The problem is asking for the best material to use for a leaf spring under two different conditions: minimizing weight and minimizing cost. The leaf spring is a simply-supported beam of width b and depth d, spanning 1 m. It is subjected to a central load of 1.5 kN and should deflect by 20 mm without yielding.

The merit index is a measure of the performance of a material under specific conditions. In this case, we need to find the merit index for each material when minimizing weight and cost.

(a) To minimize weight, we need to find the material with the highest strength-to-weight ratio. This can be calculated as the yield strength (σy) divided by the density (ρ).

For Mild steel, the strength-to-weight ratio is 220 MPa / 7850 kg/m^3 = 0.028 MPa*m^3/kg.
For High strength steel, the ratio is 1460 MPa / 7950 kg/m^3 = 0.184 MPa*m^3/kg.
For CFRP, the ratio is 1200 MPa / 1500 kg/m^3 = 0.8 MPa*m^3/kg.
For GFRP, the ratio is 200 MPa / 2000 kg/m^3 = 0.1 MPa*m^3/kg.

Therefore, the best material to minimize weight is CFRP.

(b) To minimize cost, we need to find the material with the highest strength-to-cost ratio. This can be calculated as the yield strength (σy) divided by the cost (£/kg).

For Mild steel, the strength-to-cost ratio is 220 MPa / £0.20/kg = 1100 MPa/£.
For High strength steel, the ratio is 1460 MPa / £1.80/kg = 811.11 MPa/£.
For CFRP, the ratio is 1200 MPa / £90.00/kg = 13.33 MPa/£.
For GFRP, the ratio is 200 MPa / £1.30/kg = 153.85 MPa/£.

Therefore, the best material to minimize cost is Mild steel.

Question

The problem is asking for the best material to use for a leaf spring under two different conditions: minimizing weight and minimizing cost. The leaf spring is a simply-supported beam of width b and depth d, spanning 1 m. It is subjected to a central load of 1.5 kN and should deflect by 20 mm without yielding.

The merit index is a measure of the performance of a material under specific conditions. In this case, we need to find the merit index for each material when minimizing weight and cost.

(a) To minimize weight, we need to find the material with the highest strength-to-weight ratio. This can be calculated as the yield strength (σy) divided by the density (ρ).

For Mild steel, the strength-to-weight ratio is 220 MPa / 7850 kg/m^3 = 0.028 MPa*m^3/kg.
For High strength steel, the ratio is 1460 MPa / 7950 kg/m^3 = 0.184 MPa*m^3/kg.
For CFRP, the ratio is 1200 MPa / 1500 kg/m^3 = 0.8 MPa*m^3/kg.
For GFRP, the ratio is 200 MPa / 2000 kg/m^3 = 0.1 MPa*m^3/kg.

Therefore, the best material to minimize weight is CFRP.

(b) To minimize cost, we need to find the material with the highest strength-to-cost ratio. This can be calculated as the yield strength (σy) divided by the cost (£/kg).

For Mild steel, the strength-to-cost ratio is 220 MPa / £0.20/kg = 1100 MPa/£.
For High strength steel, the ratio is 1460 MPa / £1.80/kg = 811.11 MPa/£.
For CFRP, the ratio is 1200 MPa / £90.00/kg = 13.33 MPa/£.
For GFRP, the ratio is 200 MPa / £1.30/kg = 153.85 MPa/£.

Therefore, the best material to minimize cost is Mild steel.

Knowee AI · Accepted Answer

The problem is asking for the best material to use for a leaf spring under two different conditions: minimizing weight and minimizing cost. The leaf spring is a simply-supported beam of width b and depth d, spanning 1 m. It is subjected to a central load of 1.5 kN and should deflect by 20 mm without yielding.

The merit index is a measure of the performance of a material under specific conditions. In this case, we need to find the merit index for each material when minimizing weight and cost.

(a) To minimize weight, we need to find the material with the highest strength-to-weight ratio. This can be calculated as the yield strength (σy) divided by the density (ρ).

For Mild steel, the strength-to-weight ratio is 220 MPa / 7850 kg/m^3 = 0.028 MPa*m^3/kg.
For High strength steel, the ratio is 1460 MPa / 7950 kg/m^3 = 0.184 MPa*m^3/kg.
For CFRP, the ratio is 1200 MPa / 1500 kg/m^3 = 0.8 MPa*m^3/kg.
For GFRP, the ratio is 200 MPa / 2000 kg/m^3 = 0.1 MPa*m^3/kg.

Therefore, the best material to minimize weight is CFRP.

(b) To minimize cost, we need to find the material with the highest strength-to-cost ratio. This can be calculated as the yield strength (σy) divided by the cost (£/kg).

For Mild steel, the strength-to-cost ratio is 220 MPa / £0.20/kg = 1100 MPa/£.
For High strength steel, the ratio is 1460 MPa / £1.80/kg = 811.11 MPa/£.
For CFRP, the ratio is 1200 MPa / £90.00/kg = 13.33 MPa/£.
For GFRP, the ratio is 200 MPa / £1.30/kg = 153.85 MPa/£.

Therefore, the best material to minimize cost is Mild steel.

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