Sears Tower

Statistics

In-Depth Analysis by Michael W. Su

The Sears Tower has been able to maintain its record as the world’s tallest building for over twenty years due, in large part, to its distinguishing shape. Designed by partners of Skidmore, Owings and Merrill’s Chicago office, architect Bruce Graham and structural engineers Srinivasa Iyengar and Fazlur Kahn, the tower is not only built with an unprecedented “bundled tube” structural system mostly of steel, it expresses this system fully. Its foundation begins about 30m below grade with a concrete mat foundation that is, in turn, supported by 200 rock caissons bored to reach the bedrock another 30m below. From this foundation rise nine distinct “framed tubes” of steel bound together into a 3 tube by 3 tube arrangement by, individually, deeply-sectioned spandrel girders, and collectively, one and two story tall belt trusses, or virtual outriggers of perimeter trusses and rigid floor plates. Each tube is symmetrically proportioned with 22.9m sides and formed from perimeter columns 4.6m apart on center without any interior columns. The tubes fall away with height – rather like a rocket shedding booster stages – so that two tubes end at floor 50, two end at floor 66, three end at floor 90, and only two tubes actually reach floor 108. (Interestingly, the tower deviates some 10cm from vertical due to this asymmetrical loading of the foundation.) This novel structural system allows the tower to reach heights of 413m at the highest habitable floor, 442m at the roof, and since the addition two high definition television antennas in 1982, 527m at the very top. Most remarkably, these heights are attained with great material and financial economy. According to Khan, the final structure achieves a material density of 135kg of steel per square meter of space, whereas more conventional structures utilizing interior columns would have required 207kg. In all, the Sears Tower used about 69 million kgs of steel and weighs a total of 200 million kgs – a superlative efficiency of materials for such a tall building in the “Windy City”. (For comparison, the Taipei 101 Tower weighs 635 million kgs, in large part due to its greater seismic and wind loads.)

      Bundled framed tubes are a development of the framed tube system pioneered by the legendary Fazlur Kahn – sometimes called the “father of the modern skyscraper”. Kahn was the first engineer to introduce the notion of shifting gravity-load columns from the interior to the perimeter of a building. Then, by reducing the spacing of perimeter columns, increasing their cross sections – especially at the corners, and connecting these columns with deep spandrel beams, perimeter moment resisting frames can be formed that also efficiently counter lateral forces. Specifically, the resultant structure allows the building to shift lateral loads to axial compression and tension loads on the perimeter columns so that the whole structure behaves more like a cantilever with bending – a behavior that conveniently does not require extremely high strength steel. For larger buildings, however, increased aspect ratios of height to width – either too high or too low – introduce non-negligible “shear lag” between the centers and corners of the moment resisting frames which cause the structure to deviate from cantilever response. In these cases, large-scale structural bracing is required in order to control building deflection. Ingeniously, either by introducing massive cross trusses to a single framed tube as Graham and Kahn did a few years earlier for the Hancock Tower in Chicago, or by bundling multiple, but smaller aspect ratio, tubes together as they did for the Sears Tower, the shear lag problem was virtually eliminated even as these buildings were given their distinctive forms.

      Although framed tube structures are materially very efficient, their fabrication is more complicated. The connections that form moment resistant frames need to be welded, but reliably welding moment connections either on site or vertically in the structure is extremely difficult. For the Sears Tower, steel sections of 5m x 8m in size, or about three horizontal bays and two stories high, were especially prefabricated in the controlled environment of a shop so that, among other considerations, all critical welds could be formed horizontally. These column-girder trees, or “Christmas trees”, were then hoisted into place and simply bolted to each other. The structural soundness of the resulting frames was assured by restricting bolted connections to locations where beam moment diagrams have inflection points. Construction was also accelerated by the use of an innovative flooring system of 25m span trusses just 1m deep with shear bolts tied to preformed concrete slabs. That the building was finished just three years later, in 1974, and retained its height records for 26 years testifies to the achievement of both its design and construction. In fact, it would be another twenty years before high strength steel and concrete was combined with high pressure, high altitude concrete pumps to form the requisite “super-“ and “mega-columns” of viable structural alternatives to the framed-tubes of the Sears Tower or, contemporaneously, the now-lost World Trade Center Towers.