Section 6 .steel nscp commentary

Section 6 – Steel Structures (SI)
C6 - 1
C6.1
Most of the provisions for proportioning
main elements are grouped by structural action:
 Tension and combined tension and flexure
(Article 6.8)
 Compression and combined compression
and flexure (Article 6.9)
 Flexure and flexural shear:
 I-sections (Article 6.10)
 box sections (Article 6.1 1 )
 miscellaneous sections (Article 6.12)
Provisions for connections and splices are
contained in Article 6.13.
Article 6.14 contains provisions specific to
particular assemblages or structural types, e.g.,
through-girder spans, trusses, orthotropic deck
systems, and arches.
C6.4.1
The term "yield strength" is used in
these Specifications as a generic term to denote
either the minimum specified yield point or the
minimum specified yield stress.
The main difference, and in most cases
the only difference, between AASHTO and
ASTM requirements is the inclusion of
mandatory notch toughness and weldability
requirements in the AASHTO Material
Standards. Steels meeting the AASHTO
Material requirements are prequalified for use in
welded bridges.
The yield strength in the direction
parallel to the direction of rolling is of primary
interest in the design of most steel structures. In
welded bridges, notch toughness is of equal
importance. Other mechanical and physical
properties of rolled steel, such as anisotropy,
ductility, formability, and corrosion resistance,
may also be important to ensure the satisfactory
performance of the structure.
No specification can anticipate all of the
unique or especially demanding applications that
may arise. The literature on specific properties
of concern and appropriate supplementary
material production or quality requirements,
provided in the AASHTO and ASTM Material
Specifications and the ANSI/AASHTO/AWS
Bridge Welding Code, should be considered, if
appropriate.
ASTM A 709M, Grade HPS485W, has
replaced AASHTO M 270M, Grade 485W, in
Table 1. The intent of this replacement is to
encourage the use of HPS steel over
conventional bridge steels due to its enhanced
properties. AASHTO M 270M, Grade 485W, is
still available, but should be used only with the
owners approval. The available lengths of
ASTM A 709M, Grade HPS485W, are a
function of the processing of the plate, with
longer lengths produced as as-rolled plate.
C6.4.3.1
The ASTM standard for A 307 bolts
covers two grades of fasteners. There is no
corresponding AASHTO standard. Either grade
may be used under these Specifications;
however, Grade B is intended for pipe-flange
bolting, and Grade A is the quality traditionally
used for structural applications.
The purpose of the dye is to allow a
visual check to be made for the lubricant at the
time of field installation. Black bolts must be
oily to the touch when delivered and installed.
C6.4.3.2
All galvanized nuts shall be lubricated
with a lubricant containing a visible dye.
C6.4.3.3
Installation provisions for washers are
covered in the AASHTO LRFD Bridge
Construction Specifications (1998).
C6.4.3.5

C6 - 2
Installation provisions for load-
indicating devices are covered in the AASHTO
LRFD Bridge Construction Specifications
(1998).
C6.4.4
Physical properties, test methods and
certification of steel shear connectors are
covered in the AASHTO LRFD Bridge
Construction Specifications (1998).
C6.4.5
The AWS designation systems are not
consistent. For example, there are differences
between the system used for designating
electrodes for shielded metal arc welding and the
system used for designating submerged arc
welding. Therefore, when specifying weld metal
and/or flux by AWS designation, the applicable
specification should be reviewed to ensure a
complete understanding of the designation
reference.
C6.5.2
The intent of this provision is to prevent
permanent deformations due to localized
yielding.
C6.5.4.2
Base metal  as appropriate for
resistance under consideration.
The basis for the resistance factors for
driven steel piles is described in Article 6.15.2.
Indicated values of c and f for
combined axial and flexural resistance are for
use in interaction equations in Article 6.9.2.2.
Further limitations on usable resistance during
driving are specified in Article 10.7.1.16.
C6.6.1.1
In the AASHTO Standard Specifications
for Highway Bridges (16th edition), the
provisions explicitly relating to fatigue dealt
only with load-induced fatigue.
C6.6.1.2.1
Concrete can provide significant
resistance to tensile stress at service load levels.
Recognizing this behavior will have a
significantly beneficial effect on the
computation of fatigue stress ranges in top
flanges in regions of stress reversal and in
regions of negative flexure. By utilizing shear
connectors in these regions to ensure composite
action in combination with the required 1
percent longitudinal reinforcement wherever the
longitudinal tensile stress in the slab exceeds the
factored modulus of rupture of the concrete,
crack length and width can be controlled so that
full-depth cracks should not occur. When a
crack does occur, the stress in the longitudinal
reinforcement increases until the crack is
arrested. Ultimately, the cracked concrete and
the reinforcement reach equilibrium. Thus, the
slab may contain a small number of staggered
cracks at any given section. Properly placed
longitudinal reinforcement prevents coalescence
of these cracks.
It has been shown that the level of total
applied stress is insignificant for a welded steel
detail. Residual stresses due to welding are
implicitly included through the specification of
stress range as the sole dominant stress
parameter for fatigue design. This same concept
of considering only stress range has been applied
to rolled, bolted, and riveted details where far
different residual stress fields exist. The
application to nonwelded details is conservative.
The live load stress due to the passage
of the fatigue load is approximately one-half that
of the heaviest truck expected to cross the bridge
in 75 years.
C6.6.1.2.2
Equation 1 may be developed by
rewriting Equation 1.3.2.1-1 in terms of fatigue
load and resistance parameters:

C6 - 3
C6.6.1.2.3
Components and details susceptible to
load-induced fatigue cracking have been
grouped into eight categories, called detail
categories, by fatigue resistance.
Experience indicates that in the design
process the fatigue considerations for Detail
Categories A through B' rarely, if ever, govern.
Components and details with fatigue resistances
greater than Detail Category C have been
included in Tables 1 and 2 for completeness.
Investigation of details with fatigue resistance
greater than Detail Category C may be
appropriate in unusual design cases.
Category F for allowable shear stress
range on the throat of a fillet weld has been
eliminated from Table 1 and replaced by
Category E. Category F was not as well defined.
Category E can be conservatively applied in
place of Category F. When fillet welds are
properly sized for strength considerations,
Category F should not govern.
In Table 1, "Longitudinally Loaded''
signifies that the direction of applied stress is
parallel to the longitudinal axis of the weld.
”Transversely Loaded" signifies that the
direction of applied stress is perpendicular to the
longitudinal axis of the weld.
Research on end-bolted cover plates is
discussed in Wattar et al. (1985).
Table 2 contains special details for
orthotropic plates. These details require careful
consideration of not only the specification
requirements, but also the application guidelines
in the commentary.
 Welded deck plate field splices, Cases (1),
(2), (3) - The current specifications
distinguish between the transverse and the
longitudinal deck plate splices and treat the
transverse splices more conservatively.
However, there appears to be no valid
reason for such differential treatment; in
fact, the longitudinal deck plate splices may
be subjected to higher stresses under the
effects of local wheel loads. Therefore, only
the governing fatigue stress range should
govern. One of the disadvantages of field
splices with backing bars left in place is
possible vertical misalignment and corrosion
susceptibility. Intermittent tack welds inside
of the groove may be acceptable because the
tack welds are ultimately fused with the
groove weld material. The same
considerations apply to welded closed rib
splices.
 Bolted deck or rib splices, Case (4) - Bolted
deck splices are not applicable where thin
surfacings are intended. However, bolted rib
splices, requiring "bolting windows", but
having a favorable fatigue rating, combined
with welded deck splices, are favored in
American practice.
 Welded deck and rib shop splices - Case (6)
corresponds to the current provision. Case
(5) gives a more favorable classification for
welds ground flush.
 “Window" rib splice - Case (7) is the
method favored by designers for welded
splices of closed ribs, offering the advantage
of easy adjustment in the field. According to
ECSC research, a large welding gap
improves fatigue strength. A disadvantage of
this splice is inferior quality and reduced
fatigue resistance of the manual overhead
weld between the rib insert and the deck
plate, and fatigue sensitive junction of the
shop and the field deck/rib weld.
 Ribs at intersections with floorbeams – A
distinction is made between rib walls
subjected to axial stresses only, i.e., Case
(8), closed ribs with internal diaphragm, or
open rib, and rib walls subjected to
additional out-of-plane bending, i.e., Case
(9), closed ribs without internal diaphragms,
where out-of-plane bending caused by
complex interaction of the closed-rib wall
with the "tooth" of the floorbeam web
between the ribs contributes additional
flexural stresses in the rib wall which should
be added to the axial stresses in calculations
of the governing stress range. Calculation of
the interaction forces and additional flexure
in the rib walls is extremely complex
because of the many geometric parameters
involved and may be accomplished only by

C6 - 4
a refined FEM analysis. Obviously, this is
often not a practical design option, and it is
expected that the designers will choose Case
(8) with an interior diaphragm, in which
case there is no cantilever in- plane bending
of the floorbeam "tooth" and no associated
interaction stress causing bending of the rib
wall. However, Case (9) may serve for
evaluation of existing decks without internal
diaphragms inside the closed ribs.
 Floorbeam web at intersection with the rib -
Similarly, as in the cases above, distinction
is made between the closed ribs with and
without internal diaphragms in the plane of
the floorbeam web. For the Case (l0), the
stress flow in the floorbeam web is assumed
to be uninterrupted by the cutout for the rib;
however, an additional axial stress
component acting on the connecting welds
due to the tension field in the "tooth" of the
floorbeam web caused by shear applied at
the floorbeamldeck plate junction must be
added to the axial stress f1. A local flexural
stress f2 in the floorbeam web is due to the
out-of-plane bending of the web caused by
the rotation of the rib in its plane under the
effects of unsymmetrical live loads on the
deck. Both stresses f1,and f2 at the toe of the
weld are directly additive; however, only
stress f1, is to be included in checking the
load carrying capacity of filled welds by
Equation 6.6.1.2.5-3. The connection
between the rib wall and floorbeam web or
rib wall and internal diaphragm plate can
also be made using a combination
groove/fillet weld connection. The fatigue
resistance of the combination groove/fillet
weld connection has been found to be
Category C and is not governed by Equation
6.6.1.2.5-3. See also Note e), Figure
9.8.3.7.4-1. Stress f2, can be calculated from
considerations of rib rotation under variable
live load and geometric parameters
accounting for rotational restraints at the rib
support, e.g., floorbeam depth, floorbeam
web thickness. For Case (11), without an
internal diaphragm, the stresses in the web
are very complex and comments for Case
(9) apply.
 Deck plate at the connection to the
floorbeam web - For Case (12) basic
considerations apply for a stress flow in the
direction parallel to the floorbeam web
locally deviated by a longitudinal weld, for
which Category E is usually assigned.
Tensile stress in the deck, which is relevant
for fatigue analysis, will occur in floorbeams
continuous over a longitudinal girder, or in a
floorbeam cantilever. Additional local
stresses in the deck plate in the direction of
the floorbeam web will occur in closed-rib
decks of traditional design where the deck
plate is unsupported over the rib cavity.
Resulting stress flow concentration at the
edges of floorbeam "teeth" may cause very
high peak stresses. This has resulted in
severe cracking in some thin deck plates
which were 12 mm thick or less. This
additional out-of-plane local stress may be
reduced by extending the internal diaphragm
plate inside the closed rib and fitting it
tightly against the underside of the deck
plate to provide continuous support,
Wolchuk (1999). Reduction of these stresses
in thicker deck plates remains to be studied.
A thick surfacing may also contribute to a
wider load distribution and deck plate stress
reduction. Fatigue tests on a full-scale
prototype orthotropic deck demonstrated
that a deck plate of 16 mm was sufficient to
prevent any cracking after 15.5 million
cycles. The applied load was 3.6 times the
equivalent fatigue-limit state wheel load and
there was no wearing surface on the test
specimen. However, the minimum deck
plate thickness allowed by these
specifications is 14 mm. Where interior
diaphragms are used, extending the
diaphragms to fit the underside of the deck
is suggested as a safety precaution,
especially if large rib web spacing is used.
 Additional commentary on the use of
internal diaphragms versus cutouts in the
floorbeam web can be found in Article
C9.8.3.7.4.
C6.6.1.2.5

C6 - 5
The fatigue resistance above the
constant amplitude fatigue threshold, in terms of
cycles, is inversely proportional to the cube of
the stress range, e.g., if the stress range is
reduced by a factor of 2, the fatigue life
increases by a factor of 23
.
The requirement on higher-traffic-
volume bridges that the maximum stress range
experienced by a detail be less than the constant-
amplitude fatigue threshold provides a
theoretically infinite fatigue life. The maximum
stress range is assumed to be twice the live load
stress range due to the passage of the fatigue
load, factored in accordance with the load factor
in Table 3.4.1-1 for the fatigue load
combination.
In the AASHTO 1996 Standard
Specifications, the constant amplitude fatigue
threshold was termed the allowable fatigue
stress range for more than 2 million cycles on a
redundant load path structure. The design life
has been considered to be 75 years in the overall
development of these LRFD Specifications. If a
design life other than 75 years is sought, a
number other than 75 may be inserted in the
equation for N.
Figure C1 is a graphical representation
of the nominal fatigue resistance for Categories
A through E'.
When the design stress range is less than
one-half of the constant-amplitude fatigue
threshold, the detail will theoretically provide
infinite life. Except for Categories E and E', for
higher traffic volumes, the design will most
often be governed by the infinite life check.
Table CI shows the values of (ADTT)SL, above
which the infinite life check governs, assuming a
75-year design life and one cycle per truck.
The values in the above table have been
computed using the values for A and (F)TH
specified in Tables 1 and 3, respectively. The
resulting values of the 75-year (ADTT)SL, differ
slightly when using the values for A and (F)TH,
given in the Customary US Units and SI Units
versions of the specifications. The values in the
above table represent the larger value from
either version of the specifications rounded up to
the nearest 5 trucks per day.
Equation 3 assumes no penetration at
the weld root. Development of Equation 3 is
discussed in Frank and Fisher (1979).
In the AASHTO 1996 Standard
Specifications, allowable stress ranges were
specified for both redundant and nonredundant
members. The allowables for nonredundant
members were arbitrarily specified as 80 percent
of those for redundant members due to the more
severe consequences of failure of a
nonredundant member. However, greater
fracture toughness was also specified for
nonredundant members. In combination, the
reduction in allowable stress range and the
greater fracture toughness constitute an
unnecessary double penalty for nonredundant
members. The requirement for greater fracture
toughness has been maintained. Therefore, the
allowable stress ranges represented by Equation

C6 - 6
6.6.1.2.5-1 are applicable to both redundant and
nonredundant members.
For the purpose of determining the
stress cycles per truck passage for continuous
spans, a distance equal to one-tenth the span on
each side of an interior support should be
considered to be near the support.
The number of cycles per passage is
taken as 5.0 for cantilever girders because this
type of bridge is susceptible to large vibrations,
which cause additional cycles after the truck has
left the bridge (Moses et al. 1987; Schilling
1990).
C6.6.1.3
These rigid load paths are required to
preclude the development of significant
secondary stresses that could induce fatigue
crack growth in either the longitudinal or the
transverse member (Fisher et al. 1990).
C6.6.1.3.1
These provisions appeared in previous
editions of the AASHTO Standard
Specifications in Article 10.20 "Diaphragms and
Cross Frames" with no explanation as to the
rationale for the requirements and no reference
to distortion-induced fatigue.
These provisions apply to both
diaphragms between longitudinal members and
diaphragms internal to longitudinal members.
The 90 000 N load represents a rule of
thumb for straight, nonskewed bridges. For
curved or skewed bridges, the diaphragm forces
should be determined by analysis (Keating
1990).
C6.6.1.3.2
The specified minimum distance from
the flange is intended to reduce out-of-plane
distortion concentrated in the web between the
lateral connection plate and the flange to a
tolerable magnitude. It also provides adequate
electrode access and moves the connection plate
closer to the neutral axis of the girder to reduce
the impact of the weld termination on fatigue
strength.
This requirement reduces potential
distortion- induced stresses in the gap between
the web or stiffener and the lateral members on
the lateral plate. These stresses may result from
vibration of the lateral system.
C6.6.1.3.3
The purpose of this provision is to
control distortion-induced fatigue of deck details
subject to local secondary stresses due to out-of-
plane bending.
C6.6.2
Material for main load-carrying
components subjected to tensile stress require
supplemental impact properties as specified in
the AASHTO Material Specifications. The basis
and philosophy for these requirements is given
in AISI (1975).
The Charpy V-notch impact
requirements vary, depending on the type of
steel, type of construction, whether welded or
mechanically fastened, and the applicable
minimum service temperature.
FCMs shall be fabricated according to
Section 12 of the ANSI/AASHTO/AWS D1.5
Bridge Welding Code.
C6.7.4.1
The arbitrary requirement for
diaphragms spaced at not more than 7600 mm in
the 16th edition of the AASHTO Standard
Specifications has been replaced by a
requirement for rational analysis that will often
result in the elimination of fatigue-prone
attachment details.
C6.7.4.3
Temporary diaphragms or cross-frames
in box sections may be required for
transportation and at field splices and the Ming
points of each shipping piece. In designs outside
the limitations of Article 6.11.1.1.1, distortional
stresses can be reduced by the introduction of
intermediate diaphragms or cross-frames within
the girders.

C6 - 7
C6.7.5.2
Wind-load stresses in I-sections may be
reduced by:
 Changing the flange size,
 Reducing the diaphragm or cross-frame
spacing, or
 Adding lateral bracing.
The relative economy of these methods should
be investigated.
C6.7.5.3
Investigation will generally show that a
lateral bracing system is not required between
straight multiple box sections.
In box sections with sloping webs, the
horizontal component of web shear acts as a
lateral horizontal force on the flange of the box
girder. Internal lateral bracing or struts may be
required to resist this force prior to deck
placement.
For straight box sections with spans less
than about 45 000 mm, at least one panel of
horizontal lateral bracing should be provided on
each side of a lifting point. Straight box sections
with spans greater than about 45 000 mm may
require a full length lateral bracing system to
prevent distortions brought about by temperature
changes occurring prior to concrete slab
placement.
C6.7.6.2.1
The development of Equation 1 is
discussed in Kulicki (1983).
C6.8.1
The provisions of the AISC (1993) may
be used to design tapered tension members.
C6.8.2.1
The reduction factor, U, does not apply
when checking yielding on the gross section
because yielding tends to equalize the
nonuniform tensile stresses caused over the
cross-section by shear lag.
Due to strain hardening, a ductile steel
loaded in axial tension can resist a force greater
than the product of its gross area and its' yield
strength prior to fracture. However, excessive
elongation due to uncontrolled yielding of gross
area not only marks the limit of usefulness but
can precipitate failure of the structural system of
which it is a part. Depending on the ratio of net
area to gross area and the mechanical properties
of the steel, the component can fracture by
failure of the net area at a load smaller than that
required to yield the gross area. General yielding
of the gross area and fracture of the net area both
constitute measures of component strength. The
relative values of the resistance factors for
yielding and fracture reflect the different
reliability indices deemed proper for the two
modes.
The part of the component occupied by
the net area at fastener holes generally has a
negligible length relative to the total length of
the member. As a result, the strain hardening is
quickly reached and, therefore, yielding of the
net area at fastener holes does not constitute a
strength limit of practical significance, except
perhaps for some builtup members of unusual
proportions.
For welded connections, An, is the gross
section less any access holes in the connection
region.
C6.8.2.2
For shear lag in flexural components,
see Article 4.6.2.6. These cases include builtup
members, wide-flange shapes, channels, tees,
and angles. For bolted connections, Munse and
Chesson (1963) observed that the loss in
efficiency at the net section due to shear lag was
related to the ratio of the length, L, of the
connection and the eccentricity, x, between the
shear plane and the centroidal axis of the
connected component. They concluded that a
decrease in joint length increases the shear lag
effect. To approximate the efficiency of the net

C6 - 8
section by taking into account joint length and
geometry, the following expression may be used
for U in lieu of the lower bound value of 0.85:
For rolled or builtup shapes, the distance
x is to be referred to the center of gravity of the
material lying on either side of the centerline of
symmetry of the cross-section, as illustrated
below.
C6.8.2.3
Interaction equations in tension and
compression members are a design
simplification. Such equations involving
exponents of 1.0 on the moment ratios are
usually conservative. More exact, nonlinear
interaction curves are also available and are
discussed in Galambos (1988). If these
interaction equations are used, additional
investigation of service limit state stresses is
necessary to avoid premature yielding.
C6.8.3
In the metric bolt standard, the hole size
for standard holes is 2 mm larger than the bolt
diameter for 24 mm and smaller bolts, and 3 mm
larger than the bolt diameter for bolts larger than
24 mm in diameter. Thus, a constant width
increment of 3.2 mm applied to the bolt diameter
will not work. Also, the deduction should be 2
mm and not 1.6 mm (the soft conversion) since
metric tapes and rulers are not read to less than a
mm.
The development of the "s2
/4g" rule for
estimating the effect of a chain of holes on the
tensile resistance of a section is described in
McGuire (1968). Although it has theoretical
shortcomings, it has been used for a long time
and has been found to be adequate for ordinary
connections.
In designing a tension member, it is
conservative and convenient to use the least net
width for any chain together with the full tensile
force in the member. It is sometimes possible to
achieve an acceptable, slightly less conservative
design by checking each possible chain with a
tensile force obtained by subtracting the force
removed by each bolt ahead of that chain, i.e.,
closer to midlength of the member from the full
tensile force in the member. This approach
assumes that the full force is transferred equally
by all bolts at one end.
C6.8.5.1
Perforated plates, rather than tie plates
and/or lacing, are now used almost exclusively
in builtup members. However, tie plates with or
without lacing may be used where special
circumstances warrant. Limiting design
proportions are given in AASHTO (1996) and
AISC (1994).
C6.8.6.1
Equation 6.8.2.1-2 does not control
because the net section in the head is at least
1.35 greater than the section in the body.
C6.8.6.2

C6 - 9
The limitation on the hole diameter for
steel with yield strengths above 485 MPa, which
is not included in the 16th edition of the
AASHTO Standard Specifications, 1996, is
intended to prevent dishing beyond the pin hole
(AISC 1994).
C6.8.6.3
The eyebar assembly should be detailed
to prevent corrosion-causing elements from
entering the joints. Eyebars sometimes vibrate
perpendicular to their plane. The intent of this
provision is to prevent repeated eyebar contact
by providing adequate spacing or by clamping.
C6.8.7.3
The proportions specified in this article
assure that the member will not fail in the region
of the hole if the strength limit state is satisfied
in the main plate away from the hole.
C6.8.7.4
The pin-connected assembly should be
detailed to prevent corrosion-causing elements
from entering the joints.
C6.9.1
Conventional column design formulas
contain allowances for imperfections and
eccentricities permissible in normal fabrication
and erection. The effect of any significant
additional eccentricity should be accounted for
in bridge design.
Torsional buckling or flexural-torsional
buckling of singly symmetric and unsymmetric
compression members and doubly symmetric
compression members with very thin walls
should be investigated. Pertinent provisions of
AISC (1994) can be used to design tapered
compression members.
C6.9.2.2
These equations are identical to the
provisions in AISC LRFD Specification (1994).
They were selected for use in that Specification
after being compared with a number of
alternative formulations with the results of
refined inelastic analyses of 82 frame sidesway
cases (Kanchanalai 1977). Pu, Mux, and Muy, are
simultaneous axial and flexural forces on cross-
sections determined by analysis under factored
loads. The maximum calculated moment in the
member in each direction including the second
order effects, should be considered. Where
maxima occur on different cross-sections, each
should be checked.
C6.9.4.1
These equations are identical to the
column design equations of AISC (1993). Both
are essentially the same as column strength
curve 2P of Galambos (1988). They incorporate
an out-of-straightness criterion of L/500. The
development of the mathematical form of these
equations is described in Tide (1985), and the
structural reliability they are intended to provide
is discussed in Galambos (1988).
Singly symmetric and unsymmetric
compression member, such as angles or tees,and
doubly symmetric compression members, such
as cruciform members or builtup members with
very thin walls, may be governed by the modes
of flexural-torsional buckling or torsional
buckling rather than the conventional axial
buckling mode reflected by Equations 1 and 2.
The design of these members for these less
conventional buckling modes is covered in
AISC (1993).
Member elements not satisfying the
width/thickness requirements of Article 6.9.4.2
should be classified as slender elements. The
design of members including such elements is
covered in AISC (1993).
C6.9.4.2
The purpose of this article is to ensure
that uniformly compressed components can
develop the yield strength in compression before
the onset of local buckling. This does not
guarantee that the component has the ability to
strain inelasticity at constant stress sufficient to
permit full plastification of the cross-section for
which the more stringent width-to-thickness
requirements of the applicable portion of Article
6.10 apply.

C6 - 10
The form of the width-to-thickness
equations derives from the classical elastic
critical stress formula for plates: Fcr =
[π2
kE]/[12(1-2
)(b/t)2
], in which the buckling
coefficient, k, is a function of loading and
support conditions. For a long, uniformly
compressed plate with one longitudinal edge
simply supported against rotation and the other
free, k = 0.425, and for both edges simply
supported, k = 4.00 (Timoshenko and Gere
1961). For these conditions, the coefficients of
the b/t equation become 0.620 and 1.90l,
respectively. The coefficients specified herein
are the result of further analyses and numerous
tests and reflect the effect of residual stresses,
initial imperfections, and actual (as opposed to
ideal) support conditions.
The Specified minimum wall
thicknesses of tubing are identical to those of the
1995 AC1 Building Code. Their purpose is to
prevent buckling of the steel pipe or tubing
before yielding.
C6.9.5.1
The procedure for the design of
composite columns is the same as that for the
design of steel columns, except that the yield
strength of structural steel, the modulus of
elasticity of steel, and the radius of gyration of
the steel section are modified to account for the
effect of concrete and of longitudinal reinforcing
bars. Explanation of the origin of these
modifications and comparison of the design
procedure, with the results of numerous tests,
may be found in SSRC Task Group 20 (1979)
and Galambos and Chapuis (1980).
C6.9.5.2.1
Little of the test data supporting the
development of the present provisions for design
of composite columns involved concrete
strengths in excess of 40 MPa. Normal density
concrete was believed to have been used in all
tests. A lower limit of 20 MPa is specified to
encourage the use of good-quality concrete.
C6.9.5.2.3
Concrete-encased shapes are not subject
to the width/thickness limitations specified in
Article 6.9.4.2 because it has been shown that
the concrete provides adequate support against
local buckling.
C6.10.1
Noncomposite sections are not
recommended but are permitted.
C6.10.2.1
The ratio of Iyc/Iy determines the
location of the shear center of a singly
symmetric section. Girders with ratios outside of
the limits specified are like a "T" section with
the shear center located at the intersection of the
larger flange and the web. The formulas for
lateral torsional buckling used in the
Specification are not valid for such sections.
C6.10.2.2
The specified web slenderness limit for
sections without longitudinal stiffeners
corresponds to the upper limit for transversely
stiffened webs in AASHTO (1996). This limit
defines an upperbound below which fatigue due
to excessive lateral web deflections is not a
consideration (Yen and Mueller 1966; Mueller
and Yen 1968).
The specified web slenderness limit for
longitudinally stiffened webs is retained from
the Load Factor Design portion of AASHTO
(1996). Static tests of large-size late girders
fabricated from A 36 steel with D/tw ratios
greater than 400 have demonstrated the
effectiveness of longitudinal stiffeners in
minimizing lateral web deflections (Cooper
1967). Accordingly, the web slenderness limit
given by Equation 2 is used for girders with
transverse and longitudinal stiffeners. The
specified web slenderness limit is twice that for
girders with transverse stiffeners only. Practical
upper limits are specified on the limiting web
slenderness ratios computed from either
Equation 1 or 2. The upper limits are slightly
above the web slenderness limit computed from
Equation 1 or 2 when fc is taken equal to 250
MPa.

C6 - 11
When the compression flange is at a
dead-load tress of fc, considering the deck-
placement sequence, the corresponding stress in
a web of slenderness 2Dc/tw between the limit
specified by Equation 1 and a slenderness of
λb(E/fc,)1/2
, where λb is defined in Article
6.10.4.2.6a, will be slightly above the elastic
web buckling stress. For this case, the nominal
flexural resistance of the steel section must be
reduced accordingly by an Rb factor less than
1.0.
C6.10.2.3
The minimum compression flange width
on fabricated I-sections, given by Equation 1, is
specified to ensure that the web is adequately
restrained by the flanges to control web bend
buckling. Equation 1 specifies an absolute
minimum width. In actuality, it would be
preferable for b, to be greater than or equal to
0.4Dc. In addition, the compression flange
thickness, tf, should preferably be greater than or
equal to 1.5 times the web thickness, tw. These
recommended proportions are based on a study
(Zureick and Shih 1994) on doubly symmetric
tangent I-sections, which clearly showed that the
web bend buckling resistance was dramatically
reduced when the compression flange buckled
prior to the web. Although this study was
limited to doubly symmetric I-sections, the
recommended minimum flange proportions from
this study are deemed to be adequate for
reasonably proportioned singly symmetric I-
sections by incorporating the depth of the web of
the steel section in compression in the elastic
range, Dc, in Equation 1. The advent of
composite design has led to a significant
reduction in the size of compression flanges in
regions of positive flexure. These smaller
flanges are most likely to be governed by these
proportion limits. Providing minimum
compression flange widths that satisfy these
limits in these regions will help ensure a more
stable girder that is easier to handle.
The slenderness of tension flanges on
fabricated I-sections is limited to a practical
upper limit of 12.0 by Equation 2 to ensure the
flanges will not distort excessively when welded
to the web. Also, an upper limit on the tension
flange slenderness covers the case where the
flange may be subject to an unanticipated stress
reversal.
C6.10.3.1.2
The yield moment, My, of a composite
section is needed only for the strength limit state
investigation of the following types of
composite sections:
 Compact positive bending sections in
continuous spans,
 Negative bending sections designed by the
Q formula,
 Hybrid negative bending sections for which
the neutral axis is more than 10 percent of
the web depth from middepth of the web,
 Compact homogeneous sections with
stiffened webs subjected to combined
moment and shear values exceeding
specified limits, and
 Noncompact sections used at the last plastic
hinge to form inelastic designs.
A procedure for calculating the yield
moment is presented in Appendix A.
C6.10.3.1.3
The plastic moment of a composite
section in positive flexure can be determined by:
 Calculating the element forces and using
them to determine whether the plastic
neutral axis is in the web, top flange, or slab,
 Calculating the location of the plastic neutral
axis within the element determined in the
first step; and
 Calculating Mp. Equations for the five cases
most likely to occur in practice are given in
Appendix A.
The forces in the longitudinal reinforcement
may be conservatively neglected. To do this, set

C6 - 12
Prb, and Prt, equal to 0 in the equations in
Appendix A.
The plastic moment of a composite section
in negative flexure can be calculated by an
analogous procedure. Equations for the two
cases most likely to occur in practice are also
given in Appendix A.
C6.10.3.1.4a
For composite sections, Dc, is a function
of the algebraic sum of the stresses caused by
loads acting on the steel, long-term composite,
and short-term composite sections. Thus, Dc, is a
function of the dead-to-live load stress ratio. At
sections in positive flexure, Dc, of the composite
section will increase with increasing span
because of the increasing dead-to-live load ratio.
As a result, using Dc, of the short-term
composite section, as has been customary in the
past, is unconservative. In lieu of computing Dc,
at sections in positive flexure from the stress
diagrams, the following equation may be used:
At sections in negative flexure, using Dc, of the
composite section consisting of the steel section
plus the longitudinal reinforcement is
conservative.
C6.10.3.1.4b
The location of the neutral axis may be
determined from the conditions listed in
Appendix A.
C6.10.3.2.1
The entire concrete deck may not be cast
in one stage; thus parts of the girders may
become composite in sequential stages. If certain
deck casting sequences are followed, the
temporary moments induced in the girders
during the deck staging can be considerably
higher than the final noncomposite dead load
moments after the sequential casting is
complete, and all the concrete has hardened.
Economical composite girders normally
have smaller top flanges than bottom flanges in
positive bending regions. Thus, more than half
of the noncomposite web depth is typically in
compression in these regions during deck
construction. If the higher moments generated
during the deck casting sequence are not
considered in the design, these conditions,
coupled with narrow top compression flanges,
can lead to problems during construction, such
as out-of-plane distortions of the girder
compression flanges and web. Limiting the
length of girder shipping pieces to
approximately 85 times the minimum
compression-flange width in the shipping piece
can help to minimize potential problems.
Sequentially staged concrete placement
can also result in significant tensile strains in the
previously cast deck in adjacent spans.
Temporary dead load deflections during
sequential deck casting can also be different
from final noncomposite dead load deflections.
This should be considered when establishing
camber and screed requirements. These
constructability concerns apply to deck
replacement construction as well as initial
construction.
During construction of steel girder
bridges, concrete deck overhang loads are
typically supported by cantilever forming
brackets placed every 900 or 1200 mm along the
exterior members. Bracket loads applied
eccentrically to the exterior girder centerline
create applied torsional moments to the exterior
girders at intervals in between the cross-frames,
which tend to twist the girder top flanges

C6 - 13
outward. As a result, two potential problems
arise:
 The applied torsional moments cause
additional longitudinal stresses in the
exterior girder flanges, and
 The horizontal components of the resultant
loads in the cantilever-forming brackets are
oíten transmitted directly onto the exterior
girder web. The girder web may deflect
laterally due to these applied loads.
Consideration should be given to these
effects in the design of exterior members. Where
practical, forming brackets should be carried to
the intersection of the bottom flange and the
web.
C6.10.3.2.2
For composite sections, the flow charts
represented by Figures C6.10.4-1 and C6.10.4-2
must be used twice: first for the girder in the
final condition when it behaves as a composite
section, and second to investigate the
constructibilitv of the girder prior to the
hardening of the concrete deck when the girder
behaves as a noncomposite section.
Equation 1 limits the maximum
compressive flexural stress in the web resulting
from the various stages of the deck placement
sequence to the theoretical elastic bend-
buckling stress of the web. The bend-buckling
coefficient, k, for webs without longitudinal
stiffeners is calculated assuming partial
rotational restraint at the flanges and simply
supported boundary conditions at the transverse
stiffeners. The equation for k includes the depth
of the web in compression of the steel section,
Dc, in order to address unsymmetrical sections.
A factor α of 1.25 is applied in the numerator of
Equation 1 for webs without longitudinal
stiffeners. The factor offsets the specified
maximum permanent-load load factor of 1.25
applied to the component dead load flexural
stresses in the web. Thus, for webs without
longitudinal stiffeners, local web buckling
during construction is essentially being checked
as a service limit state criterion. In the final
condition at the strength limit state, the
appropriate checks are made to ensure that the
web has adequate postbuckling resistance.
Should the calculated maximum
compressive flexural stress in a web without
longitudinal stiffeners fail to satisfy Equation 1
for the construction condition, the Engineer has
several options to consider. These options
include providing a larger top flange or a smaller
bottom flange to decrease the depth of the web
in compression, adjusting the deck-casting
sequence to reduce the compressive stress in the
web, or providing a thicker web. Should these
options not prove to be practical or cost-
effective, a longitudinal stiffener can be
provided.
The derivation of the bend-buckling
coefficient k in Equation 1 specified for webs
with longitudinal stiffeners is discussed in
C6.10.4.3.2a. An. a factor of 1.0 is
conservatively applied in the numerator of
Equation 1 for webs with longitudinal stiffeners,
which limits the maximum compressive flexural
stress in the web during the construction
condition factored by the maximum permanent-
load load factor of 1.25 to the elastic web bend-
buckling stress. As specified in Article
6.10.8.3.1, the longitudinal stiffener must be
located vertically on the web to both satisfy
Equation 1 for the construction condition and to
ensure that the composite section has adequate
factored flexural resistance at the strength limit
state. For composite sections in regions of
positive flexure in particular, several locations
may need to be investigated in order to
determine the optimum location.
C6.10.3.2.3
The web is investigated for the sum of
the factored permanent loads acting on both the
noncomposite and composite sections during
construction because the total shear due to these
loads is critical in checking the stability of the
web during construction. The nominal shear
resistance for this check is limited to the shear
buckling or shear yield force. Tension field
action is not permitted under factored dead load
alone. The shear force in unstiffened webs and
in webs of hybrid sections is limited to either the
shear yield or shear buckling force at the
strength limit state, consequently the

C6 - 14
requirement in this article need not be
investigated for those sections.
C6.10.3.3.1
The plastic moment of noncomposite
sections may be calculated by eliminating the
terms pertaining to the concrete slab and
longitudinal reinforcement from the equations in
Appendix A for composite sections.
C6.10.3.3.2
If the inequality is satisfied, the neutral
axis is in Fyw, the web. If it is not, the neutral
axis is in the flange, fc, and Dcp, is equal to the
depth of the web.
C6.10.3.4
In line with common practice, it is
specified that the stiffness of the steel section
alone be used for noncomposite sections, even
though numerous field tests have shown that
considerable unintended composite action
occurs in such sections.
Field tests of composite continuous
bridges have shown that there is considerable
composite action in negative bending regions
(Baldwin et al. 1978; Roeder and Eltvik 1985).
Therefore, it is conveniently specified that the
stiffness of the full composite section may be
used over the entire bridge length, where
appropriate.
The Engineer may use other stiffness
approximations based on sound engineering
principles. One alternative is to use the cracked-
section stiffness for a distance on each side of
piers equal to 15 percent of each adjacent span
length. This approximation is used in Great
Britain (Johnson and Buckby 1986).
C6.10.3.5.1
Compact sections are designed to
sustain the plastic moment, which theoretically
causes yielding of the entire cross-section.
Therefore, the combined effects of wind and
other loadings cannot be accounted for by
summing the elastic stresses caused by the
various loadings. Instead, it is assumed that the
lateral wind moment is carried by a pair of fully
yielded widths that are discounted from the
section assumed to resist the vertical loads.
Determination of the wind moment in the flange
is covered in Article 4.6.2.7.
C6.10.3.5.2
For noncompact sections, the combined
effects of wind and other loadings are accounted
for by summing the elastic stresses caused in the
bottom flange by the various loadings. The wind
stress in the bottom flange is equal to the wind
moment divided by the section modulus of the
flange acting in the lateral direction.
The peak wind stresses may be
conservatively combined with peak stresses
from other loadings, even though they may
occur at different locations. This is justified
because the wind stresses are usually small and
generally do not control the design.
For investigating wind loading on
sections designed by the optional Q formula
specified in Article 6.10.4.2.3, it is necessary to
apply the procedures specified in Article
6.10.3.5.1 for compact sections, even if the
actual sections are not compact, because the
design using the optional Q formula is
performed in terms of moment, rather than
stresses.
C6.10.3.6
Equation 1 defines an effective area for
a tension flange with holes to be used to
determine the section properties for a flexural
member at the strength limit state. The equation
replaces the 15 percent rule given in past
editions of the Standard Specifications and the
First Edition of the LRFD Specifications. If the
stress due to the factored loads on the effective
area of the tension flange is limited to the yield
stress, fracture on the net section of the flange is
theoretically prevented and need not be
explicitly checked.
The effective area is equal to the net
area of the flange plus a factor ß times the gross
area of the flange. The sum is not to exceed the
gross area. For AASHTO M 270M, Grade 690
or 690W steels, with a yield-to-tensile strength

C6 - 15
ratio of approximately 0.9, the calculated value
of the factor β from Equation 1 will be negative.
However, since β cannot be less than 0.0
according to Equation 1, β is to be taken as 0.0
for these steels resulting in an effective flange
area equal to the net flange area. The factor is
also defined as 0.0 when the holes exceed 32
mm in diameter, AASHTO (1991). For all other
steels and when the holes are less than or equal
to 32 mm in diameter, the factor β depends on
the ratio of the tensile strength of the flange to
the yield strength of the flange and on the ratio
of the net flange area to the gross flange area.
For compression flanges, net section
fracture is not a concern and the effective flange
area is to be taken as the gross flange area as
defined in Equation 2.
C6.10.3.7
The use of 1 percent reinforcement with
a size not exceeding No. 19 bars is intended to
provide rebar spacing that will be small enough
to control slab cracking. Reinforcement with a
yield strength of at least 420 MPa is expected to
remain elastic, even if inelastic redistribution of
negative moments occurs. Thus, elastic recovery
is expected to occur after the live load is
removed, and this should tend to close the slab
cracks. Pertinent criteria for concrete crack
control are discussed in more detail in AASHTO
(1991) and in Haaijer et al. (1987). Previously,
the requirement for 1 percent longitudinal
reinforcement was limited to negative flexure
regions of continuous spans, which are often
implicitly taken as the regions between points of
dead load contraflexure. Under moving live
loads, the slab can experience significant tensile
stresses outside the points of dead load
contraflexure. Placement of the concrete slab in
stages can also produce negative flexure during
construction in regions where the slab has
hardened and that are primarily subject to
positive flexure in the final condition. Thermal
and shrinkage stresses can also cause tensile
stresses in the slab in regions where such
stresses might not otherwise be anticipated. To
address at least some of these issues, the 1
percent longitudinal reinforcement is to be
placed wherever the tensile stress in the slab due
to either factored construction loads, including
during the various phases of the deck placement
sequence, or due to Load Combination Service
II in Table 3.4.1-1 exceeds φfr. By controlling
the crack size in regions where adequate shear
connection is also provided, the concrete slab
can be considered to be effective in tension for
computing fatigue stress ranges, as permitted in
Article 6.6.1.2.1, and flexural stresses on the
composite section due to Load Combination
Service II, as permitted in Articles 6.10.5.1 and
6.10.10.2.1.
C6.10.4
Article 6.10.4 is written in the form of a
flow chart, shown schematically in Figure C1, to
facilitate the investigation of the flexural
resistance of a particular I-section. Figure C2
shows the expanded flow chart when the
optional Q formula of Article 6.10.4.2.3 is
considered. For compact sections, the calculated
moments in simple and continuous spans are
compared with the plastic moment capacities of
the sections, even though the moments may have
been based upon an elastic analysis.
Nevertheless, unless an inelastic structural
analysis is made, it is customary to call the
process an "elastic" one. The AASHTO
Standard Specifications recognize inelastic
behavior by:
 Utilizing the plastic moment capacity of
compact sections, and
 Permitting an arbitrary 10 percent
redistribution of peak negative moments at
both overload and maximum load.
The Guide Specifications for Alternate
Load Factor Design (ALFD) permit inelastic
calculations for compact sections (AASHTO
1991). Most of the provisions of those Guide
Specifications are incorporated into Article
6.10.10 of these Specifications.
C6.10.4.1.1
Two different entry points for the flow
charts are required to characterize the flexural
resistance at the strength limit state, in part
because the moment-rotation behavior of steels
having yield strengths exceeding 485 MPa has

C6 - 16
not been sufficiently documented to extend
plastic moment capacity to those materials.
Similar logic applies to flexural members of
variable depth section and with longitudinal
stiffeners. At sections of flexural members with
holes in the tension flange, it has also not been
fully documented that complete plastification of
the cross-section can be achieved prior to
fracture on the net section of the flange.
In general, compression flange
slenderness and bracing requirements need not
be investigated and can be considered
automatically satisfied at the strength limit state
for both compact and noncompact composite
sections in positive flexure because the hardened
concrete slab prevents local and lateral
compression flange buckling. However, when
precast decks are used with shear connectors
clustered in block-outs spaced several feet apart,
consideration should be given to checking the
compression flange slenderness requirement at
the strength limit state and computing the
nominal flexural resistance of the flange
according to Equation 6.10.4.2.4a-2.
C6.10.4.1.2
The web slenderness requirement of this
article is adopted from AISC (1993) and gives
approximately the same allowable web
slenderness as specified for compact sections in
AASHTO (1996). Most composite sections in
positive flexure will qualify as compact
according to this criterion because the concrete
deck causes an upward shift in the neutral axis,
which greatly reduces the depth of the web in
compression.
C6.10.4.1.3
The compression-flange requirement for
compact negative flexural sections is retained
from AASHTO (1996).
C6.10.4.1.4
The slenderness is limited to a practical
upper limit of 12.0 in Equation 1 to ensure the
flange will not distort excessively when welded
to the web. The nominal flexural resistance of
the compression flange for noncompact sections,
other than for noncompact composite sections in
positive flexure in their final condition, that
satisfy the bracing requirement of Article
6.10.4.1.9 depends on the slenderness of the
flange according to Equation 6.10.4.2.4a-2. For
sections without longitudinal web stiffeners, the
nominal flexural resistance is also a function of
the web slenderness. For compression-flange
slenderness ratios at or near the limit given by
Equation 1, the nominal flexural resistance will
typically be below Fyc, according to Equation
6.10.4.2.b-2. To utilize a nominal flexural
resistance at or near Fyc, a lower compression-
flange slenderness ratio will be required.
C6.10.4.1.6a
The slenderness interaction relationship
for compact sections is retained from the
Standard Specifications. A review of the
moment-rotation test data available in the
literature suggests that compact sections may not
be able to reach the plastic moment when the
web and compression-flange slenderness ratios
both exceed 75 percent of the limits given in
Equations 6.10.4.1.2-1 and 6.10.4.1.3-1,
respectively. The slenderness interaction
relationship given in Equation 6.10.4.1.6b-1
redefines the allowable limits when this occurs
(Grubb and Carskaddan 1981).
C6.10.4.1.7
This article provides a continuous
function relating unbraced length and end
moment ratio. There is a substantial increase in
the allowable unbraced length if the member is
bent in reverse curvature between brace points
because yielding is confined to zones close to
the brace points. The formula was developed to
provide inelastic rotation capacities of at least
three times the elastic rotation corresponding to
the plastic moment (Yura et al. 1978);
C6.10.4.1.9
This article defines the maximum
unbraced length for which a section can reach
the specified minimum yield strength times the
applicable flange stress reduction factors, under

C6 - 17
a uniform moment, before the onset of lateral
torsional buckling. Under a moment gradient,
sections with larger unbraced lengths can still
reach the yield strength. This larger allowable
unbraced length may be determined by equating
Equation 6.10.4.2.5a-1 to Rb,Rh,Fyc, and solving
for Lb resulting in the following equation:
C6.10.4.2.1
If the limiting values of Articles
6.10.4.1.2, 6.10.4.1.3, 6.10.4.1.6, and 6.10.4.1.7
are satisfied, flexural resistance at the strength
limit state is defined as the plastic moment for
compact sections.
C6.10.4.2.2a
For simple spans and continuous spans
with compact interior support sections, the
equation defining the nominal flexural resistance
depends on the ratio of Dp, which is the distance
from the top of the slab to the neutral axis at the
plastic moment to a defined depth D’. D’ is
specified in Article 6.10.4.2.2b and is defined as
the depth at which the composite section reaches
its theoretical plastic moment capacity, Mp,
when the maximum strain in the concrete slab is
at its theoretical crushing strain. Sections with a
ratio of Dp, to D’ less than or equal to 1.0 can
reach as a minimum Mp, of the composite
section. Equation 1 limits the nominal flexural
resistance to Mp. Sections with a ratio of Dp, to
D’ equal to 5.0 have a specified nominal flexural
resistance of 0.85 My. For ratios in between 1.0
and 5.0, the linear transition Equation 2 is given
to define the nominal flexural resistance.
Equations 1 and 2 were derived as a result of a
parametric analytical study of more than 400
composite steel sections, including
unsymmetrical as well as symmetrical steel
sections, as discussed in Wittry (1 993). The
analyses included the effect of various steel and
concrete stress-strain relationships, residual
stresses in the steel, and concrete crushing
strains. From the analyzes, the ratio of Dp to D’
was found to be the controlling variable defining
the nominal flexural resistance and ductility of
the composite sections. As the ratio of Dp/D’
approached a value of 5.0, the analyses indicated
that crushing of the slab would theoretically
occur upon the attainment of first yield in the
cross-section. Thus, the reduction factor of 0.85
is included in front of My in Equation 2 because
the strength and ductility of the composite
section are controlled by crushing of the
concrete slab at higher ratios of Dp/D’. For the
section to qualify as compact with adequate
ductility at the computed nominal flexural
resistance, the ratio of Dp, to D’ cannot exceed
5.0, as specified. Also, the value of the yield
moment My to be used in Equation 2 may be
computed as the specified minimum yield
strength of the beam or girder Fy, times the
section modulus of the short-term composite
section with respect to the tension flange, rather
than using the procedure specified in Article
6.10.3.1.2. The inherent conservatism of
Equation 2 is a result of the desire to ensure
adequate ductility of the composite section.
However, in many cases, permanent deflection
service limit state criteria will govern the design
of compact composite sections. Thus, it is
prudent to initially design these sections to
satisfy the permanent deflection service limit
state and then check the nominal flexural
resistance of the section at the strength limit
state.
The shape factor (Mp/My,) for composite
sections in positive flexure can be as high as 1.5.
Therefore, a considerable amount of yielding is
required to reach Mp, and this yielding reduces
the effective stiffness of the positive flexural
section. In continuous spans, the reduction in
stiffness can shift moment from positive flexural
regions to negative flexural regions. Therefore,
the actual moments in negative flexural regions
may be higher than those predicted by an elastic
analysis. Negative flexural sections would have
to have the capacity to sustain these higher
moments, unless some limits are placed on the

C6 - 18
extent of the yielding of the positive moment
section. This latter approach is used in the
Specification for continuous spans with
noncompact interior-support sections.
The live loading patterns causing the
maximum elastic moments in negative flexural
sections are different than those causing
maximum moments in positive flexural sections.
When the loading pattern causing maximum
positive flexural moments is applied, the
concurrent negative flexural moments are
usually below the flexural resistance of the
sections in those regions. Therefore, the
specifications conservatively allow additional
moment above My to be applied to positive
flexural sections of continuous spans with
noncompact interior support sections, not to
exceed the nominal flexural resistance given by
Equations 1 or 2 to ensure adequate ductility of
the composite section. Compact interior support
sections have sufficient capacity to sustain the
higher moments caused by the reduction in
stiffness of the positive flexural region. Thus,
the nominal flexural resistance of positive
flexural sections in members with compact
interior support sections is not limited due to the
effect of this moment shifting.
Note that Equation 4 requires the use of
the absolute value of the term (Mnp-Mcp).
C6.10.4.2.2b
The ductility requirement specified in
this Article is equivalent to the requirement
given in AASHTO (1995).
The ratio of Dp, to D' is limited to a
value of 5.0 to ensure that the tension flange of
the steel section reaches strain hardening prior to
crushing of the concrete slab. D' is defined as the
depth at which the composite section reaches its
theoretical plastic moment capacity Mp, when
the maximum strain in the concrete slab is at its
theoretical crushing strain. The term
(d+ts+th)/7.5 in the definition of D', hereafter
referred to as D', was derived by assuming that
the concrete slab is at the theoretical crushing
strain of 0.3 percent and that the tension flange
is at the assumed strain-hardening strain of 1.2
percent. The compression depth of the
composite section, Dp, was divided by a factor
of 1.5 to ensure that the actual neutral axis of the
composite section at the plastic moment is
always above the neutral axis computed using
the assumed strain values (Ansourian 1982).
From the results of a parametric analytical study
of 400 different composite steel sections,
including unsymmetrical as well as symmetrical
steel sections, as discussed in Wittry (1993), it
was determined that sections utilizing 250 MPa
steel reached Mp, at a ratio of Dp/D’ equal to
approximately 0.9, and sections utilizing 345
MPa steel reached Mp, at a ratio of Dp to D’
equal to approximately 0.7. Thus, 0.9 and 0.7 are
specified as the values to use for the factor,
which is multiplied by D* to compute D’ for 250
MPa and 345 MPa yield strength steels. A value
of 0.7, thought to be conservative based upon
limited data available in late 1998, is specified
for ASTM A709M, Grade HPS485W, until
more data is available. Equation 1 need not be
checked at sections where the stress in either
flange due to the factored loadings does not
exceed Rh, Fyf, because there will be insufficient
strain in the steel section at or below the yield
strength for a potential concrete crushing failure
of the deck to occur.
C6.10.4.2.3
Equation 2 defines a transition in the
nominal flexural resistance from Mp, to
approximately 0.7 My.
The nominal flexural resistance given by
Equation 2 is based on the inelastic buckling
strength of the compression flange and results
from a fit to available experimental data. The
equation considers the interaction of the web and
compression-flange slenderness in the
determination of the resistance of the section by
using a flange buckling coefficient, k, =
4.92/(2Dcp,/tw)1/2
, in computing the Qfl,
parameter in Equation 7. Qfl, is the ratio of the
buckling capacity of the flange to the yield
strength of the flange. The buckling coefficient
given above was based on the test results
reported in Johnson (1985) and data from other
available composite and noncomposite steel
beam tests. A similar buckling coefficient is
given in Section B5.3 of AISC (1993). Equation
6 is specified to compute Qfl, if the compression-
flange slenderness Is less than the value
specified in Article 6.10.4.1.3 to effectively limit

C6 - 19
the increase in the bending resistance at a given
web slenderness with a reduction in the
compression-flange slenderness below this
value. Equation 6 is obtained by substituting the
compression-flange slenderness limit from
Article 6.10.4.1.3 in Equation 7.
Equation 2 represents a linear fit of the
experimental data between a flexural resistance
of Mp, and 0.7 My. The Qp, parameter,defined as
the web and compression-flange slenderness to
reach a flexural resistance of Mp, was derived to
ensure the equation yields a linear fit to the
experimental data. Equation 2 was derived to
determine the maximum flexural resistance and
does not necessarily ensure a desired inelastic
rotation capacity. Sections in negative flexure
that are required to sustain plastic rotations may
be designed according to the procedures
specified in Article 6.10.10. If elastic procedures
are used and Equation 2 is not used to determine
the nominal flexural resistance, the resistance
shall be determined according to the procedures
specified in Article 6.10.4.2.4.
C6.10.4.2.4a
For composite noncompact sections in
positive flexure in their final condition, the
nominal flexural resistance of the compression
flange at the strength limit state is equal to the
yield stress of the flange, Fyc, reduced by the
specified reduction factors. For all other
noncompact sections in their final condition and
for constructibility, where the limiting value of
Article 6.10.4.1.9 is satisfied, the nominal
flexural resistance of the compression flange is
equal to Fcr, times the specified reduction
factors. Fcr, represents a critical compression-
flange local buckling stress, which cannot
exceed Fyc. For sections without longitudinal
web stiffeners, Fcr, depends on the actual
compression flange and web slenderness ratios.
This equation for Fcr, was not developed for
application to sections with longitudinal web
stiffeners. For those sections, the expression for
Fcr, was derived from the compression- flange
slenderness limit for braced noncompact
sections specified in the Load Factor Design
portion of the AASHTO Standard Specifications
(1996). By expressing the nominal flexural
resistance of the compression flange as a
function of Fcr, larger compression-flange
slenderness ratios may be used at more lightly
loaded sections for a given web slenderness. To
achieve a value of Fcr, at or near Fyc, at more
critical sections, a lower compression-flange
slenderness ratio will be required.
The nominal flexural resistance of the
compression-flange is also modified by the
hybrid factor Rh, and the load-shedding factor
Rb. Rh, accounts for the increase in flange stress
resulting from web yielding in hybrid girders
and is computed according to the provisions of
Article 6.10.4.3.1. Rh, should be taken as 1.0 for
constructibility checks because web yielding is
limited. Rh, accounts for the increase in
compression-flange stress resulting from local
web bend buckling and is computed according to
the provisions of Article 6.10.4.3.2. Rh, is
computed based on the actual stress fc, in the
compression flange due to the factored loading
under investigation, which should not exceed
Fyc.
C6.10.4.2.5a
The provisions for lateral-torsional
buckling in this article differ from those
specified in Article 6.10.4.2.6 because they
attempt to handle the complex general problem
of lateral-torsional buckling of a constant or
variable depth section with stepped flanges
constrained against lateral displacement at the
top flange by the composite concrete slab. The
equations provided in this article are based on
the assumption that only the flexural stiffness of
the compression flange will prevent the lateral
displacement of that element between brace
points, which ignores the effect of the restraint
offered by the concrete slab (Basler and
Thurlimann 1961). As such, the behavior of a
compression flange in resisting lateral buckling
between brace points is assumed to be analogous
to that of a column. These simplified equations,
developed based on this assumption, are felt to
yield conservative results for composite sections
under the various conditions listed above.
The effect of the variation in the
compressive force along the length between
brace points is accounted for by using the factor
Cb. If the cross-section is constant between brace
points, Ml/Mh, is expressed in terms of Pl/Ph and

C6 - 20
may be used in calculating Cb. The ratio is taken
as positive when the moments cause single
curvature within the unbraced length.
Cb has a minimum value of 1.0 when
the flange compressive force and corresponding
moment are constant over the unbraced length.
As the compressive force at one of the brace
points is progressively reduced. Cb, becomes
lamer and is taken as 1.75 when this force is 0.0.
For the case of single curvature, it is
conservative and convenient to use the
maximum moments from the moment envelope
at both brace points in computing the ratio of
Ml/Mh, or Pl/Ph, although the actual behavior
depends on the concurrent moments at these
points.
If the force at the end is then
progressively increased in tension, which results
in reverse curvature, the ratio is taken as
negative and, continues to increase. However, in
this case, Using the concurrent moments at the
brace points, which are not normally tracked in
the analysis, to compute the ratio in Equation 4
gives the lowest value of Cb, Therefore, Cb, is
conservatively limited to a maximum value of
1.75 if the moment envelope values at both
brace points are used to compute the ratio in
Equation 4. If the concurrent moment at the
brace point with the lower compression-flange
force is available from the analysis and is used
to compute the ratio, Cb, is allowed to exceed
1.75 up to a maximum value of 2.3.
An alternative formulation for Cb is
given by the following formula (AISC 1993):
This formulation gives improved results
for the cases of nonlinear moment gradients and
moment reversal.
The effect of a variation in the lateral
stiffness properties, rt, between brace points can
be conservatively accounted for by using the
minimum value that occurs anywhere between
the brace points. Alternatively, a weighted
average rt, could be used to provide a reasonable
but somewhat less conservative answer.
The use of the moment envelope values
at both brace Points will be conservative for
both single and reverse curvature when this
formulation is used.
Other formulations for Cb, to handle
nontypical cases of compression flange bracing
may be found in Galambos (1998).
C6.10. 4.2.6a
Much of the discussion of the lateral
buckling formulas in Article C6.10.4.2.5a also
applies to this article. The formulas of this
article are simplifications of the formulas
presented in AISC (1993) and Kitipornchai and
Trahair (1980) for the lateral buckling capacity
of unsymmetrical girders.
The formulas predict the lateral buckling
moment within approximately 10 percent of the
more complex Trahair equations for sections
satisfying the proportions specified in Article
6.10.2.1. The formulas treat girders with slender
webs differently than girders with stocky webs.
For sections with stocky webs with a web
slenderness less than or equal to λb(E/Fyc)ln, or
with longitudinally stiffened webs, bend-
buckling of the web is theoretically prevented.
For these sections, the St. Venant torsional
stiffness and the warping torsional stiffness are
included in computing the elastic lateral
buckling moment given by Equation 1. For
sections with thinner webs or without
longitudinal stiffeners, cross-sectional distortion
is possible; thus, the St. Venant torsional
stiffness is ignored for these sections. Equation 3
is the elastic lateral torsional buckling moment
given by Equation 1 with J taken as 0.0.
Equation 2 represents a straight line
estimate of the inelastic lateral buckling
resistance between Rb Rh My and 0.5 Rb Rh My.

C6 - 21
A straight line transition similar to this is not
included for sections with stocky webs or
longitudinally stiffened webs because the added
complexity is not justified.
A discussion of the derivation of the
value of λb, may be found in Article
C6.10.4.3.2a.
The equation for J herein is a special
case of Equation C4.6.2.1-1.
C6.10.4.3.1a
This factor accounts for the nonlinear
variation of stresses caused by yielding of the
lower strength steel in the web of a hybrid beam.
The formulas defining this factor are the same as
those given in AASHTO (1996) and are based
on experimental and theoretical studies of
composite and noncomposite beams and girders
(ASCE 1968; Schilling 1968; and Schilling and
Frost 1964). The factor applies to noncompact
sections in both shored and unshored
construction.
C6.10.4.3.1c
Equation 1 approximates the reduction
in the moment resistance due to yielding for a
girder with the neutral axis located at middepth
of the web. For girders with the neutral axis
located within 10 percent of the depth from the
middepth of the web, the change of the value of
Rh from that given by Equation 1 is thought to
be small enough to ignore. Equation 2 gives a
more accurate procedure to determine the
reduction in the moment resistance.
The following approximate method
illustrated in Figure C1 may be used in
determining the yield moment resistance, Myr,
when web yielding is accounted for. The solid
line connecting Fyf, with fr represents the
distribution of stress at My if web yielding is
neglected. For unshored construction, this
distribution can be obtained by first applying the
proper permanent load to the steel section, then
applying the proper permanent load and live
load to the composite section, and combining the
two stress distributions. The dashed lines define
a triangular stress block whose moment about
the neutral axis is subtracted from My to account
for the web yielding at a lower stress than the
flange. My may be determined as specified in
Article 6.10.3.1.2. Thus,
Figure 1 is specifically for the case
where the elastic neutral axis is above middepth
of the web and web yielding occurs only below
the neutral axis. However, the same approach
can be used if web yielding occurs both above
and below the neutral axis or only above the
neutral axis. The moment due to each triangular
stress block due to web yielding must be
subtracted from My.
This approach is approximate because
web yielding causes a small shift in the location
of the neutral axis. The effect of this shift on
Myr, is almost always small enough to be
neglected. The exact value of Myr, can be
calculated from the stress distribution by
accounting for yielding (Schilling 1968).

C6 - 22
C6.10.4.3.2a
The Rb factor is a postbuckling strength
reduction factor that accounts for the nonlinear
variation of stresses caused by local buckling of
slender webs subjected to flexural stresses. The
factor recognizes the reduction in the section
resistance caused by the resulting shedding of
the compressive stresses in the web to the
compression-flange.
For webs without longitudinal stiffeners
that satisfy Equation 1 with the compression-
flange at a stress fc, the Rb factor is taken equal
to 1.0 since the web is below its theoretical elask
bend-buckling stress. The value of λb, in
Equation 1 reflects different assumptions of
support provided to the web by the flanges. The
value of 4.64 for sections where Dc, is greater
than D/2 is based on the theoretical elastic bend-
buckling coefficient k of 23.9 for simply
supported boundary conditions at the flanges.
The value of 5.76 for members where Dc, is less
than or equal to D/2 is based on a value of k
between the value for simply supported
boundary conditions and the theoretical k value
of 39.6 for fixed boundary conditions at the
flanges (Timoshenko and Gere 1961).
For webs with one or two longitudinal
stiffeners that satisfy Equation 2 with the
compression-flange at a stress fc, the Rb factor is
again taken equal to 1.0 since the web is below
its theoretical elastic bend-buckling stress. Two
different theoretical elastic bend-buckling
coefficients k are specified for webs with one or
two longitudinal stiffeners. The value of k to be
used depends on the location of the closest
longitudinal web stiffener to the compression-
flange with respect to its optimum location
(Frank and Helwig 1995).
Equations 4 and 5 specify the value of k
for a longitudinally stiffened web. The equation
to be used depends on the location of the critical
longitudinal web stiffener with respect to a
theoretical optimum location of 0.4Dc, (Vincent
1969) from the compression-flange. The
specified k values and the associated optimum
stiffener location assume simply supported
boundary conditions at the flanges. Changes in
flange size along the girder cause Dc, to vary
along the length of the girder. If the longitudinal
stiffener is located a fixed distance from the
compression-flange, which is normally the case,
the stiffener cannot be at its optimum location
all along the girder. Also, the position of the
longitudinal stiffener relative to Dc, in a
composite girder changes due to the shift in the
location of the neutral axis after the concrete
slab hardens. This shift in the neutral axis is
particularly evident in regions of positive
flexure. Thus, the specification equations for k
allow the Engineer to compute the web bend-
buckling capacity for any position of the
longitudinal stiffener with respect to Dc. When
the distance from the longitudinal stiffener to the
compression-flange ds, is less than 0.4Dc, the
stiffener is above its optimum location and web
bend-buckling occurs in the panel between the
stiffener and the tension flange. When ds, is
greater than 0.4Dc, web bend- buckling occurs in
the panel between the stiffener and the
compression-flange. When d, is equal to 0.4Dc,
the stiffener is at its optimum location and bend-
buckling occurs in both panels. For this case,
both equations yield a value of k equal to 129.3
for a symmetrical girder (Dubas 1948).
Since a longitudinally stiffened web
must be investigated for the stress conditions at
different limit states and at various locations
along the girder, it is possible that the stiffener
might be located at an inefficient location for a
particular condition resulting in a very low bend-
buckling coefficient from Equation 4 or 5.
Because simply-supported boundary conditions
were assumed in the development of Equations 4
and 5, it is conceivable that the computed web
bend-buckling resistance for the longitudinally
stiffened web may be less than that computed
for a web without longitudinal stiffeners where
some rotational restraint from the flanges has
been assumed. To prevent this anomaly, the
specifications state that the k value for a
longitudinally stiffened web must equal or
exceed a value of 9.0(D/Dc)2
, which is the k
value for a web without longitudinal stiffeners
computed assuming partial rotational restraint
from the flanges. Also, near points of dead load
contraflexure, both edges of the web may be in
compression when stresses in the steel and
composite sections due to moments of opposite
sign are accumulated. In this case, the neutral
axis lies outside the web. Thus, the
specifications also limit the minimum value of k

C6 - 23
to 7.2, which is approximately equal to the
theoretical bend-buckling coefficient for a web
plate under uniform compression assuming fixed
boundary conditions at the flanges (Timoshenko
and Gere 1961).
Equation 3 is based on extensive
experimental and theoretical studies (Galambos
1988) and represents the exact formulation for
the Rb, factor given by Basler (1961). For rare
cases where Equation 3 must be used to compute
Rb, at the strength limit state for composite
sections in regions of positive flexure, a separate
calculation should be performed to determine a
more appropriate value of Ac, to be used to
calculate ar, in Equation 6. For this particular
case, to be consistent with the original derivation
of Rb, it is recommended that Ac, be calculated
as a combined area for the top flange and the
transformed concrete slab that gives the
calculated value of D, for the composite section.
The following equation may be used to compute
such an effective combined value of Ac:
In addition, when the top flange is
composite, the stresses that are shed from the
web to the flange are resisted in proportion to
the relative stiffness of the steel flange and
concrete slab. The Rb, factor is to be applied
only to the stresses in the steel flange. Thus, in
this case, a modified & factor for the top flange,
termed R’b, can be computed as follows:
For a composite section with or without
a longitudinally stiffened web, Dc, must be
calculated according to the provisions of Article
6.10.3.1.4a.
C6.10.4.3.2b
Rb is 1.0 for tension flanges because the
increase in flange stresses due to web buckling
occurs primarily in the compression flange, and
the tension flange stress is not significantly
increased by the web buckling (Basler 1961).
C6.10.4.4
This provision gives partial recognition
to the philosophy of plastic design. Figure C1
illustrates the application of this provision in a
two-span continuous beam:
C6.10.5.1
The provisions are intended to apply to
the design live load specified in Article 3.6.1.1.
If this criterion were to be applied to a permit

C6 - 24
load situation, a reduction in the load factor for
live load should be considered.
This limit state check is intended to
prevent objectionable permanent deflections due
to expected severe traffic loadings that would
impair rideability. It corresponds to the overload
check in the 1996 AASHTO Standard
Specifications and is merely an indicator of
successful past practice, the development of
which is described in Vincent (1969).
Under the load combinations specified
in Table 3.4.1-1, the criterion for control of
permanent deflections does not govern for
composite noncompact sections; therefore, it
need not be checked for those sections. This may
not be the case under a different set of load
combinations.
Web bend buckling under Load
Combination Service II is controlled by limiting
the maximum compressive flexural stress in the
web to the elastic web bend buckling stress
given by Equation 6.10.3.2.2-1. For composite
sections, the appropriate value of the depth of
the web in compression in the elastic range, Dc,
specified in Article 6.10.3.1.4a, is to be used in
the equation.
Article 6.10.3.7 requires that 1 percent
longitudinal reinforcement be placed wherever
the tensile stress in the slab due to either
factored construction loads or due to Load
Combination Service II exceeds the factored
modulus of rupture of the concrete. By
controlling the crack size in regions where
adequate shear connection is also provided, the
concrete slab can be considered to be effective
in tension for computing flexural stresses on the
composite section due to Load Combination
Service II. If the concrete slab is assumed to be
fully effective in negative flexural regions, more
than half of the web will typically be in
compression increasing the susceptibility of the
web to bend buckling.
C6.10.5.2
A resistance factor is not applied
because the specified limit is a serviceability
criterion for which the resistance factor is 1.0.
C6.10.6.1
If the provisions specified in Articles
6.10.6.3 and 6.10.6.4 are satisfied, significant
elastic flexing of the web is not expected to
occur, and the member is assumed to be able to
sustain an infinite number of smaller loadings
without fatigue cracking.
These provisions are included here,
rather than in Article 6.6, because they involve a
check of maximum web buckling stresses
instead of a check of the stress ranges caused by
cyclic loading.
C6.10.6.3
The elastic bend-buckling capacity of
the web given by Equation 2 is based on an
elastic buckling coefficient, k, equal to 36.0.
This value is between the theoretical k value for
bending-buckling of 23.9 for simply supported
boundary conditions at the flanges and the
theoretical k value of 39.6 for fixed boundary
conditions at the flanges (Timoshenko and Gere
1961). This intermediate k value is used to
reflect the rotational restraint offered by the
flanges. The specified web slenderness limit of
5.70 (E/Fyw)1/2
is the web slenderness at which
the section reaches the yield strength according
to Equation 2.
Longitudinal stiffeners theoretically
prevent bend-buckling of the web; thus, the
provisions in this article do not apply to sections
with longitudinally stiffened webs.
For the loading and load combination
applicable to this limit state, it is assumed that
the entire cross-section will remain elastic and,
therefore, Dc, can be determined as specified in
Article 6.10.3.1 .4a.
C6.10.6.4
The shear force in unstiffened webs and
in webs of hybrid sections is already limited to
either the shear yielding or the shear buckling
force at the strength limit state by the provisions
of Article 6.10.7.2. Consequently, the
requirement in this article need not be checked
for those sections.
C6.10.7.1
This article applies to:

C6 - 25
 Sections without stiffeners,
 Sections with transverse stiffeners only, and
 Sections with both transverse and
longitudinal stiffeners.
A flow chart for shear capacity of I-
sections is shown below.
Unstiffened and stiffened interior web
panels are defined according to the maximum
transverse stiffener spacing requirements
specified in this article. The nominal shear
resistance of unstiffened web panels in both
homogeneous and hybrid sections is defined by
either shear yield or shear buckling, depending
on the web slenderness ratio, as specified in
Article 6.10.7.2. The nominal shear resistance of
stiffened interior web panels of homogeneous
sections is defined by the sum of the shear-
yielding or shear-buckling resistance and the
post-buckling resistance from tension-field
action, modified as necessary by any moment-
shear interaction effects, as specified in Article
6.10.7.3.3. For compact sections, this nominal
shear resistance is specified by either Equation
6.10.7.3.3a-1 or Equation 6.10.7.3.3a-2. For
noncompact sections, this nominal shear
resistance is specified by either Equation
6.10.7.3.3b-1 or Equation 6.10.7.3.3b-2. For
homogeneous sections, the nominal shear
resistance of end panels in stiffened webs is
defined by either shear yielding or shear
buckling, as specified in Article 6.10.7.3.3c. For
hybrid sections, the nominal shear resistance of
all stiffened web panels is defined by either
shear yielding or shear buckling, as specified in
Article 6.10.7.3.4.
Separate interaction equations are given
to define the effect of concurrent moment for
compact and noncompact sections because
compact sections are designed in terms of
moments, whereas noncompact sections are
designed in terms of stresses. For convenience, it
is conservatively specified that the maximum
moments and shears from the moment and shear
envelopes be used in the interaction equations.
C6.10.7.2
The nominal shear resistance of
unstiffened webs of hybrid and homogeneous
girders is limited to the elastic shear buckling
force given by Equation 1. The consideration of
tension-field action (Basler 1961) is not
permitted for unstiffened webs. The elastic shear
buckling force is calculated as the Product of the
constant C specified in Article 6.10.7.3.3a times
the plastic shear force, Vp, given by Equation 2.
The plastic shear force is equal to the web area
times the assumed shear yield strength of
Fyw/(3)0.5
. The shear bucking coefficient, k, to be
used in calculating the constant C is defined as
5.0 for unstiffened web panels, which is a
conservative approximation of the exact value of
5.35 for an infinitely long strip, with simply
supported edges (Timoshenko and Gere 1961).
C6.10.7.3.1
Longitudinal stiffeners divide a web
panel into subpanels. The shear resistance of the
entire panel can be taken as the sum of the shear
resistance of the subpanels (Cooper 1967).
However, the contribution of the longitudinal
stiffener at a distance of 2Dc/5 from the
compression flange is relatively small. Thus, it is
conservatively recommended that the influence
of the longitudinal stiffener be neglected in

C6 - 26
computing the nominal shear resistance of the
web plate.
C6.10.7.3.2
Transverse stiffeners are required on
web panels with a slenderness ratio greater than
150 in order to facilitate handling of sections
without longitudinal stiffeners during fabrication
and erection. The spacing of the transverse
stiffeners is arbitrarily limited by Equation 2
(Basler 1961). Substituting a web slenderness of
150 into Equation 2 results in a maximum
transverse stiffener spacing of 3D, which
corresponds to the maximum spacing
requirement in Article 6.10.7.1 for web panels
without longitudinal stiffeners. For higher web
slenderness ratios, the maximum allowable
spacing is reduced to less than 3D.
The requirement in Equation 2 is not
needed for web panels with longitudinal
stiffeners because maximum transverse stiffener
spacing is already limited to 1.5D.
C6.10.7.3.3a
Stiffened interior web panels of
homogeneous sections may develop post-
buckling shear resistance due to tension-field
action (Basler 1961). The action is analogous to
that of the tension diagonals of a Pratt truss. The
nominal shear resistance of these panels can be
computed by summing the contributions of
beam action and of the post-buckling tension-
field action. The resulting expression is given in
Equation 1, where the first term in the bracket
relates to either the shear yield or shear buckling
force and the second term relates to the post-
buckling tension-field force.
The coefficient, C, is equal to the ratio
of the elastic hear buckling stress of the panel,
computed assuming simply supported boundary
conditions, to the shear yield strength assumed
to be equal to Fyw/(3)0.5
. Equation 7 is applicable
only for C values not exceeding 0.8 (Basler
1961). Above 0.8, C values are given by
Equation 6 until a limiting slenderness ratio is
reached where the shear buckling stress is equal
to the shear yield strength and C = 1.0. Equation
8 for the shear buckling coefficient is a
simplification of two exact equations for k that
depend on the panel aspect ratio.
When both shear and flexural moment
are high in a stiffened interior panel under
tension-field action, the web plate must resist the
shear and also participate in resisting the
moment. Panels whose resistance is limited to
the shear buckling or shear yield force are not
subject to moment-shear interaction effects.
Basler (1961) shows that stiffened web plates in
noncompact sections are capable of resisting
both moment and shear, as long as the shear
force due to the factored loadings is less than
0.6φvVn or the flexural stress in the compression
flange due to the factored loading is less than
0.75φfFy. For compact sections, flexural
resistances are expressed in terms of moments
rather than stresses. For convenience, a limiting
moment of 0.5φfMp is defined rather than a
limiting moment of 0.75φfMy in determining
when the moment-shear interaction occurs by
using an assumed shape factor (Mp/My) of 1.5.
This eliminates the need to compute the yield
moment to simply check whether or not the
interaction effect applies. When the moment due
to factored loadings exceeds 0.5φfMp, the
nominal shear resistance is taken as Vn, given by
Equation 2, reduced by the specified interaction
factor, R.
Both upper and lower limits are placed
on the nominal shear resistance in Equation 2
determined by applying the interaction factor, R.
The lower limit is either the shear yield or shear
buckling force. Sections with a shape factor
below 1.5 could potentially exceed Vn,
according to the interaction equation at moments
due to the factored loadings slightly above the
defined limiting value of 0.5φfMp. Thus, for
compact sections, an upper limit of 1.0 is placed
on R.
To avoid the interaction effect,
transverse stiffeners may be spaced so that the
shear due to the factored loadings does not
exceed the larger of:
 0.60φvVn, where Vn, is given by Equation 1
or
 The factored shear buckling or shear yield
resistance equal to φvCVp.

C6 - 27
k is known as the shear buckling coefficient.
C6.10.7.3.3b
The commentary of Article 6.1 0.7.3.3a
applies, except that for noncompact sections,
flexural resistances are expressed in terms of
stress rather than moment in the interaction
equation. The upper limit of 1.0 applied to R in
Equation 6.10.7.3.3a-3 applies to compact
sections and need not be applied to Equation
6.10.7.3.3b-3 for noncompact sections.
C6.10.7.3.3c
The shear in end panels is limited to
either the shear yield or shear buckling force
given by Equation I in order to provide an
anchor for the tension field in adjacent interior
panels.
C6.10.7.3.4
Tension-field action is not permitted for
hybrid sections. Thus, the nominal shear
resistance is limited to either the shear yield or
the shear buckling force given by Equation 1.
C6.10.7.4.1b
The parameters I and Q should be
determined using the deck within the effective
flange width. However, in negative flexure
regions, the parameters I and Q may be
determined using the reinforcement within the
effective flange width for negative moment,
unless the concrete slab is considered to be fully
effective for negative moment in computing the
longitudinal range of stress, as permitted in
Article 6.6.1.2.1.
The maximum fatigue shear range is
produced by to the right of the point under
consideration. For the load in these positions,
positive moments are placing the fatigue live
load immediately to the left and produced over
significant portions of the girder length. Thus,
the use of the full composite section, including
the concrete deck, is reasonable for computing
the shear range along the entire span. Also, the
horizontal shear force in the deck is most often
considered to be effective along the entire span
in the analysis. To satisfy this assumption, the
shear force in the deck must be developed along
the entire span. An option is permitted to ignore
the concrete deck in computing the shear range
in regions of negative flexure, unless the
concrete is considered to be fully effective in
computing the longitudinal range of stress, in
which case the shear force in the deck must be
developed. If the concrete is ignored in these
regions, the specified maximum pitch must not
be exceeded.
C6.10.7.4.1d
Stud connectors should penetrate
through the haunch between the bottom of the
deck and top flange, if present, and into the
deck. Otherwise, the haunch should be
reinforced to contain the stud connector and
develop its load in the deck.
C6.10.7.4.2
For development of this information, see
Slutter and Fisher (1966).
C6.10.7.4.3
The purpose of the additional connectors
is to develop the reinforcing bars used as part of
the negative flexural composite section.
C6.10.7.4.4b
Composite beams in which the
longitudinal spacing of shear connectors has
been varied according to the intensity of shear
and duplicate beams where the number of
connectors were uniformly spaced have
exhibited essentially the same ultimate strength
and the same amount of deflection at service
loads. Only a slight deformation in the concrete
and the more heavily stressed connectors is
needed to redistribute the horizontal shear to
other less heavily stressed connectors. The
important consideration is that the total number
of connectors be sufficient to develop the shear,
Vh, on either side of the point of maximum
moment.
In negative flexure regions, sufficient
shear connectors are required to transfer the

C6 - 28
ultimate tensile force in the reinforcement from
the slab to the steel section.
C6.10.7.4.4c
Studies have defined stud shear
connector strength as a function of both the
concrete modulus of elasticity and concrete
strength (Ollgaard et al. 1971). Note that an
upper bound on stud shear strength is the
product of the cross-sectional area of the stud
times its ultimate tensile strength.
Equation 2 is a modified form of the
formula for the resistance of channel shear
connectors developed in Slutter and Driscoll
(1965), which extended its use to low-density as
well as normal density concrete.
C6.10.8.1.2
The requirements in this article are
intended to prevent local buckling of the
transverse stiffener.
C6.10.8.1.3
For the web to adequately develop the
tension field, the transverse stiffener must have
sufficient rigidity to cause a node to form along
the line of the stiffener. For ratios of (do/D) less
than 1.0, much larger values of It, are required,
as discussed in Timoshenko and Gere (1961).
Lateral loads along the length of a
longitudinal stiffener are transferred to the
adjacent transverse stiffeners as concentrated
reactions (Cooper 1967). Equation 3 gives a
relationship between the moments of inertia of
the longitudinal and transverse stiffeners to
ensure that the latter does not fail under the
concentrated reactions. Equation 3 is equivalent
to Equation 10-111 in AASHTO (1996).
C6.10.8.1.4
Transverse stiffeners need sufficient
area to resist the vertical component of the
tension field. The formula for the required
stiffener area can give a negative result. In that
case, the required area is 0.0. A negative result
indicates that the web alone is sufficient to resist
the vertical component of the tension field. The
stiffener then need only be proportioned for
stiffness according to Article 6.10.8.1.3 and
satisfy the projecting width requirements of
Article 6.10.8.1.2. For web panels not required
to develop a tension field, this requirement need
not be investigated.
C6.10.8.2.1
Inadequate provision to resist
concentrated loads has resulted in failures,
particularly in temporary construction.
If an owner chooses not to utilize
bearing stiffeners where specified in this article,
the web crippling provisions of AISC (1993)
should be used to investigate the adequacy of the
component to resist a concentrated load.
C6.10.8.2.2
The provision specified in this article is
intended to prevent local buckling of the bearing
stiffener plates.
C6.10.8.2.3
To bring bearing stiffener plates tight
against the flanges, part of the stiffener must be
clipped to clear the web-to-flange fillet weld.
Thus, the area of direct bearing is less than the
gross area of the stiffener. The bearing
resistance is based on this bearing area and the
yield strength of the stiffener.
C6.10.8.2.4a
A portion of the web is assumed to act
in combination with the bearing stiffener plates.
The end restraint against column
buckling provided by the flanges allows for the
use of a reduced effective length.
The web of hybrid girders is not
included in the computation of the radius of
gyration because the web may be yielding due to
longitudinal flexural stress. At end supports
where the moment is 0.0, the web may be
included.
C6.10.8.3.1

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