CHARLOTTE, N.C. -- When Nucor Corp. begins melting scrap steel next summer at a factory on the Arkansas bank of the Mississippi River, the plant may squeeze one of three Big Steel firms out of a $1.6 billion market.

Charlotte-based Nucor expects to capture 15 percent of the market for large- and medium-sized structural steel shapes -- such as I-beams -- by building the $175 million plant with a Japanese partner and the latest technology. That would take sales from the current producers, Bethlehem Steel Corp., Inland Steel Industries Inc. and USX Corp.

"Each loses a big chunk of the market -- or one of them goes," said Donald Barnett, a steel industry consultant with the Brookings Institution. "Over the long term, I think there's a good chance one of them will stop producing."

Though the Arkansas plant represents the most immediate challenge to Big Steel, it's only the start of Nucor's ambitious expansion program, which is a major challenge to companies such as Bethlehem and USX. Nucor is also building a $225 million Indiana steel plant that could prove even more of a long-term threat.

"In both cases, we're going into a market where there is overcapacity," said Ken Iverson, 62, Nucor's chairman and chief executive. "We're in a situation where we have to push somebody out."

Steel analysts say Nucor, by invading Big Steel's turf to an unprecedented degree, is likely to speed the decline of the larger, less efficient companies. They are impressed by Nucor's track record and by Iverson, who built the firm from near bankruptcy in the 1960s to a Fortune 500 company that's the largest steel minimill and the 9th largest U.S. steelmaker.

"Nucor is invading traditional, integrated mills' territory," said consultant Barnett, who added, "Their chances of success are excellent."

Analysts said that minimills, including Florida Steel Corp., Birmingham Steel Corp. and others, have grown by building smaller modern plants using scrap steel. They also depend partly on nonunion labor and have more flexible work rules. The larger producers have "integrated" production -- that is, from iron ore to finished products -- older technology and union work forces.

With the rise of minimills, consultant Barnett predicted that traditional steelmakers will be forced to close 50 percent of their factories by the end of the century. That's on top of the 30 percent of their plants they have closed in the past 10 years.

Meanwhile, for Nucor, sales could double to $1.9 billion and profits may more than triple to perhaps $170 million by 1995, analysts said. Of course, Nucor is also taking somewhat greater risks, including a union organizing drive in Indiana.

Plans for Nucor's construction program started as the company's treasury bulged with cash, $185 million by 1985. Earning low returns on short-term investments, Nucor looked for ways to expand.

Other steel companies moved into far-flung businesses, with U.S. Steel changing its name to USX after buying Marathon Oil. But Iverson rejected diversification. "We wanted to do a lot of work to see if we could expand in the steel business successfully," he said. "We didn't want to buy a bank."

Though Nucor has a few small projects under way, including a new plant that makes bolts and another making metal structures, the heart of its expansion is in two huge projects.

The first started in fall 1985, when Yamato Kogyo Co. of Japan approached Nucor about building a structural steel factory. Last year, the companies reached an agreement under which Nucor will own 51 percent of the plant.

The plant, in Blytheville, Ark., will produce 650,000 tons of heavy structural shapes used in construction, or 19 percent of the 3.5 million tons produced east of the Rockies.

Nucor said it can make the steel products 25 percent cheaper than today's price of $400 per ton. Bethlehem Steel has upgraded its structural steel mill in Bethlehem, Pa., but plant manager Andrew Futchko recently told an Allentown, Pa., newspaper, "When it {Nucor's structural plant} comes on stream, we're going to have a real crisis on our hands."

But Nucor is mounting an even more formidable challenge to Big Steel with a second plant, 35 miles west of Indianapolis. That's because financially strong Nucor, which will produce 800,000 tons of sheet steel annually at this plant, may expand in the giant U.S. market of 38 million tons annually.