$4.$ In a small dam, the hydrostatic pressure loading is supported by vertical W$8$x$17$ beams. $($Horizontal cross members not shown$).$ Determine the peak flexural stresses in section cut a$-$a $($midpoint between supports$)$ in the beam. $($ans: $3930$ psi $)$

Hints:

$-$ The total load acting on the beam is the area of the distributed load force triangle $($units: $\backslash (\backslash$mathrm$\{$lb$\}/\backslash$mathrm$\{$ft$\}\backslash$mathrm$\{$x$\}\backslash$mathrm$\{$ft$\}=\backslash$mathrm$\{$lb$\}\backslash )).$ This load can be concentrated at the centroid of the triangle for the purpose of determining the support reactions.

$-$ In order to determine the internal moment at section a$-$a$,$ make a cut there and consider the portion of the beam and load above the cut $($easier than working with the portion below the cut$).$ You will again have to determine an equivalent load and application point for the reduced $($smaller$)$ force triangle that remains.

$-$ Once you have $\backslash ($ M $\backslash )$ at the cut, you will need to convert it to in$-$lb prior to determining stresses in psi.

$-$ You might want to rotate the diagram $\backslash (90^\{\backslash$circ$\}\backslash$mathrm$\{$CCW$\}\backslash )$ and work with a horizontal beam!