Let's study the Geometrical moment of inertia.
In the second moment of the area, inertia is used instead of area.
The second moment of area is closely related to
the bending strength (stiffness) of the material.
The inertia (= stiffness) that an object does not want to change
when an external force that tries to bend occurs Because it has.
Let's see Fig. 1!!
When a load (F) is applied to the end of the fixed cantilever beam
A moment occurs at the end of the fixed point.
If the material is in equilibrium,
a support moment is generated in the fixed part.
Thus, the moment bends the material.
Once it begins to bend,
the material exhibits a load distribution as shown in Fig. 4.
Therefore, the moment applied to an arbitrary micro-surface is as follows.
(Based on the neutral axis of the material)
Since the load is 'pressure x area'
In Fig. 6, since the load increases linearly with y,
the linear equation for y of pressure P is
So, if you substitute Equation.3 to Eq.2,
Moment is
The moment over the total area is
At this time, I is the 'Geometrical moment of inertia' or'Second moment of the area'.
Why does I affect the stiffness of the material?
For example, when there are two objects with different bending strengths,
a larger load is required to give the object with the higher bending strength
the same deformation as the object with the lower bending strength.
That is, there must be more moments as shown in Fig. 2 and Equation 1.
In other words, in Equation 5, M is large means I is large.
As a result, it can be seen that the greater the bending strength (stiffness),
the greater the I.
