When LTV Corp., the second largest steel producer in the nation, went belly-up last week, Cleveland Mayor George V. Voinovich begged the Reagan administration for ''a Chrysler-like solution or bail-out of the steel industry.''

It's easy enough to sympathize with a big-city politician who sees the fifth largest employer in the area file a bankruptcy petition: Cleveland is in the heart of the rust belt of declining American industries. What's more, it's altogether probable that the desperate plight of LTV in particular and of the steel industry in general will strengthen the protectionist sentiment that already grips Congress.

But the Voinovich lament is 180 degrees off the track: LTV and the steel industry are in a terrible bind today precisely because the steel moguls have sought and been spoon-fed protectionist help by Democratic and Republican administrations alike.

sk,3 According to the American Iron and Steel Institute, domestic steel companies have closed about 700 manufacturing units since 1974. Seven steel companies have gone out of business, and the United Steelworkers Union has seen half of its 1.4 million membership disappear.

This tragedy has taken place because the industry and the union, instead of meeting the pressure of foreign competition by modernizing and boosting productivity, cut a deal: They engineered a cartel to share the market with European and Japanese producers. And the companies use precious resources to buy retail shopping centers, S&Ls or almost any other business, instead of concentrating on their own.

As far back as 1977, the Carter administration knuckled under to the steel industry's pleas for protection. When the industry lost sales to more efficient companies abroad, former White House adviser Robert Strauss promised ''a creative and innovative program.'' In the end, former Treasury undersecretary Anthony Solomon devised a ''trigger price mechanism'' designed to keep steel imports down and allow domestic producers to raise prices.

Now, despite the Reagan administration's free-trade rhetoric, it has created a full-fledged cartel: The import share is supposed to be slashed to 18.5 percent of the market, with the pieces shared among a dozen foreign producers.

But a funny thing happened to the protected steel industry as it attempted to cash in on an intended artificial scarcity. Consuming manufacturers, notably auto makers, discovered the virtues of plastic and other materials that reduce car weight, thus encouraging mileage efficiency. Today, the typical car uses hundreds of pounds less steel than one of equivalent size 10 years ago.

LTV, meanwhile, was following its own self-destruct scenario. Originally an aerospace company with an unquenchable acquisition thirst, LTV went deep into debt to gobble up the Jones and Laughlin steel company and then the Republic Steel Corp. It also acquired oil properties at the height of the overvalued oil boom. Like a Third World country unable to pay its bills, LTV has now told the bankruptcy court that its debt payments will average $567 million a year for the next three years. It also needs, and doesn't have, $375 million to pay pension and retirement benefits.

LTV's steel acquisitions were questioned at the time, inside and outside the industry. But those who protested that industrial concentration was not good for the country -- and that big was not necessarily better for the company or its stockholders -- were generally dismissed at the Department of Justice as knee-jerk liberals.

LTV hasn't earned a dime since 1981. From the beginning of 1982 through the first quarter of this year, it has managed to lose $1.55 billion. It has unfunded pension liabilities running many times the $375 million in payments due this year.

The federal government's insurer of pension funds, the Pension Benefit Guarantee Corp., ultimately will have to bear some or all of the cost of those pensions. This is another way of saying that you and I and all other taxpayers will be footing the bill.

Now, finally, LTV has figured out a way to make a profit: Its Chapter 11 bankruptcy proceeding means that the court will insulate LTV from its banks and other creditors while it tries to work out a plan to pay off its debt. Thus, bankruptcy provides industry a wonderful cost-cutting tool. LTV doubtless will persuade the court to let it weasel out of its last labor contract, and it will be able to undersell all of its competitors.

This will bring market prices down fast, and some other steel companies into the bankruptcy courts. There will be a cacophony of screams for exemption from taxes, for special credits and protection from imports. If politicians of both parties have learned anything from the past 10 years, they will turn a deaf ear to steel. But I wouldn't bet on it.