Question:
Good evening,
I have a model (attached) of a 3 span continuous multi girder bridge. Some of the reactions are unexpected. I am finding difficulty finding the cause. I have looked at your other responses and see this may be due to the section offset, however the section offsets were as per the steel composite bridge module, so I expected them to not cause issues. There is also a skew angle of 20 degrees, so this may be a cause.
1) The first unexpected result is for the "girder uniform expansion" / "girder uniform contraction" load case. The Fz reactions are shown as an example below for the fixed end. The reversal was not expected.
2) The other load case causing issues is combination "CBmin: ULS Abutment Uplift". Shown below:
We were hoping for no uplift but as shown there is some. We have even extended the side spans from 35m to 40m but it remains. We can not extend further. However, we are surprised there is still uplift mainly because the span ration is 0.7 (40m/57m). But also because the uplift is at the obtuse corner. If anywhere, we would expect is at the acute corner.
3) With regards to the support positions in relation to the grillage. Would it be more accurate to add new nodes at the actual support position (-1.75m at the ends and -3.5m at the piers), with rigid links connected them to the grillage. Or is this not right?
I have attached the model. If you could help with these I would be very grateful.
Regards,
Answer:
Hello ,
Here are the answers to your questions:
1) The varying reactions at the supports (compression/tension) are explained by the transverse behaviour of the deck and the non-uniform distribution of transverse elements. All following results shown are for the expansion case.
To illustrate this, let's just see the behaviour of a girder from your model under uniform temperature. Due to the tapering at the end the beam will have a small vertical component of deformation due to the inclination of the element axis defined by the centroid following the tapering the section:
The girders of your deck each wants to take this shape when heated if they are not connected to each other, and under simply supported conditions there are no reactions (note that there are no transverse elements yet):
If we add intermediate support to make each beam indeterminate so that it cannot deform freely, we observe compression reactions at the ends and tension at the intermediate supports, caused by the restrain of the upwards displacement which the free body beam would like to take (see the first image):
So far everything is uniform and symmetric. However, when we add transverse elements what happens is that one node along girder 1 is transferring deformation to another node on girder 2. Close to the support on girder 1, the nodes of girder 1 have small vertical displacement, however the adjacent node on girder two has large vertical deformation as it is further away from the support (due to the skew of the deck and the dx offset of each girder from the adjacent ones). This causes one beam to push up or down onto the adjacent ones near the support through the transverse elements. As a result, the reactions increase as we have introduced additional restraining to the free temperature deflections and some of the reactions may reverse. The reactions for the same model as above but with transverse elements become:
If we check the deformed shape of the deck, we can see the twist which it experiences:
If we change the transverse element to ones which are skewed, then the above effects are much less pronounced as we are connecting similar nodes between the adjacent beam. Thus, the free deformation of the beams is less restrained as all beams go up together and the deformed shape is dictated by the intermediate support and not the transverse behaviour of the deck.
Note that having transverse elements to the deck is more correct and we are providing the above case purely for the purpose of demonstrating these effects, rather than recommending a solution.
2) Uplift due to CBmin: ULS Abutment Uplift
The uplift is caused by the moving load case gr5. When the large vehicles are positioned at mid-span of the main span, then the abutment supports go into tension, with the support at the obtuse corner providing the stiffest backspan compared to the other being slightly further away.
You can use the Moving Load Tracer to see the vehicle position causing the uplift effect, which is almost 500kN
If we extract this as a static load and solve it, we can check the deformed shape which illustrates how the support is seeing uplift:
3) I am not sure I fully understand you. Providing support at the exact position they are is always good as it will give you directly the forces in the bearings. However, simplifications are often possible without any noticeable loss of accuracy, so it may be perfectly OK with approximated supports (if yours currently are).
I hope this clarifies your questions.
Kind regards,
Technical Support Team
MIDAS UK
