phaadu...we have done this several times using dynamic strain monitoring equipment while load testing the bridge using a loaded truck, typically a heavily loaded dump truck. While it is nice to have design data, it isn't absolutely necessary.
From the strain data, you can back into the capacity or anticipated capacity based on the load response.
Essentially bonded strain gauges are placed at various points on the bridge structure (primarily extreme fiber stress points in bending, but not the only locations), then the load testing is done with a moving truck load. Data evaluation include developing load response curves and then fitting perceived design data back into the mix.
You should also use some nondestructive measures to get rebar locations (R-meter, Rebar Scan, radiography, etc.) and determine the compressive strength of the concrete with cores if possible. Most nondestructive concrete strength methods have to be correlated to cores for accuracy anyway.