Second Moment of Area - semicircular groove in a beam?

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SUMMARY

The discussion focuses on calculating the second moment of area for a semicircular groove in a beam, a topic relevant to structural engineering and mechanics. The user, Spen, seeks guidance on finding equations specific to this shape, as most resources cover standard shapes like I-beams and hollow cylinders. A key insight shared is that the second moment of area is additive; thus, one can determine the moment of area of the groove and subtract it from the ungrooved beam's moment of area to find the effective moment of area. This approach provides a clear method for addressing the problem presented in Spen's Surf Science coursework.

PREREQUISITES
  • Understanding of second moment of area concepts
  • Familiarity with structural mechanics
  • Basic knowledge of beam theory
  • Ability to perform geometric calculations
NEXT STEPS
  • Research the formula for the second moment of area for semicircular shapes
  • Study additive properties of moments of area in structural analysis
  • Explore examples of moment of area calculations for non-standard shapes
  • Learn about beam deflection and stress analysis in engineering
USEFUL FOR

This discussion is beneficial for structural engineers, civil engineering students, and anyone involved in mechanical design or analysis of beams with non-standard geometries.

Spennn
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Second Moment of Area - semicircular "groove" in a beam?

Hi there guys, I've been looking into a problem that has been set as part of my Surf Science course (have your laughs I'm more than used to it! ;D) and not had much joy.

The problem that I have been having is that I can only find equations that relate to the second moment of area of I beams, Hollow cylinders etc. but, I am struggling to find anything relating to the shape that I need to investigate online or in books.

The shape I need to look at is a semicircle shaped groove in the surface of a beam.

So, I don't want to waste anybodies time, I'd just like to either know if I can relate someother shape to this or know if anybody can just point me in the right direction or let me know what I would call this shape so that I might have more luck searching myself :)

Thanks a bunch

Spen :)
 
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Welcome to PF!

Hi Spen! Welcome to PF! :smile:

Spennn said:
Hi there guys, I've been looking into a problem that has been set as part of my Surf Science course (have your laughs I'm more than used to it! ;D) …

No! sounds groovy! :wink:

(I'm not sure exactly what the shape is, but anyway …)

moment of area is additive, so you can find the moment of area of the groove, and then subtract that from the moment of area of the ungrooved beam. :smile:
 


Cheers buddy :)

Big help, now to get on with the coursework! meh!

Thanks again,

Spen
 

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