If you are among those Philadelphians who have spent the last 15 years fretting about the desecrations that architect Frank Gehry might inflict on our great temple of art, you can rest easy now.

When the Philadelphia Museum of Art opens its new galleries and public spaces Friday, you won’t see any of the exploded geometric forms or billowing waves that have become Gehry’s signature. There are none of the crude vernacular materials that Gehry adores and traditionalists hate. No chain-link fencing. No humble plywood. No shiny, industrial-grade titanium. Our beloved Rocky steps remain intact (for now, anyway), and so do the museum’s buff-colored walls. Instead of wreaking havoc, the 92-year-old architectural radical has played against type and given museum officials precisely what they wanted: clarity, light, and space.

Gehry may be best known for his paradigm-busting Guggenheim Bilbao, a pileup of shimmering, silvery shapes that resembles a deconstructed battleship, but he has also had a varied career that includes stints designing shopping malls and office buildings. Only a few months before Bilbao opened in 1997, Gehry transformed the chaotic, ’60s-era Norton Simon Museum into a serene ensemble of classically arranged galleries. It was that project that convinced Philadelphia’s former museum director Anne d’Harnoncourt that he was the right architect to untangle the muddled interior here. The Gehry that the museum hired back in 2006 was Gehry the respectful classicist.

Gehry started by reinstating the Philadelphia museum’s original, Neoclassical axial floor plan, which had been interrupted by several ill-conceived additions. First, he reopened the stunning, Guastavino-designed, vaulted corridor that runs north-south through the stone ramparts at the base of the museum. Then he yanked out a 1959 auditorium that had been blocking the east-west route. Once the cross-axis was reestablished, Gehry was able to capture space inside the museum for two new, large galleries and a handsome new public room, called the Forum.

Through it all, Gehry has rigorously deferred to the architecture of Philadelphia’s iconic museum, collaboratively designed during the 1920s by Horace Trumbauer, Julian Abele, Paul Cret, C. Clark Zantzinger, and Charles Borie Jr. To maintain the building’s aesthetic cohesion, Gehry brought in truckloads of latte-hued Kasota stone, cutting it from the quarry that supplied the museum a century ago. While Gehry’s details are more streamlined and modern than his predecessors’, his love of swooping curves has been kept in check. Rarely have I seen a better architectural ventriloquist, speaking in the voice of the building.

And that’s what makes this $233 million project a little bit of a letdown after all these years of patiently waiting to see the “bomb” that Gehry promised to sneak into the design. Every inch of this project is rendered with elegance and sensitivity. But how is it possible that Philadelphia hired one of the most creative and provocative architects of our times, and all we got is a very good renovation?

That’s not nothing, of course. The ability to take a great building and make it even better is a much underrated art. Gehry’s improvements put the building in top form as it enters its second century. New mechanical and electrical systems have been installed throughout the museum, along with a multitude of elevators. With fewer obstructions, visitors should finally be able to find their way from Cezanne’s Bathers to Peale’s Staircase Group without getting lost. The museum is now fully accessible on the north and west entrances. And with the addition of several modern restrooms, the days of lining up to get into the three-stall ladies’ room on the first floor are thankfully over.

It says a lot that when I toured the building last week with the museum’s current director, Timothy Rub, the first thing he showed me was the new mechanical room. The snaking ventilation pipes — which may be the most curvaceous and sculptural forms in the whole project — consumed a big chunk of the construction budget, Rub told me. It’s admirable that the museum spent its money so practically. You just wish it had budgeted in a little more playfulness.

Gehry comes closest to eking out some fun in the new Forum, the soaring room that replaced the auditorium. Forty feet high, the Forum is to the museum what City Hall is to Philadelphia’s street grid: a civic meeting place. Because all the new spaces orbit around the Forum, it acts as the guide star, directing visitors to their destinations.

Apart from a gently curved ceiling, the room is entirely faced in buff Kasota stone, giving it the spare serenity of an ancient temple. For the moment, the museum has left the Forum empty, though its plainness makes it suitable for a range of museum activities, from sculpture installations to weddings.

The museum is famous for two monumental staircases: the Rocky steps and the Great Stair Hall. Gehry’s Forum was intended to add a third. Although more modest than the two others, this staircase was meant to be the project’s marquee event, the sole moment when Gehry was allowed to let loose. But loose is a relative term. The curving stairs in the Forum are a long way from the dramatic sculptures and flowing coils that Gehry created for places like the Art Gallery of Ontario or Miami’s New World Center.

Gehry told me in a Zoom interview that the stair design was inspired by Piranesi’s etchings of crisscrossing stairs, but you have to look down from the second floor to get a sense of that intricacy. It doesn’t help that the treads and risers are crafted from the same weighty Kasota stone as the rest of the Forum. Perhaps Gehry intended to wow us by suspending the heavy stone steps in the space. But all the necessary anchoring and hardware take the magic out of his sleight of hand.

While Gehry and the museum made the right choice in putting restraint first everywhere else, not here. Even a venerable institution needs an occasional jolt of fresh creativity. It’s an art museum, after all, and its job is to nurture things that stop us in our tracks and make us see.

During construction, the museum limited access to the north entry on Kelly Drive, the only one of the three entrances at street level. The east entrance, facing Eakins Oval, will remain closed for the near term, so it will be interesting to see whether visitors return to the west entrance, known as Lenfest Hall, after the reopening. If they do, they will discover a more spacious, newly brightened room, with views into the Forum.

It’s hard to believe, but visitors were once funneled into the west foyer through a single revolving door. Gehry eliminated that obstacle by removing the vestibule, as well as the wall where Chagall’s sunny theater backdrop hung. He also purged the brightly colored furniture and ceiling coffers that were installed during Venturi, Scott Brown’s 1989 renovation. While the room is now more user-friendly, it’s also more monochrome and subdued. Given the importance of Venturi, Scott Brown to architectural history, and to Philadelphia, it’s a shame that some vestige of their work wasn’t retained in the space.

These days, museum renovations frequently mean giving more prominence to the museum store, and things are no different here. Instead of being drawn into the museum by the sight of Chagall’s big red sun, visitors will have to pass the gift shops located just off Lenfest Hall to reach the new galleries.

Like everything else in Gehry’s design, those galleries are understated and refined. They don’t have as much natural light as d’Harnoncourt might have hoped for, and their ceilings aren’t as high as the ones on the second floor, but they are nevertheless a game-changer for the museum.

It’s not just that they offer an additional 20,000 square feet of exhibition space for American and contemporary art. The new galleries will enable the museum to present its collection in a more modern, inclusive way. While we’ve grown used to seeing a diverse array of artists and subjects presented in contemporary shows, it’s been more challenging to get that same breadth in exhibitions of early American art.

The Art Museum uses its new American gallery to make the point that the nation’s cultural achievements would not have been possible without the labor of enslaved Africans and Native Americans. So, the first thing you see when you step into the American galleries are the dignified portraits of two Lenape chiefs by Gustavus Hesselius. Beneath their images is a finely beaded wampum belt that was once displayed in the Philadelphia History Museum. Putting it in the Art Museum raises it to the level of fine art. The same is true for the wedding portraits of Hiram and Elizabeth Montier, which hang nearby. The pair, which date from 1841, are the oldest known paintings of free Black people.

As you walk through the new spaces, there are architectural moments that will take your breath away — the Guastavino corridor, the new terrace cafe overlooking the Waterworks. But presenting the collection in a more inclusive and welcoming way is the real triumph of the expansion.

Gehry’s Forum sets the stage for the next phase, a much larger suite of galleries that would be built under the terrace facing Eakins Oval. Because they would extend under the Rocky steps, Gehry proposed cutting a window into those 72 treads to bring in natural light and open views of the skyline. Rub told me he still strongly supports the idea, as does Gehry.

Given how much respect they showed the building during this phase, it seems odd that they would tinker with this particularly iconic element. The museum steps are as essential to Philadelphia’s identity as Independence Hall. Fortunately, this project is a good 10 years off, so there is time to keep the museum from tripping up on the steps.

Better they concentrate their efforts on infusing Gehry’s design with some of its missing irreverence. The Forum cries out for public events and participatory art installations, the kind that bring Philadelphians of all backgrounds together. Gehry has provided the canvas. Now it’s up to the museum to make the most of it.