Problem $7$

Problem $7.$ The stiffness matrix for the frame depicted below is to be determined, with degrees of freedom depicted as numbers next to nodes. Determine the value in the global stiffness matrix corresponding to the horizontal degree of freedom at node $E$ and the rotational degree of freedom at node $E.$ These correspond to degrees of freedom with indices $10$ and $12.$ Assume that the directions of bars point from nodes with earlier order in the alphabet to nodes later in the alphabet. $($For example, member $CG$ points from $C$ to $G$ because $C$ is the third letter of the alphabet and $G$ is the seventh letter of the alphabet.$)$ Assume a Young's modulus of $200$GPa$=2*{10}^{8}k\frac{N}{m^2},$ cross section areas of $400m{m}^2,$ and second moment of inertia of $350*{10}^{6}m{m}^4.$ Use units of kilonewtons and meters in all calculations. Round to the nearest $4$ significant digits.

$14.$ What is the value in the global stiffness matrix corresponding to degrees of freedom $10$ and $12?$ Report your answer as indicated above.