Fig. $1($a$)$ shows the structural frame for a new building. One of the features is

the use of mass timber frames.

$($a$)$ If the glulam beams for these frames have the cross$-$section shown in Fig. $1($b$),$ and are made from wood with a density of $510$ kg$/$m$3,$ determine the self$-$weight of the beam as a uniformly distributed load $($like that shown in Fig. $1($c$)).$

$($b$)$ Now apply your load from $($a$)$ to the beam shown in Fig. $1($c$).$ Determine the support reactions.

$($c$)$ You know what$$s next: sketch the shear force and bending moment diagram for the beam. Be sure to indicate the sign conventions. Also determine the location of zero shear and location$($s$)$ of zero moment.

$($d$)$ What forces do the columns in the frame need to resist from the weight of each glulam beam?

$($e$)$ Determine the location $($along the length of the beam$)$ and magnitude of the maximum compression and tensile normal stress on the top of the beam, and on the bottom of the beam.

$($f$)$ Compare these stresses to the typical bending strengths of Grade $2-$f$-$E Douglas Fir glulam: $25\mathrm{.}6$ MPa for

positive bending moment, and $19\mathrm{.}2$ MPa for negative bending moment. Comment on the safety of these bFig. $1($b$)$eam under their self$-$weight