forms a curve intermediate between a catenary curve and a parabola. The simplifying assumption can be made that it approximates a circular arc (of radius R). By equilibrium: The horizontal and vertical reactions : By geometry: The length of the cable: The tension in the cable: By substitution: The tension is also equal to: The extension of the cable upon being loaded is (from Hooke's Law, where the axial stiffness, k, is equal to ): where E is the Young's modulus of the cable and A is its cross-sectional area. If an initial pretension, is added to the cable, the extension becomes: Combining the above equations gives: By plotting the left hand side of this equation against T, and plotting the right hand side on the same axes, also against T, the intersection will give the actual equilibrium tension in the cable for a given loading w and a given pretension . Cable with central point load A similar solution to that above can be derived where: By equilibrium: By geometry: This gives the following relationship: As before, plotting the left hand side and right hand side of the equation against the tension, T, will give the equilibrium tension for a given pretension, and load, W. Tensioned cable oscillations The fundamental natural frequency, f1 of tensioned cables is given by: where T = tension in newtons, m = mass in kilograms and L = span length. Notable structures Shukhov Rotunda, Russia, 1896 Canada Place, Vancouver, British Columbia for Expo '86 Yoyogi National Gymnasium by Kenzo Tange, Yoyogi Park, Tokyo, Japan Ingalls Rink, Yale University by Eero Saarinen Khan Shatyry Entertainment Center, Nur-Sultan, Kazakhstan Tropicana Field, St. Petersburg, Florida Olympiapark, Munich by Frei Otto Sidney Myer Music Bowl, Melbourne The O2 (formerly the Millennium Dome), London by Buro Happold and Richard Rogers Partnership Denver International Airport, Denver Dorton Arena, Raleigh Georgia Dome, Atlanta, Georgia by Heery and Weidlinger Associates (demolished in 2017) Grantley Adams International Airport, Christ Church, Barbados Pengrowth Saddledome, Calgary by Graham McCourt Architects and Jan Bobrowski and Partners Scandinavium, Gothenburg, Sweden Hong Kong Museum of Coastal Defence Modernization of the Central Railway Station, Sofia, Bulgaria Redbird Arena, Illinois State University, Normal, Illinois Retractable Umbrellas, Al-Masjid an-Nabawi, Medina, Saudi Arabia Killesberg Tower, Stuttgart Gallery of well-known tensile structures Classification numbers The Construction Specifications Institute (CSI) and Construction Specifications Canada (CSC), MasterFormat 2018 Edition, Division 05 and 13: 05 16