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Gnoma [55]
3 years ago
5

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 i

n. 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?

Engineering
1 answer:
ruslelena [56]3 years ago
3 0

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

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