Transverse member in Grillage analysis 1

[TewitC]

Hi recently there has been a question occured in my mind. When we do grillage model, let's say I girder bridge with cast in-situ deck, we assign the properties of I section plus those of deck slab with its appropriate effective width.
For transverse member, we simply assign the property of slab (width and thickness). My question lies here when the applied loads try to distribute transversely, or in other words, when we look at how adjacent girders are connected. The transverse distribution is generally influenced by two factors: the torsional stiffness in longitudinal members (Ixx) and the bending stiffness in transverse members (Iyy). The latter doesn't make sense to me since the slab is actually above the centroid of the longitudinal member. The contribution should be both from its own Iyy and the translation of rotating axis (Ad^2), but we generally just ignored the latter term.

So in short, When develop a grillage model, should I modify the Iyy stiffness in transverse members so that the offset is taken into account?

 

[r13]

I don't understand your question, can you show a sketch? BTW, I don't think Ixx is the torsional stiffness.

 

[HTURKAK]

The elements of Grillage model are line elements. The element section properties shall be defined . (Moment of inertia, effective polar moment of inertia,and effective shear area )

The slab strips for transversal direction shall be modelled using rigid links. The rigid link height will be, 0.5*( I beam height + slab thickness )

 

[TewitC]

HTURKAK Thanks for your answer.
still some questions here.
1. If I lift the transverse element up (slab) to represent the actual height, isn't that considered as "Downstand Grillage/3D Grillage". In this case it makes sense. But many people prefer to use 2D grillage. my question is : is it more proper to use downstand if I want accurate transversal stiffness?
2. In general, is it necessary to use downstand grillage? what's the main advantages?

 

[TewitC]

retired13

here are some sketches, hope this helps! (sorry for bad drawings) BTW, we usually define local x axis along the direction of line element, ergo torsional stiffness

 

[r13]

Your sketch is good enough, quite clear. However, I am not qualified to offer any opinion/advice on something that I am not familiar with. But, here is a PPT that might be useful. Link

 

[HTURKAK]

Without rigid link, you can not see the effect of composite action. If you perform 2D analysis, the composite action will disappear.

 

[TewitC]

HTURKAK
Thanks, clear on the differences.
So, in general, grillage with rigid link is better, right? Do you prefer to model it with rigid link if you had to design a bridge yourself?

 

[HTURKAK]

I would prefer to model the slab with plate bending element rather than grillage model. IMO, grillage model gives poor results for skew bridges and you can not see exactly the torsional effects.

I will suggest you to post this thread to the forum of structural engineers or bridge engineering to see the responds of others.

 

[r13]

In the old design, the bridge deck is treated as one way element supported by the girders, then position the wheel loads to obtain girder design load. The girder design load will be placed on a single composite beam, in the longitudinal direction, to obtain design reactions. Two way analysis seems an over kill, but maybe it is the trend.