Show all work $2\mathrm{.}1-9$ Beam Influence Lines.

Given:

Uniform dead load, $w_D=1\frac{k}{f}t$

Uniform live load, $w_L=3\frac{k}{f}t$

Concentrated live load, $P_L=30$kips

Find:

Using qualitative influence lines, show the position the above loads to produce the maximum positive internal shear $(+V_{\text{D}\text{m}\text{a}\text{x}})$ at Section D$.$

Using qualitative influence lines, show the position of the above loads to produce the maximum negative internal moment $(-M_{D_{\text{m}\text{a}\text{x}}})$ at Section D$.$

Use a quantitative influence line to calculate the value of $-M_{D_{\text{m}\text{a}\text{x}}}$ based on the loads above.