Question 3 (20marks) A fast food chain looking for an eco-friendly cutiry set ispoons) it is chosen to give enough bending-stiffness to hold without excessive bending. The width, length, are fixed, thickness is free and the spoon is loaded in bending. The fast food chain are conscious of its environmental image by minimizing the energy content of there throw-away tableware. a) list the design requirements b) Derive a material index ( assume a beam) for selecting materials for energy-economic using (1) a stiffness constraint (1) using a strength constraint b) based on your answer of part (b) use the suitable chart to comment on the energy content used for polystyrene (PS) and aluminum alloys Hint: The objective-function is the volume of material in the spoon times its energy content, pH per unit volume (He is the embodied energy per kg, and p the density). mass-density x volume for the failure load of a beam : Fr=101/6L and I = bt/12; 1 is the second moment of area; for a beam of rectangular section, For the elastic bending; S=12E1/L :S; the stiffness of the beam;L; length and I= A/12 is the second moment of area E and or are the modulus and failure stress of the material of the beam. Question 3 (20marks) A fast food chain looking for an eco-friendly cutiry set ispoons) it is chosen to give enough bending-stiffness to hold without excessive bending. The width, length, are fixed, thickness is free and the spoon is loaded in bending. The fast food chain are conscious of its environmental image by minimizing the energy content of there throw-away tableware. a) list the design requirements b) Derive a material index ( assume a beam) for selecting materials for energy-economic using (1) a stiffness constraint (1) using a strength constraint b) based on your answer of part (b) use the suitable chart to comment on the energy content used for polystyrene (PS) and aluminum alloys Hint: The objective-function is the volume of material in the spoon times its energy content, pH per unit volume (He is the embodied energy per kg, and p the density). mass-density x volume for the failure load of a beam : Fr=101/6L and I = bt/12; 1 is the second moment of area; for a beam of rectangular section, For the elastic bending; S=12E1/L :S; the stiffness of the beam;L; length and I= A/12 is the second moment of area E and or are the modulus and failure stress of the material of the beam