The two large red cranes on Chapel Street, the scaffolding and protective fencing around the periphery of Egerton Swartwout’s Old Art Gallery and Street Hall, and the occasional disruption of traffic on High Street are signs of progress.

The Yale University Art Gallery renovation, scheduled for completion in 2012 is currently in the middle of the demolition phase. As walls are torn down, staircases removed and old amenities stripped away, the gallery prepares for the addition of a modern new floor and terrace to the old Gothic building.

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“We’re right on schedule,” said Leslie Myers, project manager for the gallery, on a tour of the construction Wednesday.

She explained that the year-long delay in the project — a consequence of the economic downturn — gave the gallery staff, construction crew and architect more time to plan up front. The extra time has prevented any serious problems since construction started in October, she added.

The construction company, Dimeo, has overseen the actual work on the buildings, bringing in between 80 and 120 workers each day, depending on the amount and type of work that needs to be done. This week, there are 120 workers on site.

Workers and visitors must ascend a flight of stairs covered with plywood to protect the original stone, and much of the building’s brick and stone features have been similarly covered.

“The objective of the renovation is to make the buildings look as wonderful as possible,” said Jill Westgard, deputy director for museum resources and stewardship. “We don’t want to damage them in the process,”

The sculpture hall of Egerton Swartwout’s Old Art Gallery, a vast space with high, arched ceilings and wall-sized windows, did not require significant structural work, and mostly underwent cleaning, Myers said. The room will house the gallery’s collection of ancient art when the building reopens in 2012.

The third floor of Swartwout hints at what will become the renovation’s most dramatic change: The room is being prepared for the removal of the high glass ceiling and the addition of another floor, which will be home to “tower galleries,” so called because of their location on the top floor of the building. One such gallery will be the Jane and Richard C. Levin Teaching Gallery — a space that will house temporary, rotating exhibitions connected to specific Yale courses.

Though an additional floor will be placed on top of Swartwout, the building will still be about the same height — thanks to its high ceilings — in order to maintain the look of the edifice, Westgard said.

“It was important for us to have respect for the Gothic architecture of the building and the skyline of campus,” Myers added.

Still, the “tower” will be a more modern addition, with the same steel, glass and the zinc-coated copper used on the Jeffrey H. Loria Center. An exterior balcony and terrace will also be added to the gallery’s facade, providing a space for outdoor sculptures.

Across the bridge on the Old Campus side of High Street, Street Hall will be home to the American Painting and Sculpture and the American Decorative Arts departments. The building, which once housed the History of Art Department, still bears many features of its academic past: Chalkboards hang in some of the rooms, and a former auditorium has a projector screen on the back wall. Workers are in the process of removing the ubiquitous drywall; in one room, the process revealed an original stone column that will be worked into the design of the room.

A small room in the back of Street Hall, closest to Linsly-Chittenden Hall, is being built out as a test room for the gallery: The new windows, moldings and wall finishes will be put in place so gallery designers can visualize the overall look of the project before it is implemented on a large-scale level. The room will also allow engineers to test the efficacy of the materials used to maintain humidity and temperature. This summer, a chamber will be built on the outside of the room and filled with cooled nitrogen to test the effect of winter conditions on the building.

Away from the construction site, curators and exhibition specialists are working to design the configuration of the galleries, deciding on the location of artwork, light fixtures and seating for visitors. Associate Director of Exhibitions Jeffrey Yoshimine oversees this process, scheduled to start next year. He said an exhibition designer, the gallery curators and in-house technical staff are currently finalizing the plans and submitting them for review to various gallery departments to see if anything has been missed in terms of security, traffic flow and educational use.

In designing the galleries, curators are focusing on more than just the look of the art itself, head curator Susan Matheson said.

“We’re thinking a lot about continuity and the visitor’s experience,” she said, “providing comfortable places for visitors to sit, thinking about how visitors will navigate the collections.”

After the renovation is completed, the Ancient Art, Coins and Medals, Early European Art, and Modern and Contemporary Art collections will be on display at the Swartwout Building.