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Encyclopedia > Area moment of inertia

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. ...

Contents


Definition

I_x = int y^2 dA

  • Ix - the second moment of inertia about the axis x
  • dA - an elemental area
  • y - the perpendicular distance to the element dA from the axis x

Unit

The SI unit for second moment of area is metre to the fourth power (m4) The International System of Units (abbreviated SI from the French phrase, Système International dUnités) is the most widely used system of units. ... The metre, symbol: m, is the basic unit of distance (or of length, in the parlance of the physical sciences) in the International System of Units. ...


Second moment of area - rectangular cross section

Rectangle: I_{x}=frac{bh^3}{12}

  • b = width (x-dimension),
  • h = height (y-dimension)

See List of second moments of area for other shapes. The following is a list of moments of inertia. ...


Parallel axes rule

I_z = I_{CG}+Ad^2,

  • 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). ...

{sigma}= frac{M y}{I_x}
  • σ is the bending stress
  • M - the moment at the neutral axis
  • y - the perpendicular distance to the neutral axis
  • Ix - the second moment of inertia about the neutral axis x

Stress tensor In physics, stress is the internal distribution of forces within a body that balance and react to the loads applied to it. ...

External links


  Results from FactBites:
 
Moment of inertia - Wikipedia, the free encyclopedia (1428 words)
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.
List of moments of inertia - Wikipedia, the free encyclopedia (571 words)
The following is a list of moments of inertia and area moments of inertia (also known as the second moment of area).
Moments of inertia have units of dimension mass × length
, and should not be confused with the mass moment of inertia.
  More results at FactBites »

 

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