The talks also cover smaller trade unions such as painters and tile setters.
A strike could affect the $786 million Pennsylvania Convention Center expansion.
General Building Contractors Association president Walter Palmer says the labor agreement for the expansion has a no-work-stoppage clause that was signed by Building Trades Council chief Pat Gillespie, but the individual unions did not sign the agreement.
The United Brotherhood of Carpenters held a two-day strike in May 2006.
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