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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).

Effective Width

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

Back to Grillage Modelling Issues


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