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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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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 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 )
Ef = 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
nf = number of plies of FRP reinforcement in Article 5.8.3.3
tf = thickness of one ply of FRP reinforcement in Article 5.8.3.3 (in.)
wf = width of FRP shear reinforcement in Article 5.8.3.3 (in.)
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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.
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SPECIFICATIONS COMMENTARY
5.8.2.7 Maximum Spacing of Transverse C5.8.2.7 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 5.8.2.9
(ksi)
dv = 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 C5.8.2.8
Transverse steel reinforcement shall be anchored at both Figure C5.8.2.8-1 shows different possible configurations
ends in accordance with the provisions of Article 5.11.2.6. 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 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 (a) (b) (c)
nonprestressed transverse steel reinforcement with yield
strength in excess of 60.0 ksi, the design yield strength shall Figure C5.8.2.8-1 - 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 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
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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.
5.8.3.3 Nominal Shear Resistance C5.8.3.3
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 (5.8.3.3-1)
and
Width of FRP Strips (wf )
Vn 0.25 fcbv dv Vp (5.8.3.3-2)
Center-to-Center Spacing of FRP Strip (sf)
in which:
V c = 0.0316 fc b v d v
, if the procedures of Articles
(5.8.3.3-3)
5.8.3.4.1 or 5.8.3.4.2 are used
Width of FRP Strips (wf )
Vc = the lesser of Vci and Vcw, if the procedure of Article
5.8.3.4.3 are used
Figure C5.8.3.3-1 Illustration of the Terms sf and wf
Av f y d v (cot + cot ) sin
Vs (5.8.3.3-4)
s
Af f fe d f
Vf (sin f + cos f ) (5.8.3.3-5)
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 5.8.2.9
(in.)
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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 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 5.8.3.4.1 and 5.8.3.4.2 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 5.8.3.4.3. 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
5.8.3.4. 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 5.8.3.4 (°) 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 (5.8.3.3-6)
in which
fe Rf fu (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.
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. 5.8.3.3-8 and
wrap configurations
5.8.3.3-9 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 (5.8.3.3-8)
f value of Rf shown in the two equations.
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SPECIFICATIONS COMMENTARY
For Un-anchored U-wrap or Two-side bonding
configurations
.67
Rf 0.066 3( f Ef ) 1.0 (5.8.3.3-9)
where:
f = FRP shear reinforcement ratio
The FRP shear reinforcement ratio, f, shall be
determined as:
For discrete strips
The factor 2 in Equations 5.8.3.3-10 and 5.8.3.3-11
2n f t f w f
(5.8.3.3-10) 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 (5.8.3.3-11)
bv
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:
Mu Nu Vu
Aps f ps As f y 0.5 Vp 0.5Vs 0.5V f cot
dv f c v
(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)
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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:
Vu
As f y Aps f ps 0.5Vs 0.5V f V p cot (5.8.3.5-3)
v
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.
