– Given the depth of talent in American women’s gymnastics, many believed that the most challenging part of this Olympic year would be simply making the five-member team for the Rio Games. For Gabby Douglas, that turned out to be only partially true.

Douglas, the 2012 Olympic gold medalist in the all-around, fell off the balance beam twice during last weekend’s Olympic trials. She still was chosen for the roster, thanks to Martha Karolyi’s faith in her. But Karolyi, the U.S. women’s national team coordinator, made it clear that she expects Douglas — and everyone else — to sharpen up considerably during a nine-day training camp later this month.

Monday morning, many of the women who finished the trials Sunday night were dealing with the emotional hangover of a grueling event. Simone Biles, Laurie Hernandez, Aly Raisman and Madison Kocian beamed as they were fitted for their Team USA gear. Maggie Nichols of Little Canada, who was left off the roster, found her disappointment salved by the kindness of her fans and her excitement at beginning her college gymnastics career.

Then there was the visibly relieved Douglas, who promised that her work has only begun.

“I’m just really grateful and honored,’’ Douglas said. “For Martha to believe in me and trust in me, it really means a lot. And I’m going to prove to her that I’m not going to falter.

“It’s a relief to make the team. But I’m not easing up. I’m going to push so hard in the gym and prove to everyone I am more determined than ever.’’

Karolyi said the surplus of talent made the final decision the most difficult in her 15 years as national team coordinator. Based on performances at the U.S. championships and other major meets in recent months, she entered the Olympic trials with five names on a list and did not change her mind.

Biles, Hernandez and Raisman, the top three in the all-around standings, continued to set themselves apart. Kocian — a bars specialist whose score is essential to the team competition — recovered from an ankle injury to prove she can contribute on other events as well.

The final place came down to Douglas and Ashton Locklear, another bars specialist. Though Douglas has struggled in training and competition for several weeks, she got the nod because she is an all-arounder whose bars score helps the team on its weakest event — and because Karolyi is convinced she can whip Douglas into top form in time for Rio.

“Gabby gave me some concerns,’’ Karolyi said. “I feel if we put Gabby in regimented training, with daily planning and daily assignments, we will see improvement.

“We’re putting big importance on this training camp. It’s not only Gabby. We need to refine little things with other team members, also.’’

While Douglas still was feeling the heat, Nichols was feeling the love. Her fans helped her heal with an outpouring of support on social media and in person, swarming her at the San Jose airport on Monday as she waited for her flight home.

Nichols hit all four of her routines Sunday to move up to sixth in the all-around standings, generating some hope she could be one of the five team members or three alternates. But Karolyi assembles her rosters based on the calculus of the team competition — when three gymnasts compete and all three scores count — and left Nichols off because she did not finish in the top three in any event at trials.

Even Karolyi admitted that was “harsh,’’ and many were cheering for Nichols as she fought her way back from a knee injury three months ago.

“It’s very disappointing, but everything happens for a reason,’’ Nichols said. “I’m ready to turn the page, and I’m really excited to start my next chapter.

“It’s been a crazy year. There have been a lot of good times, and bad times too. I’m proud of the way I handled myself. And I enjoyed every second of it. I’ll never get an opportunity like the past year ever again.’’

With the trials over, Nichols will move on to college gymnastics at the University of Oklahoma. Douglas will be sweating it out in the gym at Karolyi’s ranch, bearing the burden of the returning Olympic champion.

“I’ll be focusing on being consistent in every event,’’ Douglas said. “No mistakes. No falls. I want to prove to everyone that you can believe in me.’’