Shear Center of thing circular section

[Mish4444]

Hi there, i have a problem trying to derive the equation for the shear centre of a thin walled slit circular section of uniform section.

I have attached a photo of the question bellow. it is taken from mechanics of materials. I hope someone can help.

 

[nvn]

Mish4444: You must list relevant equations yourself, and show your work. And then someone might check your math. We are not allowed to give you the relevant equations for your homework. Hint 1: Do you think you should first compute second moment of area, Iz, of the cross section? Do you think Iz will be needed to solve this problem?

 

[Mish4444]

Hi NVN thanks for the reply.

This is where i have got to so far:

 

[nvn]

Mish4444: Some of your current work is rather sloppy, and I cannot read some of it. How do you expect people to read characters if you do not make them legible? Also, the current work is poorly labeled, and is not making much sense yet. What is Z*D in the denominator of tau_D, and why is it there? What is Zo = t? Why did you integrate statistical moment of area in the tau_D equation from zero to pi, instead of from zero to alpha? And what does subscript D mean? Hint 2: Do you think you also need to integrate moment from zero to pi? Hint 3: Iz is currently wrong; try again. Can you make your work clearer? And label your parameters more carefully, so we know what you mean? Try it again.