A simply supported rectangular beam of span $L=2$ m carries a uniformly distributed load of $w=5$ kN/m. The beam cross‑section is a square of side $s$. Two material options are considered:

- Material A: modulus of elasticity $E_A=200$ GPa, density $\rho_A=7850$ kg/m³.
- Material B: modulus of elasticity $E_B=70$ GPa, density $\rho_B=2700$ kg/m³.

The design requires the maximum deflection not to exceed $5$ mm and the total weight of the beam not to exceed $150$ kg. Determine the minimum side $s$ (in mm) that satisfies the deflection requirement for each material, compute the corresponding weight, and state which material meets the weight limit while giving the lower weight.

Question

A simply supported rectangular beam of span $L=2$ m carries a uniformly distributed load of $w=5$ kN/m. The beam cross‑section is a square of side $s$. Two material options are considered:

- Material A: modulus of elasticity $E_A=200$ GPa, density $\rho_A=7850$ kg/m³.
- Material B: modulus of elasticity $E_B=70$ GPa, density $\rho_B=2700$ kg/m³.

The design requires the maximum deflection not to exceed $5$ mm and the total weight of the beam not to exceed $150$ kg. Determine the minimum side $s$ (in mm) that satisfies the deflection requirement for each material, compute the corresponding weight, and state which material meets the weight limit while giving the lower weight.

Accepted Answer

Material A: minimum side ≈ 59.5 mm, weight ≈ 55.6 kg; Material B: minimum side ≈ 77.3 mm, weight ≈ 32.3 kg. Both meet the weight limit, and aluminium (Material B) gives the lower weight.

City Guilds Model Questions Vol1 2019 Engineering Question 31

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