Frameworks dgn files would need to be exported to another CAD application not just simply converted.
All you do converting a dgn file is transfer the graphics and quite often things get dropped into the simplest forms.
From Frameworks you can export to Frameworks own SDNF format which seems to be accepted by most other CAD packages, or if you are using the 'latest and greatest' from Intergraph you will find Intergraph dropped support for SDNF and only support CIS/2 format which is a bigger more complex format.
There are fewer CAD applications that can import CIS/2 but I think STAAD-PRO does.
Even if you export and import a model using either SDNF or CIS/2 you might find the model still loses something.
That's mod Leif.