The pin connected truss has a pin support at point C and a roller support at point B$.$ For the truss loaded with the vertical point load at point A shown:

$2$ points $(1)$ Find the support reaction at the roller support $B$ for the load shown. Use the given sign convention to report your answer.

$4$ points $(1)$ Find the axial force in member $AB.$ Is $AB$ in tension or compression?

$1$ point Show the virtual system you would use to find the horizontal deflection at the roller support at joint $B.$

$4$ points $(1)$ Find all three of the truss member forces for the virtual system you defined in Part $3.$ Clearly indicate your results in your calculations and use the given sign convention. Note that there may be zero force members;

$4$ points $(1)$ Find the horizontal deflection of the roller support at joint $B$ due to the load shown using the principle of virtual work. Please state your result in inches and indicate if the deflection is to the right or left.

Use $AE=4000k$ for all truss members.