Forces of Tension and Compression for a simply supported bridge:
Bridge members can be in tension or compression and bridge geometry determines which force is present.
Modern material (steel and concrete) are good in tension and compression (respectively), but not vice versa.
The "End conditions" also determine bridge forces
Spectacular Bridge failures: The Tacoma Narrows Bridge in Washington state failed in Nov 1940 due to torsional vibration forces building up as a result of wind blowing and exciting the bridge at it's natural resonant frequency.
Want to build a strong bridge: Look here!
These are the equations which govern the shape and deflections and stresses for different end conditions and beams
For a more complete description of what this all means see here