“We are making our steel at four mills instead of six,” said John Armstrong, a spokesman for the United States Steel Corporation, adding that two mills were recently idled and the four still operating are running at less than full capacity.

“The third quarter was one of the best in U.S. Steel’s history,” Mr. Armstrong added. “And it has been a very precipitous drop from there.”

The cutback has been particularly hard on workers at the big integrated mills like those at U.S. Steel and Arcelor Mittal USA, with their blast furnaces and coke ovens converting iron ore and other materials into steel. Operated at less than full capacity, these mills are less efficient than the equally large “minimills,” like Nucor, whose electric arc furnaces can be operated efficiently at lower speeds.

So the plant closings have been mostly at the integrated mills, whose 50,000 workers  roughly 40 percent of the nation’s steelworkers  are represented by the United Steelworkers. The union says that early this year it expects 20,000 workers to be on furlough.

Ten thousand already have been. Kathleen Loepker, a millwright and mechanic, is among the most recent to join their ranks. She was laid off on Dec. 19 from the U.S. Steel plant in Granite City, Ill., which shut, putting more than 2,000 employees out of work. With nearly 30 years seniority, Ms. Loepker, 48, has worked through bankruptcies, union concessions and consolidations during which her mill was acquired by U.S. Steel in 2003.

Her income today is tied more to incentive bonuses than in the past. On layoff, she is collecting $20 an hour, which is 80 percent of her base pay of $25.12 an hour. That base pay, rather than rising significantly, is fattened by incentive bonuses tied to amounts of steel produced and to profits. It had been averaging an additional $7 an hour  money now gone until the mill reopens.