📘 structural mechanics

1. **Problem Statement:** Find the value of $\Psi_B$ given the parameters $S_1 = 10.0$ ft, $S_2 = 15.5$ ft, $H_1 = 8.0$ ft, $H_2 = 16.0$ ft, $EI_{beam} = 30100$ k-ft$^2$, and $EI_{