(Solved): A flanged wooden shape is used to support the loads shown on the beam. The di ...

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A flanged wooden shape is used to support the loads shown on the beam. The dimensions of the shape are shown in the second figure. Assume \( L_{A B}=5 \mathrm{ft}, L_{B C}=2 \mathrm{ft}, L_{C D}=2 \mathrm{ft}, L_{D E}=3 \mathrm{ft}, P_{C}= \) \( 2160 \mathrm{lb}, P_{E}=1670 \mathrm{lb}, w_{A B}=900 \mathrm{lb} / \mathrm{ft}, b_{1}=9 \) in., \( b_{2}=2 \) in., \( b_{3}=6 \) in., \( d_{1}=2 \) in., \( d_{2}=6 \) in., \( d_{3}=2 \mathrm{in} \). Consider the entire 12- \( \mathrm{ft} \) length of the beam and determine: (a) the maximum tension bending stress \( \sigma_{T} \) at any location along the beam, and (b) the maximum compression bending stress \( \sigma_{C} \) at any location along the beam.