고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.9-12

6.9-12 The cross section of a sign post of constant thickness is shown in the figure. Derive the formula for the distance \( e \) from the centerline of the wall of the post to the shear center \( S \): \[ e = \frac{1}{I_z} \cdot \frac{1}{3} t b a [4a^2 + 3ab \sin(\beta) + 3ab + 2 \sin(\beta) b^2] \cos(\beta) \] where \( I_z = \) moment of inertia about the \( z \) axis. Also, compare this formula with that given in Problem 6.9-11 for the special case of \( \beta = 0 \) here and \( a = h/2 \) in both formulas.