Question

A 10-ft-long simply supported laminated wood beam consists of eight 1.5-in. by 6-in. planks glued together to form a section 6 in. wide by 12 in. deep. The beam carries a 9-kip concentrated load at midspan. Which point has the largest Q value at section a–a?

Answer 1

Answer:

point B where $Q_B = 101.25 \ in^3$  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 ; $Q_A = Area \times y_1$

where ;

$y_1 = (6 - \dfrac{1.5}{2})$

$y_1 = (6- 0.75)$

$y_1 = 5.25 \ in$

$Q_A =(L \times B) \times y_1$

$Q_A =(6 \times 1.5) \times 5.25$

$Q_A =47.25 \ in^3$

For point B ;

Let Q be the moment of the Area B;

SO ; $Q_B = Area \times y_2$

where ;

$y_2 = (6 - \dfrac{1.5 \times 3}{2})$

$y_2= (6 - \dfrac{4.5}{2}})$

$y_2 = (6 -2.25})$

$y_2 = 3.75 \ in$

$Q_B =(L \times B) \times y_1$

$Q_B=(6 \times 4.5) \times 3.75$

$Q_B = 101.25 \ in^3$

For point C ;

Let Q be the moment of the Area C;

SO ; $Q_C = Area \times y_3$

where ;

$y_3 = (6 - \dfrac{1.5 \times 2}{2})$

$y_3 = (6 - 1.5})$

$y_3= 4.5 \ in$

$Q_C =(L \times B) \times y_1$

$Q_C =(6 \times 3) \times 4.5$

$Q_C=81 \ in^3$

For point D ;

Let Q be the moment of the Area D;

SO ; $Q_D = Area \times y_4$

since there is no area about point D

Area = 0

$Q_D =0 \times y_4$

$Q_D = 0$

Thus; from the foregoing ; point B where $Q_B = 101.25 \ in^3$  has the largest Q value at section a–a