Shear Flow in a Tube/Pipe: Understanding the Effects of Shear Force on Point B

[lizzyb]

Question
Given that the tube is given a shear force V = 8 kip, what is the shear flow at points A and B?
http://img268.imageshack.us/img268/144/scannedimage031.jpg

Work Completed Thus Far
I determined I:
http://img187.imageshack.us/img187/9821/scannedimage033.jpg

Q for a circle in general (second moment of inertia of an area for a circle):
http://img43.imageshack.us/img43/2042/scannedimage034.jpg

Q for this particular problem:
http://img30.imageshack.us/img30/5831/scannedimage035.jpg

Q for point B:
http://img257.imageshack.us/img257/6681/scannedimage036.jpg

q for point B:
http://img21.imageshack.us/img21/5307/scannedimage037.jpg

Yet the solution is twice what is in the back of the book.

The Big Question
It seems that for some problems we take into account that the shear force in a specific part of the object (pipe, or wooden structure) as being, say half or a third of the entire V - like in this question, take V = P/2 where P is the original, given V (P = 8 kip). But other times I've arrived at the correct answer by using the original, unmodified V.

What gives?

 

[nvn]

lizzyb: Your answer is correct for the total shear flow on both sides of the tube at y = 0. But the question asks for the shear flow on only side B, not both sides. Therefore, divide your answer by 2. Also, Q is not called second moment of inertia of area; look up the correct name.

 

[lizzyb]

Thank you for your response. I understand why I should take P = V/2 and use P in determining the shear flow however I do not understand why that should be applied in some situations and not employed in others. Here is a case in point:

Question
Determine the maximum shear flow in the channel.

http://img223.imageshack.us/img223/6509/scannedimage039.jpg

Attempt at Solution
I actually have the right answer, but why wouldn't I do the P = V/2 thing in this situation?

http://img223.imageshack.us/img223/571/scannedimage040.jpg

http://img443.imageshack.us/img443/1425/scannedimage041.jpg

http://img33.imageshack.us/img33/1313/scannedimage042.jpg

http://img443.imageshack.us/img443/5933/scannedimage043.jpg

Again, this is the right answer but why didn't I take P = V/2 in this situation? Thank you.

 

[lizzyb]

First Moment of Area: http://en.wikipedia.org/wiki/First_moment_of_area
Thank you.

 

[nvn]

Very good. Can you post the exact wording of the given question for post 3, so I can see how they worded it?

 

[lizzyb]

Question #3 (exact wording)
The channel is subjected to a shear of V = 75 kN. Determine the maximum shear flow in the channel.

Question #1 (exact wording)
The pipe is subjected to a shear force of V = 8 kip. Determine the shear flow in the pipe at points A and B.

 

[nvn]

V and I are always constant on a cross section; therefore, you never divide V by 2. Q varies depending on your section cut(s).

Therefore, in question 1, notice the actual section cut for Q is at B and A, to section off one fourth of the tube. But the shear flow at A is zero; therefore, the total shear flow on the sectioned-off portion of the cross section is the shear flow at B.

Question 3 is actually poorly written, because it can be interpreted two ways. It can mean the shear flow on the entire channel, or it can mean the shear flow on one flange. Let's assume they mean the shear flow on one flange. As always, V never changes. We see Q is half of what it would be for both flanges. Hence, q is half of the shear flow on the entire channel.

 

[lizzyb]

Yes that explains it quite well; thank you.