Cantilever Hoist Bracket: Substituted Section and a Weld-Toe Crack
A cantilever bracket carries a 12 kN static hoist load at its tip, 2.0 m from the welded support. The specified section is a 150 × 100 × 8 RHS in S275 steel with I = 11.3 × 10⁶ mm⁴, S = 150 × 10³ mm³ and E = 200 GPa. The design criteria are a bending stress not greater than 0.66 Fy and a tip deflection not greater than L/250. During fabrication the 8 mm wall was unavailable, so a 150 × 100 × 6 RHS was substituted (I = 8.85 × 10⁶ mm⁴, S = 118 × 10³ mm³) without a change note. After eight years in service, magnetic particle inspection during a routine shutdown found a 6 mm long toe crack at the support weld on the tension side. The hoist duty is about 40 cycles per day.
1. Check the bracket as originally designed against both criteria and state which one governs.
Read the worked answer
Bending moment
M = P·L = 12 kN × 2.0 m = 24 kN·m = 24 × 10⁶ N·mm
Stress check
σ = M / S = 24 × 10⁶ / 150 × 10³ = 160 MPa
Allowable = 0.66 Fy = 0.66 × 275 = 181.5 MPa
Utilisation = 160 / 181.5 = 0.88 → passes, with only 12% margin.
Deflection check
δ = P·L³ / (3·E·I) = (12,000 × 2000³) / (3 × 200,000 × 11.3 × 10⁶)
= 9.6 × 10¹³ / 6.78 × 10¹² = 14.2 mm
Limit = L/250 = 2000/250 = 8.0 mm
14.2 mm exceeds 8.0 mm by 78% → fails.
Conclusion
Deflection governs, and the as-designed bracket does not meet it. The stress check is passing at 0.88 utilisation, which is exactly the kind of result that gets waved through when only strength is checked. Two further points belong in the report: the 12 kN is a static value on a hoist, so a dynamic factor (commonly 1.5–2.0 for hoisting) should be applied before either check, which would fail the stress check too; and a tip deflection of 14 mm on a 2 m cantilever changes the geometry the operator sees. The stiffening should come from depth, not wall thickness - a deeper section is far more efficient for deflection.
2. Assess the as-built substitution. What load may the bracket carry, if any?
Read the worked answer
As-built check (150 × 100 × 6)
σ = 24 × 10⁶ / 118 × 10³ = 203 MPa vs 181.5 MPa allowable → fails, utilisation 1.12
δ = 9.6 × 10¹³ / (3 × 200,000 × 8.85 × 10⁶) = 18.1 mm vs 8.0 mm → 2.26 × the limit
So the substitution fails both criteria; it is not a marginal call.
Back-calculating an allowable load
Stress-limited: M = 181.5 × 118 × 10³ = 21.4 × 10⁶ N·mm → P = 21.4 / 2.0 = 10.7 kN
Deflection-limited: P = 8.0 × 3 × 200,000 × 8.85 × 10⁶ / 2000³ = 5.3 kN
Deflection governs again, at 5.3 kN - less than half the rated load. Applying a dynamic factor of 1.5 for hoisting takes the permissible static hoist mass to roughly 3.5 kN, which is barely more than the rigging itself.
Judgement
The bracket should not be returned to full service on the basis of a calculation alone. The substitution was made without a change note, which means the design file, the fabrication record and the as-built structure disagree - and the crack suggests the bracket has been running at a stress range above what the detail can tolerate. Put it out of service or lock it to a verified reduced load, issue a non-conformance, and require a documented re-design before reinstatement. Whether the fabricator carries the cost is a commercial matter; that the load is restricted is not.
3. The 6 mm toe crack has been found. What is your immediate disposition and what engineering do you require before it goes back into service?
Read the worked answer
Immediate
Take the bracket out of service, or restrict it to a verified low load and tag it. The crack is on the tension side at the weld toe - the point of maximum calculated stress plus a weld-toe stress concentration of roughly 2 to 3. Nominal 160 MPa with an SCF of 2.5 puts the local hot-spot stress at around 400 MPa, above yield, so local plastic cycling is entirely plausible. Do not weld over it; a crack that is not removed will re-initiate from its tip.
Engineering required
Size it properly. MPI or dye penetrant gives length only. Use UT or TOFD to get the depth through the 6 mm wall - a 6 mm surface length with a 5 mm depth is a very different problem from one with a 1 mm depth, and the assessment cannot proceed without it. Inspect the whole weld, not just the found indication.
Fitness-for-service assessment (BS 7910 or API 579 level 2): fracture assessment against the wall thickness and toughness, plus a fatigue assessment using the measured stress range and the detail category for a welded attachment. The cycle count is about 40/day × 250 days × 8 years ≈ 80,000 cycles - enough, at that stress range, to exceed the detail's constant-amplitude limit and accumulate real damage.
Root cause. The substituted 6 mm section raised the stress by about 27%, so the detail has been running harder than designed for its whole life. That is the likely accelerant and it must be corrected, not just repaired.
Repair and re-inspect. Grind out to sound metal with a documented excavation profile and a dye-penetrant check, re-weld to a qualified procedure with a smooth toe profile, and consider adding a gusset or increasing the section to bring the deflection within L/250. Re-inspect by MPI after the repair.
Record. Update the inspection interval based on the assessed remaining life, and register the reduced rating on the equipment until the repair is proven.