The sex abuse scandal that shook Penn State University in 2011, sinking its president and legendary football coach, yielded another effect that still lingers. It is the university with the highest number of reports of forcible sex offenses on any campus in the nation.

In 2012, federal data show, Penn State tallied 56 reports of forcible sex offenses on its flagship University Park campus. That was up from four in 2010 and 24 in 2011.

The University of Michigan at Ann Arbor had the second-highest total in 2012 — 34 — followed by Harvard University (31), Indiana University-Bloomington (27), Stanford (26) and Emory University (26).

Penn State officials say the reporting spike from 2011 to 2012 — the latest years for which data is available — included numerous crimes from prior years attributable to convicted sex abuser Jerry Sandusky. He was a longtime assistant to Penn State football coach Joe Paterno, who was fired amid the scandal before he died. Graham Spanier, the university’s president at the time, also was ousted.

A Washington Post analysis of federal crime data found that 55 percent of about 1,570 colleges and universities with 1,000 or more students received at least one report of a forcible sex offense on campus in 2012. Forcible sex offenses include forcible rape, forcible sodomy, forcible fondling, and sexual assault with an object.

Colleges report the data to the Education Department under the campus safety law known as the Clery Act.

The flip side of the finding: 45 percent of those schools reported no forcible sex offenses on campus at all.

Sen. Claire McCaskill (D-Mo.), who is studying campus sex assault issues, said she is more concerned about schools with no reported offenses than those with many. She said she wonders whether the schools with zero reports are doing enough to encourage victims to step forward.

“We’ve got to explain to the public that they should not hold a university responsible for some failure if the number of sexual assault reports go up,” she said.

McCaskill said many schools with rising numbers of reported sex offenses fear their public image will suffer. “They’re worried that people won’t understand that means they’re doing a better job,” she said.

Among large schools with no reports of forcible sex offenses on campus in 2012: California State University-Fullerton, University of Nevada-Las Vegas, San Francisco State University and the University of North Carolina at Greensboro.

The numbers should be read with caution, because they reflect the total of alleged incidents. That could include offenses related to cases that went to criminal trial, such as those in the Sandusky scandal. But a large number of reported incidents result in no prosecutions or convictions.

Like Harvard, Indiana and dozens of other schools, Emory is under federal investigation for its handling of sexual violence reports. The government requires colleges to give a prompt and equitable response when students report an offense.

Many of the institutions under investigation for potential violations of the anti-discrimination law known as Title IX were the subject of complaints from individuals on those campuses.

Others, including Emory, were selected by the government for what is known as a compliance review. Emory said it has taken significant steps to prevent sex assault, encourage reports and streamline how it handles cases.

“We’re not upset that we’re on some list,” said Ajay Nair, Emory’s senior vice president and dean of campus life. “This issue we don’t want to be hidden at all.”

In Virginia, The Post’s analysis found the schools with the highest total of reports of forcible sex offenses on campus in 2012 were the University of Virginia (11), Virginia Tech (8) and the University of Richmond (8). In Maryland, they were the University of Maryland at College Park (9), Salisbury University (6) and Johns Hopkins University (5).

In the District, the analysis found Gallaudet University had the highest total in 2012: 18. It was followed by George Washington University (10), American University (7), Howard University (6), Georgetown University (4), Catholic University (4) and the University of the District of Columbia (1). There were no such reports at Trinity Washington University.

Gallaudet also had the highest rate of reported forcible sex offenses among all colleges the The Post analyzed: more than 11 per thousand students in 2012.

Gallaudet, which specializes in education of the deaf and hard of hearing, said it has taken many measures to prevent sex assault and facilitate reporting of incidents. The university said it closely tracks cases and helps students when they make a report to police.

“We believe the reason why our numbers measure higher than other universities, both in terms of raw data as well as per capita, is due to the ability of students to have direct access in terms of communication and language with on-campus personnel without requiring the need for an interpreter,” said Dwight Benedict, Gallaudet’s dean of student affairs and academic support.

Nationwide, several prestigious liberal arts colleges had some of the highest rates of reported offenses per thousand students. Among them were Grinnell (more than 10), Reed (more than 9), Amherst (more than 9), Hampshire (more than 8) and Swarthmore (more than 7). The reporting rates for larger universities, which were significantly lower, might have been affected by the number of graduate students they have.