CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
REFERENCES
 S16: §17 (Sub-clauses are specified in context below.)
 Handbook (11th Ed.): pp. 5-74–5-125; Tables 5-5, 5-6, 5-7.
KEY DEFINITIONS
Cover Slab: the concrete above the flutes of the steel deck.
Full Composite Action: the state where the interconnection between the steel and
the concrete is sufficient for the two materials to behave as if monolithic.
Partial Composite Action: the state where the interconnection between the steel
and the concrete permits some degree of horizontal slip at the interface.
Shear Stud: a “headed” solid cylindrical steel bar that is welded to the steel beam
top flange and encased in the concrete slab to permit composite action to occur.
Steel Deck: a light-gauge fluted galvanized steel stay-in-place form that is often
designed to carry the weight of the wet concrete without shoring.
INTRODUCTION
Engineers are always striving to optimise the use of materials. In both steel
buildings and steel bridges, concrete is placed as a floor or deck on the steel
framework to provide a loading surface. Particularly in positive moment regions, it
makes sense to interconnect the two materials to take advantage of the concrete
compressive capacity to increase the moment resistance of the section. This way,
the concrete is not merely more weight from the point of view of the steel beam,
but rather it contributes significantly to the strength of the system after it has cured.
If the materials are interconnected sufficiently so as to act together, it leads to what
we call composite action. Depending on whether the job is of a sufficient scale
(and the spans of sufficient length) to justify bringing the specialised welding
equipment onto the site and introducing another operation into the construction
sequence, this often leads to great economic advantages, in part by reducing the
sizes of the steel beams required. The composite system is also very stiff—
reducing the likelihood of vibration or deflection problems—and ductile.
We will focus on composite beams typical for building applications, although the
principles apply equally to composite bridge girders. Moreover, we will focus on
rolled steel W-shapes as the steel section, but composite flexural systems using
other rolled sections, welded plate girders, trusses, or joists are also used.
–1–
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R.G. DRIVER
SHEAR CONNECTION
Since shear connection is the whole reason that composite action can be attained, it
is useful to begin by discussing why it is called “shear” connection, what it
achieves, and how it is accomplished. To understand this, think back to your
Strength of Materials course and the development of shear stresses within a beam
under a moment gradient. Not only do vertical shear stresses develop to equilibrate
the applied transverse loads, but horizontal (longitudinal) shear stresses are also
required for complete equilibrium of the beam. It is implicit in a monolithic beam
made of a single material that these shear stresses can be resisted by the material,
and for most structural materials used for beams this does not represent a problem.
However, if the beam is made of individual pieces—say, the flanges and web
(could be either the same material or different)—the pieces have to be connected
by a means that provides enough strength to resist these longitudinal shear stresses.
In the case of a built-up welded steel I-girder, the welds between the web and
flanges are checked to ensure sufficient longitudinal shear capacity. In the case of a
composite beam, it is the steel section and the concrete slab that must be connected
for these shear stresses. This is the reason we refer to this connection as a shear
connection and the means by which it is achieved as shear connectors.
Consider the simple composite beam in the figure below, where it is assumed that
the concrete carries all of the compression and the steel all of the tension.
Technical
Stuff
The shear stresses arise due to
the moment gradient. Within a
constant-moment region,
therefore, theoretically no
interconnection is required.
Furthermore, under a
uniformly-distributed load, the
shear connectors theoretically
should be spaced closer together
near the pinned supports or
points of inflection than near the
maximum moment. Why?
Note that longitudinal shear stresses must develop
at the interface between the two materials to
maintain equilibrium of the two components
between the point of maximum moment and the
point of zero moment. (If no shear transfer occurs on this interface, the materials
act as two individual beams and the behaviour is then non-composite.) To resist the
longitudinal shear effectively, some form of interconnection is required.
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COMPOSITE BEAMS
R.G. DRIVER
Typically, the interconnection between the steel and concrete is made mechanically
by welding shear connectors to the beam top flange so that they extend up into the
concrete after it is cast. Although conceptually nearly any shape of connector could
be used, certain types are more common and have been proven in-service, as well
as in the lab. The following figure shows three methods of interconnection, with
the headed shear studs (or simply shear studs) in Figure (b) being by far the most
common (often with only one line of studs down the centre of the beam) and the
only kind discussed in detail in this course. Another possible, but less common,
type is similar to those shown in Figure (b) except that instead of a formed “head”,
they are simply hooked at the top. Headed or hooked shear connectors are referred
to in S16 as “end-welded studs” (although this term is rarely used in practice).
Tip
“Shear connector” is
a generic term and
“shear stud” refers to
a specific type of
shear connector.
Please never call
shear studs “bolts”!
Headed shear studs are commonly referred to by the proprietary name Nelson®
studs; however, they really should be referred to generically unless they really are
made by Nelson Stud Welding, Inc. These studs are welded to the top flange using
a specialised stud-welding “gun” that allows very rapid installation by a single
worker, either in the shop or in the field. Studs are available in several diameters,
but 19 mm (3/4 inch) and 22 mm (7/8 inch) are most
commonly used, although S16 [§17.6.5] requires
that the stud diameter, d, not exceed 2.5 times the
 If the flange is flexible as
thickness of the part to which it is welded (normally
compared to the force that the
the top flange). It also stipulates [§17.9.1] that the
attached stud is expected to
width of the part to which it is welded not be less
resist (assumed proportional
than 1.4d + 20 mm. This latter requirement is really
to the diameter), it can
for truss chords, since the width of the top flange of
a standard wide-flange section would provide plenty deform (or even tear),
reducing the effectiveness of
of room for the stud.
the shear transfer.
–3–
Technical
Stuff
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
Often it is more economical to use partial shear connection (as opposed to full
shear connection), where the number of shear studs provided is fewer than that
which would develop the full flexural capacity of the composite cross-section. This
can be because the design is controlled by deflection criteria and the full capacity
is not required, or simply that the savings in shear studs and associated labour is
greater than the additional cost of providing a slightly larger steel section. This
latter situation occurs frequently because the number of shear studs provided is not
directly proportional to the composite section capacity. In fact, as a rule-of-thumb,
providing about 50% of the shear studs required for full composite action results in
about 80% of the flexural capacity of the fully composite beam.
SOLID SLABS VS. RIBBED SLABS WITH STEEL DECK
Composite beams can incorporate solid slabs atop the steel section (left figure
below) or ribbed slabs (right figure below). The former provides more concrete
area for the same overall depth, but has a drawback in that the concrete usually
needs to be shored (i.e., temporarily supported by posts at a close spacing) during
curing due to the flat (traditional) formwork required.
t
Ribbed slabs are very common, primarily because they
arise from the use of galvanized corrugated—or
fluted—steel deck (with a variety of available
proprietary profiles and depths). The steel deck acts as
the concrete formwork and spans between steel section
top flanges. It can be designed with enough flexural
stiffness to support the wet concrete without shoring,
keeping the work area below free of obstructions.
Composite deck is used that incorporates embossments
that improve the interconnection between the concrete
–4–
Tip
Deck manufacturers
provide catalogues that
indicate allowable deck
spans for a given slab
thickness and under a
variety of conditions.
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
and the deck itself and allow the deck to act as slab reinforcement, with a similar
effect to reinforcing bars. The deck flutes can run either parallel or perpendicular
to the beam, a difference that is accounted for in the design procedures (discussed
below).
Tip
According to S16 [§17.3.4], the maximum deck The use of ribbed slabs and steel
depth, hd , is 80 mm and the minimum average
deck interconnected with steel
flute width, wd , is 50 mm. The thicknesses of
beams is sometimes referred to as
steel deck material used most commonly are
“hollow composite” construction.
0.76 mm (22 gauge), 0.91 mm (20 gauge), and
1.21 mm (18 gauge), although other thicknesses are available (these thicknesses
exclude coatings). If the material is too thin it can be damaged during construction.
The shear studs can be welded to the steel top flange right through up to two layers
of overlapping deck sheets as long as neither sheet is more than 1.52 mm thick
(16 gauge) excluding the zinc coating [§17.6.3]. Otherwise, holes must be cut in
the deck with a clearance sufficient for welding the stud directly to the flange.
SLAB REINFORCEMENT
Although the composite steel deck provides some reinforcement to the slab, S16
[§17.5] has other miscellaneous requirements where standard reinforcing bars need
to be provided, primarily for crack control. This section is simply to make you
aware that these provisions exist. We will not focus on these clauses in this course.
Usually welded wire mesh (WWM) is also provided in the slab for crack control.
DESIGN
Design of composite beams for flexure is dramatically different from the
procedures for either steel or concrete beams because the influence of both
materials must be accounted for and the appropriate interconnection must be
provided. By contrast, in the design of composite beams for shear the steel beam is
assumed to resist the full shear force [§17.3.2]. Therefore, the design method for
shear (described in CIVL 331) for steel beams applies also to composite beams and
it won’t be repeated here.
Effective Concrete Width, Thickness, and Area
Similar to what we did for concrete T-beams, an effective concrete slab width is
used in the design of composite beams. For slabs extending on both sides of the
steel section, the effective slab width, b, is the lesser of [§17.4.1]:
 0.25 times the composite beam span; and
 a distance extending half way to the next parallel support on each side.
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COMPOSITE BEAMS
R.G. DRIVER
For slabs extending on one side only of the steel section, the effective slab width,
b, is the width of the top flange of the steel section plus the lesser of [§17.4.2]:
 0.10 times the composite beam span; and
 half of the clear distance to the next parallel support.
If there is a small slab overhang on the other side of the steel section, which is
commonly the case, the overhang is included in the overall effective slab width, b.
Normally only the concrete above the flutes (the effective cover slab thickness, t) is
considered effective in contributing to the resistance of the design moments in
ribbed slabs. The minimum effective cover slab thickness permitted by S16 [§17.2]
is 65 mm. The full thickness, t, is effective in solid slabs.
The maximum effective concrete area is simply the effective width, b, multiplied
by the effective thickness, t. The contribution of any concrete in tension is
neglected. [§17.9.2]
Trap
Flexural Capacity
The factored moment resistance of a composite
Don’t forget that until the concrete
beam is based upon the ultimate capacity of the gains its strength it does not provide
cross-section; the slab is considered to provide
lateral support. However, the steel
full lateral support to the steel section (i.e., no
deck, when properly fastened to the
LTB!). The method for determining the flexural steel section, also provides lateral
capacity of a composite beam depends on the
support if the flutes run perpendicular
location of the plastic neutral axis. Three cases
to the axis of the steel member.
are addressed in S16 [§17.9.3]:
1. Full shear connection with the plastic neutral axis in the slab;
2. Full shear connection with the plastic neutral axis in the steel section; and
3. Partial shear connection (plastic neutral axis is always in the steel section).
Let’s consider solid slabs first. In each case, the location of the neutral axis can be
determined from an assessment of horizontal equilibrium. The moment capacity is
then determined from the force resultant magnitudes and their respective moment
arms. Note in advance that the maximum compressive force possible in the slab is
1cfcbt, where c = 0.65, and the maximum tensile force possible in the steel
section is AsFy , where  = 0.9. As was the case with conventional reinforced
concrete members, 1 = 0.85–0.0015fc  0.67. Now, consider three composite
beams with solid slabs that correspond to the three cases enumerated above.
–6–
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COMPOSITE BEAMS
R.G. DRIVER
Case 1—Full shear connection with the plastic neutral axis in the slab
The figure below depicts this situation, which occurs when 1cfcbt > AsFy .
Since the steel section is entirely in tension, the factored tensile force, Tr , is simply
equal to AsFy . However, the factored compressive force in the concrete, Cr, must
be less than 1cfcbt.
1 c fc
Tip
The forces act at
the centroids of the
areas over which
they are distributed
(i.e., a uniform
stress is assumed).
Denoting the depth of the compressive stress block as “a”, the compressive force in
the slab, Cr, and the tensile force in the steel, Tr , are:
Tip
Cr  1 c f cba
[1]
[2]
Tr  A s Fy
From horizontal equilibrium and Equations [1] and [2],
the depth of the compressive stress block is:
A s Fy
a
t
[3]
 1 c f cb
The “prime” symbol is
used with Cr when the
force is in the concrete.
[§17.9.3(a)]
The factored moment capacity, Mrc , of the composite section is therefore:
M rc  Tr e  A s Fy e
[4]
[§17.9.3(a)]
Finally, in order to ensure full composite action the longitudinal shear force that
develops between the two materials, Vh , must be resisted by shear connectors.
Therefore, the required sum of the factored resistances of all shear connectors
between the points of maximum and zero moment, Qr , is determined as follows:
Q r  Tr  A s Fy  Vh
[5]
[§17.9.3(a); §17.9.5]
–7–
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
Case 2—Full shear connection with the plastic neutral axis in the steel section
This case occurs when AsFy > 1cfcbt , resulting in a part of the total
compressive force being resisted by the steel section. The figure below depicts this
situation. Since the steel section is not entirely in tension, the tensile force in the
steel, Tr , is less than AsFy and the compressive force in the concrete, Cr, is equal
to 1cfcbt.
1 c fc
The compressive force in the concrete, Cr, is:
Cr   1 c f cbt
[6]
[§17.9.3(b)]
From equilibrium, the compressive force in the steel, Cr , is:
[7]
C r  Tr  Cr  A s Fy  C r   Cr 
A s Fy  Cr
2
[§17.9.3(b)]
The factored moment capacity, Mrc , of the composite section is therefore:
M rc  C r e  Cr e
[8]
[§17.9.3(b)]
Finally, in order to ensure full composite action, the required sum of the factored
resistances of all shear connectors between the points of maximum and zero
moment, Qr , is determined as follows:
Q r  Cr  1 c f cbt  Vh
[9]
[§17.9.3(b); §17.9.5]
Case 3—Partial shear connection (plastic neutral axis always in the steel section)
Partial shear connection implies that only some fraction of the number of shear
studs required for full composite action is provided. S16 permits this fraction to be
as low as 40% if the design is governed by strength requirements and 25% if it is
governed by serviceability considerations. If the shear transfer capacity falls below
these levels, the behaviour is assumed to be non-composite. [§17.9.4]
–8–
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
The figure below depicts partial composite action. Since the steel section is not
entirely in tension, the tensile force in the steel, Tr , is less than AsFy . Due to the
partial composite action, the compressive force in the concrete, Cr, is less than
1cfcbt.
1 c fc
Technical
Stuff
Actually, the entire
slab depth is in
compression, but
at a stress lower
than 1cfc. The
stress distribution
shown is idealised.
Because of the partial composite action, the part of the total concrete slab strength
that can develop is directly related to the capacity of the shear studs actually
provided, Qr . Therefore:
Cr  Q r  Vh  1 c f cbt
[10]
[§17.9.3(c); §17.9.6]
The depth of the compressive stress block is calculated as:
Cr
a

t
[11]
1 c f cb
[§17.9.3(c)]
From equilibrium, the compressive force in the steel, Cr , is (same as Case 2):
[12]
C r  Tr  Cr  A s Fy  C r   Cr 
A s Fy  Cr
2
[§17.9.3(c)]
The factored moment capacity, Mrc , of the partially composite section is therefore:
[13]
M rc  C r e  Cr e
[§17.9.3(c)]
Composite construction using corrugated steel deck (hollow composite constr.)
The flexural requirements discussed above for Cases 1 to 3 apply equally to
composite beams constructed with corrugated steel deck. The only difference is
that the concrete within the flutes is considered to be ineffective, so the maximum
depth of the compressive stress block, t, is taken as being from the top of the slab
to the top of the steel deck. No force (neither tension nor compression) is assumed
to be present within the depth of the deck flutes.
–9–
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COMPOSITE BEAMS
R.G. DRIVER
Negative moment capacity
Under a negative moment, the concrete is in tension and therefore considered to be
ineffective. Although S16 has provisions to include rebar (if properly anchored and
if sufficient shear studs are provided) in negative moment capacity calculations
[§17.9.7], normally the steel section is considered to act alone and the rebar
provided merely for crack control.
Class of Steel Section for Use in Composite Construction (Local Buckling)
You may have noticed that the composite flexural capacity equations presented
above are all based on the steel section reaching the fully plastic condition. Since
local buckling checks are required only when the flanges and web are at least
partially in compression, no such check is required as long as the neutral axis is in
the slab. Furthermore, if the neutral axis is in the top flange of the steel section, the
web is still fully in tension and the flange is only partially in compression with the
strains remaining very low. If the neutral axis is in the web of the steel section, the
chance of local buckling occurring increases, although the presence of the slab
reduces the compressive strains that will develop as compared to those in a
non-composite beam. S16 does not address local buckling of steel sections used in
composite beams head-on, but it is considered prudent to limit your choice to
Class 1 and 2 sections whenever the neutral axis falls within the steel section. (If
the neutral axis is within the top flange, checking the web is unnecessary.)
Design of Shear Studs
For headed shear studs to qualify for use, they must have a height, h, to diameter,
d, ratio of at least 4.0 and, in the case of hollow composite construction, they must
project above the deck flutes by at least two stud diameters, 2d, (heights are taken
prior to welding) in order to engage the concrete effectively
Tip
[§17.7.2.1]. Moreover, the longitudinal spacing of studs
along the steel flange must be at least six stud diameters, 6d,
No minimum clear
to ensure that each stud is surrounded by sufficient concrete
cover above the stud
[§17.7.2.5], and the spacing should be at most 1000 mm, to
head is specified in
ensure that the slab and steel section do not separate
S16. I recommend
significantly under factored loads [§17.7.2.5; §17.8]. The
20 mm as a minimum
average stud spacing in a span should not exceed 600 mm
for interior exposure.
[§17.8]. Finally, the transverse spacing of studs must be at
least four stud diameters, 4d, when more than one stud is needed at a cross-section
[§17.7.2.5]. (All stud spacing requirements above are given centre-to-centre.)
The factored capacity of a single shear stud, qr , has been defined mainly from test
results and it depends on several factors, including the environment of concrete
within which it is embedded. S16 addresses three cases [§17.7.2]:
– 10 –
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R.G. DRIVER
A. Solid slabs;
B. Ribbed slabs with ribs running parallel to the beam; and
C. Ribbed slabs with ribs running perpendicular to the beam.
Case A—Solid slabs
This is the “best-case scenario”. In fact, the other two cases (B and C) include a
check to ensure that the strength calculated is not greater than the capacity of the
same stud in a solid slab. The factored capacity of a single shear stud in a solid
slab, qrs (second subscript stands for “solid”), is:
[14]
q rs  0.50 sc A sc f c E c   sc A sc Fu
where Asc is the cross-sectional area of the shear
connector, Fu is the nominal ultimate tensile
strength of the shear connector (most commonly
450 MPa), and the other variables are well
known to you from the concrete part of the
course. The resistance factor used in the design
of the shear connectors, sc , is 0.80 [§17.7.1].
[§17.7.2.2]
Tip
Unless a better value is available,
Ec = 21,000 MPa is generally
conservative. Alternatively,
equations are available in A23.3
§8.6.2.2 and §8.6.2.3.
The second part of Equation [14] is from the observation that if shear studs do not
fail by crushing the concrete around the stud, they will eventually bend over and
fail in tension.
Case B—Ribbed slabs with ribs running parallel to the beam
In this case, the factored capacity of a single shear stud, qrr (second subscript stands
for “ribbed”), is:

 wd

 1.5   q rs
 hd

[15] if 3.0 > wd/hd ≥ 1.50 (“wide rib profile”), q rr  q rs 0.75  0.167

[§17.7.2.3(a)]

[16] if wd/hd < 1.50 (“narrow rib profile”), q rr   sc 0.92

wd
0.8
0. 2 
dh f c   11sd f c    0.75q rs
hd

[§17.7.2.3(b)]
where wd is the average (they are usually trapezoidally shaped) width of the deck
flutes that are filled with concrete, hd is the depth of the flutes, s is the longitudinal
stud spacing, and the other variables have been defined previously.
Case C—Ribbed slabs with ribs running perpendicular to the beam
In this case, the factored capacity of a single shear stud, qrr , is:
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[17] if hd = 75 mm,
q rr  0.35scA p f c  q rs
[§17.7.2.4(a)]
[18] if hd = 38 mm,
q rr  0.61scA p f c  q rs
[§17.7.2.4(b)]
where  = 1.0 for normal density and
 = 0.85 for semi-low-density concrete,
and Ap is the concrete pull-out area
taking the deck profile and stud welding
burn-off into account, and the other
variables have been defined previously.
Trap
Note that the deck profile depths, hd , that
distinguish between Equations [17] and
[18] might be misleading. Steel deck is
very often provided as 3 inch (76.2 mm)
or 1.5 inch (38.1 mm) deck. This is still
well within the spirit of the clause.
Calculating Ap is tedious. The following
figure from the S16 Commentary depicts the intent (lines are at 45°). Thankfully,
the Handbook provides assistance with these calculations in Tables 5-3 and 5-4.
I will not make you
do Ap calculations.
If studs are provided in pairs (i.e., two studs at the same
cross-section, and therefore in a single flute), Ap is
determined for the stud pair, with a ridge extending
between the tops of the two studs [§17.7.2.4]. In this case,
qrr is the capacity of the stud pair (which cannot be greater
than qrs for two studs).
Distribution of shear studs
The required sum of the factored resistances of all shear
studs between the points of maximum and zero moment,
Vh , was specified in the section entitled “Flexural
Capacity” above. The number of shear studs, n, required
within this region, therefore, is:
V
n h
[19]
qr
– 12 –
Tip
It is not unusual to have
a combination of single
studs and stud pairs on a
beam in Case C.
Trap
The total number of
studs on the beam will
be 2n, not n!
[§17.9.8]
CIVL 432
In general, the ductility
of the system allows the
shear studs to be spaced
uniformly (which is
especially convenient
when the deck ribs are
perpendicular to the
beam axis!). However,
in a region of positive
moment, the number of
shear studs, n, between
any concentrated load
and the nearest point of
zero moment must not
be less than:
[20]
COMPOSITE BEAMS
R.G. DRIVER
Tip
When deck flutes are perpendicular to the beam axis and
there are no concentrated loads, it is common practice to
specify that one stud be placed in every second flute
starting from each end of the beam until all “2n” studs
have been installed. If there are any studs remaining after
reaching mid-span, they are filled in from the ends of the
beam in the alternate flutes. If there are still studs left
over when every flute has a stud, they can be “doubled
up” where they are needed most (near the ends where the
moment gradient is steepest). If doubling-up is necessary,
recall that stud pairs may have a lower capacity than the
combined capacity of two single studs.
 M  Mr 

n  n  f 1

M
M
r 
 f
where Mf1 = factored moment at the concentrated load;
Mr = factored moment resistance of the steel; and
Mf = maximum positive factored moment.
Since the capacity of the steel section alone, Mr , does not
depend on the presence of shear studs, it is subtracted from
both Mf1 and Mf .
[§17.9.8]
Tip
Even if Equation [20]
needs to be checked, a
uniform stud spacing may
still turn out to be adequate.
Trap
If n results in a wider
Additional Shear Check on Vertical Planes for Solid Slabs
spacing in the region where
and Ribbed Slabs with Ribs Running Parallel to the Beam
the BMD is steepest, use a
As discussed previously, the compressive force present in
uniform spacing instead.
the slab at the point of maximum moment must be
equilibrated entirely by the point of zero moment through shear at the interface
between the steel and the concrete, and the requirements for selecting the shear
studs ensure that sufficient capacity is provided for this force transfer to take place.
For the same reason, certain other planes within the slab need to be checked to
ensure sufficient shear capacity.
Note that the general forms of the equations in S16 that are used to check these
shear planes account for the fact that rebar may be present in the slab in the two
directions. However, it is always conservative to neglect the rebar in the demand
and/or capacity equations presented below.
– 13 –
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
Consider the following figure of a composite beam with a ribbed slab extending
from the point of maximum moment to the point of zero moment.
Technical
Stuff
You might think that
qr in the Vu equation
should really be Vh
(i.e., the actual shear
force rather than the
shear strength).
However, the original
research recommends
that the capacity of all
of the studs be
developed prior to
failing the concrete
shear plane, even if
more studs are
provided than required,
in order to ensure a
ductile failure mode.
Tip
This check is
also required
for solid slabs.
The planes marked with the area Acv are the ones being checked. Any force that is
applied within the shaded area Ac does not need to be transferred across these
planes. Take Ac to be the area of the rectangular compressive stress block with the
depth “a” between the vertical planes marked Acv in the figure. (Using the depth
“a” is conservative, since more of the shaded area would attract compressive force
if the vertical planes actually started to fail.) The total shear force, Vu , to be
resisted on these vertical planes is:
[21]
Vu   q r   1 c f cA c   r A r Fyr
– 14 –
[§17.9.10]
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
where Ar (Arl in the figure) is the total area of the longitudinal reinforcing steel
within the shaded area Ac , Fyr is the nominal yield strength of these bars, and the
other variables have been defined previously. The resistance factor for the
reinforcing steel, r , is (as always) 0.85.
For normal-density concrete (equations for semi-low-density are available in the
literature), the factored shear resistance along the vertical planes marked Acv is:
Vr  0.80r A r Fyr  2.76c A cv   0.50c f cA cv
[§17.9.10]
[22]
Technical
Stuff
where Ar (Art in the figure) is the total
Note that no benefit is considered for
area of the transverse reinforcing steel
the shear resistance of the steel deck since
crossing the shear planes that constitute
no research is available to substantiate it.
Acv (i.e., counting two planes in this
Neglecting it is conservative.
case), and the other variables have been
defined previously. For determining the area Acv , use the full depth of concrete at
that section with the length equal to the distance from between the points of
maximum and zero moment.
For a solid slab, check the vertical planes at the edges of the top flange of the steel
section. While planes closer to the studs theoretically carry slightly more force, the
zone around the studs themselves is considered to be accounted for by the
procedures used to select the studs. Use of the depth “a” is also quite conservative.
As long as Vr ≥ Vu , the shear capacity along these planes is adequate.
Unshored Beams
Although beams can be shored until the concrete gains its design strength to ensure
that all loads are carried by the composite section, it is common to omit shoring to
keep the work areas below unobstructed and to avoid the associated direct and
indirect expenses. In unshored construction, S16 requires that the stresses in the
tension flange of the steel section be checked to ensure that they do not exceed the
nominal yield stress, Fy , under service loads [§17.11]. The purpose of this check is
to limit deflections, so it is a serviceability check.
To perform this check, the loads are separated into those that are applied prior to
the slab reaching 75% of its nominal design capacity (usually about 7 days) and
those applied thereafter. The former are assumed to be applied to the bare steel
section and the latter to the composite section. Although no equation is provided in
S16, this requirement is satisfied by the following:
– 15 –
CIVL 432
[23]
COMPOSITE BEAMS
M1 M 2

 Fy
Ss
St
R.G. DRIVER
Trap
Don’t apply this to
shored construction.
where M1 = moment from specified loads that are applied prior to the concrete
reaching 0.75fc (excludes loads that are present only during
construction, such as construction LL, plywood formwork, etc.);
M2 = moment from any specified loads that are applied after the concrete
reaches 0.75fc;
Ss = elastic section modulus of the steel section (to the bottom fibre); and
St = elastic section modulus of the composite section (to the bottom
fibre) determined using the transformed area method (from your
Strength of Materials course) to obtain an equivalent steel section.
Beam Design for Construction Loads
Since wet concrete has no strength, during
Construction live loads should be
construction the bare steel section must be
estimated as closely as possible for
designed to carry all factored construction
the case considered, but a common
loads—including the weight of the wet concrete
nominal value for light construction
itself—until the slab reaches its design strength,
taking into account the lateral bracing and shoring is 1 kPa (picture one 225 lb dude on
conditions furnished during construction [§17.12]. every square metre of floor area).
The design procedures for non-composite beams were all covered in CIVL 331.
Tip
Deflections
A part of the total deflection of a composite beam occurs prior to the beam
becoming composite. This deflection is computed based on the stiffness of the steel
section alone. The remainder of the deflection, due to loads applied after the
concrete has cured, is calculated assuming composite action.
Deflections of composite beams under specified loads are affected by many things
including creep and shrinkage of the concrete and the potential for interfacial slip
between the two materials in the case of partial shear connection. The latter effect
is accounted for by determining an effective moment of inertia, Ie , as follows:
[24]
Ie  Is  0.85p 
0.25
I t  Is 
where Is = moment of inertia of the steel section;
p = fraction of full shear connection; and
It = transformed moment of inertia of
composite beam (equivalent steel
section) based on the modular ratio,
n = E/Ec .
– 16 –
[§17.3.1(a)]
Technical
Stuff
Even for full composite action
(p = 1.0), there is still a reduction
in the moment of inertia because
there is some flexibility in the
shear studs that can lead to slip,
increasing deflections.
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
To account for creep, the elastic deflections caused by dead loads and long-term
live loads using the effective moment of inertia defined by Equation [24] are
amplified by 15% [§17.3.1(b)].
The concrete in a composite beam is not able to shrink freely since it is connected
to the steel section. The resulting restrained shrinkage tends to induce curvature in
the composite beam that has the effect of increasing deflections, as indicated in the
figure below. Figure (a) indicates how the slab would shrink if unrestrained, while
Figure (b) shows the results of the shrinkage when restrained by connection to the
steel by the use of studs.
The force applied to the section due to the concrete shrinkage can be considered to
act at the centroid of the slab. This, in turn, leads to a moment acting at a distance y
above the elastic neutral axis of the composite section, as shown in the figure
below.
– 17 –
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
 f A c L2 y
8n s I es
[§17.3.1(c)]
The resulting deflection is:
[25]
s  c
where c = empirical coefficient to adjust theoretical relationship to better match
with test results (accounts for things such as concrete cracking and
the non-linear stress vs. strain relationship of concrete)
f = free shrinkage strain of the concrete (use 580 in the absence of a
more accurate value);
Ac = effective area of the concrete slab;
L = beam span;
y = distance from the centroid of the effective area of the concrete slab to
the elastic neutral axis of the composite beam;
ns = modular ratio suitable for shrinkage calculations, E/Ec;
E = modulus of elasticity of steel;
Ec = age- and creep-adjusted effective modulus of concrete in tension; and
Ies = effective moment of inertia (Equation [24]), with the transformed
moment of inertia of the composite beam (equivalent steel section)
based on the modular ratio ns instead of n.
The effective modulus of concrete, Ec , is time-dependent, but since the modular
ratio and the effective moment of inertia (denominator of Equation [25]), as well as
the distance y (numerator of Equation [25]), vary with it, the net result is that it has
a relatively small effect on the deflection. Annex H of S16 provides some guidance
for determining Ec .
If deflections are calculated assuming simple supports, even when simple shear
connections are used at the beam ends this can overestimate the deflection by a
significant amount due to the continuity at the supports provided by the composite
system. It has been suggested that applying negative end moments equal to 25% of
the midspan moment of a uniformly loaded, simply-supported beam will give a
good estimate of the true deflection.
– 18 –
CIVL 432
COMPOSITE BEAMS
R.G. DRIVER
SUMMARY OF IMPORTANT CONCEPTS
 Composite beams take advantage of benefits of both steel and concrete by
connecting them together so they act (more-or-less) as one.
 Composite action is achieved through the use of shear connectors (usually
headed shear studs).
 The longitudinal shear at the interface between the two materials must be
transferred between the point of maximum moment and the point of zero
moment (for equilibrium) and there are special stud distribution requirements
when there are concentrated loads.
 A designer can select either full composite action or partial composite action.
 For full composite action, whether the neutral axis falls within the slab or the
steel section depends on the relative proportions and material strengths of the
two components.
 If only a fraction of the shear connectors required for full composite action is
provided (must be ≥ 40% for strength and ≥ 25% for serviceability), partial
composite action results, and the neutral axis will always be in the steel section.
 Slabs can be either solid or ribbed, the latter resulting from the use of
corrugated steel deck forms.
 Ribbed slabs may have the ribs parallel or perpendicular to the steel section,
and the rib orientation affects the capacity of the shear studs.
 In solid slabs and ribbed slabs with the ribs parallel to the steel section, the slab
could fail on vertical shear planes adjacent to the steel section. These planes
must be checked to ensure adequate capacity.
 In unshored construction, a serviceability check is required to ensure that the
maximum tensile stress in the steel under unfactored loads does not exceed Fy .
 Deflection calculations (under service loads) for composite beams must account
for interfacial slip, as well as creep and shrinkage of the concrete.
Credits: The figures used in this document are © Kulak, G.L. and Grondin, G.Y. (2002) Limit
States Design in Structural Steel, Canadian Institute of Steel Construction, Toronto,
ON, © CISC (2000) Handbook of Steel Construction, Canadian Institute of Steel
Construction, Toronto, ON, or © Chien, E.Y.L. and Ritchie, J.K. (1984) Design and
Construction of Composite Floor Systems, , Canadian Institute of Steel Construction,
Toronto, ON.
steelcentre.ca
– 19 –