$8\mathrm{.}14.$ For the case $($or cases$)$ assigned by the instructor, select the lightest $W$ section, using the $$ modified flexure analogy approach, to carry uniform loading $w,$ in addition to the weight of the beam.

The ends of the span are assumed to be fixed fist both flexure and torsion. If "exact" solution way obtained in Prob. $8\mathrm{.}11,$ check maximum stres. using that solution.

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