Second Moment of Area - semicircular groove in a beam?

In summary, the conversation is about a problem related to the second moment of area in a beam with a semicircular groove. The speaker is struggling to find relevant equations and is asking for advice or direction in regards to this shape. Another person suggests using the additive property of moment of area to solve the problem.
  • #1
Spennn
2
0
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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  • #2
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:
 
  • #3


Cheers buddy :)

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

Thanks again,

Spen
 

1. What is the Second Moment of Area for a semicircular groove in a beam?

The Second Moment of Area for a semicircular groove in a beam refers to the resistance of a beam to bending when a load is applied. It is a measure of the beam's cross-sectional shape and size, and is calculated by squaring the distance of each point on the beam from the neutral axis and multiplying it by the area of that point.

2. How is the Second Moment of Area calculated for a semicircular groove?

The Second Moment of Area for a semicircular groove can be calculated by dividing the cross-sectional area of the groove into smaller elements and then using the formula for a semicircle (I = πr^4/8) to determine the moment of inertia for each element. The moments of inertia for each element are then summed up to find the overall Second Moment of Area for the semicircular groove.

3. What is the significance of the Second Moment of Area for a semicircular groove in a beam?

The Second Moment of Area for a semicircular groove in a beam is important because it determines the beam's ability to resist bending and maintain its structural integrity when a load is applied. A larger Second Moment of Area indicates a stronger beam that is less likely to deform or fail under stress.

4. How does the depth of the semicircular groove affect the Second Moment of Area?

The depth of the semicircular groove directly affects the Second Moment of Area, as it is one of the variables used in the calculation. The deeper the groove, the larger the Second Moment of Area, which results in a stronger beam with a higher resistance to bending.

5. Can the Second Moment of Area be increased for a semicircular groove in a beam?

Yes, the Second Moment of Area for a semicircular groove in a beam can be increased by increasing the depth of the groove or by adding reinforcement to the beam. Reinforcement such as steel bars or plates can be added to increase the overall strength and resistance to bending of the beam, resulting in a larger Second Moment of Area.

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