Solve Shear Center Problem: Find Length b in Cross Section

[womanengineer]

Homework Statement

The problem and cross section are attached. (#2 on the PDF)

I have to find the length of b if the shear center is at point O.

The horizontal lines that are not labeled are of length a.

The Attempt at a Solution

I took the Moment about O to get the equation for e.
I have split the cross section into 3 different sections, used tau=VQ/IT
Took the integral of tau to get V of the particular section.
I then found I total.
All of these values are respect to t,b, and a.

After I've done all this, do I set the e=0 and solve the equation for b in terms of a and t?

I am not sure if I am doing this right.
Will post the work I've done if necessary.

Thanks!

 

[KataKoniK]

Hello,

Thank you for sharing your attempt at solving this problem. It seems like you are on the right track by using the equation for shear stress, tau=VQ/IT, to find the shear force, V, of each section. However, when finding the total moment, it is important to consider the contribution of each section to the overall moment. This means that the moment equation should include the distance from the shear center, e, for each section.

Additionally, setting e=0 and solving for b in terms of a and t may not be the most efficient approach. It may be easier to solve for e in terms of b, a, and t and then substitute that value into the moment equation to solve for b. This will give you a direct relationship between b and a, which may make it easier to find the length of b.

I hope this helps and I look forward to seeing your work. Good luck!