$($a$)$ Calculate the vertical deflection at joint $U_3$ on the truss shown below, $AE=84\mathrm{.}5{10}^{3}kN$ for all members.a$)$ For the beams shown below, draw the influence lines from points $($A$)$ through$($E$)$ For:

i$)$ bending moment at point $($B$)$

ii$)$ shear force immediately left of point $($C$),$ and

iii$)$ bending moment at point $($D$)$

For each influence line, calculate and indicate the value of the influence

coefficient that has the maximum absolute value.

b$)$ A vehicle, which is idealized as three point loads shown on the left below, moves across

the beam structure shown. Calculate and show the influence line for shear force at point

$($B$).$ Also calculate the largest shear force at the point$($B$)$ that would occur while the

idealized vehicle crosses the structure.

$($b$)$ If the $40kN$ vertical load were at joint $U_3$ instead of joint $U_2,$ what would be the vertical deflection be at join! $U_2?$