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Geometric Properties for Grillages
"Grillage" geometric properties should be used
in preference to "Thick Beam" geometric properties
for a 2D grillage. This is particularly important
if you may later wish to extract Wood-Armer
moments, since this allows the input of "effective
width".
Second moment of area about y axis (Iyy)
When performing a static analysis Iyy is the only I value used* in a 2D engineering grillage
model with GRIL elements. The second moment of inertia about
the local z, (Izz), is only required when assembling the
mass matrix. Therefore Izz in GRIL elements is used in an
eigen value or dynamics analysis.
In a 2D static grillage it is
perfectly acceptable to specify only one I value (e.g. Izz =
Iyy or Izz = 0). This ensures that the
relevant bending stiffness has been specified in the
analysis. For eigen value or dynamics analysis Izz must be specified.
Where an upstand / downstand grillage is being considered
3D thick beam elements are used and thus Izz value must be defined
correctly in such a static analysis.
* This is indicated in the Help menu:
Help Topics > Contents > Element reference manual > Elements >
Beam Elements > 2D Engineering Grillage Thick Beam Element > Output
- since only Fz, Mx and My output will be reported.
Torsional Properties
Torsional properties are often very important to the
behaviour of a grillage model and are the subject of several
texts which cannot be readily summarised. The derivation
of torsional properties should be carefully considered and
cross-checked where possible. Users may find the following
references on torsional constant helpful:
Help topics > Contents > Element reference
manual > Appendices > Shear Area and Torsional Constant > Torsional Constant
"Recommendations On The Use Of
Grillage Analysis For Slab And Pseudo-Slab Bridge
Decks" R West (C&CA/CIRIA)
C(solid beam)=kb³b(max)
"Bridge Deck Behaviour" Edmund C
Hambly (Chapman & Hall)
C(continuous slab)=BD³/6
It is advisable to give a figure (even if small) rather
than zero. In steel/ concrete composite bridges some
engineers find it is simpler to assess torsional constants by
converting to equivalent concrete units throughout rather than
equivalent steel units. However care should be taken to
consider long-term and short-term effects properly.
More bridge modelling
notes including voided
slab decks and steel/concrete
composite decks
Shear areas
You can find guidance on an appropriate value to use for
this parameter in the Help menu:
Help topics > Contents > Element reference
manual > Appendices > Shear Area and Torsional Constant > Shear areas
As = zero should not be used as this results in mechanisms
in the model. To neglect shear deformations, As must be
set to a large value (e.g. As=1000A).
To use the Wood-Armer
equations for grillages the bending and twisting moments
obtained from the analysis have to be converted into "equivalent
plate moments" in global directions. An extra geometric
property (effective width) has to be defined for the grillage
members in order to compute the "equivalent plate
moments". In the normal way the "effective width"
will be the width of slab assigned to the member in question.
More on
Wood-Armer
calculations
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