The warnings were terse: Set up tents in violation of campus policies and the police will remove them. The images were startling — officers wrestling students to the ground and cuffing them with zip ties.

As pro-Palestinian protests rippled outward from Columbia University over the past several days, many campuses saw clashes between demonstrators and the police officers who’d been ordered by administrators to clear the encampments. Other campuses saw peaceful encampments set up as protesters demanded that colleges divest from Israeli companies or companies doing business in Israel. Students have been arrested on at least 14 campuses, including four over the weekend.

At each of those colleges, presidents and other senior leaders are struggling to respond to the latest wave of mass protests to roil American higher education. While many of those leaders champion free speech in statements, they say they are also concerned about safety. They wonder when they should send in the police and when they should hang back, decisions complicated by what experts say is a uniquely complex situation when compared with mass protests of previous years. At some institutions, including Yale University and Indiana University at Bloomington, encampments have been cleared and then reappeared within hours or days. Complicating matters is heavy pressure from donors, alumni, and politicians to take action against protesters they view as antisemitic.

“At high-profile institutions, presidents are in impossible situations,” said Timothy R. Cain, a professor at the University of Georgia who studies student activism. But when presidents decide to bring in the police to those situations, they often raise tensions, he said. “Efforts to quash through police power can backfire.”

Faculty at the Massachusetts Institute of Technology made that point in a recent open letter supporting the students’ right to have an encampment: “We remind the administration that engaging police to dismantle peaceful protests can prove profoundly destructive to the students, our campus climate, and to the institute’s reputation. Such peaceful expression of moral and political concerns in academic settings is a part of a long tradition in which young people find their voice to participate in democracy, and their voices should not be chilled or silenced by threats of arrest or disciplinary proceedings.”

There is no debate in the mind of Chancellor Daniel Diermeier, of Vanderbilt University, about whether directing officers to arrest pro-Palestinian student protesters on his campus in late March was a violation of their free speech.

“That’s a simple violation of rules of how to behave on campus,” Diermeier said. The protesters, he said, entered a locked administration building and injured a community-service officer. “They weren’t arrested for the content” of their message,” the chancellor said. “That’s not a free-speech issue. Do not confuse free speech with disruptive conduct.”

Occupying a building and camping out in a quad are different methods of disrupting business as usual. But protests are supposed to be disruptive, Vanderbilt faculty members argued in an open letter following the arrests. “Thus, stipulating that protests violate handbook policy when they disrupt university operations potentially bans many meaningful forms of protest,” the letter states.

Tense campus protests are a rich tradition in American higher education, dating back to at least the 1930s, when college students protested economic policy around the Great Depression and the rise of fascism. The 1960s saw a wave of protests around civil rights and against the Vietnam War. The 1980s saw students rallying for disinvestment from companies doing business in South Africa in a push to end apartheid. In the 1990s, students railed against sweatshop labor practices, and more recent years have seen Occupy Wall Street rallies and Black Lives Matter demonstrations and marches.

Robert J. Birgeneau was chancellor at the University of California at Berkeley during the height of the Occupy movement in 2011. While traveling in China and Japan, he helped decide to enlist the police to clear an encampment at the university. A clash ensued in which police officers used batons on protesters. Birgeneau, on his return to campus, said he did not condone the use of excessive force by the police. However, the encampment had to be cleared, he recently told The Chronicle.

“We were more than willing to have the student protesters put up a small number of tents which could be monitored for safety,” he said. “However, in these and previous protests, there were serious challenges with a group of outside anarchists who were prone to violence. One such group literally tried to burn down the chancellor’s residence with my wife and I in it. Maintaining a safe environment is extremely difficult with a large number of tents. In addition, such encampments violate university time, place, and manner rules, and ultimately one must enforce such rules.”

Adding tents to protests can change the tenor, said Cain, the Georgia scholar. “There’s something about the physicality of encampments that changes the stakes” for those making decisions about protests, he said. “It claims space. It can also be read as something scarier than something that is moving through, like a march or a rally that ends.”

In a recent column in the student newspaper at Princeton University, President Christopher L. Eisgruber spelled out explicitly his issues with encampments.

“Encampments can obstruct others from moving freely or conducting university business,” he wrote. “They can create health and safety risks. They require significant staff time to keep occupants and bystanders safe, thereby diverting people and resources from fulfilling their primary purpose. They can intimidate community members who must walk past them. There is no practical way to bar outsiders from joining the encampments.”

Setting up encampments also gets university lawyers involved in evaluating risks, said Demetri L. Morgan, an associate professor of higher education at Loyola University Chicago. General counsels, who are increasingly influential in university decision making, may bring up the possibility of the institution being liable if something goes wrong in the encampment and a student is hurt.

“A march has known risks,” Morgan said, unlike an encampment, which can raise a host of unknown legal issues. Right now, one of them is attracting the scrutiny of the federal government. This week, just days after nationwide attention focused on Columbia, the Department of Education opened an investigation into shared-ancestry discrimination at the institution.

All of this has led colleges to take what Liliana M. Garces, a professor in the department of educational leadership and policy at the University of Texas at Austin, has labeled repressive legalism, where colleges are acting “from a place of fear.”

Whatever their motivations, colleges may have trouble rationalizing the decision to use force by invoking safety concerns. “What is safety and who gets to decide what is safety and security?” Morgan asked. Many protesters say they don’t feel safe on their campus and that is why they are demonstrating. Students are using the resources they have — their bodies — to disrupt and make their message heard, Morgan said.

Even decisions about what constitutes disruption can be fraught, and on some campuses, the rules are changing in real time. Is marching through an academic building while classes are going on a disruption? Is holding a vigil that clogs the center of campus for a few hours a disruption? Why is setting up tents the tipping point?

It all depends on the circumstances, several presidents told The Chronicle. At Michigan State University, students gathered on Thursday morning to try to set up an encampment, but were told they needed a permit from the Board of Trustees to do so. The protesters filed a permit application. While they were waiting, the new president, Kevin M. Guskiewicz, arrived to talk with the students. He told the student newspaper he supported the petition to hold the encampment. Shortly thereafter, the board approved the petition and allowed the encampment until Sunday.

Steps like these embody an approach that some presidents said is key to avoiding violent confrontation: clear communication before tensions are at their highest.

At DePauw University, a recent panel involving board members was greeted with a silent protest from students who stood around the edges of the auditorium with various posters making their points. At the end of the panel, President Lori S. White invited the students to come to the front of the auditorium and hold the signs so the entire audience could see them. She said a discussion then took place between the people on the stage and those protesting.

“Higher education has a fundamental role in sustaining our democracy,” said White, who is part of the College Presidents for Civic Preparedness, a consortium aimed at instilling students with the skills to be good citizens. That includes having students express themselves. She said she wants to work with students to figure out “other strategies before we go to protest and you hand me a list of demands.”

At Skidmore College, President Marc C. Conner says disruption isn’t allowed. Students “can’t block access to education” other students are trying to acquire. But, what constitutes disruption is “a judgment call,” he said. “We try to be lenient. To me, it’s really got to cross a line before we would respond.”

The University of Denver is gearing up for its annual Day of Free Expression and Pluralism, on Tuesday. Applying an institutional focus on the value of free expression has helped encourage a culture of pluralism, said the chancellor, Jeremy Haefner.

“It defuses a lot of the negative impacts that happen,” he said. “I love the passion our students are bringing to the issues of the day. What we need to do is to help them develop the skills” around expressing those passions. When it comes to protests, working with students in advance to plan out the event and desired outcomes helps as well. His campus currently doesn’t have an encampment, but if it did, he said he wouldn’t step in to squelch it right away.

“Peaceful sit-ins and encampments are forms of freedom of expression and we have to respect that,” he said. Where they cross the line is when physical safety is threatened, property is damaged, or when people are harassing or using discriminatory language against other people. “Freedom of expression is not unlimited, as we all know.”