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

point B where
`Q_B = 101.25 \ in^3` has the largest Q value at section a–a

Step-by-step 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 * y_1`

where ;

`y_1 = (6 - (1.5)/(2))`

`y_1 = (6- 0.75)`

`y_1 = 5.25 \ in`

`Q_A =(L * B) * y_1`

`Q_A =(6 * 1.5) * 5.25`

`Q_A =47.25 \ in^3`

For point B ;

Let Q be the moment of the Area B;

SO ;
`Q_B = Area * y_2`

where ;

`y_2 = (6 - (1.5 * 3)/(2))`

`y_2= (6 - (4.5)/(2)})`

`y_2 = (6 -2.25})`

`y_2 = 3.75 \ in`

`Q_B =(L * B) * y_1`

`Q_B=(6 * 4.5) * 3.75`

`Q_B = 101.25 \ in^3`

For point C ;

Let Q be the moment of the Area C;

SO ;
`Q_C = Area * y_3`

where ;

`y_3 = (6 - (1.5 * 2)/(2))`

`y_3 = (6 - 1.5})`

`y_3= 4.5 \ in`

`Q_C =(L * B) * y_1`

`Q_C =(6 * 3) * 4.5`

`Q_C=81 \ in^3`

For point D ;

Let Q be the moment of the Area D;

SO ;
`Q_D = Area * y_4`

since there is no area about point D

Area = 0

`Q_D =0 * 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