The workers are unhappy with the termination of long-standing agreements and the perceived de-skilling of construction workers.
Electricians, plumbers and heating and ventilating engineers voted by two to one for strike action.
Seven major contractors want to replace long-standing Joint Industry Boards agreements with new arrangements.
Unite national officer, Bernard McAulay, said: “This high 'yes' vote for strike action indicates the resentment felt by our members.
“Balfour Beatty needs to recognise it has lost the support of its employees. The company needs to re-join the industry wide agreements which have served the industry so well.”
Unite has given an undertaking to the court that it will not call for industrial action until after the outcome of next Tuesday’s (7 February) court hearing.
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