How can the issue of not being able to find the modes of buckling shapes corresponding to the Eigen values vibration mode when performing buckling analysis with a plate model be resolved?

However, I expect that you would still get a significant amount of modes of buckling in the web. This is because buckling analysis is a linear eigenvalue analysis, and this finds the weakest points that will buckle first. These are usually thin plates, like webs. You have quite well braced main girders, so I would expected a lot of web buckling to occur before the main girders experience any global buckling.

Unfortunately, there is no easy way to find the global modes, however, there are some methods which can be used to narrow the search down. You can artificially stiffen the web of the girders in the out-of-plane, and leave the in-plane behaviour as it is. This will increase significantly the critical load for the local buckling modes of the web, while the global buckling of the main girders will not be significantly affected as this is not governed by out-of-plane bending of the web. You can do this by assigning separately in-plane and out-of-plane thickness for the web thickness property:

This will allow you to observe the global buckling mode of the girder as Mode 1 and see what is the critical factor for this approximately. Note that the factor is slightly higher than the true solution due to the for the global buckling if the out-of-plane of the web had not been stiffened, usually a few percent. However, you can then reduce the stiffness of the web back to its design value and limit the buckling analysis to the expected range of value where you expect the global mode to be.

Alternatively, you can model a longitudinal stiffener along the web of the main girders. While not real, this will significantly reduce the web buckling effects with a minimal effect on the global buckling of the girders. Again, this can guide you to the critical load for the global buckling.