Beam Bending

• Bending is a deformation that puts one edge of a member in compression and the other edge in tension.

  

• Navier's hypothesis: The assumption that plane sections remain plane (Navier's hypotheses) leads to the conclusion that the distribution of strains through the depth of the beam is a straight line.

  • Navier's hypothesis is generally valid when the span to depth ratio of the beam exceeds about 10 (i.e. the beam is reasonably slender).

• Assume homogenous, linear elastic material: The additional assumption that the material is homogeneous and linear elastic leads to the conclusion that the distribution of stresses through the depth is also a straight line.

• Flexure formula: This distribution of stresses leads to the "Flexure Formula" that relates bending stress, internal moment, and cross section properties:

  

• Bending strength is sensitive to depth: The relationship between bending moment and bending stress is more sensitive to section depth than section width.

• This is because at the same stress level, a deeper beam has larger tension and compression resultants, and the resultants are farther apart.