Exhibit 8.2

2727 NORTH HARWOOD STREET • DALLAS, TEXAS 75201.1515

TELEPHONE: +1.214.220.3939 • JONESDAY. COM

January 13, 2026

Olympic Steel, Inc.

22901 Millcreek Boulevard, Suite 650

Highland Hills, Ohio 44122

Ladies and Gentlemen:

We have acted as counsel to Olympic Steel, Inc. (“Olympic Steel”) in connection with the preparation and filing with the Securities and Exchange Commission (the “Commission”) of the Registration Statement on Form S-4, filed with the Commission on January 13, 2026 (the “Registration Statement”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the Agreement and Plan of Merger, dated as of October 28, 2025 (the “Merger Agreement”), by and among Ryerson Holding Corporation, a Delaware corporation (“Ryerson”), Crimson MS Corp., an Ohio corporation and a direct wholly owned subsidiary of Ryerson (“Merger Sub”), and Olympic Steel, an Ohio corporation. Any capitalized terms used but not defined herein have the meaning given to such terms in the Merger Agreement.

In providing our opinion, we have examined the Merger Agreement, the Registration Statement and such other documents as we have deemed necessary or appropriate for purposes of this opinion. In addition, we have assumed that (i) the Merger will be consummated in accordance with the provisions of the Merger Agreement and as described in the Registration Statement (and no transaction or condition described therein will be waived by any party), (ii) the statements concerning the Merger and the parties thereto set forth in the Merger Agreement and in the Registration Statement are true, complete and correct and will remain true, complete and correct at all times up to and including the Effective Time, (iii) the representations to be made by Ryerson and Olympic Steel in their respective tax representation letters pursuant to Section 5.13(b) of the Merger Agreement in the forms attached as Exhibit C and Exhibit D of the Merger Agreement (the “Representation Letters”) are true, complete and correct and will remain true, complete and correct at all times up to and including the Effective Time, (iv) any such statement or representation set forth in the Merger Agreement, the Registration Statement or the Representation Letters that is qualified by belief, knowledge, intention, materiality or any comparable or similar qualification, is and will be true, complete and correct as if made without such qualification, (v) the parties to the Merger Agreement and their respective subsidiaries will treat the Merger for U.S. federal income tax purposes in a manner consistent with this opinion, (vi) such parties have complied with and will continue to comply with the obligations, covenants and agreements contained in the Merger Agreement and (vii) there will be no change in applicable U.S. federal income tax law from the date hereof through the Effective Time. If any of

AMSTERDAM  •  ATLANTA  •  BEIJING  •  BOSTON  •  BRISBANE  •  BRUSSELS  •  CHICAGO  •  CLEVELAND  •  COLUMBUS  •  DALLAS DETROIT  •  DUBAI  •  DÜSSELDORF  •  FRANKFURT  •  HONG KONG  •  HOUSTON  •  IRVINE  •  LONDON  •  LOS ANGELES  •  MADRID MELBOURNE  •  MEXICO CITY  •  MIAMI  •  MILAN  •  MINNEAPOLIS  •  MUNICH  •  NEW YORK  •  PARIS  •  PERTH  •  PITTSBURGH SAN DIEGO  •  SAN FRANCISCO  •  SÃO PAULO  •  SHANGHAI  •  SILICON VALLEY  •  SINGAPORE  •  SYDNEY  •  TAIPEI  •  TOKYO

•  WASHINGTON

January 13, 2026

Page 2

the above described assumptions is untrue for any reason or if the Merger is consummated in a manner that is different from the manner described in the Merger Agreement, the Registration Statement or the Representation Letters, this opinion may be adversely affected. We have not undertaken any independent investigation of any factual matter set forth in any of the foregoing.

Based upon and subject to the foregoing, and our consideration of such other matters of fact and law as we have considered necessary or appropriate, it is our opinion that, subject to the assumptions, exceptions, limitations and qualifications set forth herein and in the Registration Statement, the Merger will be treated for U.S. federal income tax purposes as a reorganization within the meaning of Section 368(a) of the Code.

We express no opinion on any issue relating to the tax consequences of the Merger other than the opinion set forth above. Our opinion set forth above is based on the Code, Treasury Regulations promulgated thereunder, published pronouncements of the Internal Revenue Service and judicial precedents, all as of the date hereof. The foregoing authorities may be repealed, revoked or modified, and any such change may have retroactive effect. Any change in applicable laws or facts and circumstances surrounding the Merger, or any inaccuracy in the statements, facts, assumptions and representations on which we have relied may affect the validity of the opinion set forth herein. We assume no responsibility to inform Olympic Steel of any such change or inaccuracy that may occur or come to our attention. In addition, our opinion is being delivered prior to the consummation of the Merger and therefore is prospective and dependent on future events.

This opinion is furnished to you solely in connection with the Registration Statement and this opinion is not to be relied upon for any other purpose without our prior written consent. We hereby consent to the filing of this opinion with the Commission as an exhibit to the Registration Statement, and to the references therein to us. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

/s/ Jones Day