Homework $4$

Part $1.$ Use equation III$-2$ for $[$k$]$ to develop $[$K$]$ for the $2-$beam$-$member structure shown. Assume constant $El$ along both members $1$ and $2.$

Part $2.$ Identify the DOF to allow partitioning into $\{F_f\},\{F_s\},\{{}_f\}$ and $\{{}_s\}$

Part $3.$ Re$-$number the nodes to allow $K$ to be partitioned. Write the expression for $K_{ff}.$

Part $4.$ Use $K_{ff}$ to solve for the rotations ${}_z^B$ and ${}_2^C.$ Note that an exact formula to invert a $22$ matrix was presented in class.