Methodology
Each case checks an unstiffened rectangular plate field for in-plane
buckling under combined axial, transverse and shear stress, following
DNV-RP-C201 (Buckling Strength of Plated Structures).
- Elastic buckling: classical plate theory,
σE = k·π²E/[12(1−ν²)]·(t/b)², with the
buckling coefficient k for a simply-supported field under uniform
compression (and the shear coefficient kτ for the
shear term).
- Johnson–Ostenfeld correction: where the elastic
stress exceeds half the yield, the critical stress is reduced
inelastically, σcr = fy(1 − fy/4σE).
- Interaction check: utilisation =
σx/(σcr/γM) +
[τ/(τcr/γM)]², compared against
unity. A material factor γM = 1.15
is applied to all capacities.
- Materials: IACS marine grades — Grade A
(fy 235 MPa), AH36 (355 MPa) and EH40 (390 MPa), all with
E = 206 GPa. Toughness suffix does not change buckling capacity.
Applicable Codes & Standards
- DNV-RP-C201 (2010)
- IACS UR W11 (hull steel grades)
Assumptions & Limitations
- Simply-supported plate field on four edges (no rotational restraint credited).
- Uniform in-plane compression across the loaded edge; no lateral pressure.
- Marine grades Grade A / AH36 / EH40 with E = 206 GPa, Poisson's ratio 0.3.
- Effective width of attached plating equals the stiffener spacing — the stiffener itself is NOT modelled; this is unstiffened plate-field buckling only.
- Material factor gamma_M = 1.15; results are preliminary screening estimates and require review by a qualified engineer.
- Charts reference a 800 mm breadth x 2400 mm span plate under sigma_x=150, sigma_y=0, tau=0 MPa.
AH36 plate-field check — representative thickness range
AH36 at 800 mm breadth under axial sigma_x=150 MPa. Minimum acceptable thickness ≈ 12.2 mm (utilisation crosses unity).
| Thickness (mm) |
Slenderness beta |
sigma_cr (MPa) |
Utilisation |
Status |
| 8.0 |
4.1513 |
74.47 |
2.3162 |
FAIL |
| 9.0 |
3.6900 |
94.26 |
1.8301 |
FAIL |
| 10.0 |
3.3210 |
116.37 |
1.4824 |
FAIL |
| 11.0 |
3.0191 |
140.80 |
1.2251 |
FAIL |
| 12.0 |
2.7675 |
167.57 |
1.0294 |
FAIL |
| 13.0 |
2.5546 |
194.79 |
0.8856 |
PASS |
| 14.0 |
2.3722 |
216.86 |
0.7954 |
PASS |
| 15.0 |
2.2140 |
234.67 |
0.7351 |
PASS |
| 16.0 |
2.0756 |
249.24 |
0.6921 |
PASS |
| 17.0 |
1.9535 |
261.31 |
0.6601 |
PASS |
| 18.0 |
1.8450 |
271.43 |
0.6355 |
PASS |
| 19.0 |
1.7479 |
280.00 |
0.6161 |
PASS |
| 20.0 |
1.6605 |
287.31 |
0.6004 |
PASS |
| 21.0 |
1.5814 |
293.60 |
0.5875 |
PASS |
| 22.0 |
1.5096 |
299.06 |
0.5768 |
PASS |
| 23.0 |
1.4439 |
303.82 |
0.5678 |
PASS |
| 24.0 |
1.3838 |
307.99 |
0.5601 |
PASS |
| 25.0 |
1.3284 |
311.68 |
0.5535 |
PASS |
From parametric screening to live measured loads
This study screens a fixed grid of design stresses overnight. The same
DNV-RP-C201 plate-buckling model can instead be driven by
measured in-service loads — strain-gauge or hull-monitoring
derived stress histories — to report utilisation against the identical
capacity envelope shown above, turning the static utility curves into a
continuous structural-margin readout.
Buckling utilisation vs plate thickness
Reference: 800 mm breadth, axial sigma_x=150 MPa. Below the dashed unity line the plate field is acceptable.
Critical buckling stress vs plate thickness
Per-grade sigma_cr at 800 mm breadth (DNV-RP-C201 + Johnson–Ostenfeld).
Utilisation vs plate slenderness beta
Markers coloured by zone: green util≤0.7, amber 0.7–0.9, red >0.9.
Combined load interaction (AH36, 12 mm plate)
Utilisation as axial sigma_x and shear tau vary; black line is the util=1.0 capacity boundary.