Shear Connection in composite beams

ADVISORY DESK
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AD 266
Shear Connection in
composite beams
Following some recent questions on the requirements given in
BS 5950-3: 1990 for the design of the shear connection in composite
beams, a clarification of three major issues is given in this advisory desk
article. These issues are:
• Effective breadth of the concrete flange (BS 5950-3: 1990 Clause 4.6)
• Partial shear connection (BS 5950-3: 1990 Clause 5.5)
• Transverse reinforcement (BS 5950-3: 1990 Clause 5.6)
Effective breadth of the concrete flange
(BS 5950-3: 1990 Clause 4.6)
In normal composite construction, a relatively thin concrete floor slab
acts as the compression flange of the composite beam. The longitudinal
compressive bending stresses in the slab cause shear stresses in the
plane of the slab as shown in Figure 1.
The effective width is defined mathematically by the following equation:
Be = 2
b
0
σx
σxmax dy
The above equation allows the actual flange width B to be replaced by
an effective width Be , such that the area GHJK equals the area ACDEF
(see Figure 2). Previous research, based on elastic theory, has shown that
the ratio of Be/B depends in a complex way on:
• the ratio of B to the span L
• the type of loading
• the boundary conditions at the supports
• other variables.
The results of this work have been simplified and incorporated in
BS 5950-3: 1990 Clause 4.6. According to this code of practice, the total
effective breadth of the concrete flange Be should be taken as the sum of
the effective breadths of the portions of flange be each side of the centreline of the steel beam. In the absence of any more accurate determination,
the effective breadth of each portion may be taken to be:
a) for a slab spanning perpendicular to the beam,
be = Lz / 8 >b
/
b) for a slab spanning parallel to the beam
be = Lz / 8 >0.8b
/
Figure 1. Shear stresses in a composite beam
The shear stresses cause shear strains in the plane of the slab. One effect
of these shear strains is that the areas of slab furthest from the steel
beams are not as effective at resisting longitudinal bending stresses as
the areas close to the steel beams. This effect is called shear lag. As a
result, the longitudinal bending stress across the width of the slab is not
constant, see Figure 2. The longitudinal stress tends to be a maximum
over the web of the steel section, and reduces non-uniformly away from
the centre-line of the beam.
In order that simple “engineers” bending theory may be applied (i.e.,
plane sections remain plane in bending), the effective width concept is
introduced. The section properties are calculated using the effective
width, Be , which is assumed to carry a uniform stress across the width
Be. The value of the stress in the concrete calculated using these effective
section properties is equal to the maximum stress resulting from the
effects of shear lag in the actual slab.
Figure 2. Use of effective width to allow for shear lag
where Lz is the distance between points of zero moment (taken as the
span L for simply-supported beams) and b is the actual breadth of each
portion of the concrete flange (taken as half the beam spacing or, when
the beam is adjacent to a free edge, the distance between the centre-line
of the web and the free edge).
It should be noted that unless a reduction in composite action has been
justified by tests or numerical analyses, it is not appropriate to consider
a smaller effective width than given by the expressions shown above.
This is because an underestimate of the effective width of the concrete
flange will result in unsafe designs for the shear connectors. For this
particular reason, the values of the effective breadth given in Eurocode 4
are generally higher than those in Eurocode 2 for reinforced concrete
T-beams.
Partial shear connection
(BS 5950-3: 1990 Clause 5.5)
The basic requirement for shear connectors is that they are capable of
maintaining their design resistance to shear at large slips, to enable the
composite beam to have sufficient rotation capacity to develop its full
design bending resistance. The ductility of a shear connector is defined
by its slip capacity, which is established from a standard push test, and
is defined by the maximum slip that the connector can resist while still
maintaining its design resistance. Provided that studs have a slip
capacity greater than required in a beam design, they are considered to
be “ductile”, allowing a plastic distribution of force to be assumed at the
shear connection. This means that the studs may be spaced equally
along the beam and assumed to be equally loaded under flexural failure
of the beam. Note that the deformations of the connectors will not be
equal, but will be much greater at the ends of the beam than at mid-span.
From extensive numerical analyses and full-scale beam tests, it has been
shown that, to enable a beam to develop its full bending resistance, the
slip required increases with the beam span and the degree of shear
connection. In addition, for steel sections that have a bottom flange area
greater than the top flange (i.e., asymmetric sections), the slip required
increases further, due to the neutral axis lying further down within the
steel section.
ADVISORY DESK
Rather than stating slip capacities directly, the current codes of practice
allow designers to assume a plastic distribution of force at the shear
connection by specifying minimum degrees of shear connection in terms
of the beam span and, in the case of Eurocode 4, the degree of
asymmetry of the steel section. These code rules are based on numerical
studies of composite beams that considered the slip capacity of the shear
connection explicitly.
According to BS 5950-3: 1990, for a steel beam with equal flanges, the
following relationship for the degree of shear connection should be
satisfied:
For spans up to 10m
Na / Np ≥ 0.4
For spans between 10 and 16m
Na / Np ≥ (L - 6) / 10 but
Na / Np ≥ 0.4
For typical internal composite beams that are equally spaced, the
effective breadth of each portion of the concrete flange be is equal. In this
case, the longitudinal shear force in each portion of the concrete flange is
equal, and the longitudinal shear force that has to be transferred along
potential shear planes such as a-a and e-e has a value of V/2. Due to the
fact that it is normal to assume a plastic distribution of force at the shear
connection, it is often more convenient to work in terms of a longitudinal
shear force per unit length v, in which case the following equation may
be used:
where Na is the actual number of shear connectors provided,
Np is the number of shear connectors required for full shear
connection and
• for full shear connection, taken as either the lesser of resistance of the
concrete flange or the steel section,
• for partial shear connection, taken as the resistance of the shear
connection
L is the beam span in metres.
and s is the spacing of the shear connectors.
The partial shear connection rules given in Eurocode 4 are applicable for
much larger spans and additional guidance is given for steel sections
with unequal flanges (provided that the bottom flange area does not
exceed three times the upper flange area). In these cases, ‘ductile’
connectors are defined as those with a characteristic slip capacity of
6mm. Although BS 5950-3: 1990 and Eurocode 4 give different
expressions for partial shear connection, they are identical in one respect
viz. the degree of shear connection provided in a composite beam should
not be less than 0.4.
v = V / 2s
where V is the longitudinal shear force, and is:
However, for cases when composite beams are not spaced equally, or
when a beam is adjacent to a free edge (such as at a hole in the slab), the
longitudinal shear force per unit length along potential shear planes
either side of the beam is no longer equal. This design case is illustrated
in Figure 4.
Transverse reinforcement
(BS 5950-3: 1990 Clause 5.6)
In composite beams, the longitudinal shear force that has to be
transferred between the steel beam and the concrete flange is dependent
on whether full shear connection or partial shear connection is provided.
If the shear connectors are "ductile" (see requirements for partial shear
connection above), a plastic distribution of force may be assumed at the
shear connection. For full shear connection, the magnitude of this
longitudinal shear force V is equal to the lesser of either the crosssectional resistance of the concrete flange or the cross-sectional
resistance of the steel section. For partial shear connection, the
longitudinal shear force is equal to the resistance of the shear connection
(i.e., the design resistance of the stud multiplied by the number of
connectors provided between the support and the critical section under
consideration).
For composite beams using composite or solid slabs, BS 5950-3: 1990
requires that sufficient transverse reinforcement should be provided to
resist the longitudinal shear force V, to prevent longitudinal splitting of
the concrete flange along the potential shear planes shown in Figure 3.
Figure 4. Composite beam with an unsymmetrical concrete flange
For the special case shown in Figure 4, the longitudinal shear force per
unit length along shear planes f-f and g-g may be calculated from the
following expressions:
v
v
f-f
g-g
= Vb2 / Bes
= Vb1 / Bes
For further information contact:
Dr Stephen Hicks, SCI.
Tel: 01344 623345
E-mail: [email protected]
Figure 3. Potential shear planes according to BS5950-3: 1990
A) Solid slab
B) Composite slab with the sheeting spanning
perpendicular to the beam
C) Composite slab with the sheeting spanning
parallel to the beam
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