Section 3 Buckling

3.1.1 This Section contains the requirements for buckling control of plate panels subject to in-plane compressive and/or shear stresses and buckling control of primary and secondary stiffening members subject to axial compressive and shear stresses.

3.1.2 The requirement for buckling control of plate panels is contained in Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements. The requirements for secondary stiffening members are contained in Vol 1, Pt 6, Ch 2, 3.7 Secondary stiffening in direction of compression. The requirements for primary members are contained in Vol 1, Pt 6, Ch 2, 3.9 Buckling of primary members and Vol 1, Pt 6, Ch 2, 3.10 Shear buckling of girder webs

3.1.3 In general all areas of the structure are to meet the buckling strength requirements for the design stresses. The design stresses are to be taken as the global hull girder bending and shear stresses derived in accordance with Vol 1, Pt 6, Ch 4 Hull Girder Strength. In addition, where the structural member is subject to local compressive loads, then the design stresses are to be based on these loads.

3.1.4 The buckling requirements are to be met using the net scantlings, hence any additional thickness for corrosion margin or enhanced scantlings is not included in the scantlings used to assess the buckling performance. For corrosion margins, see Vol 1, Pt 6, Ch 6, 3.8 Corrosion margin.

3.2.1 The symbols used in this Section are defined below and in the appropriate sub-Section:

3.3.1 The section gives methods for evaluating the buckling strength of plate panels subjected to the following load fields:

1. uni-axial compressive loads;

2. shear loads;

3. bi-axial compressive loads;

4. uni-axial compressive loads and shear loads;

5. bi-axial compressive loads and shear loads.

3.3.2 The plate panel buckling requirements will be satisfied if the buckling interaction equations given in Table 2.3.1 Plate panel buckling requirements for the above load fields are complied with.

3.3.3 The critical compressive buckling stresses and critical shear buckling stresses required for Table 2.3.1 Plate panel buckling requirements are to be derived in accordance with Vol 1, Pt 6, Ch 2, 3.4 Derivation of the buckling stress for plate panels

3.3.4 The buckling factors of safety λ _σ and λ _τ required by Table 2.3.1 Plate panel buckling requirements are to be extracted from Vol 1, Pt 6, Ch 5 Structural Design Factors for the structural member concerned.

3.3.5 For all structural members which contribute to the hull girder strength, the plate panel buckling requirements for uni-axial compressive loads, Table 2.3.1 Plate panel buckling requirements, and shear loads, Table 2.3.1 Plate panel buckling requirements are to be complied with.

3.3.6 In addition to Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements 3.3.5, structural members which are subjected to local compressive loads and/on shear loads are to be verified using the plate panel buckling requirements in Table 2.3.1 Plate panel buckling requirements to Table 2.3.1 Plate panel buckling requirements.

3.3.7 However, where some members of the structure have been designed such that elastic buckling of the plate panel between the stiffeners is allowable, then the requirements of Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically must be applied to the buckling analysis of the stiffeners supporting the plating. In addition, panels which do not satisfy the panel buckling requirements must be indicated on the appropriate drawing and the effect of these panels not being effective in transmitting compressive loads taken into account for the hull girder strength calculation, see Vol 1, Pt 6, Ch 4, 1.4 Calculation of hull section modulus 1.4.9 and Vol 1, Pt 6, Ch 4, 1.4 Calculation of hull section modulus 1.4.10

3.3.8 In general the plate panel buckling requirements for more complex load fields, see Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements 3.3.1.(c), Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements 3.3.1.(d) and Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements 3.3.1.(e), are to be complied with. Where this is not possible, due to elastic buckling of the panel, then the critical buckling stress, σ_c, may be based on the ultimate collapse strength of the plating, σ_u from Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically 3.5.4, instead of the elastic buckling stress, σ_e, derived in Vol 1, Pt 6, Ch 2, 3.3 Plate panel buckling requirements 3.3.5. In addition, the requirements of Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically are to be met for the supporting secondary stiffeners and primary members.

3.4.1 The critical compressive buckling stress, σ_c, for a plate panel subjected to uni-axial in-plane compressive loads is to be derived in accordance with Table 2.3.2 Buckling stress of plate panels

3.4.2 The critical shear buckling stress, τ_c, for a plate panel subjected to pure in-plane shear load is to be derived in accordance with Table 2.3.2 Buckling stress of plate panels.

3.4.3 For welded plate panels with plating thicknesses below 8 mm, the critical compressive buckling stress is to be reduced to account for the presence of residual welding stresses. The critical buckling stress for plating is to be taken as the minimum of:

or

where

t_p and σ _o are defined in Vol 1, Pt 6, Ch 2, 1.3 Symbols and definitions 1.3.1

σ_c is derived in Vol 1, Pt 6, Ch 2, 3.4 Derivation of the buckling stress for plate panels 3.4.1

b is defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1

3.4.4 In general the effect of lateral loading on plate panels (for example hydrostatic pressure on bottom shell plating) may be neglected and the critical buckling stresses calculated considering the in-plane stresses only.

3.4.5 Unless indicated otherwise, the effect of initial deflection on the buckling strength of plate panels may be ignored.

3.5.1 Elastic buckling of plate panels between stiffeners occurs when both the following conditions are satisfied:

1. The design compressive stress, σ_d, is greater than the elastic buckling stress of the plating, σ _e

1. The elastic buckling stress is less than half the yield stress

   

3.5.2 Elastic buckling of local plating between stiffeners, including girders or floors etc. may be allowed if all of the following conditions are satisfied:

1. The critical buckling stress of the stiffeners in all buckling modes is greater than the axial stress in the stiffeners after redistribution of the load from the elastically buckled plating into the stiffeners, hence

1. Maximum predicted loadings are used in the calculations.

2. Functional requirements will allow a degree of plating deformation.

where

σ _de is the stiffener axial stress given in Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically 3.5.5

σ _c(i) is given by Table 2.3.3 Buckling stress of secondary stiffeners

• where
• i is a, t, w or f depending on the mode of buckling.

λ _σ is the buckling factor of safety given in Table 5.3.2 Allowable stress factors f 1.

3.5.3 The effective breadth of attached plating for stiffeners, girder or beams that is to be used for the determination of the critical buckling stress of the stiffeners attached to plating which buckles elastically is to be taken as follows:

where

b is given in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1

3.5.4 The ultimate buckling strength of plating, σ _u, which buckles elastically, may be determined as follows:

1. shortest edge loaded, i.e. A _R ≥ 1:

   

2. longest edge loaded i.e. A _R < 1:

   

where

A _R and s are defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1

t_p, E and σ _ow are defined in Vol 1, Pt 6, Ch 2, 1.3 Symbols and definitions 1.3.1.

3.5.5 The axial stress in stiffeners attached to plating which is likely to buckle elastically is to be derived as follows:

where

σ _d is the axial stress in the stiffener when the plating can be considered fully effective

where

b and b _eu are given in Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically 3.5.3

t is the plating thickness, in mm

A _s is the stiffener area in cm².

3.6.1 The shear buckling capability of longitudinally stiffened panels between primary members is to satisfy the following condition:

where

τ _c is derived from Vol 1, Pt 6, Ch 2, 3.6 Shear buckling of stiffened panels 3.6.3

τ _d is the design shear stress

λ _τ is given in Table 5.3.2 Allowable stress factors f 1.

3.6.2 The elastic shear buckling stress of longitudinally stiffened panels between primary members may be taken as:

where

s, , E and S _p are as defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1, see also Figure 2.3.1 Shear buckling

3.6.3 The critical shear buckling stress, τ _c, may be determined from τ _e, see Note in Table 2.3.2 Buckling stress of plate panels.

3.7.1 The buckling performance of stiffeners will be considered satisfactory if the following conditions are satisfied:

where

σ_{c (a)}, σ_{c (t)}, σ_{c (w)} and σ_{c (f)} are the critical buckling stress of the stiffener for each mode of failure, see Vol 1, Pt 6, Ch 2, 3.7 Secondary stiffening in direction of compression 3.7.2

σ _d is the design compressive stress, see also Vol 1, Pt 6, Ch 2, 3.1 General 3.1.3 and Vol 1, Pt 6, Ch 2, 3.5 Additional requirements for plate panels which buckle elastically

λ_σ is the buckling factor of safety given in Table 5.3.2 Allowable stress factors f 1 in Vol 1, Pt 6, Ch 5 Structural Design Factors The value of λ _σ to be chosen depends on the buckling assessment of the attached plating, see Note 3, Table 5.3.2 Allowable stress factors f 1

3.7.2 The critical buckling stresses for the overall, torsional, web and flange buckling modes of longitudinals and secondary stiffening members under axial compressive loads are to be determined in accordance with Table 2.3.3 Buckling stress of secondary stiffeners

3.7.3 To prevent torsional buckling of secondary stiffeners from occurring before buckling of the plating, the critical torsional buckling stress, σ _c(t), is to be greater than the critical buckling stress of the attached plating as detailed in Vol 1, Pt 6, Ch 2, 3.4 Derivation of the buckling stress for plate panels 3.4.1

3.7.4 The critical buckling stresses of the stiffener web, σ_c(w), and flange, σ_c(f), are to be greater than the critical torsional buckling stress, hence:

σ_c(w) > σ_c(t)

σ_c(f) > σ_c(t)

3.7.5 To ensure that overall buckling of the stiffened panel cannot occur before local buckling of the secondary stiffener, the critical overall buckling stress σ_c(a), is to be greater than the critical torsional buckling stress, hence:

σ_c(a) > σ_c(t)

3.8.1 Where a stiffened panel of plating is subjected to a compressive load perpendicular to the direction of the stiffeners, see Figure 2.3.2 Secondary stiffening perpendicular to direction of compression e.g. a transversely stiffened panel subject to longitudinal compressive load, the requirements of this section are to be applied.

3.8.2 The minimum moment of inertia of each stiffener including attached effective plating of width, b _eb, to ensure that overall panel buckling does not precede plate buckling is to be taken as:

s, l and S are defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1 and shown in Figure 2.3.2 Secondary stiffening perpendicular to direction of compression

t _p and E are defined in Vol 1, Pt 6, Ch 2, 1.3 Symbols and definitions 1.3.1.

3.9.1 Where primary girders are subject to axial compressive loading, the buckling requirements for lateral, torsional, web and flange buckling modes detailed in Vol 1, Pt 6, Ch 2, 3.7 Secondary stiffening in direction of compression are to be satisfied.

3.9.2 To prevent global buckling from occurring before local panel buckling, transverse primary girders supporting axially loaded longitudinal stiffeners are to have a sectional moment of inertia, including attached plating, of not less than the following:

S _p and s are as defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1

σ _d is design stress, in N/mm²

σ _o and A _te are as defined in Vol 1, Pt 6, Ch 2, 3.2 Symbols 3.2.1

σ _e(a) is the elastic column buckling stress, see Vol 1, Pt 6, Ch 2, 3.7 Secondary stiffening in direction of compression 3.7.2

E is defined in Vol 1, Pt 6, Ch 2, 1.3 Symbols and definitions 1.3.1

_e is defined in Table 2.3.3 Buckling stress of secondary stiffeners

3.10.1 Local panels in girder webs subject to in-plane shear loads are to satisfy the shear buckling requirements in Table 2.3.1 Plate panel buckling requirements, item (b).

3.10.2 The critical shear buckling stress, τ_c, is to be determined using the following formula for τ_e and the Note in Table 2.3.2 Buckling stress of plate panels

where

t_p and E are defined in Vol 1, Pt 6, Ch 2, 1.3 Symbols and definitions 1.3.1

3.11.1 Pillars and pillar bulkheads are to comply with the requirements of Vol 1, Pt 6, Ch 3, 12 Pillars and pillar bulkheads