Originally Posted by plinko
I find it really interesting that the 2nd setback occurs at the 66th floor rather than the 70th (in line with the 20 floor sections along the rest of the building).
The diagram is a little misleading. For instance the top portion of the building isn't 20 floors. The elevator penthouse roof is the 110th floor. The roof of the topmost section is the 108th floor.
As to what floors the setbacks ended up at, I don't think there is a single simple answer. They were optimized by the design team. It's a combination of the building program (sq ft of floor space, # of corner offices, the whole marketing & business equation stuff), visual aesthetics, and structural requirements. For instance, Sears needed immediately 2 million square feet of large open floorplan office space. Some studies indicated that 50,000ft^2 per floor was was optimum, so the first setback floor height was primarily set by this need. Above the 50th floor, you start dealing with asymmetric structure and controlling the aeroelastic torsion modes of the building. It wouldn't surprise me if belt truss placement to control of these dynamic modes at least partially dictated the setback heights. Supposedly the topmost (double tube) section of the tower helps in this regard, but it isn't clear to me if the wind loading performance drove that arrangement or merely confirmed it.