Beam Deflection Homework: Finding Centroid Distance from Point B

[chetzread]

Homework Statement

http://www.mathalino.com/reviewer/m...ution-to-problem-625-moment-diagrams-by-parts)
from the link , why the distance of centroid from B is (4/3) and (9/4) as shown?

Homework Equations

The Attempt at a Solution

it should be (4- (2/3) ) and (4-0.75) , am i right ?

 

[SteamKing]

Homework Statement

http://www.mathalino.com/reviewer/m...ution-to-problem-625-moment-diagrams-by-parts)
from the link , why the distance of centroid from B is (4/3) and (9/4) as shown?

Homework Equations

The Attempt at a Solution

it should be (4- (2/3) ) and (4-0.75) , am i right ?

For the right triangle, the centroid is located 1/3 the base from the right angle or 2/3 the base from the acute angle.

For the second degree curve, the centroid is also shown correctly.

You can look these things up to check yourself:

https://en.wikipedia.org/wiki/List_of_centroids

http://www.engineering.com/Library/...articleId/109/Centroids-of-Common-Shapes.aspx

 

[chetzread]

For the right triangle, the centroid is located 1/3 the base from the right angle or 2/3 the base from the acute angle.

For the second degree curve, the centroid is also shown correctly.

You can look these things up to check yourself:

https://en.wikipedia.org/wiki/List_of_centroids

http://www.engineering.com/Library/...articleId/109/Centroids-of-Common-Shapes.aspx

but , the problem is (area AB) x B , so the location should be measured from B , am i right ?

 

[SteamKing]

but , the problem is (area AB) x B , so the location should be measured from B , am i right ?

Beats me. The locations of the centroids shown are correct.

 

[chetzread]

Beats me. The locations of the centroids shown are correct.

then , what is the purpose of having (areaAB) XA and (areaAB) X B ?

 

[chetzread]

Beats me. The locations of the centroids shown are correct.

then , what is the purpose of having (areaAB) XA and (areaAB) X B ?

 

[SteamKing]

then , what is the purpose of having (areaAB) XA and (areaAB) X B ?

It appears that the problem is trying to show how to calculate beam deflection by the area-moment method.

http://www.engr.mun.ca/~katna/5931/Deflections_Area-moment2p.pdf

 

[chetzread]

It appears that the problem is trying to show how to calculate beam deflection by the area-moment method.

http://www.engr.mun.ca/~katna/5931/Deflections_Area-moment2p.pdf

yes i don't understand, why the author using 2 different approaches?

 

[SteamKing]

yes i don't understand, why the author using 2 different approaches?

Because beam deflections can be calculated using different methods, and he is trying to show the area-moment method in particular.

 

[chetzread]

Because beam deflections can be calculated using different methods, and he is trying to show the area-moment method in particular.

i don't understand what is the purpose of having (areaAB) XA and (areaAB) X B ...
does he mean measure centroid from A and B??

 

[chetzread]

Because beam deflections can be calculated using different methods, and he is trying to show the area-moment method in particular.

does he mean measure centroid from A and B??
why he need to do do?

 

[chetzread]

why is it so?

 

[chetzread]

Beats me. The locations of the centroids shown are correct.

how do you know? can you explain further?

 

[SteamKing]

how do you know? can you explain further?

You can look these things up on the internet. That's what it's for. There's probably a list of them also in your textbook.

https://en.wikipedia.org/wiki/List_of_centroids

http://www.engineering.com/Library/...articleId/109/Centroids-of-Common-Shapes.aspx

This is the second time I've given you websites to find this information. Why are you so eager to waste people's time and not even read the replies to your posts?

 

[chetzread]

You can look these things up on the internet. That's what it's for. There's probably a list of them also in your textbook.

https://en.wikipedia.org/wiki/List_of_centroids

http://www.engineering.com/Library/...articleId/109/Centroids-of-Common-Shapes.aspx

This is the second time I've given you websites to find this information. Why are you so eager to waste people's time and not even read the replies to your posts?

ok, for Parabolic spandrel , the centroid is 3a/4 , so it's 3(3)/4, but, it'should be measured from B, am i right?
So is it 1 +9/4 = 13/4 ?

 

[SteamKing]

ok, for Parabolic spandrel , the centroid is 3a/4 , so it's 3(3)/4, but, it'should be measured from B, am i right?
So is it 1 +9/4 = 13/4 ?

If you want to measure it from B, sure.

But the location as shown in the OP is also correct, since the spandrel starts 1 m away from B.

 

[chetzread]

If you want to measure it from B, sure.

But the location as shown in the OP is also correct, since the spandrel starts 1 m away from B.

so,

If you want to measure it from B, sure.

But the location as shown in the OP is also correct, since the spandrel starts 1 m away from B.

sorry, it's my fault, then for the smaller triangle part , it should be -0.5(2)(1000)( (4/3) +2 ) , is it true?
Why the author left out +2 ?
(area AB) x B means area x distance of centroid measured from B,am i right?

 

[SteamKing]

so,

sorry, it's my fault, then for the smaller triangle part , it should be -0.5(2)(1000)( (4/3) +2 ) , is it true?
Why the author left out +2 ?
(area AB) x B means area x distance of centroid measured from B,am i right?

For the smaller triangle, the centroid location measured from A is correct, but the location measured from B is off by 2 m. The 4/3 m should actually be measured from the tip of this triangle.

 

[chetzread]

For the smaller triangle, the centroid location measured from A is correct, but the location measured from B is off by 2 m. The 4/3 m should actually be measured from the tip of this triangle.

so, 4/3 is incorrect?
the author used (area AB) x B, which means the centroid should be measured from B, right?

 

[chetzread]

I m not sure what does (area AB x B ) means, can someone clarify?