$3.(25$pts$)$ A flitch beam consisting of a $200$ mm wide douglas fir beam sandwiched between two A$36$ steel beams, each of width $20$mm is shown. The beam experiences an internal $\backslash (\backslash$mathrm$\{$M$\}=100\backslash$mathrm$\{$kN$\}-\backslash$mathrm$\{$m$\}\backslash )$ bending moment about the horizontal axis $($as shown$).$

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a$.$ Convert the beam to an equivalent allsteel beam. Show that the equivalent width of "wood as steel equivalent" is approximately $13$ mm $,$ giving an equivalent all$-$steel beam as approximately $53$ mm wide total. Give answers to $4$ significant figures. b$.$ Convert the beam to an equivalent allwood beam. Show that the equivalent width of "steel as wood equivalent" is approximately $600$ mm $,$ giving an equivalent all$-$wood beam as approximately $800$ mm wide total. Give answers to $4$ significant figures.

c$.$ Show that the magnitude of the maximum normal stress in the steel is approximately $70$ MPa and the maximum normal stress in the wood is approximately $4\mathrm{.}6$MPa. Give answers to $4$ significant figures.