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$4.$ composite beam is formed using a $400mm180mm$ timber beam with a $300m12mm$ steel plate securely fixed to each side, as shown in the sketch.

The maximum stress in the steel and timber may not exceed $140$ and $9$MPa respectively, and the modular ratio is $20.$

$($a$)$ What will be the actual stresses used for $($i$)$ the steel and $($ii$)$ the timber?

$($b$)$ What is the safe moment of resistance in $kNm$ for the beam section?