Problem VIX. $1$ Consider the beams shown in Figure IX$\mathrm{.}1,$ having Young's modulus E and

moment of inertia I.

$(1)$ Is the beam symmetric? Are the loads and reaction forces symmetric or antisymmetric?

$(2)$ Use symmetry to compute the elastic curve.

Problem IX$.2$ Consider the frame shown in Figure IX$\mathrm{.}2.$ The columns and the beam have the same

Young's modulus E and moment of inertia I.

$(1)$ Is the frame isostatic?

$(2)$ Use symmetry: is the reduced structure isostatic?

$(3)$ Compute the reaction forces on constraints;

$(4)$ Plot the internal moment.

Problem IX$\mathrm{.}3$ Consider the frame shown in Figure IX$\mathrm{.}3.$ The columns and the beam have the same

Young's modulus, E$,$ and moment of inertia, I. Can the elastic curve be solved using

symmetry$/$antisymmetry$?$