This is for a bridge design project.
We went for an arch bridge over the roughly parabolic valley. The arch is parabolic and rises 1.3 meters above the deck of the bridge. The deck is divided in 20 sections and supported by both vertical and diagonal members (hollow structural steel sections) connecting arch and deck.
It is no problem to figure out angles, load forces and reaction forces. The bridge is completely supported by the arch, which thrusts into the wall of the river (concrete footings for our purpose). The arch, too, is made out of discrete members (so that a true parabola is approximated). All joints are assumed to be pin joints (hinges).
These are my assumptions for my calculations:
- The arch is hinged at the footings as well
- All forces in members have a horizontal and vertical component, and therefore give two values (sin and cos) to be used in equations
- The end of the deck of the bridge is supported by nothing but the arch. The ends of the bridge don't touch the riverbank.
I have 88 equations now, and 87 members. I created a huge matrix in Matlab to solve them for me, but I get ridiculous answers. Supposed I did iron out all the typos, does this bridge actually have any chance of being statically determinate? Can I work with 88 equations (44 joints, horizontal and vertical forces for each) and 87 unknowns? Can I just add a random member somewhere to make up for the missing member?
It's really hard to find easily information on the static determinacy of arch bridges for very simple model calculations like this. It seems like there's a lot of stuff on basic trusses, but whoever's doing arch bridges needs to really know what they're doing.
So should I scrap the arch bridge and go for something simple, or how do I fix my design?