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Steel/Concrete Composite Decks
In modelling steel/concrete
composite decks a grillage model
may be appropriate, although the deck may be modeled using
plate elements for the deck slab with beam elements modelling
the beams (a "ribbed plate"). Alternatively
you
may wish to consider a 3D shell model, or even a 3D solids
model. However, it is always instructive to build
up understanding of the behaviour of a structure from simple
models. Advice is available from a variety
of references including:
- "Bridge Deck Behaviour" Edmund C Hambly
(Chapman & Hall), last revised 1990, in particular pages 8-11
and chapters 4 ("Beam-and-slab decks"), 8 and 9.
- "Bridge Deck Analysis" Eugene J.
O'Brien and Damien L. Keogh (E&FN SPON, 1999)
Benefits / drawbacks of modelling options
In LUSAS a ribbed plate can be assembled simply and quickly using a
single line feature for each span, on the centreline of each beam, and
a long thin surface feature for the slab which spans between these
beams. Mesh, geometric
properties, materials, support and loads are then assigned to the
features in order to complete the model.
There are at least three potential areas of difficulty with a model constructed from beam & shell elements:
- Eccentricities/ transverse
bending
- Cracking of the RC slab in hogging
areas
- Post-processing.
Eccentricities are required but this causes problems with transverse stiffness.
For longitudinal bending, it is intuitive to model the nodal plane of the bridge deck model as lying at the composite neutral axis (NA) of the structure. 3D beam elements would represent the bridge beams, with an eccentricity to account for the beam NA being below the overall deck NA. 3D shell elements would represent the RC slab, with an eccentricity to account for the slab NA being above the overall deck NA. However, for transverse bending, the slab alone is effective; bending about the NA of the slab alone rather than that of the overall deck i.e. an eccentricity of zero is required. Thus the shell elements would require different eccentricity in two directions. This is not possible and the
engineer should therefore be aware of this approximation. If more
accuracy is required it is possible to model beams with shell elements
in details.
For a model with transverse bending loading a workaround to the
transverse stiffness problem might be to use beam elements representing the longitudinal stiffness of a composite section (as for a grillage model) and with
total eccentricity from plate centerline, using plate elements to represent the slab,
with zero eccentricity.
In "Bridge Deck Analysis" (Eugene J O'Brien & Damien L Keogh), E&FN
Spon, 1999, section 6.5, the authors describe how such a model may be constructed using beam elements to represent the composite section, subtracting the stiffness of the RC slab at the neutral axis level, as an improvement on the workaround described above. While this seems suitable extracting results from such a model
may not be straightforward.
Cracking in hogging areas.
The longitudinal stiffness contributed by the RC slab should be lower in hogging regions to account for the effect of cracking - the stiffness there being normally based upon the reinforcement provided rather than gross concrete section. The transverse stiffness of the slab would be unchanged in such areas. If attempting to use a beam & shell model with eccentricities included this would pose a problem. However, the issue is eliminated if using
a grillage modelling approach. In such a model it is possible to
include the cracked section properties of the longitudinal beams as appropriate.
Post- processing and subsequent design calculations
Codes of practice (such as BS5400: Part 5) may not have been written with post-processing for a beam & shell model in mind, often being written when grillages were the only practical available option. However, again, using the workaround described in 1 above, the composite design using (for example) BS5400: Part 5 should be possible.
Although it seems that a grillage beam & 2D plate model may be suitable, the relative advantages over a grillage model are not quantified and it would be appropriate for the engineer to consider the case for a specific bridge structure. It may, for example, be useful in heavily skewed decks.
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