Disclaimers: My background for "Abnormal Indivisible Loads" (AILs) is UK based. I don't know what the bridge rating and assessment requirements are in your state.
Searching on "abnormal load" will give some background on the UK legal requirements there but doesn't answer your question.
is a UK system being introduced that will include appraisal using influence lines for comparison with existing bridge ratings and maximum axle loads.
If I were in your situation, I'd look at the known history of overweight vehicles crossing that structure first. It may have already been 'proof loaded'. If the bridge condition and loading is similar, the effects are likely to be similar.
Have a good idea how the structure is likely to fail under excessive vehicle loading (sagging, hogging, shear, punching shear, transverse bending, etc) and how your overweight vehicle compares to the rated load capacity. Influence lines may give you a quick and dirty comparison method, if required. To deal with this problem, my previous employer had a semi-automated system and, before that, comparison spreadsheets and extensive records of specific loaded vehicles traversing specific bridges.
If you are dealing with something that is a couple of tonnes over a standard vehicle, it would be rare for it to be a problem. If you are shifting 350-450 tonnes of loaded vehicle (eg transformer) over a new route, I would expect that some calculations would be involved.
