The dizzying heights achieved by skyscraper designers in the early 20th century were directly dependent upon the development of the cantilever method of analysis. While land speculation, a mature financial infrastructure, elevators, and many other factors were necessary to create the explosion of scrapers in Manhattan in the early 20th century, the ability to reliably design steel frames to support the buildings was a fundamental factor in the rise of the skyscraper.
In the 1890s perceptive engineers working on bridge portals understood that a column rigidly fixed into a framework will deflect into an S-shape when subjected to lateral forces. Recognizing the relationship between shear, moment, and slope, it was understood that internal moments in the column are, by definition, zero at the point of contraflexure. Publications by J. B. Johnson in 1893, Ernst F. Jonson in 1905, and A.C. Wilson in 1908 track the progress in developing the cantilever method which assumes points of contraflexture at the midpoints of columns and reliably calculates tall building frames.
Purdy and Henderson had already used stacks of bridge portals to stiffen the frame of the Old Colony Building in Chicago. Based on their subsequent work on Chicago and New York, it is apparent that they, and other engineers, used the key understanding of the point of contraflexure and the opportunity to simplify frame calculations in their design work. Initially used on slender buildings, such as The New York Times building of 1905, the efficacy of the technique was proven in these lower but slender buildings. Confidence with the procedure encouraged engineers to abandon the restrictive X-bracing used in the Singer Building, and instead design frames with rigid connections that led to world record heights in the Metropolitan Life, Woolworth, Chrysler, and Empire State buildings.