Assume that the structure in Part A (free vibration displacement response of an undamped structure with natural frequency fn = 1 Hz, u(0) = 1 in, u'(0) = 3 in/s) is a water tower, with mass m (concentrated at the top with assumed massless column), height H (i.e., length for base of the tower to the center of mass at the top of the tower), with a column cross section with constant sectional stiffness EI. The gravitational constant is g. The tower is fixed at its base (all degrees of freedom are equal to zero).

• Please derive the equations that describe the bending moment, the shear force, and the axial force at the base of the tower as a function of time t and the known properties of the system. Find the expression of the maximum (over time) bending moment, shear force, and axial force.
• Please find the expression of the maximum normal stress at the base section of the column of the tower.
• Someone proposed to build a wall close to the water tower. How far does the wall has to be to avoid the impact of the water tower with the wall during the vibration of the water tower mass?