Civil Engineering Reference
In-Depth Information
the diameters
2.9 N/mm
2
.
For other concrete strengths, the diameter is given in EN 1994-1-1 by
φ
*, for concrete with the reference strength
f
ct,0
=
φ
=
φ
*
f
ct,eff
/
f
ct,0
The stress
σ
s
may not exceed
f
sk
for the bars to be used.
4.2.5.3
Control of load-induced cracking
A global analysis is required, to determine the bending moment at the
cross-section considered. This is usually a cross-section at an internal
support, where the hogging bending moment is a maximum.
In EN 1992-1-1, the use of the quasi-permanent load combination
(Section 1.3.2.3) is recommended. Imposed loads are then lower than for
the characteristic combination, which is used for deciding where minimum
reinforcement is required. The resulting bending-moment envelope thus
has a lower proportion of each span subjected to hogging bending.
The use of the quasi-permanent combination also implies that there are
no adverse effects if the cracks are wider for short periods when heavier
variable loads are present. It may sometimes be necessary to check crack
widths for a less probable load level, either 'frequent' or 'characteristic'.
Where unpropped construction is used, load resisted by the steel member
alone is excluded.
Elastic global analysis (Section 4.3.2) is used. If relative stiffnesses are
based on uncracked concrete in regions where the slab is in tension, the
hogging moments will be overestimated, typically by about 10%.
The tensile stress in the reinforcement nearest to the relevant concrete
surface is calculated by elastic section analysis, neglecting concrete in
tension. This stress,
σ
s,o
, is then increased to a value
σ
s
by a correction for
tension stiffening, given by
σ
s
=
σ
s,o
+
0.4
f
ctm
A
ct
/(
α
st
A
s
)
(4.34)
where
AI
2
/A
a
I
a
. The values
A
and
I
2
are for the cracked transformed
composite section, and
A
a
and
I
a
are for the structural steel section. Elastic
properties of the uncracked section are also needed, to find
A
ct
, the area of
concrete in tension. This is not divided by the modular ratio.
A
s
is the area
of reinforcement within the area
A
ct
.
The correction to
α
st
=
σ
s,o
is largest for lightly reinforced slabs (high
A
ct
/
A
s
)
of strong concrete (high tensile strength,
f
ctm
). The basis of Equation 4.34 is
that, until cracking is fully developed, the curvature of the steel beam equals
the mean curvature of the slab, which is above-average at cracks (which
increases the mean stress
σ
s,o
to
σ
s
), and below-average between cracks.
