Solving for (0.35)(0.025) Difference in 0.18676 and 0.175

[fonseh]

Homework Statement

For this question , i am not sure how to get the Q , Can i use the middle part instead of the right part ?

Homework Equations

The Attempt at a Solution

if i use middle part , my ans would be (0.35)(0.025)(0.18676-0.175) = 1.03x10^-4 , which is different from the ans . Is it wrong ? If it's wrong , why can't i take the middle section ( green part) ?

 

[PhanthomJay]

Homework Statement

For this question , i am not sure how to get the Q , Can i use the middle part instead of the right part ?

Homework Equations

The Attempt at a Solution

if i use middle part , my ans would be (0.35)(0.025)(0.18676-0.175) = 1.03x10^-4 , which is different from the ans . Is it wrong ? If it's wrong , why can't i take the middle section ( green part) ?

That is a good observation, you certainly can take the green part, but your calculation is wrong because the neutral axis dimension of 0.18676 is measured from the top and I think you measured from the bottom. If you adjust your calc accordingly, the shear flow is exactly twice the other method, because there are 2 shear planes in the bolts when you do it this way, so you must divide that value by 2 to determine the bolt shear force.

 

[fonseh]

If you adjust your calc accordingly, the shear flow is exactly twice the other method,

Whta do you mean ? can you show it ?

 

[fonseh]

That is a good observation, you certainly can take the green part, but your calculation is wrong because the neutral axis dimension of 0.18676 is measured from the top and I think you measured from the bottom. If you adjust your calc accordingly, the shear flow is exactly twice the other method, because there are 2 shear planes in the bolts when you do it this way, so you must divide that value by 2 to determine the bolt shear force.

why the area that we take not this area only ? refer to the attachment i uploaded ( green part) , i said so because when the planes area sheared , the green area is connected to the each other , right ?

Here's the definition of Q to support my answer

 

[PhanthomJay]

why the area that we take not this area only ? refer to the attachment i uploaded ( green part) , i said so because when the planes area sheared , the green area is connected to the each other , right ?

Here's the definition of Q to support my answer

No, the book has it right and you would have had it right in your first post if you had not made the calc error for y'_bar and not forgotten to divide by 2. The area you show in your last post is incorrect.
These shear flow problems can be challenging. You are taught that Q is calculated using the atea above or below he section of interest, but that does not apply for connected parts when you are looking for connection bolt stresses and not the wood itself stresses. You must use the full area of the connected part like you did in your original post.

 

[fonseh]

No, the book has it right and you would have had it right in your first post if you had not made the calc error for y'_bar and not forgotten to divide by 2. The area you show in your last post is incorrect.
These shear flow problems can be challenging. You are taught that Q is calculated using the atea above or below he section of interest, but that does not apply for connected parts when you are looking for connection bolt stresses and not the wood itself stresses. You must use the full area of the connected part like you did in your original post.

do you meanit is correct also to use the green area , if i use the green area in the first post , i must divide it by 2 ?

 

[PhanthomJay]

do you meanit is correct also to use the green area , if i use the green area in the first post , i must divide it by 2 ?

Yes! Redo it using the correct value for the distance from the centroid of your area to the neutral axis.