Problem $2$

For the beam shown below:

$($a$)$ Determine the degree of kinematic indeterminacy, DKI. Show your work for credit. Neglect axial deformations and take advantage of the zero moment condition $($free rotation$)$ at the hinge location.

$($b$)$ Determine the joint force vector, hat$(Q).$

$($c$)$ Determine the fixed$-$end force vector, $Q^0.$

$($d$)$ Determine the coefficients for ALL columns of the stiffness matrix for the structure shown below. Assume that all members have an $EI=100,000$ kip$-$ft ${?}^2$

$($e$)$ Solve for the unknown displacements.

$($f$)$ Using these results from $(2.$e$)$ compute the shear forces at critical sections needed to develop the shear force diagram.

$($g$)$ Draw the shear force diagram.