WASHINGTON — Few relationships in Washington are as complex as that of president and vice president, a partnership forged of political necessity and often defined by rivalry and competing self-interests.

For President Barack Obama and Vice President Joe Biden, there have been trying moments since they took office more than six years ago.

But the recent death of Biden's son, Beau, has magnified a striking personal bond between Obama and Joe Biden, men from different generations and backgrounds.

"Joe, you are my brother," Obama said in a deeply personal eulogy at the younger Biden's funeral Saturday in Delaware. "I'm grateful every day that you've got such a big heart, and a big soul, and those broad shoulders."

Obama's voice cracked throughout his remarks, a rare public display of emotion for a president with a typically cool demeanor. Biden, on the other hand, can overflow with emotion at even mundane White House events.

The 53-year-old Obama and his 72-year-old vice president overlapped for a few years in the Senate, but they were not particularly close. After winning the Democratic presidential nomination in 2008, Obama picked Biden as his running mate in part because he hoped the Delaware senator's 36 years in Washington would offset his own inexperience.

Once in the White House, Obama showed his confidence in Biden by putting him in charge of meaty issues, including Iraq policy and the economic stimulus. Biden also would become the point person on Ukraine and gun control.

As the White House and Congress barreled toward a tax increase deadline in the closing days of 2012, it was Biden who called on his deep Capitol Hill relationships to avert a crisis, filling the void for a president who has struggled with the kind of personal touch that appears to come so easily for the vice president.

But Biden's free-wheeling style has caused headaches for the White House, most notably when he appeared to force the president's hand on gay marriage in the months before the 2012 election. Biden said in a television interview that he was "absolutely comfortable" with gay couples marrying. At the time, Obama professed to still be "evolving" on the issue.

Obama's political advisers were frustrated that Biden had pushed the president to weigh in on an issue they had planned to avoid until after the election. But Obama himself appeared far less exercised by his vice president's misstep.

"I think (Obama) understood before a lot of people that all of the value you get from having Joe Biden on your team, it just overwhelms a minor hiccup if he says something impolitic," said Jay Carney, who worked for both Obama and Biden in the White House before leaving the administration last year.

The closing years of an administration can be trying for relations between the president and vice president, particularly if the second-in-command is running for the top job. Even the ties between President Bill Clinton and Vice President Al Gore, who were seen as close during most of their two terms in office, grew distant as Gore tried to separate himself from Clinton as he ran for president in 2000.

Biden hasn't officially ruled out a presidential run in 2016, though there are few signs he is moving in that direction.

More than Biden's political or policy skill, aides say it's the vice president's closeness with his family that appeals to Obama. While Biden's family is large and close-knit, Obama barely knew his father and was raised by his grandparents and single mother.

"I think the president is just really drawn to the emotional power of the Biden family — the intensity of the commitment the vice president has to his family and they have to him," Carney said.

Biden largely kept his son's health struggles private, but White House officials say Obama and the vice president had several conversations in recent weeks about Beau Biden's recurrence of cancer.

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When Obama addressed the large crowd packed into a Roman Catholic church in Wilmington, it was clear he was speaking not as a political ally but as someone suffering alongside the Biden family.

After sharing a long embrace with Biden, Obama said of his own family, "We've become part of the Biden clan."

"The Biden family rule applies," he continued. "We're always here for you, we always will be — my word as a Biden."

Follow Julie Pace at http://twitter.com/jpaceDC

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