$($b$)$ The beam is initially made from a Glass Fibre Reinforced Polymer $($GFRP$)$ cross section. The beam is to be strengthened by fully bonding another polymer composite $($DMC$)$ to the top surface, as shown in Figure $1$b$.$ The DMC has Young's modulus $14$ GPa and uniaxial yield strength of $90$ MPa $.$ The GFRP has Young's modulus $10$ GPa and uniaxial yield strength of $155$ MPa $.$

i$)$ The unreinforced GFRP section has a moment capacity of $43\mathrm{.}59$ kNm $.$ Using your bending moment diagram from part $($a$),$ how far either side of the support at B should the strengthening be applied to prevent yield in bending?

ii$)$ Check if the reinforced section in Figure $1$b yields at the bending moment over point B$.$ What is its maximum moment capacity?

A

B

C

Figure $1$a: Floor beam structure and geometry.