Three-Point Bending at Large Deflections

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Abstract
A complete investigation of three-point bending at large deflections was attempted with the view of applying it as a test method for the determination of the effective modulus of elasticity of materials. A general solution of the problem was attempted by considering friction forces at the supports, axial forces along the beams tested at large deflections, and the effect of finite depth. The solution was carried out for homogeneous, perfectly elastic materials with equal tensile and compressive moduli under the assumption that plane sections remain plane at large deflections and that no appreciable effect of shear or stress concentrations at the position of load application exists. The effect of roller supports of finite radius was also considered. The results obtained by the present theory provide sufficient data for the design of a bending test under any given conditions or accuracy required.

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