Assumptions in Theory of Pure Bending
Theory of Pure Bending
- The material of the beam is homogeneous, isotropic, and linear elastic, in which Hooke’s law is valid.
- The beam is straight before loading.
- The cross-section of the beam is prismatic throughout the length.
- The plane section before bending remains plane after bending. It means the longitudinal strain varies linearly from zero at the neutral axis to maximum at the surface, and the longitudinal strain at any distance y is directly proportional to its distance (y) from the neutral axis.
- Every layer of material is free to expand or contract longitudinally and laterally under stress and does not exert pressure upon each other. Thus, the Poisson’s effect at the interface of the adjoining differently stressed fibers is ignored.
- The value of Young’s modulus (E) for the material is the same in tension and in compression.
- The section of the beam is symmetrical in the loading plane. If the section is nonsymmetrical, then twisting and warping may occur apart from bending.
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