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The Differential Equation of the Elastic Line
Interpretation of the Integration Constants
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antisymmetrical applied approximation assumed beam of finite buckling calculated circumferential components compression concentrated force corresponding cos2 Cosh2 cross section crossbeams cylindrical deflection curve deflection line deformation denote derived determined differential equation displacement elastic foundation elastic line elastically supported End Fig end points end-conditioning forces expressions finite length flexural rigidity formulas free ends functions Hence hoop Ibs./in infinite beam infinitely long beam integration constants Loading Fig longitudinal element main girders maximum bending method middle modulus modulus of elasticity moments normal force obtained point of application Poisson's ratio pressure problem produced radial rail reaction forces semi-infinite beam shearing force shell shown in Figure sign convention sin2 Sinh XZ Sinh2 slope solution subjected Substituting symmetrical theory tion tube values Xx cos Xx Xx Cosh Xx Xx sin Xx XZ cos XZ XZ Cosh Xz sin Xz XZ Sinh Xx