Internal Continuum
The Internal Continuum Mechanics Perspective (Newton’s Third Law)
When viewing the beam as a deformable physical body rather than an idealized rigid entity, load transmission between to points occurs through an internal stress field:
Intermolecular Bonding:
The load applied at one point generates localized strains, setting up internal stresses across the material lattice.
Action and Reaction:
Governed by Newton's third law, each infinitesimal volume element of the beam transmits internal contact forces to adjacent elements throughout the continuous body.
Internal Resultants:
If an imaginary cut is made through the beam at cross-section \(A_j\) , the cumulative action of all external forces acting on one side of the cut resolves into internal stress resultants:
- Normal Force (N): Resultant of normal stresses parallel to the longitudinal axis (axial tension or compression).
- Shear Force (V): Resultant of transverse shear stresses perpendicular to the beam axis.
- Bending Moment (M): Resultant moment of normal stress distributions, balancing the external moments about section \(A_j\).