Construction and exposure to Hepatitis B (or C or HIV) doesn’t arise very often since construction workers are usually not around blood, bodily fluids, or patients. There are times when construction must occur at wastewater treatment facilities, municipals, or in active sewers. Occasionally exposure can come from illegal drug use or the remnants of it (think of a project underneath a downtown bridge).
Currently there is not a specific rule for bloodborne pathogens in construction (1926). However, if it is reasonably anticipated that an employee might have exposure, you should take precaution.
What are the dangers? First, you must have occupational exposure to skin, eye, or mucous membrane with contact to blood or infected material.  Exposure may then cause the employee the diseases of Hepatitis B, C and HIV. Occasionally construction companies want to know if they need to offer their employees the Hep B vaccine.
The real-threat is contact with blood. Here is a question to ask… Do you anticipate seeing any blood on the jobsite? If the answer is NO…then you probably are under what is called the COLLATERAL DUTY clause. 
In this case, the hepatitis B vaccination does not need to be given…until the presence of blood. Once this happens (and employees must be trained beforehand) you have certain steps to take in order to offer the Hep B vaccination. Oregon OSHA (and others) have adopted this stance.
If you have probable exposures you must:
- make an exposure control plan
- train your employees
- universal precautions – google it…there’s a lot to know
- protect your employees (engineering controls, work practices)
- housekeeping – cleanup
- label
- keep records
Oregon OSHA has some good info here.