Coastal Wind-Turbine Bracket: Lightness, Stiffness and Galvanic Risk
A portable 3 kW wind-turbine demonstrator uses a cantilever bracket to hold a 6.5 kg generator at 120 mm from a mast clamp. The bracket must carry a design point load of 250 N at its free end, with a maximum deflection of 1.5 mm and a safety factor of at least 2 on yield. Three candidates are available: 6061-T6 aluminium (E = 69 GPa, σy = 276 MPa, ρ = 2700 kg/m³), 30% glass-fibre-reinforced PA66 (E = 9 GPa, σy = 150 MPa, ρ = 1400 kg/m³), and 316 stainless steel (E = 193 GPa, σy = 205 MPa, ρ = 8000 kg/m³). The bracket will be bolted to the mast with stainless-steel A4 bolts and will be used outdoors near the sea. The team wants the lightest bracket that still meets stiffness, strength and a five-year service life, and is considering anodising only the aluminium option. Manufacturing is limited to cutting, drilling and bolting; no welding or autoclave is available.
1. Using δ = FL³/(3EI), calculate the minimum second moment of area required for each candidate and recommend a material. Compare masses with the stiffness-limited index M = ρ/E^0.5 and state what the strength check adds.
Read the worked answer
Take L = 0.120 m, F = 250 N, δ = 0.0015 m, so FL³ = 250 × 0.001728 = 0.432 N·m³.
I_req = FL³/(3Eδ):
- 6061-T6: 0.432/(3 × 69×10⁹ × 0.0015) = 1.39×10⁻⁹ m⁴
- PA66-GF30: 0.432/(3 × 9×10⁹ × 0.0015) = 1.07×10⁻⁸ m⁴
- 316: 0.432/(3 × 193×10⁹ × 0.0015) = 4.97×10⁻¹⁰ m⁴
For geometrically similar sections the mass scales with M = ρ/E^0.5: aluminium 0.0103, PA66-GF30 0.0148, stainless 0.0182. Aluminium is the lightest; PA66-GF30 is about 1.44 times the aluminium mass for equal stiffness, and stainless about 1.77 times. PA66-GF30 also creeps and absorbs moisture, so its long-term deflection outdoors is worse than the short-term calculation suggests.
The strength check is separate: with SF = 2, allowable stresses are 138 MPa, 75 MPa and 102.5 MPa. Bending moment is 250 × 0.120 = 30 N·m, so required section modulus is S = M/σallow: 2.17×10⁻⁷, 4.00×10⁻⁷ and 2.93×10⁻⁷ m³. A rectangular section must satisfy both I and S; for aluminium a section near 8 mm × 13 mm can do this, but local buckling and the bolted joint must be checked. Recommendation: 6061-T6, anodised, with galvanic isolation at the bolts.
2. Explain the galvanic risk of using A4 stainless bolts in the aluminium bracket near the sea, and propose two design changes that do not change the bracket material.
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In a chloride-containing marine atmosphere, stainless steel is cathodic to aluminium. If water bridges the bolt and bracket, the aluminium becomes the anode and corrodes, especially at scratches, cut edges and crevices under washers. The area ratio is unfavourable: a small aluminium anode near a relatively large stainless cathode concentrates attack and can cause deep pitting. Anodising raises surface resistance but does not remove the risk once the film is damaged or the joint is wet.
Two practical changes are: (1) isolate the joint electrically with nylon or PTFE washers and a insulating sleeve on each bolt, and seal the faying surfaces with a marine-grade sealant; (2) redesign for drainage and inspection, for example by adding a drain path and avoiding upward-facing crevices, and specify a maintenance check of the bolt area. A sacrificial zinc anode or aluminium-compatible fasteners are alternatives, but isolation and drainage are the minimum. The stainless bolts should not be replaced by plain steel, which would corrode even faster.
3. The team wants to advertise the bracket as 'fully recyclable'. Compare the end-of-life implications of the three candidates and state one limitation of that claim.
Read the worked answer
Aluminium and stainless steel are both technically recyclable and have established scrap value, but both carry significant embodied energy. Aluminium recycling saves most of the primary energy, yet anodising and mixed fasteners complicate separation. Stainless steel is highly recyclable but dense, so transport and handling impacts are higher. PA66-GF30 is the weakest option: glass-fibre-reinforced thermoplastic is difficult to separate and reprocess, and it may end up in energy recovery or landfill.
The claim 'fully recyclable' is limited because recyclability depends on disassembly. If stainless bolts, washers and anodised aluminium are left assembled, the material stream is mixed and the practical recovery rate falls. The design should therefore use removable fasteners, avoid bonded joints and mark materials. The claim should say 'recyclable when dismantled into labelled metal streams', not 'fully recyclable' without conditions.