The Origin, Development, and Application of Hyperstatic Rigid Frames

Han, Shuyuan [UCL] Zastavni, Denis [UCL]

The research presented in this seminar is the first part of the author’ PhD project. This project is comprised of two parts: a history study of hyperstatic rigid frames, and developing the historical analysis method graphic statics into a geometric-based design method for hyperstatic rigid frames. Hyperstatic rigid frames are frames characterized by moment-resisting connections and static indeterminacy. Despite their ubiquitous use nowadays, some questions related to the history of their origin, development, and application are still unclear. The first part of the project tries to answer these questions through the investigation of archival evidence. The review of the historical graphical method also provides the foundation for the second part of the project. An overview of the historical research of hyperstatic rigid frames The intent of the history study is to reveal how new materials, spatial need, new construction technologies and structural theories have advanced the development and application of hyperstatic rigid frames. This kind of frames had already existed before the first industrial revolution. Ancient wooden ships used bracing knees in joints. The members could thus resist bending together, the ship frames became stronger and more integrated. During the age of first industrial revolution, the increasing need for prompt construction promoted rigid connections. The frame of the Crystal Palace derived its stability from rigid connection during construction. Without the supporting falsework, the construction became faster. Many iron frames at that time adopted brackets or curved girders in joints to realize the momentresisting capacity, imitating the strategy of timber frames. It is believed until the Godfrey Greene’s Royal Navy Boat Store that the rigid connection finally had its modern elegant construction. Then with the burgeoning highrise building in Chicago and New York in the late 1860s and 1870s, the demand for reducing floor area occupied by thick masonry walls gave an impetus for the adoption of “portal actions” to resist lateral loading. For example, the Old Colony Building built in the 1890s was laterally braced by its sophisticated portal arch system. With the extensive application of steel and reinforced concrete in building industry, the elegancy and simplicity of the rigid joints became more effortless to achieve. Electric welding and high-strength bolts further simplified the detail of steel frames. Meanwhile, pioneering architects and engineers were exploring the potential of visual expression of hyperstatic rigid frames. The structural theories had also been evolving along. At the time of Renaissance, Leonardo da Vinci was able to illustrate the basic bending action of portal frames. Then at the time of first Industrial Revolution, analytical methods advanced continuously with the introduction of mathematical means like calculus and matrix. At the beginning of the twentieth century, the force method and the displacement method quickly reached their limits with the blossom of high-rise building. To address high degree of static indeterminacy, iterative methods such as those of Hardy Cross was proposed and extensively used. Besides the well-known numeric methods, geometricbased method graphic statics was also developed and applied on hyperstatic rigid frames by some researchers. Milo Ketchum and Jerome Sondericker devised methods that could solve portal frames partly rigid. William Wolfe adapted Otto Mohr’ method to solve a three-degreeindeterminate continuous portal frame under vertical loading. Though almost forgotten, these graphical methods can offer special insight into the relation between structural definition and bending performance.