Comparisons between the resistance of materials and the theory of elasticity - Reflections.

The resistance of materials and the theory of elasticity are two disciplines with common objectives: both address the study of the resistance (state of tensions) and the rigidity (state of deformations) of solid bodies deformable subjected to the action of systems of forces in static equilibrium.

In mechanical engineering the study that deals with the mechanics of solids is of the utmost importance, since we as future mechanical engineers work with many pieces of solid physical texture, many of these pieces of solid characteristics depending on the function they are executing are subjected to efforts, many of these efforts are in tension and understanding, the power to elucidate to what extent they can endure these efforts is our primary objective, since this will depend on the design of many operations in the world of the mechanics of many machines.

The resistance of the materials within the mechanics that the solid bodies follow limit their field of application to certain types of structural elements such as beams, columns among others, supported in some predetermined way in supports, recesses, joints that in turn are subject to certain types of actions as punctual forces, all these considerations within the resistance of the materials causes that the solution to certain problems of analytical character and of daily life are given within the field of structural engineering.

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In contrast to the resistance of materials, we have the elasticity theory, which in turn, faces the problem of mechanical origin in terms of geometries, boundary conditions and types of actions considered. For this it is necessary to apply a series of mathematical approaches that prevent obtaining a series of analytical solutions for the resolution of most problems of practical interest.

It is necessary to evaluate the sciences that study the behavior of solids when subjected to an effort within what is the resistance of materials and the theory of elasticity, since the resistance of materials and elasticity although they had parallel paths in their beginnings , it is currently under the understanding of many within the mechanical engineering and related engineering that we can approach the issue under a modern and avant-garde perspective, where we can consider the material resistance as a branch within the great theory of elasticity, that yes always being conscious and considering that both disciplines are handled between multitude of common concepts such as:

• Force.
• Displacement.
• Tension.
• Deformation.
• Balance.
• Compatibility

Which leads us to conclude that both disciplines consider that for a solid to be able to deform there must be a series of forces acting on it, some of these forces are given in compression, that is acting the sense of the force vector all towards a same point. Other forces occur in the opposite direction, these forces acting on the solid in the form of tension. If the solid undergoes a deformation it is because there is a displacement of elongation or compression compared to the original dimensions of the solid, that is why both the deformation of materials and the elasticity theory handle the displacement dimension. For a solid to be subjected to a series of stresses and not suffer deformation, it is because these efforts did not exceed the limits of elasticity of the material, or that they did not exceed the limits of material overload. However, the other thing that can happen is that there is a balance between the forces that act and the resistance of the material.