But in September, workers dismantling the east span heard a loud popping sound and soon discovered that the structure was unstable. Taking that part of the bridge apart piece by piece could lead to collapse, Tappan Zee Constructors, the company responsible for the demolition, determined.

“Through extensive engineering analysis, it has been determined that this is the safest method to proceed with lowering the span given its current state,” the company said in a statement.

After the demolition, only a portion of the west span, nearer Rockland County, will remain; it will continue to be dismantled piece by piece, according to Tappan Zee Constructors.

The instability of the east span was discovered a day after Gov. Andrew M. Cuomo led a ceremony to open the second span of the Mario M. Cuomo Bridge, the $4 billion structure named after his father. That bridge was built to replace the Tappan Zee, which opened in 1955.

State Senator David Carlucci, a Democrat who represents Rockland County and parts of Westchester, said on Saturday that he was disappointed at the change of plans because engineers have “known since September that the structure was not sound.”