“Hamilton” opens its run at the Kennedy Center on June 12. (Joan Marcus/Joan Marcus)

“Hamilton” mania hit the Kennedy Center website Wednesday morning, when all online visitors were placed in a virtual waiting room for its members-only sale of tickets to the mega-hit show.

There were huge lines outside the Kennedy Center to get to the box office, while thousands more logged on to the website for the chance to purchase seats to the long-awaited run of Lin-Manuel Miranda’s award-winning hip-hop musical.

If you wanted to buy tickets to any of the hundreds of other Kennedy Center events, you were placed in the “Hamilton” waiting room with everyone else. At one point, more than 70,000 users were in the system.

The arts center anticipated high demand for the members’ sale for the show, which begins a 14-week run at the Opera House on June 12. The virtual waiting room was an attempt to prevent the demand from crashing the site, as has happened in the past.

“Everyone going to the website today will go to the waiting queue. That’s the way it’s working today,” spokesman Brendan Padgett said. “It’s helping facilitate the people getting on to purchase tickets.”

It also clogged the line for tickets. The Kennedy Center won’t disclose how many members it has — or how many it gained with the “Hamilton” promotion — but the number of people online was inflated by those who had multiple browsers open, as well as those seeking information or tickets for other events.

Tim Neumark of Falling Waters, W.Va., logged on to the website a few minutes before 9 a.m. An hour later, his random spot in line was between 32,000 and 34,000, he said.

“I was surprised I didn’t have to log in for the Kennedy Center to verify that I am a member before I would get in line,” Neumark said. “Up until this morning I was impressed with the way this works. Since we’re members, we get a priority, and there’s a waiting room. It does not seem like they executed it well.”

Padgett said an external site that has been used by a number of other theaters hosting the “Hamilton” tour was hired to help control the traffic. Once visitors reached the front of the line, they were directed to the Kennedy Center website and asked to sign in. About 2,000 people an hour were moving through the waiting room, Padgett said. Altogether, there are about 260,000 tickets for the entire run.

Hundreds of members also waited outside early in the morning to buy tickets in person at the box office. The first person in line arrived around 11:30 p.m. Tuesday, Padgett said.

The Kennedy Center has plenty of experience with website crashes during popular sales. High demand for “The Book of Mormon” brought its website down more than once, as did sales for “Wicked” in 2011.

The idea of the virtual waiting room was to control traffic to the website and therefore keep it running.

Kati Brown became a Kennedy Center member for Wednesday’s presale, and she logged on to the website at 7 a.m. “hoping to get a good spot,” she said via email.

“I figured if I’d gotten them it would have been $60 well spent,” said Brown, who lives in Bristow, Va. “My spot is 44,016, so no, I did not get a good spot in line.”

Not everyone was disappointed. Ruth Dewa Ayu of Bethesda, Md., bought a membership for the opportunity to purchase “Hamilton” tickets. She logged on at 6 a.m. and went back to the computer just before 10. Her randomly assigned place was 250, and about 20 minutes later she was buying four $99 tickets.

“It was really straightforward,” she said. She bought the maximum number at the cheapest price and plans to take her husband and his sister and her partner to the show.

“I was really being militant about it,” she said of her strategy, which included opening no other programs. “I didn’t want to slow my Internet down.”

The Kennedy Center sent messages to members reminding them to create or verify their online accounts and even produced a video to explain how its new Fast Find system works. Still, when the sale began at 10 a.m., everyone who visited the site was placed in the waiting room in random order. One user was No. 4,887, another 15,622, another 51,101. All of their wait times were listed as “more than an hour.”

Others were annoyed that the “Hamilton” sale was preventing them from accessing the center’s other programs. “I don’t want Hamilton Tickets. I just want to access your regular website,” posted one Twitter user.

Still others fumed about high-price tickets available almost immediately on resale sites, many for more than $1,000.

Padgett said the arts center is trying to prevent bots and brokers from buying tickets and noted that some of the online offers are speculative, meaning sellers don’t actually own the tickets they are promoting. He said online purchasers will not receive their tickets for seven to 10 days, allowing producers to make sure they were bought by real people.

Padgett said he expected that the website would direct patrons to the virtual waiting room for several hours. Tickets for the general public will be sold in late March.