Composite beams

sublimefrontUrban and Civil

Nov 15, 2013 (3 years and 8 months ago)

175 views

Chapter 21
Composite beams
by MARK LAWSON and PETER WICKENS
601
21.1 Applications of composite beams
In buildings and bridges,steel beams often support concrete slabs.Under load each
component acts independently with relative movement or slip occurring at the inter-
face.If the components are connected so that slip is eliminated,or considerably
reduced,then the slab and steel beam act together as a composite unit (Fig.21.1).
There is a consequent increase in the strength and stiffness of the composite beam
relative to the sum of the components.
The slab may be solid in situ concrete or the composite deck slab considered in
Chapter 20.It may also comprise precast concrete units with an in situ concrete
topping.In buildings,steel beams are usually of standard UB scction,but UC and
asymmetric beam sections are sometimes used where there is need to minimize the
beam depth.A typical building under construction is shown in Fig.21.2.Welded fab-
ricated sections are often used for long-span beams in buildings and bridges.
Design of composite beams in buildings is now covered by BS 5950:Part 3,
1
although guidance was formerly available in an SCI publication.
2
The design of com-
posite beams incorporating composite slabs is affected by the shape and orientation
of the decking,as indicated in Fig.21.3.
One of the advantages of composite construction is smaller construction depths.
Services can usually be passed beneath,but there are circumstances where the beam
depth is such that services can be passed through the structure,either by forming
large openings,or by special design of the structural system.A good example of this
is the stub-girder.
3
The bottom chord is a steel section and the upper chord is the
concrete slab.Short steel sections or ‘stubs’ are introduced to transfer the forces
between the chords.
Openings through the beam webs can be provided for services.Typically,these
can be up to 70% of the beam depth and can be rectangular or circular in shape.
Guidance on the design of composite beams with web openings is given in Refer-
ence 4.Examples of the above methods of introducing services within the structure
are shown in Fig.21.4.
21.2 Economy
Composite beam construction has a number of advantages over non-composite
construction:
noncomposite
composite beam
beam
support
force in
(1) savings in steel weight are typically 30% to 50% over non-composite beams.
(2) the greater stiffness of the system means that beams can be shallower for the
same span,leading to lower storey heights and savings in cladding,etc.
It also shares the advantage of rapid construction.
The main disadvantage is the need to provide shear-connectors at the interface
between the steel and concrete.There may also be an apparent increase in com-
plexity of design.However,design tables have been presented to aid selection of
member sizes.
2
602 Composite beams
Fig.21.1 Behaviour of composite and non-composite beams
Fig.21.2 Composite building under construction showing decking and shear-connectors
deck
(a) (b)
overlap
The normal method of designing simply-supported beams for strength is by plastic
analysis of the cross-section.Full shear connection means that sufficient shear-
connectors are provided to develop the full plastic capacity of the section.Beams
designed for full shear connection result in the lightest beam size.Where fewer
shear-connectors are provided (known as partial shear connection) the beam size is
heavier,but the overall design may be more economic.
Partial shear connection is most attractive where the number of shear-connectors
is placed in a standard pattern,such as one per deck trough or one per alternate
trough where profiled decking is used.In such cases,the resistance of the shear-
connectors is a fixed quantity irrespective of the size of the beam or slab.
Conventional elastic design of the section results in heavier beams than with
plastic design because it is not possible to develop the full tensile resistance of the
steel section.Designs based on elastic principles are to be used where the
compressive elements of the section are non-compact or slender,as defined in
BS 5950 Part 1.This mainly affects the design of continuous beams (see section
21.6.3).
21.3 Guidance on span-to-depth ratios
Beams are usually designed to be unpropped during construction.Therefore,the
steel beam is sized first to support the self-weight of the slab before the concrete
has gained adequate strength for composite action.Beams are assumed to be lat-
erally restrained by the decking in cases where the decking crosses the beams (at
an angle of at least 45° to the beam) and is directly attached to them.These beams
can develop their full flexural capacity.
Where simply-supported unpropped composite beams are sized on the basis of
their plastic capacity it is normally found that span-to-depth ratios can be in the
Guidance on span-to-depth ratios 603
Fig.21.3 Composite beams incorporating composite deck slabs:(a) deck perpendicular to
beam,(b) deck parallel to beam
column
,shearconnector._mesh
beam
"sti1fener
(a)
(c)
bolt
E
I.
opening
Q
opening
L1 0°
services
(b)
range of 18 to 22 before serviceability criteria influence the design.The ‘depth’ in
these cases is defined as the overall depth of the beam and slab.S355 steel is often
specified in preference to S275 steel in composite beam design because the stiffness
of a composite beam is often three to four times that of the non-composite beam,
justifying the use of higher working stresses.
The span-to-depth ratios of continuous composite beams are usually in the range
of 22 to 25 for end spans and 25 to 30 for internal spans before serviceability crite-
ria influence the design.Many continuous bridges are designed principally to satisfy
the serviceability limit state.
604 Composite beams
Fig.21.4 Different methods of incorporating services within the structural depth
21.4 Types of shear connection
The modern form of shear-connector is the welded headed stud ranging in diameter
from 13 to 25mm and from 65 to 125mm in height.The most popular size is 19mm
diameter and 100mm height before welding.When used with steel decking,studs
are often welded through the decking using a hand tool connected via a control unit
to a power generator.Each stud takes only a few seconds to weld in place.Alter-
natively,the studs can be welded directly to the steel beams in the factory and the
decking butted up to or slotted over the studs.
There are,however,some limitations to through-deck welding:the top flange of
the beam must not be painted,the galvanized steel should be less than around
1.25mm thick,the deck should be clean and free of moisture,and there should be
no gap between the underside of the decking and the top of the beam.The minimum
flange thickness must not be less than the diameter of the stud divided by 2.5
(typically,19/2.5 = 7.6mm).The power generator needs 415V electrical supply,and
the maximum cable length between the weld gun and the power control units should
be limited to around 70m to avoid loss of power.Currently,only 13,16 or 19mm
diameter studs can be through-deck welded on site.
Where precast concrete planks are used,the positions of the shear-connectors are
usually such that they project through holes in the slab which are later filled with
concrete.Alternatively,a gap is left between the ends of the units sitting on the top
flange of the beam on to which the shear connectors are fixed.Reinforcement
(usually in the form of looped bars) is provided around the shear-connectors.
There is a range of other forms of welded shear-connector,but most lack prac-
tical applications.The ‘bar and hoop’ and ‘channel’ welded shear-connectors have
been use in bridge construction.
5
Shot-fired shear-connectors may be used in smaller
building projects where site power might be a problem.All shear-connectors should
be capable of resisting uplift forces;hence the use of headed rather than plain studs.
The number of shear-connectors placed along the beam is usually sufficient to
develop the full flexural resistance of the member.However it is possible to reduce
the number of shear-connectors in cases where the moment resistance exceeds the
applied moment and the shear-connectors have adequate ductility (or deformation
capacity).This is known as partial shear connection and is covered in section 21.7.4.
21.5 Span conditions
In buildings,composite beams are usually designed to be simply-supported,mainly
to simplify the design process,to reduce the complexity of the beam-to-column con-
nections,and to minimize the amount of slab reinforcement and shear-connectors
that are needed to develop continuity at the ultimate limit state.
However,there are ways in which continuity can be readily introduced,in order
to improve the stiffness of composite beams.Figure 21.5 shows how a typical con-
nection detail at an internal column can be modified to develop continuity.The stub
Span conditions 605
M
bending moment
ram
M developed by
shearconnectors
in this zone
tension in
anchorage
reinforcement
lenathmesh
-
7
.,.
çIL-1I
...., .
.. ...... ..;. -y
t It
I L
bolt
compression
stiffener
girder system also utilizes continuity of the secondary members (see Fig.21.4(c)).
Other methods of continuous design are presented in References 3 and 6.
Continuous composite beams may be more economic than simply-supported
beams where plastic hinge analysis of the continuous member is carried out,pro-
vided the section is plastic according to BS 5950:Part 1.However,where the lower
flange or web of the beam is non-compact or slender in the negative (hogging)
moment region,then elastic design must be used,both in terms of the distribution
of moment along the beam,and also for analysis of the section.Lateral instability
of the lower flange is an important design condition,although torsional restraint is
developed by the web of the section and the concrete slab.
6
In bridges,continuity is often desirable for serviceability reasons,both to reduce
deflections,and to minimize cracking of the concrete slab,finishes and wearing
surface in road bridges.Special features of composite construction appropriate to
bridge design are covered in the publication by Johnson and Buckby
7
based on
BS 5400:Part 5.
5
21.6 Analysis of composite section
21.6.1 Elastic analysis
Elastic analysis is employed in establishing the serviceability performance of com-
posite beams,or the resistance of beams subject to the effect of instability,for
606 Composite beams
Fig.21.5 Representation of conditions at internal column of continuous beam
Os
Be/ae
D
elastic
neutral axis
equivalent
steel area
stress p
(a)
(b)
example,in continuous construction,or in beams where the ductility of the shear
connection is not adequate.
The important properties of the section are the section modulus and the second
moment of area.First it is necessary to determine the centroid (elastic neutral axis)
of the transformed section by expressing the area of concrete in steel units by divid-
ing the concrete area within the effective breadth of the slab,B
e
,by an appropriate
modular ratio (ratio of the elastic modulus of steel to concrete).
In unpropped construction,account is taken of the stresses induced in the non-
composite section as well as the stresses in the composite section.In elastic analy-
sis,therefore,the order of loading is important.For elastic conditions to hold,
extreme fibre stresses are kept below their design values,and slip at the interface
between the concrete and steel should be negligible.
The elastic section properties are evaluated from the transformed section as in
Fig.21.6.The term a
e
is the modular ratio.The area of concrete within the profile
depth is ignored (this is conservative where the decking troughs lie parallel to the
beam).The concrete can usually be assumed to be uncracked under positive
moment.
The elastic neutral axis depth,x
e
,below the upper surface of the slab is deter-
mined from the formula:
(21.1)
x
D D
r
D
D
r
e
s p
e s
e
=
-
+ +
Ê
Ë
ˆ
¯
+
( )
2 2
1
a
a
Analysis of composite section 607
Fig.21.6 Elastic behaviour of composite beam.(a) Elastic stress distribution.
(b) Transformed section
where r = A/[(D
s
- D
p
)B
e
],D
s
is the slab depth,D
p
is profile height (see Fig.21.6)
and A is the cross-sectional area of the beam of depth D.
The second moment of area of the uncracked composite section is:
(
21.2
)
where I is the second moment of area of the steel section.The section modulus for
the steel in tension is:
(21.3)
and for concrete in compression is:
(21.4)
The composite stiffness can be 3 to 5 times,and the section modulus 1.5 to 2.5 times
that of the I-section alone.
21.6.2 Plastic analysis
The ultimate bending resistance of a composite section is determined from its plastic
resistance.It is assumed that the strains across the section are sufficiently high that
the steel stresses are at yield throughout the section and that the concrete stresses
are at their design strength.The plastic stress blocks are therefore rectangular,as
opposed to linear in elastic design.
The plastic moment resistance of the section is independent of the order of
loading (i.e.propped or unpropped construction) and is compared to the moment
resulting from the total factored loading using the load factors in BS 5950:Part 1.
The plastic neutral axis of the composite section is evaluated assuming stresses
of p
y
in the steel and 0.45f
cu
in the concrete.The tensile resistance of the steel is
therefore R
s
= p
y
A,where A is the cross-sectional area of the beam.The compres-
sive resistance of the concrete slab depends on the orientation of the decking.Where
the decking crosses the beams the depth of concrete contributing to the compres-
sive resistance is D
s
- D
p
(Fig.21.6(a)).Clearly,D
p
is zero in a solid slab.Where the
decking runs parallel to the beams (Fig.21.6(b)),then the total cross-sectional area
of the concrete is used.Taking the first case:
(21.5)
where B
e
is the effective breadth of the slab considered in section 21.7.1.
Three cases of plastic neutral axis depth x
p
(measured from the upper surface of
the slab) exist.These are presented in Fig.21.7.It is not necessary to calculate x
p
explicitly if the following formulae for the plastic moment resistance of I-section
beams subject to positive (sagging) moment are used.The value R
w
is the axial resist-
ance of the web and R
f
is the axial resistance of one steel flange (the section is
R f D D B
c cu s p e
= -
( )
0 45.
Z I x
e c e e
= a
Z I D D x
t c s e
= + -
( )
I
A D D D
r
B D D
I
c
s p
e
e s p
e
=
+ +
( )
+
( )
+
-
( )
+
2 3
4 1 12a a
608 Composite beams
py
O451cu
assumed to be symmetrical).The top flange is considered to be fully restrained by
the concrete slab.
The moment resistance,M
pc
,of the composite beam is given by:
Case 1:R
c
> R
s
(plastic neutral axis lies in concrete slab):
(21.6)
Case 2:R
s
> R
c
> R
w
(plastic neutral axis lies in steel flange):
(21.7)
NB the last term in this expression is generally small (T is the flange thickness).
Case 3:R
c
< R
w
(plastic neutral axis lies in web):
(21.8)
where M
s
is the plastic moment resistance of the steel section alone.This formula
assumes that the web is compact i.e.not subject to the effects of local buckling.For
this to be true the depth of the web in compression should not exceed 78te,where
t is the web thickness (e is defined in BS 5950:Part 1).If the web is non-compact,a
method of determining the moment resistance of the section is given in BS 5950:
Part 3,Appendix B.
1
21.6.3 Continuous beams
Bending moments in continuous composite beams can be evaluated from elastic
global analysis.However,these result in an overestimate of moments at the sup-
ports because cracking of the concrete reduces the stiffness of the section and
M M R
D D D
R
R
D
pc s c
s p
c
2
w
= +
+ +
Ê
Ë
Á
ˆ
¯
˜
-
2 4
M R
D
R
D D
R R
R
pc s c
s p
s c
f
T
4
= +
+
Ê
Ë
Á
ˆ
¯
˜
-
-
( )
2 2
2
M R
D
D
R
R
D D
pc s s
s
c
s p
2
= + -
-
Ê
Ë
Á
ˆ
¯
˜
È
Î
Í
˘
˚
˙
2
Analysis of composite section 609
Fig.21.7 Plastic analysis of composite section under positive (sagging) moment (PNA:
plastic neutral axis)
permits a relaxation of bending moment.A simplified approach is to redistribute
the support moment based on gross (uncracked) section properties by the amounts
given in Table 21.1.Alternatively,moments can be determined using the appropri-
ate cracked and uncracked stiffnesses in a frame analysis.In this case,the permit-
ted redistribution of moment is less.
610 Composite beams
Table 21.1 Maximum redistribution of support moment based on elastic design of continuous
beams at the ultimate limit state
Classification of compression flange at supports
Assumed section
Plastic
properties at Slender Semi-compact Compact Generally Beams (with nominal
supports slab reinforcement)
Gross uncracked 10% 20% 30% 40% 50%
Cracked 0% 10% 20% 30% 30%
Table 21.2 Moment coefficients (multiplied by free moment of WL/8) for elastic design of
continuous beams
Classification of compression flange at supports
Plastic
Location Slender Semi-compact Compact Generally Beams (with
nominal slab
reinforcement)
Middle 2 spans 0.71 0.71 0.71 0.75 0.79
of end 3 or 0.80 0.80 0.80 0.80 0.82
span more
spans
First 2 spans 0.91 0.81 0.71 0.61 0.50
internal 3 or 0.86 0.76 0.67 0.57 0.48
support more
spans
Middle of 0.65 0.65 0.65 0.65 0.67
internal spans
Internal supports 0.75 0.67 0.58 0.50 0.42
(except first)
Redistribution 10% 20% 30% 40% 50%
The section classification is expressed in terms of the proportions of the com-
pression (lower) flange at internal supports.This determines the permitted redistri-
bution of moment.A special category of plastic section is introduced where the
section is of uniform shape throughout and nominal reinforcement is placed in the
slab which does not contribute to the bending resistance of the beam.In this case
the maximum redistribution of moment under uniform loading is increased to 50%.
A simplified elastic approach is to use the design moments in Table 21.2 assuming
that:
(1) the unfactored imposed load does not exceed twice the unfactored dead load;
(2) the load is uniformly distributed;
(3) end spans do not exceed 115% of the length of the adjacent span;
(4) adjacent spans do not differ in length by more than 25% of the longer span.
An alternative to the elastic approach is plastic hinge analysis of plastic sections.
Conditions on the use of plastic hinge analysis are presented in BS 5950:Part 3
1
and
Eurocode 4 (draft).
8
However,large redistributions of moment may adversely affect
serviceability behaviour (see section 21.7.8).
The ultimate load resistance of a continuous beam under positive (sagging)
moment is determined as for a simply-supported beam.The effective breadth of the
slab is based on the effective span of the beam under positive moment (see section
21.7.1).The number of shear-connectors contributing to the positive moment capac-
ity is ascertained knowing the point of contraflexure.
The negative (hogging) moment resistance of a continuous beam or cantilever
should be based on the steel section together with any properly anchored tension
reinforcement within the effective breadth of the slab.This poses problems at edge
columns,where it may be prudent to neglect the effect of the reinforcement unless
particular measures are taken to provide this anchorage.The behaviour of a con-
tinuous beam is represented in Fig.21.5.
The negative moment resistance is evaluated from plastic analysis of the section:
Case 1:R
r
< R
w
(plastic neutral axis lies in web):
(21.9)
where R
r
is the tensile resistance of the reinforcement over width B
e
,R
q
is the capac-
ity of the shear-connectors between the point of contraflexure and the point of
maximum negative moment (see section 21.7.3),and D
r
is the height of the re-
inforcement above the top of the beam.
Case 2:R
r
> R
w
(plastic neutral axis lies in flange):
(21.10)
NB the last term in this expression is generally small.
The formulae assume that the web and lower flange are compact i.e.not subject
to the effects of local buckling.The limiting depth of the web in compression is 78te
(where e is defined in Chapter 2) and the limiting breath:thickness ratio of the
flange is defined in Table 11 of BS 5950:Part 1.
If these limiting slendernesses are exceeded then the section is designed elasti-
cally – often the situation in bridge design.The appropriate effective breadth of slab
is used because of the sensitivity of the position of the elastic neutral axis and hence
the zone of the web in compression to the tensile force transferred by the rein-
forcement.The elastic section properties are determined on the assumption that the
concrete is cracked and does not contribute to the resistance of the section.
M R
D
R D
R R
R
T
snc r r
s r
f
= + -
-
( )
2 4
2
M M R
D
D
R
R
D
nc s s r
q
2
w
= + +
Ê
Ë
ˆ
¯
-
2 4
Analysis of composite section 611
point load
udi
B/L
0.8
0.2
0.3
0.6_
B
0.4
0.4
0.6
0.2
 
0.8
support
midspan
support
21.7 Basic design
21.7.1 Effective breadths
The structural system of a composite floor or bridge deck is essentially a series of
parallel T beams with wide thin flanges.In such a system the contribution of the
concrete flange in compression is limited because of the influence of ‘shear lag’.The
change in longitudinal stress is associated with in-plane shear strains in the flanges.
The ratio of the effective breadth of the slab to the actual breadth (B
e
/B) is a
function of the type of loading,the support conditions and the cross-section under
consideration as illustrated in Fig.21.8.The effective breadth of slab is therefore not
a precise figure but approximations are justified.A common approach in plastic
design is to consider the effective breadth as a proportion (typically 20%–33%) of
the beam span.This is because the conditions at failure are different from the elastic
conditions used in determining the data in Fig.21.8,and the plastic bending capac-
ity of a composite section is relatively insensitive to the precise value of effective
breadth used.
Eurocode 4 (in its ENV or pre-norm version)
8
and BS 5950:Part 3
1
define the
effective breadth as (span/4) (half on each side of the beam) but not exceeding the
actual slab breadth considered to act with each beam.Where profiled decking spans
in the same direction as the beams,as in Fig.21.3(b),allowance is made for the com-
bined flexural action of the composite slab and the composite beam by limiting the
effective breadth to 80% of the actual breadth.
In building design,the same effective breadth is used for section analysis at both
the ultimate and serviceability limit states.In bridge design to BS 5400:Part 5,
5
tabular data of effective breadths are given for elastic design at the serviceability
612 Composite beams
Fig.21.8 Variation of effective breadth along beam and with loading
limit state.If plastic design is appropriate,the effective breadth is modified to
(span/3).
5
In the design of continuous beams,the effective breadth of the slab may be based
conservatively on the effective span of the beam subject to positive or negative
moment.For positive moment,the effective breadth is 0.25 times 0.7 span,and for
negative moment,the effective breadth is 0.25 times 0.25 times the sum of the adja-
cent spans.These effective breadths reduce to 0.175 span and 0.125 span respec-
tively for positive and negative moment regions of equal-span beams.
21.7.2 Modular ratio
The modular ratio is the ratio of the elastic modulus of steel to the creep-modified
modulus of concrete,which depends on the duration of the load.The short- and
long-term modular ratios given in Table 21.3 may be used for all grades of concrete.
The effective modular ratio used in design should be related to the proportions of
the loading that are considered to be of short- and long-term duration.Typical
values used for office buildings are 10 for normal weight and 15 for lightweight con-
crete.
21.7.3 Shear connection
The shear resistance of shear-connectors is established by the push-out test,a stan-
dard test using a solid slab.A typical load–slip curve for a welded stud is shown in
Fig.21.9.The loading portion can be assumed to follow an empirical curve.
9
The
strength plateau is reached at a slip of 2–3mm.
The shear resistance of shear-connectors is a function of the concrete strength,
connector type and the weld,related to the diameter of the connector.The purpose
of the head of the stud is to prevent uplift.The common diameter of stud which can
be welded easily on site is 19mm,supplied in 75mm,100mm or 125mm heights.The
material properties,before forming,are typically:
Ultimate tensile strength 450N/mm
2
Elongation at failure 15%
Basic design 613
Table 21.3 Modular ratios (a
e
) of steel of concrete
Duration of loading
Type of concrete Short-term Long-term ‘Office’ loading
Normal weight 6 18 10
Lightweight 10 25 15
(density > 1750kg/m
3
)
load per
shear
connector
0.6 u
<0.5 mm2 to 3 mm
>5 mm
slip
Higher tensile strengths (495N/mm
2
) are required in bridge design.
5
Nevertheless,
the ‘push-out’ strength of the shear-connectors is relatively insensitive to the
strength of the steel because failure is usually one of the concrete crushing for con-
crete grades less than 40.Also the weld collar around the base of the shear-
connector contributes to increased shear resistance.
The modern method of attaching studs in composite buildings is by through-deck
welding.An example of this is shown in Fig.21.10.The common in situ method of
checking the adequacy of the weld is the bend-test,a reasonably easy method of
quality control which should be carried out on a proportion of studs (say 1 in 50)
and the first 2 to 3 after start up.
Other forms of shear-connector such as the shot-fired connector have been devel-
oped (Fig.21.11).The strength of these types is controlled by the size of the pins
used.Typical strengths are 30%–40% of the strengths of welded shear-connectors,
but they demonstrate greater ductility.
The static resistances of stud shear-connectors are given in Table 21.4,taken from
BS 5400:Part 5 and also incorporated in BS 5950:Part 3.As-welded heights are
some 5mm less than the nominal heights for through-deck welding;for studs welded
directly to beams the length after welding (LAW) is taken as the nominal height.
The strengths of shear-connectors in structural lightweight concrete (density
>1750kg/m
2
) are taken as 90% of these values.
In Eurocode 4,
8
the approach is slightly different.Empirical formulae are given
614 Composite beams
Fig.21.9 Load–slip relationship for ductile welded shear-connector
based on two failure modes:failure of the concrete and failure of the steel.The
upper bound strength is given by shear failure of the shank and therefore there is
apparently little advantage in using high-strength concrete.
In BS 5950:Part 3 and Eurocode 4,the design resistance of the shear-connectors
is taken as 80% of the nominal static strength.Although this may broadly be con-
sidered to be a material factor applied to the material strength,it is,more correctly,
a factor to ensure that the criteria for plastic design are met (see below).The design
resistance of shear-connectors in negative (hogging) moment regions is conserva-
tively taken as 60% of the nominal resistance.In BS 5400:Part 5,an additional
material factor of 1.1 is introduced to further reduce the design resistance of the
shear connectors.
Basic design 615
Fig.21.10 Welding of shear-connector through steel decking to a beam
616 Composite beams
Fig.21.11 Shot-fired shear-connector
Table 21.4 Characteristic resistances of headed stud shear-
connectors in normal weight concrete
Dimensions of stud Characteristic strength
shear-connectors (mm) of concrete (N/mm
2
)
Diameter Nominal As-welded 25 30 35 40
height height
25 100 95 146 154 161 168
22 100 95 119 126 132 139
19 100 95 95 100 104 109
19 75 70 82 87 91 96
16 75 70 70 74 78 82
13 65 60 44 47 49 52
For concrete of characteristic strength greater than 40N/mm
2
use the
values for 40N/mm
2
For connectors of heights greater than tabulated use the values for the
greatest height tabulated
loading
shear
connector
elastic shear flow
actual shear flow at failure
idealized plastic shear flow
slip
In plastic design,it is important to ensure that the shear-connectors display
adequate ductility.It may be expected that shear-connectors maintain their design
resistances at displacements of up to 5mm.A possible exception is where concrete
strengths exceed C 40,as the form of failure may be more brittle.
For beams subject to uniform load,the degree of shear connection that is pro-
vided by uniformly-spaced shear-connectors (defined in section 21.7.4) reduces
more rapidly than the applied moment away from the point of maximum moment.
To ensure that the shear connection is adequate at all points along the beam,the
design resistance of the shear-connectors is taken as 80% of their static resistance.
This also partly ensures that flexural failure will occur before shear failure.For
beams subject to point loads,it is necessary to design for the appropriate shear con-
nection at each major load point.
In a simple composite beam subject to uniform load the elastic shear flow defin-
ing the shear transfer between the slab and the beam is linear,increasing to a
maximum at the ends of the beam.Beyond the elastic limit of the connectors there
is a transfer of force among the shear-connectors,such that,at failure,each of the
shear-connectors is assumed to be subject to equal force,as shown in Fig.21.12.This
is consistent with a relatively high slip between the concrete and the steel.The slip
increases as the beam span increases and the degree of shear connection reduces.
For this reason BS 5400:Part 5
5
requires that shear-connectors in bridges are spaced
in accordance with elastic theory.In building design,shear-connectors are usually
spaced uniformly along the beam when the beam is subject to uniform load.
No serviceability limit is put on the force in the shear-connectors,despite the fact
that consideration of the elastic shear flow suggests that such forces can be high at
Basic design 617
Fig.21.12 Idealization of forces transferred between concrete and steel
working load.This is reflected in the effect of slip on deflection in cases where partial
shear connection is used.When designing bridges
5
or structures subject to fatigue
loading,a limit of 55% of the design resistance of the shear-connectors is appro-
priate for design at the serviceability limit state.
21.7.4 Partial shear connection
In plastic design of composite beams the longitudinal shear force to be transferred
between the concrete and the steel is the lesser of R
c
and R
s
.The number of shear-
connectors placed along the beam between the points of zero and maximum posi-
tive moment should be sufficient to transfer this force.
In cases where fewer shear-connectors are provided than the number required
for full shear connection it is not possible to develop M
pc
.If the total capacity of the
shear-connectors between the points of zero and maximum moment is R
q
(less than
the smaller of R
s
and R
c
),then the stress block method in section 21.6.2 is modified
as follows,to determine the moment resistance,M
c
:
Case 4:R
q
> R
w
(plastic neutral axis lies in flange):
(21.11)
NB the last term in this expression is generally small.
Case 5:R
q
< R
w
(plastic neutral axis lies in web):
(21.12)
The formulae are obtained by replacing R
c
by R
q
and re-evaluating the neutral axis
position.The method is similar to that used in the American method of plastic
design,
10
which predicts a non-linear increase of moment capacity with degree of
shear connection K defined as:
An alternative approach,which has proved attractive,is to define the moment resist-
ance in terms of a simple linear interaction of the form:
(21.13)
The stress block and linear interaction methods are presented in Fig.21.13 for a
typical beam.It can be seen that there is a significant benefit in the stress block
method in the important range of K = 0.5 to 0.7.
In using methods based on partial shear connection a lower limit for K of 0.4 is
specified.This is to overcome any adverse effects arising from the limited defor-
mation capacity of the shear-connectors.
M M K M M
c s pc s
= + -
( )
K R R R R
K R R R R
= <
= <
q s s c
q c c s
for
or for
M M R
D
D
R
R
D D R
R
D
c s q s
q
c
s p q
2
w
= + + -
-
Ê
Ë
Á
ˆ
¯
˜
È
Î
Í
˘
˚
˙
-
2 2 4
M R
D
R D
R
R
D D R R
R
T
c s q s
q
c
s p s q
f
= + -
-
Ê
Ë
Á
ˆ
¯
˜
È
Î
Í
˘
˚
˙
-
-
( )
2 2 4
2
618 Composite beams
moment
'ductile shear
rigid shear
connectors
K
3)
0.4
1.0
degree of shear
connection, K
In BS 5950:Part 3,the limiting degree of shear connection increases with beam
span (L in metres) such that:
(21.14)
This formula means that beams longer than 16m span should be designed for full
shear connection,and beams of up to 10m span designed for not less than 40%
shear connection,with a linear transition between the two cases.Partial shear con-
nection is also not permitted for beams subject to heavy off-centre point loads,
except where checks are made,as below.
A further requirement is that the degree of shear connection should be adequate
at all points along the beam length.For a beam subject to point loads,it follows that
the shear-connectors should be distributed in accordance with the shear force
diagram.
Comparison of the method of partial shear connection with other methods of
design is presented in Table 21.5.Partial shear connection can result in overall
K L£ -
( )
≥6 10 0 4.
Basic design 619
Fig.21.13 Interaction between moment capacity and degree of shear connection.(a) Stress
block method.(b) Linear interaction method
economy by reducing the number of shear-connectors at the expense of a slightly
heavier beam than that needed for full shear connection.Elastic design is relatively
conservative and necessitates the placing of shear-connectors in accordance with
the elastic shear flow.Deflections are calculated using the guidance in section
21.7.8.
21.7.5 Influence of deck shape on shear connection
The efficiency of the shear connection between the composite slab and the com-
posite beam may be reduced because of the shape of the deck profile.This is ana-
logous to the design of haunched slabs where the strength of the shear-connectors
is strongly dependent on the area of concrete around them.Typically,there should
be a 45° projection from the base of the connector to the core of the solid slab to
transfer shear smoothly in the concrete without local cracking.
The model for the action of a shear-connector placed in the trough of a deck
profile is shown in Fig.21.14.For comparison,also shown is the behaviour of a con-
nector in a solid slab.Effectively,the centre of resistance in the former case moves
towards the head of the stud and the couple created is partly resisted by bending
of the stud but also by tensile and compressive forces in the concrete,encouraging
concrete cracking,and consequently the strength of the stud is reduced.
A number of tests on different stud heights and profile shapes have been per-
formed.The following formula has been adopted by most standards worldwide.The
620 Composite beams
Table 21.5 Comparison of designs of simply-supported composite beams
Plastic design
Beam data Elastic design No connectors Partial Full shear
(BS 5950: Part 1) connection connection
Full depth (mm) 536 536 435 435
Beam size (mm) 406 ¥ 140UB 406 ¥ 140UB 305 ¥ 102UB 305 ¥ 102UB
Beam weight (kg/m) 39 46 33 28
Number of 19mm 50 0 25 50
diameter shear- (every trough) (alternate (every trough)
connectors troughs)
Imposed load 7 19 14 13
deflection (mm)
Self-weight 14 11 25 30
deflection (mm)
Beam span:7.5m (unpropped)
Beam spacing:3.0m
Slab depth:130mm
Deck height:50mm
Steel grade:50 (p
y
= 355N/mm
2
)
Concrete grade:30 (normal weight)
Imposed load:5kN/m
2
a
C
a.
0
Cb
II
gII
;:
.
C-
C
0 -
av
a.
strength reduction factor (relative to a solid slab) for the case where the decking
crosses the beams is:
(21.15)
where b
a
is the average width of the trough,h is the stud height,and n is the number
of studs per trough (n < 3).The limit for pairs of studs is given in BS 5950 Part 3
and takes account of less ductile behaviour when n > 1.This formula does not apply
in cases where the shear-connector does not project at least 35mm above the top
of the deck.A further limit is that h  2D
p
in evaluating r
p
.
Where the decking is placed parallel to the beams no reduction is made for the
number of connectors but the constant in Equation (21.15) is reduced to 0.6 (instead
of 0.85).No reduction is made in the second case when b
a
/D
p
> 1.5.
Further geometric limits on the placing of the shear-connectors are presented in
Fig.21.15.The longitudinal spacing of the shear-connectors is limited to a maximum
of 600mm and a minimum of 100mm.
r
n
b
D
h D
D
n
n
p
a
p
p
p
for
for
=
-
Ê
Ë
Á
ˆ
¯
˜
£ =
£
=
0 85 1 0 1
0 8 2
..
.
÷
Basic design 621
Fig.21.14 Model of behaviour of shear-connector.(a) Shear-connector in plain slab.(b)
Shear-connector fixed through profile sheeting
minimum
dimensions
unless stated
100 mm
II1

looped
bars
:
slab
edge
25 mm or 1.250.
21.7.6 Longitudinal shear transfer
In order to transfer the thrust from the shear-connectors into the slab,without split-
ting,the strength of the slab in longitudinal shear should be checked.The strength
is further influenced by the presence of pre-existing cracks along the beam as a
result of the bending of the slab over the beam support.
The design recommendations used to check the resistance of the slab to longi-
tudinal shear are based on research into the behaviour of reinforced concrete slabs.
The design longitudinal shear stress which can be transferred is taken as 0.9N/mm
2
for normal weight and 0.7N/mm
2
for lightweight concrete;this strength is relatively
insensitive to the grade of concrete.
11
It is first necessary to establish potential planes of longitudinal shear failure
around the shear-connectors.Typical cases are shown in Fig.21.16.The top rein-
forcement is assumed to develop its full tensile resistance,and is resisted by an equal
and opposite compressive force close to the base of the shear-connector.Both top
and bottom reinforcement play an important role in preventing splitting of the
concrete.
The shear resistance per unit length of the beam which is equated to the shear
force transferred through each shear plane (in the case of normal weight concrete)
is:
V = 0.9L
s
+ 0.7A
r
f
y
£ 0.15 L
s
f
cu
(21.16)
where L
s
is the length of each shear plane considered on a typical cross-section,
which may be taken as the mean slab depth in Fig.21.16(a) or the minimum depth
in Fig.21.16(b).The total area of reinforcement (per unit length) crossing the shear
plane is A
r
.For an internal beam,the slab shear resistance is therefore 2V.
The effect of the decking in resisting longitudinal shear is considerable.Where
622 Composite beams
Fig.21.15 Geometric limits on location of shear-connectors
cover width of decking
C
b
b_______
a
overlap
(a)
(b)
aa
a
the decking is continuous over the beams,as in Fig.21.3(a),or rigidly attached by
shear-connectors,there is no test evidence of the splitting mode of failure.It is
assumed,therefore,that the deck is able to provide an important role as transverse
reinforcement.The term A
r
f
y
may be enhanced to include the contribution of the
decking,although it is necessary to ensure that the ends of the deck (butt joints)
are properly welded by shear-connectors.In this case,the anchorage provided by
each weld may be taken as 4f t
s
p
y
,where f is the stud diameter,t
s
is the sheet thick-
ness,and p
y
is the strength of the sheet steel.Dividing by the stud spacing gives the
equivalent shear resistance per unit length provided by the decking.
Where the decking is laid parallel to the beams,longitudinal shear failure can
occur through the sheet-to-sheet overlap close to the line of studs.Failure is assessed
assuming the shear force transferred diminishes linearly across the slab to zero at
a distance of B
c
/2.Therefore,the effective shear force that is transferred across the
longitudinal overlaps is (1 – cover width of decking/effective breadth) ¥ shear force.
The shear resistance at overlaps excludes the effect of the decking.
To prevent splitting of the slab at edge beams,the distance between the line of
shear-connectors and the edge of the slab should not be less than 100mm.When
this distance is between 100mm and 300mm,additional reinforcement in the
form of U bars located below the head of the shear-connectors is to be provided.
12
No additional reinforcement (other than that for transverse reinforcement) need
be provided where the edge of the slab is more than 300mm from the shear-
connectors.
21.7.7 Interaction of shear and moment in composite beams
Vertical shear can cause a reduction in the plastic moment resistance of a compos-
ite beam where high moment and shear co-exist at the same position along the beam
Basic design 623
Fig.21.16 Potential failure planes through slab in longitudinal shear
shear
force
moment
O5P
(i.e.the beam is subject to one or two point loads).Where the shear force F
v
exceeds
0.5P
v
(where P
v
is the lesser of the shear resistance and the shear buckling resist-
ance,determined from Part 1 of BS 5950),the reduced moment resistance is deter-
mined from:
(21.17)
where M
c
is the plastic moment resistance of the composite section,and M
f
is the
plastic moment resistance of the composite section having deducted the shear area
(i.e.the web of the section).
The interaction is presented diagrammatically in Fig.21.17.A quadratic relation-
ship has been used,as opposed to the linear relationship in BS 5950:Part 1,because
of its better agreement with test data,and because of the need for greater economy
in composite sections which are often more highly stressed in shear than non-
composite beams.
21.7.8 Deflections
Deflection limits for beams are specified in BS 5950:Part 1.Composite beams are,
by their nature,shallower than non-composite beams and often are used in struc-
tures where long spans would otherwise be uneconomic.As spans increase,so tra-
M M M M F P
ccv c f v v
= - -
( )
-
( )
2 1
2
624 Composite beams
Fig.21.17 Interaction between moment and shear
ditional deflection limits based on a proportion of the beam span may not be appro-
priate.The absolute deflection may also be important and pre-cambering may need
to be considered for beams longer than 10m.
Elastic section properties,as described in section 21.6.1,are used in establishing
the deflection of composite beams.Uncracked section properties are considered to
be appropriate for deflection calculations.The appropriate modular ratio is used,
but it is usually found that the section properties are relatively insensitive to the
precise value of modular ratio.The effective breadth of the slab is the same as that
used in evaluating the bending resistance of the beam.
The deflection of a simple composite beam at working load,where partial shear
connection is used,can be calculated from:
13
(21.18)
where d
c
and d
s
are the deflections of the composite and steel beam respectively at
the appropriate serviceability load;K is the degree of shear connection used in the
determining of the plastic strength of the beam (section 21.7.4).The difference
between the coefficients in these two formulae arises from the different shear-
connector forces and hence slip at serviceability loads in the two cases.These for-
mulae are conservative with respect to other guidance.
10
The effect of continuity in composite beams may be considered as follows.The
imposed load deflection at mid-span of a continuous beam under uniform load or
symmetric point loads may be determined from the approximate formula:
(1.19)
where d¢
c
is the deflection of the simply-supported composite beam for the same
loading conditions;M
0
is the maximum moment in a simply-supported beam subject
to the same loads;M
1
and M
2
are the end moments at the adjacent supports of the
span of the continuous beam under consideration.
To determine appropriate values of M
1
and M
2
,an elastic global analysis is carried
out using the flexural stiffness of the uncracked section.
For buildings of normal usage,these support moments are reduced to take into
account the effect of pattern loading and concrete cracking.The redistribution of
support moment under imposed load should be taken as the same as that used at
the ultimate limit state (see Table 21.1),but not less than 30%.
For buildings subject to semi-permanent or variable loads (e.g.warehouses),there
is a possibility of alternating plasticity under repeated loading leading to greater
imposed load deflections.This also affects the design of continuous beams designed
by plastic hinge analysis,where the effective redistribution of support moment
exceeds 50%.In such cases a more detailed analysis should be carried out consid-
ering these effects (commonly referred to as ‘shakedown’) as follows:
(1) evaluate the support moments based on elastic analysis of the continuous beam
under a first loading cycle of dead load and 80% imposed load (or 100% for
semi-permanent load);
d d
cc c 1 0
= ¢ - +
( )( )
1 0 6
2
.M M M
d d d d
d d d d
¢ = + -
( )
-
( )
¢ = + -
( )
-
( )
¸
˝
˛
c c s c
c c s c
for propped beams
for unpropped beams
0 5 1
0 3 1
.
.
K
K
Basic design 625
(2) evaluate the excess moment where the above support moment exceeds the
plastic resistance of the section under negative moment;
(3) the net support moments based on elastic analysis of the continuous beam
under imposed load are to be reduced by 30% (or 50% for semi-permanent
loads) and further reduced by the above excess moment;
(4) these support moments are input into Equation (21.19) to determine the
imposed load deflection.
21.7.9 Vibration
Shallower beams imply greater flexibility,and although the in-service performance
of composite beams and floors in existing buildings is good,the designer may be
concerned about the susceptibility of the structure to vibration-induced oscillations.
The parameter commonly associated with this effect is the natural frequency of the
floor or beams.The damping of the vibration by a bare steel–composite structure is
often low.However,when the building is occupied,damping increases considerably.
The lower the natural frequency,the more the structure may respond dynami-
cally to occupant-induced vibration.A limit of 4Hz (cycles per second) is a com-
monly accepted lower bound to the natural frequency of each element of the
structure.Clearly,vibrating machinery or external vibration effects pose particular
problems and in such cases it is often necessary to isolate the source of the
vibration.
In practice,the mass of the structure is normally such that the exciting force is
very small in comparison,leading to the conclusion that long-span structures may
respond less than light short-span structures.Guidance is given in Reference 14 and
Chapter 12.
21.7.10 Shrinkage,cracking and temperature
It is not normally necessary to check crack widths in composite floors in heated
buildings,even where the beams are designed as simply-supported,provided that
the slab is reinforced as recommended in BS 5950:Part 4 or BS 8110 as appropri-
ate.In such cases crack widths may be outside the limits given in BS 8110,but ex-
perience shows that no durability problems arise.
In other cases additional reinforcement over the beam supports may be required
to control cracking,and the relevant clauses in BS 8110:Part 2
15
and BS 5400:Part
5
5
should be followed.This is particularly important where hard finishes are used.
Questions of long-term shrinkage and temperature-induced effects often arise in
long-span continuous composite beams,as they cause additional negative (hogging)
moments and deflections.In buildings these effects are generally neglected,but in
bridges they can be important.
5,7
626 Composite beams
The curvature of a composite section resulting from a free shrinkage (or tem-
perature induced) strain e
s
in the slab is:
(21.20)
where I
c
and r are defined in section 21.6.1 and a
e
is the appropriate modular ratio
for the duration of the action considered.The free shrinkage strain may be taken
to vary between 100 ¥ 10
-6
in external applications and 300 ¥ 10
-6
in dry heated
buildings.A creep reduction factor is used in BS 5400:Part 5
5
when considering
shrinkage strains.This can reduce the effective strain by up to 50%.The central
deflection of a simply-supported beam resulting from shrinkage strain is then
0.125K
s
L
2
.
References to Chapter 21
1.British Standards Institution (1990) Structural use of steelwork in building.Part
3,Section 3.1:Code of practice for design of composite beams.BS 5950,BSI,
London.
2.The Steel Construction Institute (SCI) (1989) Design of Composite Slabs and
Beams with Steel Decking.SCI,Ascot,Berks.
3.Chien E.Y.L.& Ritchie J.K.(1984) Design and Construction of Composite Floor
Systems.Canadian Institute of Steel Construction.
4.Lawson R.M.(1988) Design for Openings in the Webs of Composite Beams.The
Steel Construction Institute,Ascot,Berks.
5.British Standards Institution (1979) Steel,concrete and composite bridges.Part
5:Code of practice for design of composite bridges.BS 5400,BSI,London.
6.Brett P.R.,Nethercot D.A.& Owens G.W.(1987) Continuous construction in
steel for roofs and composite floors.The Structural Engineer,65A,No.10,Oct.
7.Johnson R.P.& Buckby R.J.(1986) Composite Structures of Steel and Concrete,
Vol.2:Bridges,2nd edn.Collins.
8.British Standards Institution (1994) Eurocode 4:Design of Composite steel and
concrete structures.General rules and rules for buildings.DD ENV 1994-1-1,
BSI,London.
9.Yam L.C.P.& Chapman J.C.(1968) The inelastic behaviour of simply supported
composite beams of steel and concrete.Proc.Instn Civ.Engrs,41,Dec.,651–83.
10.American Institute of Steel Construction (1986) Manual of Steel Construction:
Load and Resistance Factor Design.AISC,Chicago.
11.Johnson R.P.(1975 & 1986) Composite Structures of Steel and Concrete.Vol.1:
Beams.Vol.2:Bridges,2nd edn.Granada.
12.Johnson R.P.& Oehlers D.J.(1982) Design for longitudinal shear in composite
L beams.Proc.Instn Civ.Engrs,73,Part 2,March,147–70.
13.Johnson R.P.& May I.M.(1975) Partial interaction design of composite beams.
The Structural Engineer,53,No.8,Aug.,305–11.
K
D D D A
r I
s
s s p
e c
=
+ +
( )
+
( )
e
a2 1
References 627
14.Wyatt T.A.(1989) Design Guide on the Vibration of Floors.The Steel
Construction Institute (SCI)/CIRIA.
15.British Standards Institution (1985) Structural use of concrete.Part 2:Code of
practice for special circumstances.BS 8110,BSI,London.
16.Lawson R.M.,Mullet D.L.& Rackham J.W.(1997) Design of Asymmetric
Slimflor
®
Beams Using Deep Composite Decking.The Steel Construction
Institute,Ascot,Berks.
A series of worked examples follows which are relevant to Chapter 21.
628 Composite beams