The defining feature of a mansard roof, a sloped facade/roof, is mildly problematic as structure. Under just the gravity load of the wall’s own weight, there is a small overturning moment, which is resisted as an inward thrust at the top and an outward thrust at the base. If the sloped wall is carrying other loads – part of the weight of the flat roof above, or wind pressure, for example – those thrusts usually increase.
In older buildings with wood-framed mansards and a bunch of interior masonry bearing walls. it’s not a big deal to absorb those thrusts into the walls. It’s so much not a big deal that no one ever thought to get engineers involved. In newer (i.e. 1880s and later) buildings with metal frames and relatively light masonry walls, those thrusts had to be accounted for. Since the frame buildings typically had some level of engineering involvement, either structural engineers as designers or as employees of the steel fabricator, the solution was a designed engineering solution.
The curved knees above provide moment connections between mansard rafters and flat-roof beams. Because this building was constructed in 1905, this connection was made using rivets, so each curved knee is mostly just a plate that connects double-channel rafters and beams. (If you look closely, you can see dark lines on the flanges that mark the edges between the pairs of channels. The outer edge of each knee has a flange consisting of a pair of angles riveted to the plate. By providing a moment connection here, effectively making continuous the sloped and flat portions of the roof members, the thrusts created by the slope are spread over a larger area and their effect reduced.
In short, this steel-framed mansard is structurally quite different from its wood-framed predecessors, but looks more or less the same from the outside. Once again, structural engineering does its job well by being invisible.
