The external actions (forces) acting on the beam can be of various nature even if generally only actions referable to forces and torques are considered, both concentrated on particular sections and distributed per unit length of the beam. The internal actions are linked to the internal continuity constraint (the constituent material is continuous) which acts in correspondence with each section of the beam.
This constraint presupposes that between the two sections in which the generic section S (point of application of the agent force) ideally divides the beam by matching images, there must be no solution of continuity. For the theory of elasticity this continuity constraint is expressed on the section by means of a punctual stress system. In this system the internal forces are reciprocally exchanged by the two sections through the faces of the section plane S. The resulting vector Y and the moment T of this point distribution define the stress characteristics of the beam in the considered section S.
These solicitations are
1. Axial force (or normal force)
2. Cutting force (or cuts)
3. Torque moment
4. Bending moments
The “technical theory of the beam” makes use of the stress characteristics in order to summarize the internal stress state of the beam. The respect of the equilibrium conditions for each section leads to the definition of a system of equations of equilibrium between stress characteristics and the applied external loads valid for each section of beams.
Through the analytical formulas, known the mechanical characteristics of the materials, it is possible to calculate:
1. Axial elongation
2. Linear deformations
3. Angular deformations