The second moment of area, also known as the second moment of inertia and the area moment of inertia, is a property of a shape that is used to predict its resistance to bending and deflection. Figure 1. ... Deflection happens when an object hits a plane surface Deflection in physics is the event where an object collides and bounces against a plane surface. ...
It is derived with use of the parallel axes rule. The second moment of area is not the same as thing as the moment of inertia, which is used to calculate the angular acceleration. The parallel axes rule can be used to determine the moment of inertia of a rigid object about any axis, given the moment of inertia of the object about the parallel axis through the objects center of mass and the perpendicular distance between the axes. ... Moment of inertia quantifies the resistance of a physical object to angular acceleration. ... Angular acceleration is the rate of change of angular velocity over time. ...
Iz - the second moment of area for axis one is moving a shape to
ICG - the second moment of area for the centre of gravity (coincides with the neutral axis)
A - area of the moved shape
d - the distance between the new axis and the axis of the shape
Stress in a beam
The classic bending formula for a beam is: The elementary Euler-Bernoulli beam theory is a simplfication of the linear theory of elasticity which allows quick calculation of the load carrying capacity and deflection of common structural elements called beams. ... A beam is a structural element that carries load primarily in bending (flexure). ...
The moment of inertia can also be called the mass moment of inertia (especially by mechanical engineers) to avoid confusion with the second moment of area, which is sometimes called the moment of inertia (especially by structural engineers) and denoted by the same symbol I.
In addition, the moment of inertia should not be confused the polar moment of inertia, which is a measure of an object's ability to resist torsion.
If the moment of inertia tensor has been calculated for rotations about the centroid of the rigid body, there is a useful labor-saving method to compute the tensor for rotations offset from the centroid.
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