Exhibit 5.1

July 29, 2013   Nucor Corporation 1915 Rexford Road Charlotte, North Carolina 28211

Ladies and Gentlemen:

We have acted as counsel to Nucor Corporation, a Delaware corporation (the “Company”), in connection with the Company’s offer and sale of $500,000,000 aggregate principal amount of 4.000% Notes due August 1, 2023 (the “2023 Notes”) and $500,000,000 aggregate principal amount of 5.200% Notes due August 1, 2043 (the “2043 Notes” and, together with the 2023 Notes, the “Notes”) pursuant to the registration statement on Form S-3 (Reg. No. 333-176786) filed by the Company (the “Registration Statement”) with the Securities and Exchange Commission (the “SEC”) under the Securities Act of 1933, as amended (the “Securities Act”), and as described in the prospectus dated September 12, 2011 (the “Base Prospectus”) and the prospectus supplement dated July 24, 2013 (the “Prospectus Supplement” and, together with the Base Prospectus, the “Prospectus”). With your permission, all assumptions and statements of reliance herein have been made without any independent investigation or verification on our part except to the extent otherwise expressly stated, and we express no opinion with respect to the accuracy of such assumptions or items relied upon.

The Notes will be issued pursuant to and governed by an indenture dated January 12, 1999 (the “Base Indenture”) between the Company and The Bank of New York Mellon, as trustee (the “Trustee”), as supplemented by the sixth supplemental indenture dated July 29, 2013 between the Company and the Trustee (the “Sixth Supplemental Indenture” and, together with the Base Indenture, the “Indenture”).

In connection with this opinion, we have (i) investigated such questions of law, (ii) examined originals or certified, conformed or reproduction copies of such agreements, instruments, documents and records of the Company (including, without limitation, the Indenture), such certificates of public officials and such other documents and (iii) received such information from officers and representatives of the Company and others, in each case, as we have deemed necessary or appropriate for the purposes of this opinion. In all such investigations and examinations, we have assumed the legal capacity and competency of all natural persons executing documents and certificates submitted to us, the genuineness of all signatures, the authenticity of original and certified documents submitted to us, the conformity to original or certified documents of all copies submitted to us as conformed or reproduction copies and that any certificate or document upon which we have relied and which was given or dated earlier than the date of this letter continues to remain accurate, insofar as relevant to the opinions contained herein, from such earlier date through and including the date hereof. As to various questions of fact relevant to the opinions expressed herein, we have relied upon, and assumed the accuracy of, statements contained in the Indenture and any other documents executed, delivered or entered into in connection with the offering of the Notes and certificates and oral or written statements and other information of or from public officials and officers and representatives of the Company and others and assume compliance on the part of all parties to the Indenture with their covenants and agreements contained therein. We have also assumed that (i) the Trustee had and continues to have the power and authority to enter into and perform its obligations under the Indenture, and to

consummate the transactions contemplated thereby, (ii) the Sixth Supplemental Indenture was duly authorized, executed and delivered by, and the Indenture constitutes a legal, valid and binding obligation of, the Trustee enforceable against the Trustee in accordance with its terms, and that the Trustee will comply with all of its obligations under the Indenture, (iii) the Company will comply with all applicable laws, (iv) the Registration Statement, and any amendments thereto filed on or prior to the date hereof, are and remain effective, no stop order suspending the effectiveness of the Registration Statement or preventing its use or the use of any prospectus or prospectus supplement has been or will be issued and no proceedings for that purpose have been or will be instituted or threatened by the SEC and (v) the Notes were issued and sold in compliance with and in the manner described in the Prospectus and duly authenticated by the Trustee in the manner provided in the Indenture.

Based upon the foregoing and subject to the limitations, qualifications and assumptions set forth herein, we are of the opinion that the Notes were validly authorized and issued and are binding obligations of the Company, enforceable against the Company in accordance with their terms.

The opinions set forth above are subject to the following:

(A) bankruptcy, insolvency, reorganization, moratorium and other laws (or related judicial doctrines) now or hereafter in effect affecting creditors’ rights and remedies generally;

(B) general principles of equity (including, without limitation, standards of materiality, good faith, fair dealing and reasonableness, equitable defenses and limits as to the availability of equitable remedies), whether such principles are considered in a proceeding in equity or at law; and

(C) the application of any applicable fraudulent conveyance, fraudulent transfer, fraudulent obligation, or preferential transfer law or any law governing the distribution of assets of any person now or hereafter in effect affecting creditors’ rights and remedies generally.

The opinions expressed herein are limited to the laws of the State of New York, the Delaware General Corporation Law and the federal laws of the United States of America, each as currently in effect, and no opinion is expressed with respect to such laws as subsequently amended, or any other laws, or any effect that such amended or other laws may have on the opinions expressed herein. The opinions expressed herein are limited to the matters stated herein and no opinion is implied or may be inferred beyond the matters expressly stated herein. The opinions expressed herein are given as of the date hereof, and we undertake no obligation to advise you of any changes in applicable laws after the date hereof or of any facts that might change the opinions expressed herein that we may become aware of after the date hereof or for any other reason.

We hereby consent to the filing of this opinion with the SEC and the incorporation by reference of this opinion as an exhibit to the Registration Statement and to the references to this firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under the Securities Act or the rules and regulations of the SEC promulgated thereunder.

Very truly yours,

/s/ Moore & Van Allen PLLC