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PrEN1994-1-2 provides the simple calculation models
for determining the sagging and hogging moment resistances of unprotected
composite slabs with profiled steel decking exposed to the standard
fire. The evaluation of the temperature profiles in the slabs is
given in its Annex D (informative).
Basically, the approach allows the temperatures
of steel sheet, reinforcement bars in the ribs and the concrete
slab to be separately calculated. The temperatures of the lower
flange, web and upper flange of the steel decking, and the reinforcement
bars in the ribs can be obtained by using the empirical formulae.
However, the calculation of temperature profiles for the concrete
part of the slabs is rather complicated as the temperature distribution
across a concrete cross-section exposed to fire conditions will
not be uniform. It will be too complicated to establish the isotherms
within the concrete by using empirical formulae.
Currently, prEN1994-1-2 only provides a simple
model for establishing the isotherm for a certain limiting temperature
within the concrete, with temperatures beyond the limiting temperature
being neglected and the remaining cross section being taken as
under room temperature conditions. It must be emphasised that the
limiting temperature is derived from equilibrium over the cross
section and has no relation with temperature penetration (Both
1998). Such simplification may be adequate for the calculation
of hogging moment resistance, but not for the thermal response
analysis of the slabs. Alternatively, prEN1994-1-2 provides a conservative
approximation by treating the composite slabs as solid slabs with
the temperature distribution given in a table.
One assumption of the method is that the steel
deck remains bonded to the concrete.
Steel Decking
The temperatures Θa of the lower flange,
web and upper flange of the steel decking are given by:
 |
(1) |
| with |
 |
where
| Φ |
is the view factor of the upper flange [-]; |
| b0…b4 |
is the coefficients for determining the temperatures of various
parts of the steel decking as given in Table
1; |
| A/Lr |
is the rib geometry factor [mm]; |
| A |
is the concrete volume of the rib per m rib length [mm3/m]; |
| h2 |
is the depth of the rib [mm]; |
| Lr |
is the exposed area of the rib per m rib length [mm3/m]; |
| l1,l2 |
is the distances as shown in Figure 1 [mm]; |
| l3 |
is the width of the upper flange [mm]. |
The definition of the geometric dimensions and
factors of a typical composite slab is given in Figure 1.
Figure 1 Definition of geometric dimensions of composite
slabs (EN1994-1-2: 2003)
Reinforcement Bars
The temperature Θs of
the reinforcement bars in the rib (see Figure 2) is given by:
 |
(2) |
| with |
 |
where
| α |
is the angle of the web [degree]; |
| c0…c5 |
is the coefficients for determining the temperature of rebars
in the rib as given in Table
2; |
| A/Lr |
is the rib geometry factor [mm]; |
| A |
is the concrete volume of the rib per m rib length [mm3/m]; |
| h2 |
is the depth of the rib [mm]; |
| Lr |
is the exposed area of the rib per m rib length [mm2/m]; |
| l3 |
is the width of the upper flange [mm]; |
| u1, u2 |
is the shortest distance from the rebar centre to any point
of the webs [mm]; |
| u3 |
is the distance from the rebar centre to lower flange [mm]; |
| z |
is the factor indicating the position of rebar in the rib
[mm-½]. |
Figure 2 illustrated how to measure the distances u1 ,
u2 and u3 for the reinforcement
bars in the ribs of a composite slab.
Figure 2 Definition of u1 , u2 and u3 for
rebar in the rib (EN1994-1-2: 2003)Concrete Slab over Steel Decking
For the concrete slab over steel decking, prEN1994-1-2
does not provide a simple model for calculating the temperature
distribution. It only provides a conservative approximation by
treating the composite slabs as solid slabs with the temperature
distribution.
In the calculation, the composite slab is replaced
by a solid slab with an effective thickness heff which
is given by:
 |
(3) |
where the cross section dimensions h1 ,
h2 , l1 , l2 and l3 are
given in Figure 3.
Figure 3 Cross section dimensions of composite slabs
(EN1994-1-2: 2003) The temperature at a depth x from heff can
then be obtained from Table
3.
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