The Selly Oak viaduct is the biggest structure I've built in many years, and my normal methods need a bit of adaption.
With the sides stuck to the plywood track bed using Deluxe Materials Speedbond, the structure still felt a bit wobbly. Cue several pieces of foamboard fixed in place for added strength. I only need this while the model is free of the baseboard, but they won't hurt. It's not like they add any weight! Fixing is with the special foam-safe UHU as it's quick to grab and holds really well.
At the end, there some DIY wall filler also acting as glue and the same trick has been sued along the sides of the trackbed where there are small gaps 'cos I'm rubbish at woodwork.
The viaduct can now be waved around in the air without issue - good news as it's now time for paint.