Neutral Axis/Second Moment Of Area

In summary, the advantages of using hollow cross sections over solid sections in beam bending applications include a lower moment of inertia and a smaller radius of gyration, making them more resistant to bending. The neutral axis and second moment of area play a significant role in determining the effectiveness of these cross sections.
  • #1
headshrinker
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Homework Statement


Explain the advantages of using hollow cross sections against solid sections in beam bending applications.


Homework Equations


None


The Attempt at a Solution


I know this has something to do with the Neutral axis and the second moment of area for the beam but i don't know how!

please help!
 
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  • #2
Quantitatively, evaluate the moment of inertia of a hoop about an axis in the plane of the hoop passing through the center of the hoop (neutral axis contains the centroid if no net tension or compression of the beam exists) with a mass M. Then evaluate the same moment for a solid circle of equal mass. This geomtery is easy to evaluate. Qualitatively, you can compare the radius of gyration of the two cross sections about the neutral axis. What do you conclude about their moments? How is bending related to moment or radius of gyration?
 
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What is the neutral axis?

The neutral axis is an imaginary line that passes through the centroid of a cross-sectional shape. It divides the shape into two equal areas and experiences no stress or strain when the shape is under load.

Why is the neutral axis important?

The neutral axis is important because it is used to determine the bending stress and deflection of a beam or structure under load. It also helps to determine the location of the maximum stress in a cross-sectional shape.

What is the second moment of area?

The second moment of area, also known as the moment of inertia, is a property of a cross-sectional shape that describes its resistance to bending. It is calculated by integrating the squared distance from the neutral axis to each point on the shape.

How is the second moment of area used in engineering?

The second moment of area is used in engineering to calculate the bending stress and deflection of beams and structures. It is also used in the design and analysis of various mechanical components, such as shafts, columns, and frames.

What factors affect the value of the second moment of area?

The value of the second moment of area is affected by the shape and size of the cross-section, as well as the location of the neutral axis. The distribution of material within the cross-section also plays a role in determining the value of the second moment of area.

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