고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.9-11

6.9-11 Derive the following formula for the distance \( e \) from the centerline of the wall to the shear center \( S \) for the hat 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 case of a channel section (\( a = 0 \)).