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Solid mechanics - Review of stresses

After having seen the basics of solid mechanics and the simple pure pressure stress in the previous page, this one reviews the different kind of stresses, including shear stress, etc. The modeling used for calculation of relations between stresses and strains is also covered.
But first, we have to see the moment of inertia.

The moment of inertia

The moment of inertia, that is, in fact, the second moment of area, is a purely geometric value calculated with the cross-section of the studied object, and depends on the axis you're interested in.
As we will see later, it is very interesting in stress and strain calculations, as it represents the resistance of a geometric configuration to deformation or deflection.

Let's consider an example:

Cylindric beam with cross-section description and annotation for the calculation of the moment of inertia
Sample beam on which principle of the moment of inertia is shown

The moment of inertia is given by the integration over the cross-sectional area of the square of the distance from the considered axis:

Ix = A dA