Steel Beam Design
PROPERTIES
If a rod of steel is subjected to a tensile test (Fig. 4. 1(a) ), and the stress in the rod (load/cross
sectional area in N/mm2) is plotted against the strain (change in length/original length), as the load
is applied, a graph similar to that shown in Fig. (b) would be obtained. the stress-strain curve is linear
up to a certain value, known as the yield point. Beyond this point the steel yields without an increase
in load, although there is significant ‘strain hardening’ as the bar continues to strain towards failure.
This is the plastic range.
Stress Strain Curve
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In the elastic range the bar will return to
its original length if unloaded. However,
once past the yield point, in the plastic
range, the bar will be permanently
strained after unloading.
Idealized Stress-Strain
Fig. shows the idealised stress-strain curve for
structured steelwork which is used in the design of steel
members.
The slope of the stress-strain curve in the elastic range is
referred to as the modulus of elasticity or Young’s modulus
and is denoted by the letter E. It indicates the stiffness of
the material and is used to calculate deflections under
load. Structural steel has a modulus of elasticity of 205
kN/mm2.
Structural steel and steel sections
Structural steel is manufactured in three basic grades: S275, S355 and S460. Grade S460 is the
strongest, but the lower strength grade S275 is the most commonly used in structural applications,
for reasons that will later become apparent. In this classification system ‘S’ stands for structural and
the number indicates the yield strength of the material in N/mm2.
The geometric properties of these steel sections, including the principal dimensions, area, second
moment of area, radius of gyration and elastic and plastic section moduli have been tabulated in a
booklet entitled Structural Sections to BS4: Part 1: 1993 and BS EN10056: 1999 which is published by
Corus Construction and Industrial.
Structural steel used in the UK is specified by BS 5950: Part 2, and strengths of the more commonly
used steels are given in
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Table 9 of BS 5950,
MODES OF FAILURE
4.8.1.1 Bending
The vertical loading gives rise to bending of the beam. This results in longitudinal stresses being set
up in the beam. These stresses are tensile in one half of the beam and compressive in the other.
As the bending moment increases, more and more of the steel reaches its yield stress. Eventually, all
the steel yields in tension and/or compression across the entire cross section of the beam. At this
point the beam cross-section has become plastic and it fails by formation of a plastic hinge at the
point of maximum moment induced by the loading.
Local buckling
During the bending process outlined above, if
the compression flange or the part of the web
subject to compression is too thin, the plate
may actually fail by buckling or rippling, as
shown in Fig. before the full plastic moment is
reached.
Shear
Due to excessive shear forces, usually adjacent
to supports, the beam may fail in shear. The
beam web, which resists shear forces, may fail
as shown in Fig, as steel yields in tension and
compression in the shaded zones. The
formation of plastic hinges in the flanges
accompanies this process.
Shear buckling
During the shearing process described above, if
the web is too thin it will fail by buckling or
rippling in the shear zone, as shown in Fig.
Web bearing and buckling
Due to high vertical stresses directly over a support or under a concentrated load, the beam web
may actually crush, or buckle as a result of these stresses, as illustrated in Fig.
Lateral torsional buckling.
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When the beam has a higher bending stiffness in the vertical plane compared to the
horizontal plane, the beam can twist sideways under the load. This is perhaps best visualised
by loading a scale rule on its edge, as it is held as a cantilever – it will tend to twist and
deflect sideways. This is illustrated in Fig. Where a beam is not prevented from moving
sideways, by a floor, for instance, or the beam is not nominally torsionally restrained at
supports, it is necessary to check that it is laterally stable under load. Nominal torsional
restraint maybe assumed to exist if web cleats, partial depth end plates or fin plates, for
example, are present .
Deflection
Although a beam cannot fail as a result of excessive deflection alone, it is necessary to ensure that
deflections are not excessive under unfactored imposed loading. Excessive deflections are those
resulting in severe cracking in finishes which would render the building unserviceable.
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Example Selection of a beam section in grade S275 steel (BS 5950)
The simply supported beam in Fig. supports uniformly distributed characteristic dead and imposed
loads of 5 kN/m each, as well as a characteristic imposed point load of 30 kN at mid-span. Assuming
the beam is fully laterally restrained and there is nominal torsional restrain at supports, select a
suitable UB section in S275 steel to satisfy bending and shear considerations.
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DESIGN BENDING MOMENT AND SHEAR FORCE
Total loading = (30 × 1.6) + (5 × 1.4 + 5 × 1.6)10 = 48 + 15 × 10 = 198 kN