20.4: Flexural Stress
When analyzing bending in symmetric members, it's crucial to understand how stresses distribute when subjected to bending moments. This stress distribution is effectively described by applying fundamental mechanics and material science principles, particularly Hooke's Law for elastic materials.
Hooke's Law states that within the material's elastic limits, stress is directly proportional to strain. In a member experiencing a bending moment, the strain at any point is relative to its distance from the neutral axis, the central layer that experiences no longitudinal strain. The strain varies linearly from zero at the neutral axis to a maximum at the outermost fibers of the member.
From this, it is determined that the longitudinal stress at any point also varies linearly with distance from the neutral axis. Integrating this linear variation across the cross-sectional area of the member, where stress is zero at the neutral axis, confirms that this axis coincides with the centroid of the cross-section.
This integration process also defines the expression for the bending moment, and also defines the moment of inertia of the section. This calculation further establishes the relationship between the bending moment and the maximum stress at the furthest point from the neutral axis and gives the flexural stress caused by the member's bending.
