ABET accreditation requires “a general education component that complements the technical content of the curriculum and is consistent with the program and institution objectives”, according to http://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2015-2016/#curriculum . Actual H/SS requirements for engineering majors do vary across schools. In some cases (e.g. MIT, CSUs), the requirements are the same as those for all other majors. In other cases, where the school is divided into divisions, the requirements differ for the engineering division. In the case of Brown, there are no general education requirements for non-engineering majors, but engineering majors have an H/SS requirement along with engineering and science requirements for their majors.
The same section indicates that a minimum of 1/4 of the course work needed to graduate must be in math and sciences, and 3/8 must be in engineering science and engineering design. There can be within-major electives within these categories, and the total minimum is 5/8 of the course work needed to graduate, leaving up to 3/8 for general education and free electives. In practice, many engineering major programs require more than 5/8 of the course work needed to graduate, possibly leaving as few as no free electives once the out-of-major course work is used to cover general education requirements. At some schools, the requirements for both the major and general education exceed the usual amount of course work needed to graduate, so that a student needs to take overloads to graduate in 8 semesters or 12 quarters (although, for example, Dartmouth disallows too many overloads, so an ABET-accredited engineering degree takes more than 12 quarters there).