Some colleges or engineering divisions start frosh engineering students undeclared, but have secondary admission to major procedures which may result in some students in good academic standing (usually minimum of 2.0 GPA and C grades) being denied their first choice engineering major due to departmental capacity limitations.
Here is information and links to some such colleges and criteria. Note: all GPAs referenced below are college GPAs, and all descriptions below assume (unless otherwise specified) that the student entered in the engineering division (if applicable), has completed the pre-major courses, is not beyond the limit of the number of semesters (usually four), and is in good academic standing.
Colorado (for students initially admitted to pre-engineering): 2.7 technical and overall GPA with C grades in technical courses automatically admits to major.
Cornell: minimum GPA varies by major (currently between 2.0 and 2.5); some majors have specific grade requirements (currently between C- and B-) for specific pre-major courses.
https://www.engineering.cornell.edu/advising/choosing-major (follow links to handbook)
Michigan: 2.0 GPA and C grades in technical courses automatically admit to major.
Minnesota: 3.2 technical GPA automatically admits to major. Otherwise, admission is competitive by technical GPA, although recently most majors admitted all applicants.
North Carolina State: 2.0 pre-major GPA minimum to apply to major; admission determined competitively (biomedical engineering also requires essay).
Ohio State: minimum pre-major and overall GPA varies by major (recently between 2.0 and 3.4 for those with pre-set thresholds, but some majors determine thresholds competitively).
Penn State: minimum GPA varies by major (recently between 2.0 and 3.2); some majors have specific grade requirements for specific pre-major courses.
https://bulletins.psu.edu/undergraduate/colleges/engineering/#majorsminorsandcertificatestext (click on major, then click on “How to Get In”)
Pittsburgh: “There are no limits or restrictions on how many students can enter a major. As long as first-year engineering students finish the first-year requirements and achieve a 2.0 or higher, they may enter the department of their choice.”
Purdue: 3.2 technical and overall GPA automatically admits to major. Otherwise, admission is competitive by GPA and various other criteria listed.
Texas A&M: 3.5 GPA automatically admits to major. Otherwise, admission is competitive by GPA and three essays.
Virginia Tech: 3.0 GPA automatically admits to major (except biomedical engineering). Otherwise, admission is competitive by GPA and essays.
Washington: 2.5 GPA minimum to apply to a major, which also requires essay and resume. “Some majors will have more requests for placement than they can accommodate.”
Wisconsin: minimum technical and overall GPA to declare or continue in major varies by major (recently 2.8 to 3.5 technical, 2.5 to 3.0 overall).