고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.9-13

6.9-13 A cross section in the shape of a circular arc of constant thickness is shown in the figure. Derive the following formula for the distance \( e \) from the center of the arc to the shear center \( S \): \[ e = \frac{2r(\sin \beta - \beta \cos \beta)}{\beta - \sin \beta \cos \beta} \] in which \( \beta \) is in radians. Also, plot a graph showing how the distance \( e \) varies as \( \beta \) varies from \( 0 \) to \( \pi \).