An 8-foot span is awfully long to try that. A plate would have to be about 3 inches thick for a 4-foot wide section to resist that kind of load. Most road plates only have 2 or 3 foot spans. You might want to consider something else.
You can sum moments about one of the centerlines and find the average moment in the plate & solve for thickness. I get around 1" doing this. You might find more accurate 2-way formulas in "Formulas for Stress and Strain" or other references. The answer could vary some depending on your allowable stress and design assumptions.
Seems like some larger cities have standard tables for plates used to cover holes in pavement- make sure you're not overlooking something there.
1" is OK for strength for an effective width of 8', but static deflection is about L/100 and an 8' effective width is optimistic. What if the wheel load is on the edge of the plate, or if there are 2 wheels on the 8' wide plate?
You need to start with what size plate is available and proceed from there. Also, as mentioned above, check if standard tables are available.
Also try Roarks "Formulas for Stress and Strain" as mentioned above by JStephen. I'd check several formulas to get consistent results, some solve for peak stress and other solve for an average stress across a section. It depends on whether your needs are for a long term installation where peak stress is important or if it is for temporary use where the basic strength is adequate. However an 8' plate is probably going to have considerable deflection.
