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The Differential Equation of the Elastic Line
Interpretation of the Integration Constants
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antisymmetrical applied approximation assumed axis beam of finite buckling calculated circumferential components compression concentrated force corresponding cos2 Cosh2 cross section crossbeams cylindrical deﬂection deflection curve deflection line deformation denote derived determined differential equation displacement elastic foundation elastic line elastically supported end points end-conditioning forces expressions finite length flexural rigidity formulas free ends functions Hence hoop infinite beam infinitely long beam integration constants lbs./in 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 sin2 Sinh Xx Sinh2 slope solution subjected Substituting symmetrical theory tion tube values Xa cos X(Z Xx cos Xx Xx Cosh Xx Xx sin Xx Xx Sinh