# Beam deflection

1. Jul 5, 2016

2. Jul 5, 2016

### SteamKing

Staff Emeritus
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

3. Jul 5, 2016

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

4. Jul 5, 2016

### SteamKing

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

5. Jul 5, 2016

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

6. Jul 5, 2016

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

7. Jul 5, 2016

### SteamKing

Staff Emeritus
8. Jul 5, 2016

9. Jul 5, 2016

### SteamKing

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

10. Jul 5, 2016

i dont understand what is the purpose of having (areaAB) XA and (areaAB) X B ....
does he mean measure centroid from A and B??

11. Jul 5, 2016

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

12. Jul 8, 2016

why is it so?

13. Jul 8, 2016

how do you know? can you explain further?

14. Jul 8, 2016

### SteamKing

Staff Emeritus
15. Jul 8, 2016

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 ????

16. Jul 8, 2016

### SteamKing

Staff Emeritus
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.

17. Jul 8, 2016

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?

18. Jul 8, 2016

### SteamKing

Staff Emeritus
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.

19. Jul 8, 2016

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

20. Jul 9, 2016