Strength of materials

The resistance of materials (RoM) is a particular discipline of the mechanics of continuous media allowing the calculation of stresses and strains in slender structures made of different materials (machines, mechanical engineering, building and civil engineering). It is a 1D static modeling of a deformable solid assimilated to a beam linked to a frame and subjected to external mechanical stresses.

The RoM allows the study of the global behavior of a structure (relationship between stresses - forces or moments - and displacements) to be reduced to that of the local behavior of the materials composing it(relationship between stresses and strains). Mechanical stresses can be seen as " cohesive forces " of the material. The deformations of a physical object are observed by a variation in its dimensions or in its overall shape.

The use of my RoM has two main objectives:

1) Characterize globally themechanical behavior of a solid in small deformations.

2) To dimension mechanical structures. To do this, it is necessary to knowthestate of stresses and / ordeformations within these structures. This is what allows modeling by the RdM which allows to predict these states of stresses / strains.

This teaching is therefore an application of isothermal linear Hooke elasticity in the 1D case. The mechanical structures considered are thus represented by beams, i.e. one-dimensional elastic media, a priori curved.

Required prerequisites*:

Rigid solid mechanics

Trigonometry

Notions of derivatives and primitives of functions

Recommended prerequisites*:

Analysis and linear algebra in L1+L2

Final exam with CC and max rule + TP

It starts with a brief reminder of the fundamental principle of statics (PFS) to determine the connection forces of a beam to its frame and then by calculating the forces within a lattice of bars, going as far as determining the displacement of the nodes of the lattice.

Then, the so-called "cut-off method" is introduced to determine the internal forces. After the introduction of the internal forces in a beam, the local equilibrium equations are established as well as the method to solve them. Different cases of simple loading are studied: tension/compression, bending and torsion. Following the introduction of the notion of deformation, the behavior laws of beams are defined and their exploitation to determine the deformation of a beam is developed.

Before highlighting the link between this approach and the 3-D elasticity of deformable media (next semester), the energetic methods, which are an application of the Virtual Power Principle, are exposed.