MILWAUKEE — The architect Santiago Calatrava’s addition to the Milwaukee Art Museum, completed in 2001, quickly became the symbol of this Midwestern city, plastered prominently on the official tourism website.

The $130 million Quadracci Pavilion, the addition’s official name, has a cathedral-like reception hall topped by a soaring louvered sunscreen that opens like the wings of a giant bird. Locals refer to the structure — which holds a grand temporary exhibition space, a restaurant and other amenities — as simply “the Calatrava,” as if it were a stand-alone artwork.

But the museum has some 30,000 objects in its permanent collection that are housed in two other buildings. And while attention was being lavished on the Quadracci Pavilion, including scrambling to pay off the debt its construction incurred, the two older buildings were falling apart: Water, the great enemy of museum collections, was dripping through the ceilings of the War Memorial Center — a 1957 structure designed by Eero Saarinen — and its larger 1975 addition by David Kahler.

Gallery spaces, encroached upon for storage and offices over the years, were unnavigable. “The floor plan was a maze,” the museum’s chief curator, Brady Roberts, said. “Staff people who had been here for 10 years would get lost.”