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A force is applied to a beam at a right angle to the longitudinal axis:
The beam reacts to the external force, and a bending moment is created about the point at which it is pinned. 'M' denotes the bending moment whilst 'u' denotes the displacement from it's original position.
The beam bends in a uniform way, such that R denotes the radius of curvature, which remains uniform throughout the beam.
The radius of curvature can be calculated with the equation:
Where K is the curvature, u is the displacement from original position and R is the radius of curvature.
The following assumptions are made when calculating the curvature:
The beam is initially straight, symmetrical and unstressed.
The material of the beam is homogenous, isotropic and linearly elastic.
The limit of proportionality is not exceeded during loading.
Young's modulus for the material is the same in tension and compression
All elastic deformation is small so the planar cross-sections remain planar before and after bending.
The applied load purely causes a bending moment and no torsion (twisting)
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