고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.9-10

6.9-10 Derive the following formula for the distance \( e \) from the centerline of the wall to the shear center \( S \) for the C-section of constant thickness shown in the figure: \[ e = \frac{3bh^2(b + 2a) - 8ba^3}{h^2(h + 6b + 6a) + 4a^2(2a - 3h)} \] Also, check the formula for the special cases of a channel section (\( a = 0 \)) and a slit rectangular tube (\( a = h/2 \)).