Who knew such beauty could be found in the detritus of daily life?

Discarded prescription pill bottles, broken umbrellas, old ties, worn sweaters, losing lottery tickets, and those cheap trophies awarded to every child who’s ever played a sport — these are the materials that make up a new exhibit at the Smithsonian’s American Art Museum.

In her show “Common Threads,— artist Jean Shin has gathered the stuff that goes out in the trash and created eight impressive installations. It’s the first time this many pieces created by the 38-year-old Bethesda, Md., native have been gathered in one place for a show.

It’s a surprising exhibit, considering the materials. Shin has achieved a kind of symmetry and balance in this work, which manages to find elegance, meaning and beauty in the ordinary.

The highlight of the show, which opened Friday, is the installation “Everyday Monuments— (2009), a room-sized expanse of nearly 2,000 donated sports trophies, laid out in a rectangle patterned after the National Mall. Shin painstakingly washed each trophy, cut off its arms and removed any part related to sports (such as a basketball or a tennis racket) and then hand-sculpted new objects for each trophy. So, for example, instead of a trophy with a figure sporting a bowling ball, the figure might be pushing a stroller.

“It’s really a tribute to those labors that go unnoticed and the everyday person who shows up to work,— Shin said. The idea of taking all the secondhand trophies and giving them a “second life— allowed her to honor “all the people who have never won trophies,— she said. “I am literally deconstructing them and putting them back together in a new form.— Figures push brooms, type on a keyboard, ride a bike, carry a tray, climb a ladder, carry groceries, hold a suit on a hanger or sit behind a wheel.

Arranging those trophies in a long rectangular shape allowed Shin to bring Washington’s intimidating scale and monuments “down to an intimate level,— she said. Shin said she finds the empty expanse of the Mall in the midst of the buildings of Washington surprising.

Projected on the wall alongside the trophies is a magnified image of some of the trophy figures, blown up to larger-than-life size so that visitors could also experience the feeling of being swallowed up in a crowd with no clear sense of how large the crowd actually is.

Another fascinating installation is called “Chance City.— It’s a precarious and colorful cityscape made of $25,382 worth of losing lottery tickets, all delicately balancing against each other in giant houses of cards.

The installation is a vivid representation of the “notion of vulnerability,— says curator Joanna Marsh. “We take these chances in life and sometimes they fall apart.— The piece also reminds viewers that cities themselves are “built on risk-taking,— Marsh says. “The force of money and power is very illusory.—

So what happens when an impulsive child can’t resist touching these houses of cards and an entire building crashes? Shin “does fully expect that a portion will fall,— says Marsh. “At a certain point, you just have to let go.—

That, of course, doesn’t mean the museum encourages that much participation from viewers: The exhibit is protected by alarms. Shin and her associates spent two solid weeks painstakingly constructing the cardscape.

The act of installation — as well as the task of gathering discarded materials from volunteers around the country — is what makes “Common Threads— both labor-intensive and collaborative. For instance, Shin’s installation “Unraveling— is made up of dozens of donated sweaters from people living in Asian-American arts communities in New York; Houston; Berkeley, Calif.; Los Angeles; Honolulu and D.C.

With each city the installation visits, the exhibit grows, as Shin not only collects sweaters but also creates literal connections among them. Each person donating a sweater named the others he or she knew, and that connection was represented by a string of yarn linking the two.

The result is an overhead tapestry that perfectly illustrates the abstract idea of social networking. But that’s not to say that Shin’s social networking is limited to sweaters. The museum has set up accounts on Twitter, Facebook, Flickr, ArtBabble, iTunes and YouTube to follow the exhibition and offer glimpses of the work it took Shin and her assistants to set up the show. Others can even post their own photos of works they’ve created with found art.

“Common Threads— runs through July 26.