Track-structure interaction in Statik

Customer Question

The track-structure interaction calculation issue, what is the status of this issue (...) and now I have a bridge at hand where this calculation could be done with Statik if it is available.

Answer Technical Support

With the release of the new STATIK-9, an interesting tool has been added to model supports and members with non-linear behavior. This tool responds to the requests we have received over the years and is finally a reality.

This tool is very generic and allows the development of all types of models where it is necessary to define supports or elements whose behavior is not linear. A particular application would be, for example, the track-structure interaction, since it is a model formed by rigid bars and springs, whose scheme could be as follows:

 

 
We have introduced in STATIK a very simple model that could serve as a basis for developing much more complex models for this purpose.
 

 

With STATIK-9 it is now possible to define nonlinearities of many types in addition to the classic “no compression allowed” for cables. This allows us to define specific behaviors for members and supports and then to select members and supports that we want to behave in this way and indicate that they have a “1”, “2”, “3” behavior .....

In the above model, for example, we have defined non-linear members (those marked in red in the figure above) and assigned them the non-linear behavior “1”:

 

 

This behavior is governed by a bilinear diagram, according to which, when the bar reaches an axial force of 10 kN in compression or in tension, there is a change of behavior with zero stiffness, at which point the bar will maintain that axial force constant.

If we ask the program for the axial forces for these members for a linear and a nonlinear analysis, we see the following: 

Linear analysis:

 

 

Non-linear analysis:

 

 

In this second case, no member exceeds 10 kN in either compression or tension.

In addition to defining non-linear members, it is also necessary to define supports with non-linear behavior. To illustrate how they work, in this example, we have defined a nonlinear behavior of the supports as follows:

 

 

That is, the supports will be able to resist a certain force until they start to slip and, moreover, this slip will be limited to a certain value, 5 mm in this case. The supports will not slip as long as the reaction Fx < mu*Fz. When Fx=mu*Fz, the support will start to slip until it reaches Du, at which point Fx=0, i.e. the support will stop working.

In our example, we have defined the supports of nodes K_2 and K_3 in this way and we have left the support of K_1 fixed.

 

 
When we analyze against a given horizontal load that we are increasing, we see that at a given moment we arrive at the following situation:

 

 
Where we see that at the intermediate support there is no longer an Fx reaction because we have exceeded the ultimate displacement.