
56 SPECIFICATIONS COMMENTARY df = effective depth of FRP shear reinforcement equal to dv for rectangular sections and d - hf for T- sections(in.) dv = effective shear depth as determined in Article 5.8.2.9 (in.) ffe = effective stress of FRP shear reinforcement as determined in Article 5.8.3.3 (ksi) hf = flange thickness (in.) s = spacing of stirrups (in.) sf = center-to-center spacing of FRP shear reinforcement (in.) Vf = shear resistance provided by FRP shear reinforcement (kip); may only be used in conjunction with the provisions of Articles 5.8.3.4.1 and 5.8.3.4.2 when minimum steel shear reinforcement is provided or when the member depth or maximum spacing of distributed longitudinal reinforcement is less than 12 inches, and with the provisions of Article 5.8.3.4.3. Vf shall be taken as zero when dv/bv > 4 Vp = component in the direction of the applied shear of the effective prestressing force; positive if resisting the applied shear (kip) f = angle of inclination of FRP transverse reinforcement to longitudinal axis (°) = factor indicating ability of diagonally cracked concrete to transmit tension as specified in Article 5.8.3.4. = angle of inclination of diagonal compressive stresses as determined in Article 5.8.3.4 (°) The effective stress of FRP shear reinforcement, ffe,shall be determined as: fe f fef E (5.8.3.3-6) in which fe f fuR (5.8.3.3-7) where: Ef = modulus of elasticity of FRP reinforcement (ksi) Rf = strain reduction factor to account for the effectiveness of FRP strengthening fe = effective strain of FRP reinforcement. it is limited to 0.012 when Eq. 5.8.3.3-9 is used. fu = failure tensile strain of FRP reinforcement The strain reduction factor (Rf) shall be determined as: For completely wrapped or properly anchored U- wrap configurations .670.088 4( ) 1.0f f fR E (5.8.3.3-8) The application of FRP reinforcements on precast I- shaped sections with âslender websâ did not provide significant or reliable FRP contributions to shear capacity, Vf, and on occasion resulted in a decrease of strength relative to that of the member that did not have FRP shear reinforcement [NCHRP Project 12-75]. Changes in the experimental setup and girder details made to address this reduction was unsuccessful. It was concluded that the reason that the application of FRP shear reinforcements did not lead to strength gains in I-girders with slender webs was due to degradation of the diagonal compressive resistance of slender webs when stiff and well bonded FRP reinforcements are glued to the surface of these webs. While the members experiencing this web resistance degradation were all prestressed, it has been concluded that this degradation was due to the slenderness of the webs and not the effect of prestressing [NCHRP Project 12-75]. Based on an examination of strength gains as a function of the ratio of depth to web width (d/bv), it was concluded that the shear resistance provided by FRP shear reinforcement, Vf , should be ignored for members with a web slenderness of d/bw > 4 [NCHRP Project12-75]. According to the observation on the experimental database, the maximum effective strain that can be achieved in the beams failing due to debonding of FRP was 0.012. The upper bound for the quantity fEf in Eqs. 5.8.3.3-8 and 5.8.3.3-9 is 300 ksi [NCHRP Project 12-75]. Substituting this value in the two equations results in the lower bound value of Rf shown in the two equations.
57 SPECIFICATIONS COMMENTARY For Un-anchored U-wrap or Two-side bonding configurations .670.066 3( ) 1.0f f fR E (5.8.3.3-9) where: f = FRP shear reinforcement ratio The FRP shear reinforcement ratio, f, shall be determined as: For discrete strips 2 f f f f v f n t w b s (5.8.3.3-10) For continuous sheets 2 f f f v n t b (5.8.3.3-11) where: bv = effective web width taken as the minimum web width within the depth dv as determined in Article 5.8.2.9 (in.) nf = number of plies of FRP shear reinforcement sf = center-to-center spacing of FRP shear reinforcement strips (in.) tf = thickness of FRP plies (in.) wf = width of FRP shear reinforcement strips (in.) 5.8.3.5 Longitudinal Reinforcement At each section, the tensile capacity of the longitudinal reinforcement on the flexural tension side of the member shall be proportioned to satisfy: 0.5 0.5 0.5 cotu u ups ps s y p s f v f c v M N VA f A f V V V d (5.8.3.5-1) in which: Vs + Vf Vu/ (5.8.3.5-2) where: Vs = shear resistance provided by the transverse steel reinforcement at the section under investigation as given by Eq. 5.8.3.3-4 (kip) The factor 2 in Equations 5.8.3.3-10 and 5.8.3.3-11 accounts for the presence of FRP reinforcement on both sides of a component.
58 SPECIFICATIONS COMMENTARY Vf = shear resistance provided by the transverse FRP reinforcement at the section under investigation as given by Eq. 5.8.3.3-5 (kip) = angle of inclination of diagonal compressive stresses used in determining the nominal shear resistance of the section under investigation as determined by Article 5.8.3.4 (°); if the procedures of Article 5.8.3.4.3 are used, cot is defined therein f v c = resistance factors taken from Article 5.5.4.2 as appropriate for moment, shear and axial resistance The area of longitudinal reinforcement on the flexural tension side of the member need not exceed the area required to resist the maximum moment acting alone. This provision applies where the reaction force or the load introduces direct compression into the flexural compression face of the member. Eq. 5.8.3.5-1 shall be evaluated where simply-supported girders are made continuous for live loads. Where longitudinal reinforcement is discontinuous, Eq. 5.8.3.5-1 shall be reevaluated. At the inside edge of the bearing area of simple end supports to the section of critical shear, the longitudinal reinforcement on the flexural tension side of the member shall satisfy: 0.5 0.5 cotus y ps ps s f p v VA f A f V V V (5.8.3.5-3) Eqs. 5.8.3.5-1 and 5.8.3.5-2 shall be taken to apply to sections not subjected to torsion. Any lack of full development shall be accounted for.
