Steel

Concrete Composite Beams
Steel
–
Concrete Composite Beams
AISC Chapter I
AISC pdf 138
Figure
1
–
Plastic stress distribution with compression in concrete slab
Figure
2

Strain Compatibility
Method
AISC pdf
144
Figure
3

Effective Width
Figure
4

Negative Moment Strength

Rebars in width
Composite Moment Capacity
Fully Composite versus Partially Composite
Steel

concrete composite beams are identified as being fully composite or
partially
composite. Lets
focus on positive moment strength. A fully composite steel

concrete composite b
eam has its rolled
shape entirely in tension. For rolled shapes with compact webs, the entire shape is at yield in tension. A
beam is fully composite
when
there are a sufficient number of shear connectors provided and the
concrete slab has adequate compres
sion strength.
Positive Moment Strength
For positive moment, the concrete slab carries compression. The steel shape carries tension
(fully
composite) or tension plus some
compression
(partially composite)
. The cross section is shown in
Figure
5
.
Figure
5
There are three cases to consider. The cases correspond to three potential locations of the plastic
neutral axis (PNA).
The PNA is the vertical location, usually expressed as a y

coordinate
, of the
transition
from compression stress to tension stress. For plastic analysis, stresses change from a maximum value
in compression to a maximum value in tension.
The three potential locations for the PNA are: 1)
At the top of steel
; 2)
In the top flange of t
he steel
shape, and; 3) In the web of the steel shape. We locate the PNA using equilibrium relations for
horizontal forces.
Total compressions due to bending must equal total tensions due to bending.
Eq.
1
PNA in Slab
A full
y composite beam has its steel shape entirely in tension. A fully composite beam has its PNA
at the
top of steel
(
Figure
6
).
The compression force in the slab is large enough to yield the steel shape in
tension.
Figure
6
The parameter
is the distance from the top of
the
steel falnge to the line of
action
of
the
compression force in the slab.
The thickness of the slab is
.
Moment strength is computed using a moment balance at the top of steel. The compression force
has a momen
t arm equal to
. The tension force
has
a moment arm equal to
when the steel
shape has all
fibers at yield in tension.
Eq.
2
Since
equals
, this becomes
Eq.
3
Tension and compression forces are related as
Eq.
4
Eq.
3
is re

written as
Eq.
5
Eq.
6
PNA in Top Flange
The compression force in the concrete slab may not be large enough to yield the steel shape in tension.
How does this happen? Usually
, we make it happen. We choose to install fewer shear connectors, and
so limit the force sent into the concrete slab.
The sum of the strengths of shear connectors is the force sent to the concrete slab.
Eq.
7
We use
Eq.
7
to compute the depth of compression block
.
If the force,
, is less than the yield force
of the steel shape
, then force equilibrium requires
compression stress in a portion
of the steel shape. Let’s say that the portion of steel in compression is
contained in the top flange. The pattern of stresses is shown in
Figure
7
. A parameter
is the distance
from the top fo steel to the PNA.
Figure
7
Force equilibrium is
Eq.
8
Eq.
8
relates
total
compression to net tension in the steel shape. We use this equ
ation to
compute
.
Eq.
9
The result of
Eq.
9
allows us to check whether the PNA is actually in the top flange. We compute
in
Eq.
9
and then compare
Eq.
10
For PNA in the top flange, moment strength
is
Eq.
11
PNA in Web
If we use even few
er shear connectors, there is less force in the concrete slab, and more of the steel
shape must be in compression to maintain force equilibrium. Note that the end point to this process is
one half of the steel shape in compression and one half in tension:
An
ordinary
steel
beam
.
For PNA in the web of the steel shape, force equilibrium becomes
Eq.
12
We use
Eq.
12
to compute
Eq.
13
We use
Eq.
13
to check that the PNA is in the web.
Eq.
14
The moment strength is
Eq.
15
Example

Composite Beam Flexural Strength
, Positiv
e Moment
Given:
W18 x 40
A992
As
11.8
in2
L
60
ft
d
17.9
in
P at
20
ft
bf
6.02
in
M
2 / 9 PL
tf
0.525
in
tw
0.315
in
f'c
3
ksi
t
6
in
be
10
ft
As Fy
590
k
Shear Connector
0.75
in
N
27.
6
conns
Qn
21
.
4
k
Case 1
P
20 ft
40 ft
28
28
Connectors
Concrete Crushing
1836
k
呥n獩s攠奩敬摩ng
590
k
卨敡爠eonne捴o牳
599
k
呥n獩s攠y楥汤楮gon瑲o汳Ⱐ瑨敲敦e牥r瑨ts猠愠晵alyompo獩瑥 c瑩tn.
0.85f’c
Fy
Y2
d
a
t
a
1⸹.
楮
夲
5⸰.
楮
䵮
619
武k
Case 2
P
20 ft
40 ft
15
15
Connectors
Concrete Crushing
1836
k
Tensile Yielding
590
k
Shear connectors
32
1
k
Shear connectors control. This is a partially composite beam.
0.85f’c
Fy
PNA
Y2
Y1
d
a
t
a
1.05
in
Y2
5.4
8
in
Y1
0.4
4
7
in
䵮
㔲
3
武k
Cas
e 3
P
20 ft
40 ft
8
8
Connectors
Concrete Crushing
1836
k
Tensile Yielding
590
k
Shear connectors
171
k
Shear connectors control. This is a partially composite beam.
0.85f’c
Fy
PNA
Y2
Y1
d
a
t
a
0.55
9
in
Y2
5.7
2
in
Y1
3.7
9
in
䵮
㐴
7
武k
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