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51 ATTACHMENT A Recommended Changes to AASHTO LRFD Bridge Design Specifications 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.
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52 5.2 Definitions (only additions are shown in this section) FRP fiber-reinforced polymer laminate consisting of fibers (carbon, aramid, or glass) and an epoxy matrix. 5.3 Notation (only additions and particularly relevant notations are shown) dv = effective shear depth as determined in Article 184.108.40.206 (in.) df = effective depth of FRP shear reinforcement in Article 220.127.116.11 (in.) ffe= effective stress of FRP shear reinforcement as determined in Article 18.104.22.168 (ksi) s = spacing of stirrups (in.) sf = center-to-center spacing of FRP shear reinforcement in Article 22.214.171.124 (in.) hf = flange thickness in Article 126.96.36.199 (in.) = angle of inclination of transverse steel reinforcement to longitudinal axis (°) f = angle of inclination of transverse FRP reinforcement to longitudinal axis in Article 188.8.131.52 (°) Af = sum of area of FRP reinforcement on both faces of the web within a distance sf in Article 184.108.40.206 (in.2) Vf = shear resistance provided by externally bonded FRP shear reinforcement in Article 220.127.116.11 (kip ) Ef = modulus of elasticity of FRP reinforcement in Article 18.104.22.168 (ksi) fe = effective strain of FRP reinforcement in Article 22.214.171.124 fu = failure tensile strain of FRP reinforcement in Article 126.96.36.199 Rf = strain reduction factor to account for the effectiveness of FRP strengthening in Article 188.8.131.52 f = FRP shear reinforcement ratio in Article 184.108.40.206 nf = number of plies of FRP reinforcement in Article 220.127.116.11 tf = thickness of one ply of FRP reinforcement in Article 18.104.22.168 (in.) wf = width of FRP shear reinforcement in Article 22.214.171.124 (in.)
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53 SPECIFICATIONS COMMENTARY 126.96.36.199 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 188.8.131.52 and 184.108.40.206.3 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.
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54 SPECIFICATIONS COMMENTARY 220.127.116.11 Maximum Spacing of Transverse C18.104.22.168 Maximum Spacing of Transverse Reinforcement Reinforcement The center-to-center spacing of the transverse steel Sections that are highly stressed in shear require more reinforcement and the center-to-center spacing between closely spaced reinforcement to provide crack control. externally bonded FRP shear reinforcement shall not exceed the maximum permitted spacing, smax , determined as: ' If vu 0.125 fc then smax 0.8d v 24.0 in. ' If vu 0.125 fc then smax 0.4d v 12.0 in. where: vu = the shear stress calculated in accordance with 22.214.171.124 (ksi) dv = effective shear depth as defined in Article 126.96.36.199 (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. 188.8.131.52 Design and Detailing Requirements C184.108.40.206 Transverse steel reinforcement shall be anchored at both Figure C220.127.116.11-1 shows different possible configurations ends in accordance with the provisions of Article 18.104.22.168. of the FRP when applied to a beam. 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 22.214.171.124 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 (a) (b) (c) nonprestressed transverse steel reinforcement with yield strength in excess of 60.0 ksi, the design yield strength shall Figure C126.96.36.199-1 - Configuration of FRP Application: (a) be taken as the stress corresponding to a strain of 0.0035, but Two-side bonding, (b) U-wrap, and (c) Complete wrap 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 188.8.131.52.3. 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
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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 The direction of the fibers relative to the direction of the component shall be oriented to provide the required stresses the FRP reinforcement is meant to resist will effect resistance. The orientation of the fibers shall be shown on the the effectiveness of the FRP reinforcement. The fibers should contract documents. be oriented in the direction that maximizes the effectiveness Externally bonded FRP shear reinforcement may be of the FRP reinforcement. anchored to the concrete. Mechanical anchorage systems Anchoring externally bonded FRP shear reinforcement consisting of FRP composite plates and concrete anchor bolts helps reduce the potential for premature failure due to shall be proportioned such that the factored bearing resistance debonding. There are various types of anchorage systems of the concrete anchor bolts used to anchor one end of a FRP available in the literature [NCHRP Report 12-75]. strip is not less than the tensile force exerted from the FRP Examples of mechanical anchorage systems consisting of strip calculated on the basis of the failure tensile strain of the FRP composite plates and concrete anchor bolts are available FRP. The use of additional horizontal strips of FRP as in the literature [NCHRP Report 12-75]. anchorage for FRP shear reinforcement shall not be permitted. 184.108.40.206 Nominal Shear Resistance C220.127.116.11 The nominal shear resistance, Vn , shall be determined as Center-to-Center Spacing of FRP Strip (sf) the lesser of: Vn Vc Vs Vf Vp (18.104.22.168-1) and Width of FRP Strips (wf ) Vn 0.25 fcbv dv Vp (22.214.171.124-2) Center-to-Center Spacing of FRP Strip (sf) in which: V c = 0.0316 fc b v d v , if the procedures of Articles (126.96.36.199-3) 188.8.131.52.1 or 184.108.40.206.2 are used Width of FRP Strips (wf ) Vc = the lesser of Vci and Vcw, if the procedure of Article 220.127.116.11.3 are used Figure C18.104.22.168-1 Illustration of the Terms sf and wf Av f y d v (cot + cot ) sin Vs (22.214.171.124-4) s Af f fe d f Vf (sin f + cos f ) (126.96.36.199-5) sf 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 188.8.131.52 (in.)
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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 184.108.40.206 (in.) ffe = effective stress of FRP shear reinforcement as determined in Article 220.127.116.11 (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 The application of FRP reinforcements on precast I- reinforcement (kip); may only be used in conjunction shaped sections with "slender webs" did not provide with the provisions of Articles 18.104.22.168.1 and 22.214.171.124.2 significant or reliable FRP contributions to shear capacity, Vf, when minimum steel shear reinforcement is provided and on occasion resulted in a decrease of strength relative to or when the member depth or maximum spacing of that of the member that did not have FRP shear distributed longitudinal reinforcement is less than 12 reinforcement [NCHRP Project 12-75]. Changes in the inches, and with the provisions of Article 126.96.36.199.3. experimental setup and girder details made to address this Vf shall be taken as zero when dv/bv > 4 reduction was unsuccessful. It was concluded that the reason Vp = component in the direction of the applied shear of the that the application of FRP shear reinforcements did not lead effective prestressing force; positive if resisting the to strength gains in I-girders with slender webs was due to applied shear (kip) degradation of the diagonal compressive resistance of slender f = angle of inclination of FRP transverse reinforcement webs when stiff and well bonded FRP reinforcements are to longitudinal axis (°) glued to the surface of these webs. While the members = factor indicating ability of diagonally cracked experiencing this web resistance degradation were all concrete to transmit tension as specified in Article prestressed, it has been concluded that this degradation was 188.8.131.52. due to the slenderness of the webs and not the effect of = angle of inclination of diagonal compressive stresses prestressing [NCHRP Project 12-75]. Based on an as determined in Article 184.108.40.206 (°) examination of strength gains as a function of the ratio of depth to web width (d/bv), it was concluded that the shear The effective stress of FRP shear reinforcement, ffe,shall be resistance provided by FRP shear reinforcement, Vf , should determined as: be ignored for members with a web slenderness of d/bw > 4 [NCHRP Project12-75]. f fe Ef fe (220.127.116.11-6) in which fe Rf fu (18.104.22.168-7) 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. 22.214.171.124-9 is used. According to the observation on the experimental = failure tensile strain of FRP reinforcement database, the maximum effective strain that can be achieved in fu the beams failing due to debonding of FRP was 0.012. The strain reduction factor (Rf) shall be determined as: For completely wrapped or properly anchored U- The upper bound for the quantity fEf in Eqs. 126.96.36.199-8 and wrap configurations 188.8.131.52-9 is 300 ksi [NCHRP Project 12-75]. Substituting .67 this value in the two equations results in the lower bound Rf 0.088 4( Ef ) 1.0 (184.108.40.206-8) f value of Rf shown in the two equations.
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57 SPECIFICATIONS COMMENTARY For Un-anchored U-wrap or Two-side bonding configurations .67 Rf 0.066 3( f Ef ) 1.0 (220.127.116.11-9) where: f = FRP shear reinforcement ratio The FRP shear reinforcement ratio, f, shall be determined as: For discrete strips The factor 2 in Equations 18.104.22.168-10 and 22.214.171.124-11 2n f t f w f (126.96.36.199-10) accounts for the presence of FRP reinforcement on both sides f bv s f of a component. For continuous sheets 2n f t f f (188.8.131.52-11) bv where: bv = effective web width taken as the minimum web width within the depth dv as determined in Article 184.108.40.206 (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.) 220.127.116.11 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: Mu Nu Vu Aps f ps As f y 0.5 Vp 0.5Vs 0.5V f cot dv f c v (18.104.22.168-1) in which: Vs + Vf Vu/ (22.214.171.124-2) where: Vs = shear resistance provided by the transverse steel reinforcement at the section under investigation as given by Eq. 126.96.36.199-4 (kip)
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58 SPECIFICATIONS COMMENTARY Vf = shear resistance provided by the transverse FRP reinforcement at the section under investigation as given by Eq. 188.8.131.52-5 (kip) = angle of inclination of diagonal compressive stresses used in determining the nominal shear resistance of the section under investigation as determined by Article 184.108.40.206 (°); if the procedures of Article 220.127.116.11.3 are used, cot is defined therein f v c = resistance factors taken from Article 18.104.22.168 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. 22.214.171.124-1 shall be evaluated where simply-supported girders are made continuous for live loads. Where longitudinal reinforcement is discontinuous, Eq. 126.96.36.199-1 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: Vu As f y Aps f ps 0.5Vs 0.5V f V p cot (188.8.131.52-3) v Eqs. 184.108.40.206-1 and 220.127.116.11-2 shall be taken to apply to sections not subjected to torsion. Any lack of full development shall be accounted for.