TACOMA, Wash. — As construction crews 5,000 miles away are working to widen the Panama Canal to allow much larger ships to sail straight to the East Coast, this historic port city and others along the West Coast are doing everything they can to avoid becoming superfluous.

The Port of Tacoma is determined to keep up its rich import business, which can be traced to the 1880s when chests of tea from Asia arrived at its docks and headed to the East Coast by rail. Port officials know that by the time the Panama Canal opens in 2016, an even newer, larger fleet of cargo ships will be plying the oceans and will be so big they will not be able to squeeze through even the wider channel.

So Tacoma, Seattle and other ports are spending billions to be ready to receive the ships and keep themselves competitive in the overall scramble for foreign trade.

“The ships continue to get bigger, the cranes need to get bigger, and the docks need to be able to handle them,” said Trevor Thornsley, senior project manager for the Port of Tacoma, as he stood along the jagged rebar and broken concrete of a $22 million renovation to shore up the port’s Pier 3.