Stability and moment of inertia

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SUMMARY

The discussion centers on the calculation of the least moment of inertia for a rectangular section, specifically using dimensions of 4 feet for the base and 2 feet for the height. Participants clarify that the least moment of inertia corresponds to the minor axis, which is critical for stability analysis. It is established that the major axis moment of inertia, calculated with the base as 2 feet and height as 4 feet, is significantly greater, indicating reduced stability along the weak axis. Understanding these concepts is essential for accurate structural engineering calculations.

PREREQUISITES
  • Understanding of moment of inertia concepts
  • Familiarity with structural stability principles
  • Basic knowledge of geometry related to rectangles
  • Experience with engineering calculations
NEXT STEPS
  • Study the calculation methods for moment of inertia in various shapes
  • Learn about the implications of weak and strong axes in structural design
  • Explore software tools for structural analysis, such as AutoCAD or SAP2000
  • Research the effects of material properties on moment of inertia
USEFUL FOR

Structural engineers, civil engineering students, and professionals involved in stability analysis and design of rectangular sections will benefit from this discussion.

Jason03
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The problem and my work is below...I believe I got the problem to work out. The only question I had was if I found the LEAST moment of inertia which is what's needed for the formula at the end of my calculations. What exactly is meant by the least moment of inertia?

http://i674.photobucket.com/albums/vv106/jason03_2009/prob7-1.jpg

http://i674.photobucket.com/albums/vv106/jason03_2009/prob7-2.jpg
 
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Jason03 said:
The problem and my work is below...I believe I got the problem to work out. The only question I had was if I found the LEAST moment of inertia which is what's needed for the formula at the end of my calculations. What exactly is meant by the least moment of inertia?
You have calculated the least (minor axis) moment of inertia by assuming the 4 feet as your 'b' and 2 feet as your 'h'. The major axis moment of inertia is much greater ( using 2 feet as the 'b' and 4 feet as the 'h'); hence, the wall is much less stable along the weak axis, and thus, the least moment of inertia applies.
 
ok I see... so if the rectangle was rotated than the major axis would be calculated with the base being 2 and height being 4.
 

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