(Solved): Problem 1 (50 points). For the beam shown below with a constant EI, answer the questions with the g ...

Problem 1 (50 points). For the beam shown below with a constant EI, answer the questions with the given \( x \)-axis using Integration Method: (a) [10 points] List four boundary conditions (B.C., two force B.C. and two geometric B.C.) of the beam. Answer: (b) \( [10 \) points] Determine the equation of the external force, \( \omega(x) \). Answer: \( \omega(x)= \) (c) \( [20 \) points \( ] \) Determine the equation of the elastic curve, \( y(x) \). Answer: \( y(x)= \) (d) \( [10 \) points \( ] \) Determine the deflection at point \( \mathrm{B}, \Delta_{B} \). Answer: \( \Delta_{B}= \)