The $2$D frame structure shown in Figure P$31$ is composed of two steel members with Young's modulus E $=10$ x $106$ psi and cross sectional area $1$ x $2$ in;the $2-$in dimension is perpendicular to the plane of loading. The connection at node $2$ is treated as a welded joint and both supports at nodes $1$ and $3$ are fixed. The loading is composed of a linearly distributed load with maximum value of $20,000$ lb$/$in andconcentrated moment at node $2$ of $1,500$ lb in$.$Using a model with two beam elements, determine:

a: The global reduced stiffness matrix of the structure.

b: The global lumped load vector.

c: All displacement and rotation components at node $2.$

d: All reactions at node $3.$Figure P$31$