THE other night, Danielle Travali, 25, was listening to Kelly Clarkson’s new album, “Stronger.” Ms. Travali has fought her brigade of demons and then some, describing herself as an eating-disorders survivor.

“I am not a schmaltzy type,” said Ms. Travali, who edits an online women’s magazine in Fairfield, Conn., during a phone interview. But as Ms. Clarkson sang “The War Is Over,” she said, “tears were rolling down my face. As someone who has struggled with low self-esteem and body image, I have such a strong appreciation for powerful women who sing their truth. Kelly’s songs are not just about failed relationships with others, but failed relationships with ourselves. Boom! I’m learning here: What did I do to hurt me?”

For a decade, Ms. Clarkson has been belting power-pop hits like “I Do Not Hook Up” and “Since U Been Gone,” and dismissing withering criticism of her weight. As a result, her fans have built a distinctive relationship with her: less that of conventional adulation than of identification and admiration.

“You get a sense that she’s one of us,” Ms. Travali said.

That connection has been reinforced by “Stronger,” released last week, which the singer describes as her own journey of empowerment, addressed directly to fans. On one song, “You Can’t Win,” Ms. Clarkson, 29, sings, “If you’re thin/Poor little walking disease/If you’re not/They’re all screaming obese/If you’re straight/Why aren’t you married yet?/If you’re gay/Why aren’t you waving a flag?”