3 Definitions

3.1 General

3.1.1 Buckling definition

‘Buckling’ is used as a generic term to describe the strength of structures, generally under in-plane compressions and/or shear and lateral load. The buckling strength or capacity can take into account the internal redistribution of loads depending on the load situation, slenderness and type of structure.

3.1.2 Buckling capacity

Buckling capacity based on this principle gives a lower bound estimate of ultimate capacity, or the maximum load the panel can carry without suffering major permanent set.

Buckling capacity assessment utilises the positive elastic post-buckling effect for plates and accounts for load redistribution between the structural components, such as between plating and stiffeners. For slender structures, the capacity calculated using this method is typically higher than the ideal elastic buckling stress (minimum Eigen value). Accepting elastic buckling of structural components in slender stiffened panels implies that large elastic deflections and reduced in-plane stiffness will occur at higher buckling utilisation levels.

3.1.3 Assessment methods

The buckling assessment is carried out according to one of the two methods taking into account different boundary condition types:

Method A: All the edges of the elementary plate panel are forced to remain straight (but free to move in the in-plane directions) due to the surrounding structure/neighbouring plates.
Method B: The edges of the elementary plate panel are not forced to remain straight due to low in-plane stiffness at the edges and/or no surrounding structure/neighbouring plates.

3.2 Buckling utilisation factor

3.2.1 The utilisation factor, η, is defined as the ratio between the applied loads and the corresponding ultimate capacity or buckling strength.

3.2.2 For combined loads, the utilisation factor, η_act, is to be defined as the ratio of the applied equivalent stress and the corresponding buckling capacity, as shown in Figure 1, and is to be taken as:

where:

W_act : Applied equivalent stress, in N/mm²:

for plate
for stiffener

W_u : Equivalent buckling capacity, in N/mm², to be taken as:

for plate
for stiffener

γ_c : Stress multiplier factor at failure.

For each typical failure mode, the corresponding capacity of the panel is calculated by applying the actual stress combination and then increasing or decreasing the stresses proportionally until collapse.

Figure 1 illustrates the buckling capacity and the buckling utilisation factor of a structural member subject to σ_x and σ_y stresses.

Figure 1 : Example of buckling capacity and buckling utilisation factor

3.3 Allowable buckling utilisation factor

3.3.1 General structural elements

The allowable buckling utilisation factor is defined in Table 1.

Table 1 : Allowable buckling utilisation factor

Structural component

η_all, Allowable buckling utilisation factor

Plates and stiffeners

Stiffened and unstiffened panels

Vertically stiffened side shell plating of single side skin bulk carrier

Web plate in ways of openings

1.00 for load combination: S+D

0.80 for load combination: S

Struts, pillars and cross ties

0.75 for load combination: S+D

0.65 for load combination: S

Corrugation of vertically corrugated bulkheads with lower stool and horizontally corrugated bulkhead, under lateral pressure from liquid loads, for shell elements only.

Supporting structure in way of lower end of corrugated bulkheads without lower stool.

0.90 for load combination: S+D

0.72 for load combination: S

Corrugation of vertically corrugated bulkheads without lower stool under lateral pressure from liquid loads, for shell elements only.

0.81 for load combination: S+D

0.65 for load combination: S

Note 1: Supporting structure for a transverse corrugated bulkhead refers to the structure in longitudinal direction within half a web frame space forward and aft of the bulkhead, and within a vertical extent equal to the corrugation depth.

Note 2: Supporting structure for a longitudinal corrugated bulkhead refers to the structure in transverse direction within three longitudinal stiffener spacings from each side of the bulkhead, and within a vertical extent equal to the corrugation depth.

3.4 Buckling acceptance criteria

3.4.1 A structural member is considered to have an acceptable buckling strength if it satisfies the following criterion:

η_act ≤ η_all

where:

η_act : Buckling utilisation factor based on the applied stress, defined in [3.2.2].

η_all : Allowable buckling utilisation factor as defined in [3.3].