Editing Tie rod (section)

==Geometry==
Osgood and Graustein used the [[rectangular hyperbola]], its [[conjugate hyperbola]], and [[conjugate diameters]] to rationalize tie rods at 15 degree radial spacing, to a square of [[girder]]s, from its center. The tie-rods to the corners (45°) correspond to the asymptotes, while the pair at 15° and 75° are conjugate, as are the pair at 30° and 60°. According to this model in [[linear elasticity]], the application of a load compressing the square results in a [[deformation (mechanics)|deformation]] where the tie rods maintain their conjugate relations.<ref>[[William F. Osgood]] & William C. Graustein (1922) [http://quod.lib.umich.edu/u/umhistmath/abn6056.0001.001/324?rgn=full+text;view=pdf Plane and Solid Analytic Geometry], page 307, link from University of Michigan Historical Math Collection</ref>