Question $3$

$($a$)$ Construct the following influence lines with key influence coefficients for the beam shown in Figure Q$3($a$)$:

$1.$ Reaction force at A

$2.$ Bending moment at K

$3.$ Shear force to the left of $\backslash ($ F $\backslash )$

$4.$ Shear force to the right of $\backslash ($ F $\backslash )$

$(10$ marks$)$

$($b$)$ Consider the simply supported beam shown in Figure Q$3($b$),$ determine the maximum positive moment at C due to a series of concentrated loads moving from right to left.

$(10$ marks$)$

Figure Q$3($b$).$