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BEAMS, SLABS, COLUMNS, AND FRAMES FOR BUILDINGS
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Introduction
he design of structures for buildings and bridges is mainly concerned with the provision and
support of load-bearing horizontal surfaces. Except in long-span bridges, these floors or decks are
usually made of reinforced concrete, for no other material has a better combination of low cost,
high strength, and resistance to corrosion, abrasion, and fire.
The economical span for a reinforced concrete slab is little more than that at which its thickness
becomes just sufficient to resist the point loads to which it may be subjected or, in buildings, to
provide the sound insulation required. For spans of more than a few metres it is cheaper to support
the slab on beams or walls than to thicken it. When the beams are also of concrete, the monolithic
nature of the construction makes it possible for a substantial breadth of slab to act as the top flange
of the beam that supports it.
At spans of more than about 10 m, and particularly where the susceptibility of steel to damage
by fire is not a problem, as for example in bridges and multi-storey car parks, steel beams become
cheaper than concrete beams. It used to be customary to design the steelwork to carry the whole
weight of the concrete slab and its loading; but by about 1950 the development of shear
connectors had made it practicable to connect the slab to the beam, and so to obtain the T-beam
action that had long been used in concrete construction. The term ‘composite beam’ as used in this
book refers to this type of structure.
The same term is used for beams in which prestressed and in-situ concrete act together, and
there are many other examples of composite action in structures, such as between brick walls and
beams supporting them, or between a steel-framed shed and its cladding; but these are outside the
scope of this book.
No income is received from money invested in the construction of a multi-storey building such
as a large office block until the building is occupied. For a construction time of two years, this loss
of income from capital may be 10% of the total cost of the building; that is, about one-third of the
cost of the structure. The construction time is strongly influenced by the time taken to construct a
typical floor of the building, and here structural steel has an advantage over in-situ concrete.
Even more time can be saved if the floor slabs are cast on permanent steel formwork that acts first
as a working platform, and then as bottom reinforcement for the slab. This formwork, known as
profiled steel sheeting, has long been used in tall buildings in North America.(1) Its use is now
standard practice in most regions where the sheeting is readily available, such as Europe,
Australasia and Japan. These floors span in one direction only, and are known as composite
slabs.,where the steel sheet is flat, so that two-way spanning occurs, the structure known as a
Shear Connection
Introduction
The established design methods for reinforced concrete and for structural steel give no help with
the basic problem of connecting steel to the concrete. The force applied to this connection is
mainly, but not entirely, longitudinal shear. As with bolted and welded joints, the connection is a
region of severe and complex stress that defies accurate analysis, and so methods of connection
have been developed empirically and verified by tests. They are described in Section 2.4.
The simplest type of composite member used in practice occurs in floor structures of the type
shown in Fig.3.1. The concrete floor slab, other two together span in the x-direction as a
composite beam. The steel member has not been described as a ‘beam’, because its main function
at midspan is to resist tension, as does the reinforcement in a T-beam. The compression is assumed
to be resisted by an ‘effective’ breadth of slab, as explained in Sections 3.4.
In building, but not in bridges, these concrete slabs are often composite with profiled steel
sheeting (Fig.2.8), which rests on the top flange of the steel beam. Other type of cross-section that
can occur in composite beams are shown in Fig
Simply-supported beam of rectangular cross-section
Flitched beams, whose strength depended on shear connection between parallel timbers, were used
in mediaeval times, and survive today in the form of glued-laminated construction, such a beam,
made from two members of equal size (Fig.2.2), will now be studied. It carries a load w per unit
length over a span L, and its components are made of an elastic material with Young’s modulus E.
The weight of the beam is neglected.
Uplift
In the preceding examplem the stress normal to the interface AOB (Fig.2.2) was everywhere
compressive and equal to w/2b except at the ends of the beam .The stress would have been tensile
if the load w had been applied to the lower member. Such loading is unlikely, except when
traveling cranes are suspended from the steelwork of a composite floor above: but there are other
situations in which stresses tending to cause uplift can occur at the interface. These arise from
complex effects such as the torsional stiffness of reinforced concrete slabs forming flanges of
composite beams, the triaxial stresses in the vicinity of shear connectors and, in box-girder bridges,
the torsional stiffness of the steel box.
Tension across the interface can also occur in beams of non-uniform, Section or with partially
completed flanges. Two members without shear connection, as shown in Fig. 2.5,provide a simple
example. AB. Is sup-ported on CD and carries distributed loading. It can easily be shown by
elastic theory that if the flexural rigidity of AB exceeds about one-tenth of that of CD, then the
whole of the load on AB is transferred to CD at points A and B, with separation of the beams
between these points. If AB was connected to CD, there would be uplift forces at midspan.
Bond
Until the use of deformed bars became common, most of the reinforcement for concrete consisted
of smooth mild-steel bars. The transfer of shear from steel to concrete was assumed to occur by
bond or adhesion at the concrete-steel interface. Where the steel component of a composite
member is surrounded by reinforced concrete, as in an encased beam, Fig.2.1©, or an encased
stanchion, Fig, 5.15, the analogy with reinforced concrete suggests that no shear connectors need
be provided. Tests have shown that this is usually true for cased stanchions and filled tubes, where
bond stresses are low, and also for cased beams in the elastic range. But in design it is necessary to 33
restrict bond stress to a low value, to provide a margin for the incalculable of steel surfaces, and
stresses due to variations of temperature.
Simply-supported Composite Slabs and Beams
The subjects of this and subsequent chapters are treated in the sequence in which they developed.
Relevant structural behaviour is discovered by experience or research, and is then represented by
mathematical models. These make use of standardized properties of materials, such as the yield
strength of steel, and enable the behaviour of a member under load to be predicted. The models are
developed into design rules, as found in codes of practice, by simplifying them wherever possible,
defining their scope and introducing partial safely factors.
Research workers often propose alternative models, and language barriers are such that the
model preferred in one country may be little known elsewhere. The writers of codes try to select
the most rational and widely-applicable of the available models, but must also consider existing
design practices and the need for simplicity. The design rules used in this volume are taken from
the Eurocodes, which differ slightly from the corresponding British codes; but the underlying
models are usually the same, and significant differences will be explained.
There will inevitably be minor differences between the methods used here and those of any code
which the reader may consult. Only the preliminary (ENV) versions of the Eurocodes are yet
available, and each country can choose ‘national’ values for the partial safety factors, that may
differ from those given in the codes.
The methods to be described are illustrated by the design calculations for part of a framed
structure for a building. To avoid repetition, the results obtained at each stage are used in
subsequent work. Much of the material on beams finds application also in bridge structures, which
are treated in Volume 2.
The notation used is that of the Eurocodes. It is more consistent than that used in current British
codes, less ambiguous, but sometimes more complex. It is listed at the start of the book. The
following comments on it may be useful.
Composite floor slabs
Composite slabs have for several decades been the most widely used method of suspended floor
construction for steel-framed buildings in North America. Within the last twenty years there have
been many advances in design procedures, and a wide range of profiled sheetings has become
available in Europe. The British Standard for the design of composite floors first appeared in 1982,
and there are preliminary Eurocodes for design of both the sheeting alone and the composite slab.
The steel sheeting has to support not only the wet concrete for the floor slab, but other loads that
are imposed during concreting. These may include the heaping of concrete and pipeline or
pumping loads. The minimum characteristic value given for these in Eurocode 4 is 1.5 kN/m3
on
any area 3 m by 3 m, plus 0.75 kN/m2
on the remaining area.
Profiled steel sheeting
The sheeting is very thin, for economic reasons; usually between 0.8mm and 1.2mm. it has to be
galvanized to resist corrosion, and this adds about 0.04mm to the overall thickness. It is specified
in Eurocode 3. Part 1.3 that where design is based on the nominal thickness of the steel, the sheet
must have at least 95% of that thickness – but it is not a simple matter for the user to check this!
The sheets are pressed or cold rolled, and are typically about 1m wide and up to 6 m long. They
are designed to span in the longitudinal direction only. For many years, sheets typically 50 mm
deep, and the limiting span was about 3 m. The cost of propping the sheets during concreting led
to the development of deeper profiles; but design of composite slabs is still often governed by a
limit on deflection. There is then no advantage in using a high-yield steel, so most sheeting in the
UK is of mild stee
Continuous Beams and Slabs, and Beams in Frames
The definition of ‘continuous composite beam’ given in Eurocode 4: Part 1.1[12] is:
A beam with three or more supports, in which the steel section is either continuous over internal
supports or is jointed by full strength and rigid connections, with connections between the beam
and each support such that it can be assumed that the support does not transfer significant
bending moment to the beam. At the internal supports the beam may have either effective
reinforcement or only nominal reinforcement.
Beam-to-column connections in steelwork are classified in Eurocode 3: Part 1.1[11] both by
stiffness, as:
z nominally pinned,
z rigid, or
z semi-rigid
and by strength, as:
z nominally pinned,
z full-strength, or
z partial-strength.
In Eurocode 4: Part 1.1, a ‘composite connection’ is defined as:
A connection between a composite member and any other member in which reinforcement is
intended to contribute to the resistance of the connection.
The system of classification is as for steel connections, except that semi-rigid connections are
omitted, because design methods for them are not ye sufficiently developed.
A ‘full-strength and rigid’ connection has to be at least as stiff and strong as the beams
connected, so a ‘continuous composite beam’ can be analyzed for bending moments as one long
member without internal connections, by methods to be explained in Section 4.3. Bridge girders
(Volume 2) are usually of this type. The example to be used here is a two-span beam continuous
over a wall or supporting beam.
In multi-bay plane frames, commonly used in structures for buildings, the beam-to-column
connections are often ‘nominally pinned’. The beams are then designed as simply-supported,
where full-strength connections are used, the frame should be analysed as a whole, and the beams
are not ‘continuous’ as defined above. These beams are referred to here as ‘beams in frames’, as
are those with partial-strength connections. In comparison with simple spans, beams in frames
have the same advantages and disadvantages as continuous beams. The global analysis is more
complex than for continuous beams, because the properties of columns and connections are