Redesigning a School Bag Hook for Manufacture
A Year 12 student designed a wall-mounted bag hook for the school's design fair. The prototype is a 120 mm long cantilevered arm of 10 mm mild steel bar, bent at 90 degrees, with a 40 mm diameter disc welded to the wall end and four M6 masonry fixings. In testing, a 12 kg bag hung at the tip caused visible deflection of about 8 mm and the weld at the wall plate showed a hairline crack after 50 load cycles. The brief requires the hook to carry 15 kg with less than 3 mm deflection and survive 5000 cycles. The student proposes switching to 12 mm bar and adding a gusset. Manufacturing is one-off; the school has a MIG welder, a drill press, a bench grinder and hand tools, but no mill or lathe.
1. Diagnose why the prototype failed and evaluate the student's proposed fix.
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Deflection: a cantilever's tip deflection scales with length cubed and inversely with the second moment of area. Going from 10 mm to 12 mm bar increases I by (12/10)^4 = 2.07, roughly halving deflection. The 8 mm at 12 kg would become about 4 mm at 12 kg, and at 15 kg about 5 mm - still above the 3 mm limit. So the diameter change alone is insufficient.
Weld crack: the hairline crack at the wall plate is a fatigue failure. The weld toe is a stress raiser, and the 90-degree bend concentrates load at the junction. A gusset spreads load but adds a second weld line, which can introduce a new fatigue initiation site if not blended. The gusset helps stiffness but the weld quality and toe geometry matter more than the gusset itself.
Evaluation of the fix: partially effective. The 12 mm bar plus gusset will reduce deflection and stress, but the design still relies on a welded joint in a fatigue-critical location, and the student has not verified the numbers against the 3 mm and 5000-cycle targets. The fix treats symptoms (thicker bar, more material) rather than the root cause (bending moment at a welded junction and a long cantilever).
2. Propose a revised design the school can actually manufacture, and justify the changes against the brief.
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Revised concept: shorten the cantilever and change the load path rather than adding material.
- Shorten the arm from 120 mm to 80 mm. Tip deflection scales with L^3, so 80/120 gives (0.667)^3 = 0.30, cutting deflection to about 30% for the same section. Combined with 12 mm bar, predicted tip deflection at 15 kg is well under 3 mm.
- Replace the welded wall plate with a bent-and-bolted flange. Bend the bar through 90 degrees at the wall end and bolt through a separate 3 mm steel plate drilled on the drill press. This removes the fatigue-critical weld entirely; the bend is formed cold and the plate is a simple drilled part. Bolted joints can be inspected and retorqued.
- Add a diagonal brace from the arm to the wall plate, bolted at both ends, forming a triangulated load path. A triangle carries load in tension/compression rather than bending, so the brace takes most of the moment and the arm sees far less bending stress. This is manufacturable with a drill press and hand tools; no mill needed.
- Specify a fillet radius at the bend of at least 1.5x bar diameter to avoid cold-working cracks, and deburr all edges.
Justification against brief: 15 kg capacity is met by the triangulated path; deflection target is met by shortening the arm and bracing; 5000 cycles is met because the welded fatigue site is eliminated and bolted joints are inspectable. The design uses only available equipment and standard fixings, so it is genuinely manufacturable at one-off scale.