Deck Plating Wastage and Plate Buckling at Midship
A 32,000 dwt bulk carrier is in its third special survey. At midship, the deck plating between continuous longitudinals is nominally 14.0 mm thick, with longitudinals at 850 mm spacing and transverse frames at 2.4 m spacing. Close-up gauging over three bays shows fairly uniform wastage to 11.0 mm, with scattered pits down to 9.0 mm. The deck is in longitudinal compression. The loading computer and rule wave bending moment give a nominal hogging stress of 145 MPa at the deck, and the material is mild steel with E = 206 GPa, ν = 0.30 and yield stress 235 MPa. The superintendent argues that 11 mm is still above the 10 mm minimum thickness in the survey report, so no renewal is needed before the next voyage. The class surveyor is concerned about buckling rather than pure tensile stress. The deck plating is stiffened by longitudinals and frames and can be idealised as a simply supported rectangular plate in uniaxial compression.
1. Calculate the elastic buckling stress of the 11 mm deck plate between longitudinals and compare it with the applied 145 MPa compressive stress. What does the comparison show?
Read the worked answer
For a simply supported plate in uniaxial compression, take buckling coefficient k = 4. The plate breadth between longitudinals is b = 850 mm and thickness t = 11 mm.
σcr = [kπ²E / (12(1−ν²))] × (t/b)² = [4 × 9.8696 × 206,000 / (12 × 0.91)] × (11/850)² = 744,700 × 0.0001675 ≈ 124.7 MPa.
The applied compressive stress is 145 MPa, which exceeds the elastic buckling stress by about 16%. The plate would therefore be expected to buckle elastically before reaching the nominal hull-girder stress. Post-buckling reserve exists because the plate can shed load to the longitudinals, but class rules require a margin against buckling, not reliance on post-buckling behaviour. At the 9 mm pits, σcr falls to about 124.7 × (9/11)² ≈ 83 MPa, so local buckling is even more critical.
The superintendent's comparison with a 10 mm minimum thickness is not a buckling check. Yield is not the governing criterion here: 145 MPa is well below 235 MPa, but buckling governs.
2. Determine the minimum net thickness needed to keep the elastic buckling stress at least 10% above the applied stress, and state whether renewal is required.
Read the worked answer
The target buckling stress is 1.10 × 145 = 159.5 MPa. Rearrange the plate formula: t = b × sqrt[σcr × 12(1−ν²) / (kπ²E)] = 850 × sqrt[159.5 / 744,700] = 850 × 0.01463 ≈ 12.4 mm.
So the net thickness should be about 12.4 mm, say 12.5 mm, just to meet the 10% margin at the nominal stress. That leaves no allowance for further corrosion before the next survey. A practical renewal thickness would be greater, depending on the class rule corrosion addition and the intended service interval.
The as-gauged 11 mm is below 12.4 mm, so renewal or repair is required. The original 14 mm plate has lost about 21% of its thickness. Simply accepting 11 mm because it is above a 10 mm absolute minimum ignores the buckling margin and the scattered 9 mm pits.
3. Explain why an average thickness over three bays may be misleading, and what inspection and repair action you would require.
Read the worked answer
An average of 11 mm can hide a locally thin pit at 9 mm. Buckling and local strength are governed by the thinnest area, not the average: the critical stress scales with t², so a 9 mm pit has only (9/11)² ≈ 67% of the buckling capacity of the 11 mm plate. Corrosion is also not uniform; pitting creates local stress concentrations and can initiate cracks. The average may satisfy a crude wastage calculation while the local panel is unacceptable.
Require close-up gauging on a grid, mapping of the pits, and renewal of the affected bays or insertion of new plate to the original or class-required net thickness. After repair, verify the buckling check using net thickness and the actual span between longitudinals and frames. Also check the condition of longitudinals and their connections, because load shed from buckled plating increases demand on them. The repair should be covered by an approved welding procedure, and the area should be re-surveyed before the next intermediate survey.