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basic strut beam equation boundary conditions y=0 buckling cannot occur buckling loads Central Concentrated Force central concentrated loading central rise ratio circular curved beam clamped ends Coordinates and Geometry Cornell University critical loads curvature at s=0 Curves of Central Curves of Critical deflection deformations are considered Deformed Half-beam Loaded differential equation direct compression due to bending due to direct elastic line elastica elliptic integrals End Moment Load Equations 1.27 Fourier series Frisch-Fay Geometry of Curved Graphs of Initial half span High Rise Beam hinged end horizontal thrust inextensible and extensible inflection points initial rise initial rise/span ratio Jacobian elliptic functions linear and nonlinear linear beam theory linear theory nonlinear extensible theories nonlinear theories number of inflection point of inflection predict rectangular cross-section beam represent all possible rotational restraint shown in Fig slender beams Span of High STABILITY OF CURVED symmetrical deformations thrust Q translational spring constant values Wijngaarden