Answer:
point B where
has the largest Q value at section a–a
Explanation:
The missing diagram that is suppose to be attached to this question can be found in the attached file below.
So from the given information ;we are to determine the point that has the largest Q value at section a–a
In order to do that; we will work hand in hand with the image attached below.
From the image attached ; we will realize that there are 8 blocks aligned on top on another in the R.H.S of the image with the total of 12 in; meaning that each block contains 1.5 in each.
We also have block partitioned into different point segments . i,e A,B,C, D
For point A ;
Let Q be the moment of the Area A;
SO ; ![Q_A = Area \times y_1](https://tex.z-dn.net/?f=Q_A%20%3D%20Area%20%5Ctimes%20y_1)
where ;
![y_1 = (6 - \dfrac{1.5}{2})](https://tex.z-dn.net/?f=y_1%20%3D%20%286%20-%20%5Cdfrac%7B1.5%7D%7B2%7D%29)
![y_1 = (6- 0.75)](https://tex.z-dn.net/?f=y_1%20%3D%20%286-%200.75%29)
![y_1 = 5.25 \ in](https://tex.z-dn.net/?f=y_1%20%3D%205.25%20%5C%20%20in)
![Q_A =(L \times B) \times y_1](https://tex.z-dn.net/?f=Q_A%20%3D%28L%20%5Ctimes%20B%29%20%20%5Ctimes%20y_1)
![Q_A =(6 \times 1.5) \times 5.25](https://tex.z-dn.net/?f=Q_A%20%3D%286%20%5Ctimes%201.5%29%20%20%5Ctimes%205.25)
![Q_A =47.25 \ in^3](https://tex.z-dn.net/?f=Q_A%20%3D47.25%20%5C%20in%5E3)
For point B ;
Let Q be the moment of the Area B;
SO ; ![Q_B = Area \times y_2](https://tex.z-dn.net/?f=Q_B%20%3D%20Area%20%5Ctimes%20y_2)
where ;
![y_2 = (6 - \dfrac{1.5 \times 3}{2})](https://tex.z-dn.net/?f=y_2%20%3D%20%286%20-%20%5Cdfrac%7B1.5%20%5Ctimes%203%7D%7B2%7D%29)
![y_2= (6 - \dfrac{4.5}{2}})](https://tex.z-dn.net/?f=y_2%3D%20%286%20-%20%5Cdfrac%7B4.5%7D%7B2%7D%7D%29)
![y_2 = (6 -2.25})](https://tex.z-dn.net/?f=y_2%20%3D%20%286%20-2.25%7D%29)
![y_2 = 3.75 \ in](https://tex.z-dn.net/?f=y_2%20%3D%203.75%20%5C%20in)
![Q_B =(L \times B) \times y_1](https://tex.z-dn.net/?f=Q_B%20%3D%28L%20%5Ctimes%20B%29%20%20%5Ctimes%20y_1)
![Q_B=(6 \times 4.5) \times 3.75](https://tex.z-dn.net/?f=Q_B%3D%286%20%5Ctimes%204.5%29%20%20%5Ctimes%203.75)
![Q_B = 101.25 \ in^3](https://tex.z-dn.net/?f=Q_B%20%3D%20101.25%20%5C%20in%5E3)
For point C ;
Let Q be the moment of the Area C;
SO ; ![Q_C = Area \times y_3](https://tex.z-dn.net/?f=Q_C%20%3D%20Area%20%5Ctimes%20y_3)
where ;
![y_3 = (6 - \dfrac{1.5 \times 2}{2})](https://tex.z-dn.net/?f=y_3%20%3D%20%286%20-%20%5Cdfrac%7B1.5%20%5Ctimes%202%7D%7B2%7D%29)
![y_3 = (6 - 1.5})](https://tex.z-dn.net/?f=y_3%20%3D%20%286%20-%201.5%7D%29)
![y_3= 4.5 \ in](https://tex.z-dn.net/?f=y_3%3D%204.5%20%5C%20%20in)
![Q_C =(L \times B) \times y_1](https://tex.z-dn.net/?f=Q_C%20%3D%28L%20%5Ctimes%20B%29%20%20%5Ctimes%20y_1)
![Q_C =(6 \times 3) \times 4.5](https://tex.z-dn.net/?f=Q_C%20%3D%286%20%5Ctimes%203%29%20%20%5Ctimes%204.5)
![Q_C=81 \ in^3](https://tex.z-dn.net/?f=Q_C%3D81%20%5C%20in%5E3)
For point D ;
Let Q be the moment of the Area D;
SO ; ![Q_D = Area \times y_4](https://tex.z-dn.net/?f=Q_D%20%3D%20Area%20%5Ctimes%20y_4)
since there is no area about point D
Area = 0
![Q_D =0 \times y_4](https://tex.z-dn.net/?f=Q_D%20%3D0%20%5Ctimes%20y_4)
![Q_D = 0](https://tex.z-dn.net/?f=Q_D%20%3D%200)
Thus; from the foregoing ; point B where
has the largest Q value at section a–a