Elastic Stresses in Unshored Composite Section
The elastic stresses at any location shall be the sum of
stresses caused by appropriate loads applied separately
Steel beam
Permanent loads applied before the slab has hardened, are
carried by the steel section.
Short

term composite section
Transient loads (such as live loads) are assumed to be carried
by short

term composite action. The short

term modular ratio,
n
, should be used.
Long

term composite section.
Permanent loads applied after the slab has been hardened are
carried by the long

term composite section. The long

term
modular ratio, 3
n
, should be used.
Elastic Stresses
(6.10.1.1)
Original section
Transformed section
b
b/n
y
t
y
b
t
t
tr
b
sb
I
My
f
tr
t
ct
nI
My
f
The procedure shown in this
picture is only valid if the neutral
axis is not in the concrete.
Use iterations otherwise.
Elastic Stresses
(6.10.1.1)
Effective Width (Interior)
According to AASHTO

LRFD 4.6.2.6.1, the effective width
for interior girders is to be taken as the smallest of:
One quarter of the effective span length (span length in
simply supported beams and distance between
permanent load inflection points in continuous beams).
Average center

to

center spacing.
Twelve times the slab thickness plus the top flange width.
Hybrid Sections 6.10.3, 6.10.1.10
The web yield strength must be:
1.20 f
yf
≥
fyw
≥ 0.70 f
yf
and
f
yw
≥ 36 ksi
The hybrid girder reduction factor = R
h
Where,
b
=2 D
n
t
w
/ A
fn
D
n
= larger of distance from elastic NA to inside flange face
A
fn
= flange area on the side of NA corresponding to D
n
f
n
= yield stress corresponding to A
fn
b
b
2
12
)
3
(
12
3
h
R
Additional sections
6.10.1.4
–
Variable web depth members
6.10.1.5
–
Stiffness
6.10.1.6
–
Flange stresses and bending moments
6.10.1.7
–
Minimum negative flexure concrete deck rft.
6.10.1.8
–
Net section fracture
Web Bend

Buckling Resistance
(6.10.1.9)
For webs without longitudinal stiffeners, the nominal bend buckling
resistance shall be taken as:
When the section is composite and in positive flexure R
b
=1.0
When the section has one or more longitudinal stiffeners,
and D/t
w
≤ 0.95 (E k /F
yc
)
0.5
then R
b
= 1.0
When 2D
c
/t
w
≤ 5.7 (E / F
yc
)
0.5
then R
b
= 1.0
2
2
0.9
9
,
/
,
crw
w
c
c
Ek
F
D
t
where k bend buckling coefficient
D D
where D depth of web in compression in elastic ra
nge
Web Bend

Buckling Reduction
(6.10.1.10)
If the previous conditions are not met then:
2
1 1.0
1200 300
,5.7
2
wc c
b rw
wc w
rw
yc
c w
wc
fc fc
a D
R
a t
E
where
F
D t
and a
b t
Calculating the depth D
c
and D
cp
(App. D6.3)
For composite sections in positive flexure, the depth of the
web in compression in the elastic range D
c
, shall be the
depth over which the algebraic sum of the stresses in the
steel, the long

term composite and short term composite
section is compressive
In lieu, you can use
f
n
IM
LL
n
WS
DC
steel
DC
IM
LL
WS
DC
DC
c
t
c
f
c
f
f
c
f
f
f
f
f
D
3
2
1
2
1
0
,sec
c
c fc
c t
c t
f
D d t
f f
where d depth of steel tion
f and f are the compression and tension flange st
resses
Calculating the depth D
c
and D
cp
(App. D6.3)
For composite sections in positive flexure, the depth of the
web in compression at the plastic moment D
cp
shall be
taken as follows for the case of PNA in the web:
1
85
.
0
2
'
w
yw
r
yr
s
c
c
yc
t
yt
cp
A
F
A
F
A
f
A
F
A
F
D
D
6.10 I

shaped Steel Girder Design
Proportioning the section (6.10.2)
Webs without longitudinal stiffeners must be limited to
D/t
w
≤ 150
Webs with longitudinal stiffeners must be limited to
D/t
w
≤ 300
Compression and tension flanges must be proportioned
such that:
/6
12.0
2
1.1
0.1 10
f
f
f
f w
yc
yt
b D
b
t
t t
I
I
Slender
Noncompact
Compact
Moment
Curvature
M
p
M
y
Section Behavior
6.10 I

Shaped Steel Girder Design
Strength limit state 6.10.6
Composite sections in positive flexure (6.10.6.2.2)
Classified as compact section if:
Flange yield stress (F
yf
)
≤ 70 ksi
where, D
cp
is the depth of the web in compression at the
plastic moment
Classified as non

compact section if requirement not met
Compact section designed using Section 6.10.7.1
Non

compact section designed using Section 6.10.7.2
2
3.76
cp
w yc
D
E
t F
6.10.7 Flexural Resistance
Composite Sections in Positive Flexure
Compact sections
At the strength limit state, the section must satisfy
If D
p
≤ 0.1 D
t
, then M
n
= M
p
Otherwise, M
n
= M
p
(1.07
–
0.7 D
p
/D
t
)
Where, D
p
= distance from top of deck to the N.A. of the
composite section at the plastic moment.
D
t
= total depth of composite section
For continuous spans, M
n
= 1.3 M
y
. This limit allows for
better design with respect to moment redistributions.
1
3
n
u l xt f
M f S M
6.10.7 Flexural Resistance
Composite Sections in Positive Flexure
Non

Compact sections (6.10.7.2)
At the strength limit state:
The compression flange must satisfy
f
bu
≤
f
F
nc
The tension flange must satisfy
f
bu
+ f
l
/3
≤
f
F
nt
Nominal flexural resistance
F
nc
= R
b
R
h
F
yc
Nominal flexural resistance
F
nt
= R
h
F
yt
Where,
R
b
= web bend buckling reduction factor
R
h
= hybrid section reduction factor
Ductility requirement.
Compact and non

compact sections
shall satisfy D
p
≤ 0.42 D
t
This requirement intends to protect the concrete deck
from premature crushing. The D
p
/D
t
ratio is lowered to
0.42 to ensure significant yielding of the bottom flange
when the crushing strain is reached at the top of deck.
6.10.7 Flexural Resistance
Composite Sections in Positive Flexure
6.10 I

Shaped Steel Girder Design
Composite Sections in Negative Flexure and Non

composite Sections (6.10.6.2.2)
Sections with F
yf
≤ 70 ksi
Web satisfies the non

compact slenderness limit
Where, D
c
= depth of web in compression in elastic range.
Designed using provisions for compact or non

compact web
section specified in App. A.
Can be designed conservatively using Section 6.8
If you use 6.8, moment capacity limited to M
y
If use App. A., get greater moment capacity than M
y
2
5.7
c
w yc
D
E
t F
6.10.8 Flexural Resistance Composite Sections in
Negative Flexure and Non

Composite Section
Discretely braced flanges in compression
Discretely braced flanges in tension
Continuously braced flanges: f
bu
≤
f
R
h
F
yf
Compression flange flexural resistance = F
nc
shall be taken
as the smaller of the local buckling resistance and the
lateral torsional buckling resistance.
Tension flange flexural resistance = F
nt
= R
h
F
yt
1
3
nc
bu l f
f f F
1
3
nt
bu l f
f f F
Flange Local buckling or Lateral Torsional
Buckling Resistance
F
n
or M
n
L
b
Inelastic Buckling
(non

compact)
Elastic Buckling
(Slender)
L
p
F
max
or M
max
Inelastic Buckling
(Compact)
pf
L
r
rf
f
F
yr
or M
r
6.10.8 Flexural Resistance Composite Sections in
Negative Flexure and Non

Composite Section
F
nc
Compression flange flexural resistance
–
local buckling
0.38 0.56
2
,
,1 1
0.7
fc
f pf rf
fc yc yr
f pf nc b h yc
yr f pf
f rf nc b h yc
h yc rf pf
yr yc
b
E E
t F F
When F R R F
F
When F R R F
R F
F F
F
nc
Compression flange flexural resistance
Lateral torsional buckling
2 2
1 1
2 2
1.0
,
,1 1
,
,
1.75 1.05 0.3 2.3
b p t rf t
yc yr
b p nc b h yc
yr b p
b r nc b b h yc b h yc
h yc r p
b r nc cr b h yc
b
E E
L L r r
F F
When L L F R R F
F L L
When L L F C R R F R R F
R F L L
When L L F F R R F
Where
f f
C
f f
2
2
12 1
3
b b
cr
b
t
fc
t
c w
fc fc
C R E
F
L
r
b
r
D t
b t
Lateral Torsional Buckling
Unstiffened Web Buckling in Shear
y
F
E
46
.
2
D/t
w
Web plastification in shear
Inelastic web buckling
Elastic web buckling
y
F
E
07
.
3
w
yw
p
n
t
D
F
V
V
.
58
.
0
2
1.48
n w yw
V t EF
D
E
t
V
w
n
3
55
.
4
6.10.9 Shear Resistance
–
Unstiffened webs
At the strength limit state, the webs must satisfy:
V
u
≤
v
V
n
Nominal resistance of unstiffened webs:
V
n
= V
cr
= C V
p
where, V
p
= 0.58 F
yw
D t
w
C = ratio of the shear buckling resistance to shear yield strength
k = 5 for unstiffened webs
2
,1.12;1.0
1.12
,1.12 1.40;
1.57
,1.40;
w yw
yw w yw yw
w
w yw yw
w
D Ek
If then C
t F
Ek D Ek E k
If then C
D
F t F F
t
D Ek E k
If then C
t F F
D
t
Tension Field Action
d
0
D
g
n cr TFA
V V V
Beam Action
Tension Field Action
6.10.9 Shear resistance
–
Stiffened Webs
Members with stiffened webs have interior and end panels.
The interior panels must be such that
Without longitudinal stiffeners and with a transverse
stiffener spacing (d
o
) < 3D
With one or more longitudinal stiffeners and transverse
stiffener spacing (d
o
) < 1.5 D
The transverse stiffener distance for end panels with or
without longitudinal stiffeners must be d
o
< 1.5 D
The nominal shear resistance of end panel is
V
n
= C (0.58 F
yw
D t
w
)
For this case
–
k is obtained using equation shown on next
page and d
o
= distance to stiffener
Shear Resistance of Interior Panels of Stiffened Webs
2
2
2
sec:2.5
0.87 (1 )
0.58
1
,
5
5
,0.58
w
fc fc ft ft
n yw w
o
o
o
n
Dt
If the tion is proportioned such that
b t b t
C
V F Dt C
d
D
where d transverse stiffener spacing
k shear buckling coefficient
d
D
If not thenV
2
0.87 (1 )
1
yw w
o o
C
F Dt C
d d
D D
Transverse Stiffener Spacing
Interior panel
End
panel
D
d
o
3
D
d
o
5
.
1
D
1.5
o
d D
Types of Stiffeners
D
1.5
o
d D
1.5
o
d D
Bearing
Stiffener
Transverse
Intermediate
Stiffener
Longitudinal
Stiffener
6.10.11 Design of Stiffeners
Transverse Intermediate Stiffeners
Consist of plates of angles bolted or welded to either one or
both sides of the web
Transverse stiffeners may be used as connection plates for
diaphragms or cross

frames
When they are not used as connection plates, then they shall
tight fit the compression flange, but need not be in bearing
with tension flange
When they are used as connection plates, they should be
welded or bolted to both top and bottom flanges
The distance between the end of the web

to

stiffener weld
and the near edge of the adjacent web

to

flange weld shall
not be less than 4 t
w
or more than 6 tw.
Transverse Intermediate Stiffeners
Less than 4
t
w
or more than 6
t
w
Single Plate
Double Plate
Angle
6.10.11 Design of Stiffeners
Projecting width of transverse stiffeners must satisfy:
b
t
≥ 2.0 + d/30
and b
f
/4 ≤ b
t
≤ 16 t
p
The transverse stiffener’s moment of inertia must satisfy:
I
t
≥ d
o
t
w
3
J
where, J = required ratio of the rigidity of one transverse
stiffener to that of the web plate = 2.5 (D/d
o
)
2
–
2.0 ≥ 2.5
I
t
= stiffener m.o.i. about edge in contact with web for
single stiffeners and about mid thickness for pairs.
Transverse stiffeners in web panels with longitudinal
stiffeners must also satisfy:
3.0
t
t l
l o
b
D
I I
b d
6.10.11 Design of Stiffeners
2
2
0.15 (1 ) 18
,
0.31
,1.0
1.8 sin
2.4 sin
yw
u
s w
w v n crs
crs
crs ys
t
p
F
V
D
A B C t
t V F
where F elastic local buckling stress
E
F F
b
t
and B for stiffener pairs
B for gle angle stiffener
B for gle plate stiffener
The stiffener strength must be greater than that required for
TFA to develop. Therefore, the area requirement is:
If this equation gives A
s
negative, it means that the web alone
is strong enough to develop the TFA forces. The stiffener
must be proportions for m.o.i. and width alone
6.10.11 Design of Stiffeners
Bearing Stiffeners must be placed on the web of built

up
sections at all bearing locations. Either bearing stiffeners will
be provided or the web will be checked for the limit states of:
Web yielding
–
Art. D6.5.2
Web crippling
–
Art. D6.5.3
Bearing stiffeners will consist of one or more plates or
angles welded or bolted to both sides of the web. The
stiffeners will extend the full depth of the web and as closely
as practical to the outer edges of the flanges.
The stiffeners shall be either mille to bear against the flange
or attached by full penetration welds.
6.10.11 Design of Stiffeners
To prevent local buckling before yielding, the following
should be satisfied.
The factored bearing resistance for the fitted ends of
bearing stiffeners shall be taken as:
The axial resistance shall be determined per column
provisions. The effective column length is 0.75D
It is not D because of the restraint offered by the top and
bottom flanges.
ys
p
t
F
E
t
b
48
.
0
1.4
sb pn ys
n
R A F
6.10.11 Design of Stiffeners
Interior panel
End
panel
D
d
o
3
D
d
o
5
.
1
D
b
t
t
p
9
t
w
9
t
w
9
t
w
General Considerations
Shear studs are needed to transfer the horizontal shear
that is developed between the concrete slab and steel
beam.
AASHTO

LRFD requires that full transfer (i.e. full
composite action) must be achieved.
Shear studs are placed throughout both simple and
continuous spans.
Two limit states must be considered: fatigue and shear.
Fatigue is discussed later.
Strength of Shear Studs
u
sc
c
c
sc
n
F
A
E
f
A
Q
'
5
.
0
Cross

sectional are of the stud in square inches
Minimum tensile strength of the stud (usually 60 ksi)
n
sc
r
Q
Q
0.85
Placement
A sufficient number of shear studs should be placed
between a point of zero moment and adjacent points of
maximum moment.
It is permissible to evenly distribute the shear studs along
the length they are needed in (between point of inflection
and point of maximum moment), since the studs have the
necessary ductility to accommodate the redistribution that
will take place.
Miscellaneous Rules
Minimum length = 4 x stud diameter
Minimum longitudinal spacing = 4 x stud diameter
Minimum transverse spacing = 4 x stud diameter
Maximum longitudinal spacing = 8 x slab thickness
Minimum lateral cover = 1".
Minimum vertical cover = 2”.
Minimum penetration into deck = 2”
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