Problem $1$: Consider the beam shown below subjected to a linearly varying distributed load

assume w$.$ The boundary condition at A is pinned and B is roller. Neglect shear and axial

deformation and assume that $E$ and I are constant.

$($a$)$ Determine the slope and displacement at the end A of the beam using double integration

method.

$($b$)$ Determine the slope and displacement at the end $A$ of the beam using principles of virtual

work. $[$Problem $8-24]$

$($c$)$ Draw free$-$body diagrams, shear, bending moment and deflection diagrams for this beam.

Be sure to label values $($maximum$,$ minimum, locations, etc.$).$ Cross check your figures

similar to the questions that were posed in the previous homework.

$($d$)$ How do your results compare with those from Mastan? Assume A$=1,$ I$=1$ E$=100.$ Please

submit relevant screen shots.