Modeling Considerations

• Why Different Modeling Techniques Give Different Results, and
• How "Composite Results" can be Used, and
• Setting up Good Finite Element Models.

Comparing Simple Models

Why is it that when we use line beam analysis to derive moments and shears, we get different answers compared to grillage analysis, which in turn are different to the results from finite element analysis? And why is it that sometimes when we make the model more detailed the answers are not what we expect?

Put simply, it is because all three techniques are models of reality, none of which are completely accurate, and they are inaccurate in different ways. So we can derive different answers when comparing similar structures modeled in different ways.

It would seem reasonable to assume that all three techniques can model simple structures and to expect to derive similar results, but this is not necessarily the case! Take a simply supported square span whose side length is "L", and subjected to a uniform total load of "W" (to be clear, the loading intensity is W/L). Assume the deck is made of a concrete slab and a set of five composite steel beams.

Line beam analysis will correctly give the reactions as W/2 and the midspan moment as WL/8. However, it is wrong to assume that the midspan moment in every beam is the total moment divided by 5. We have to use distribution factors to adjust the results and whereas these are soundly based on research studies, and many decks have been built using them, there is no doubt that they can be inaccurate, sometimes by as much as 20%.

Grillage analysis will give the correct reactions if all five support reactions along one side were summed. And the same is true for moments, if we summed the moments at midspan for all five beams. Here we would see that the midspan moments for each beam would indeed be different, and it is when comparing these to the results from line beam and distribution factor analysis that we can see a difference of 20%.

Finite element analysis will also give the correct reactions if all five support reactions along one side were summed, but for midspan moments the picture is very different. Deriving the total midspan moments due to the forces in the slab added to the forces in a beam can be a very difficult operation. Having done it, we will probably have answers comparable to a grillage, but is the trouble worth it? The answer is "Yes, if we can save the trouble", and now there is a simple tool that does. It has the generic term of "Composite Results", and this is a unique feature to SAM, which is set to make analysis using finite elements significantly easier for everyone.

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Using "Composite Results"

To use Composite Results, we specify which beams and elements form a composite member, and then the total load effects for the composite member are correctly calculated. In the case of the beam and slab deck above, we include every part of the model as being the composite member, and then ask for the Composite Result, and we will see results that are tolerably close to those from line beam analysis.

This picture shows a two span grillage, where every member has been selected to become one Composite Member (shown by the series of dots).

Here are the Composite Results for the Composite Member, that is, the whole deck (negative moment over the central supports shown as below the axis).

Or, if we defined a composite member as a longitudinal girder made up of plate elements for the web and beam elements for the two flanges (all with suitable vertical offsets) and the plate elements that make up the slab, then the Composite Results would be tolerably close to those from grillage analysis.

So it is now possible easily to answer the question "How different are my results?".

The effect is even more dramatic when we are modeling a box girder using thin shell finite elements. It is extremely difficult and time consuming to derive the total moments and shears at any section of a box girder, but these figures are required for strength limit state code checks.

Setting up a composite member that consists of all the elements intersecting a section is quite straightforward (it is the series of dots on the curved line in the adjacent picture).

Having done that, it is almost a trivial exercise to derive the Composite Results for total moment for the whole girder. In short, deriving the total moment diagram becomes a very simple task.

For shear in the webs, the problem is compounded by the torsion, but Composite Results take this into account too, so yet another complex problem is easily solved.

Here is a contour plot of the membrane forces in one web of the arched box girder

And here are the Composite Shear Forces in the web.

Composite Results are very powerful in other ways too. Make the span above a simple slab, and replace the bearings under the beams by a continuous line of supports. It is worth modeling this to see what happens to the values of the reactions at the extreme nodes as the fineness of the mesh increases. As the mesh increases from 2 by 2 so the closeness to theoretical results increases (as we would expect), and a 8 by 8 mesh is tolerably accurate.

We would expect the accuracy to increase with even finer models, and to a degree this is true, but by the time the mesh becomes 64 by 64 an interesting phenomenon occurs ... the reaction at the extreme nodes becomes negative, with very high values! This is due to the fact that finite element models do not like discontinuities, but the coarser meshes hide this problem.

Now when modeling real structures we can sometimes encounter this problem, but for other modeling reasons we may not want to make the mesh more coarse, so what can we do?

Certainly one solution would be to take (say) the two outer rows of the mesh along one of the unsupported sides and make them a composite member, and then ask for the Composite Result.

So we can use Composite Results to overcome some of the limitations of the modeling process.