2 Buckling Capacity of Plates and Stiffeners

2.1 Overall stiffened panel capacity

2.1.1 The elastic stiffened panel limit state is based on the following interaction formula:

where c_f and P_z are defined in [2.3.4].

2.2 Plate capacity

2.2.1 Plate limit state The plate limit state is based on the following interaction formulae:

with

γ_c = min(γ_c1,γ_c2,γ_c3,γ_c4)

where:

σ_x , σ_y : Applied normal stress to the plate panel, in N/mm², to be taken as defined in [2.2.7].

τ : Applied shear stress to the plate panel, in N/mm².

σ_cx’ : Ultimate buckling stress, in N/mm², in direction parallel to the longer edge of the buckling panel as defined in [2.2.3].

σ_cy’ : Ultimate buckling stress, in N/mm², in direction parallel to the shorter edge of the buckling panel as defined in [2.2.3].

τ_c’ : Ultimate buckling shear stresses, in N/mm², as defined in [2.2.3].

γ_c1, γ_c2, γ_c3, γ_c4: Stress multiplier factors at failure for each of the above different limit states. γ_c2 and γ_c3 are only to be considered when σ_x ≥ 0 and σ_y ≥ 0 respectively.

B : Coefficient given in Table 1.

e₀ : Coefficient given in Table 1.

2.2.2 Reference degree of slenderness

The reference degree of slenderness is to be taken as:

where:

K : Buckling factor, as defined in Table 3 and Table 4.

2.2.3 Ultimate buckling stresses

The ultimate buckling stresses of plate panels, in N/mm², are to be taken as:

σ_cx’ = C_x R_{eH_P}

σ_cy’ = C_y R_{eH_P}

The ultimate buckling stress of plate panels subject to shear, in N/mm², is to be taken as:

where:

The boundary conditions for plates are to be considered as simply supported, see cases 1, 2 and 15 of Table 3. If the boundary conditions differ significantly from simple support, a more appropriate boundary condition can be applied according to the different cases of Table 3 subject to the agreement of the Society.

2.2.4 Correction factor F_long

The correction factor F_long depending on the edge stiffener types on the longer side of the buckling panel is defined in Table 2. An average value of F_long is to be used for plate panels having different edge stiffeners. For stiffener types other than those mentioned in Table 2, the value of c is to be agreed by the Society. In such a case, value of c higher than those mentioned in Table 2 can be used, provided it is verified by buckling strength check of panel using non-linear FE analysis and deemed appropriate by the Society.

2.2.5 Correction factor F_tran

2.2.6 Curved plate panels

This requirement for curved plate limit state is applicable when R/t_p ≤ 2500. Otherwise, the requirement for plate limit state given in [2.2.1] is applicable.

The curved plate limit state is based on the following interaction formula:

where:

σ_ax : Applied axial stress to the cylinder corresponding to the curved plate panel, in N/mm². In case of tensile axial stresses, σ_ax = 0.

σ_tg : Applied tangential stress to the cylinder corresponding to the curved plate panel, in N/mm². In case of tensile tangential stresses, σ_tg = 0.

C_ax, C_tg, C_τ : Buckling reduction factor of the curved plate panel, as defined in Table 4.

The stress multiplier factor, γ_c, of the curved plate panel need not be taken less than the stress multiplier factor, γ_c, for the expanded plane panel according to [2.2.1].

2.2.7 Applied normal stress to plate panel

2.3 Stiffeners

2.3.1 Buckling modes

2.3.2 Web thickness of flat bar

For accounting the decrease of the stiffness due to local lateral deformation, the effective web thickness of flat bar stiffener, in mm, is to be used in [2.3.4] for the calculation of the net sectional area, A_s, the net section modulus, Z, and the moment of inertia, I, of the stiffener and is taken as:

2.3.3 Idealisation of bulb profile

Bulb profiles are to be considered as equivalent angle profiles, as defined in Ch 3, Sec 7, [1.4.1].

2.3.4 Ultimate buckling capacity

When σ_a + σ_b + σ_w > 0, the ultimate buckling capacity for stiffeners is to be checked according to the following interaction formula:

where:

σ_a : Effective axial stress, in N/mm², at mid span of the stiffener, acting on the stiffener with its attached plating.

ψ : Edge stress ratio for case 2 according to Table 3.

w_na: : Distance from the mid-point of attached plating to the neutral axis of the stiffener calculated with the effective width of the attached plating according to [2.3.5].

I_P : Net polar moment of inertia of the stiffener, in cm⁴, about point C as shown in Figure 1, as defined in Table 5.

I_T : Net St. Venant’s moment of inertia of the stiffener, in cm⁴, as defined in Table 5.

I_ω : Net sectional moment of inertia of the stiffener, in cm⁶, about point C as shown in Figure 1, as defined in Table 5.

A_w : Net web area, in mm².

Af : Net flange area, in mm².

2.3.5 Effective width of attached plating

where:

2.3.6 FE corrected stresses for stiffener capacity

2.4 Primary supporting members

2.4.1 Web plate in way of openings

The web plate of primary supporting members with openings is to be assessed for buckling based on the combined axial compressive and shear stresses.

The web plate adjacent to the opening on both sides is to be considered as individual unstiffened plate panels as shown in Table 6.

where:

2.4.2 Reduction factors of web plate in way of openings

The reduction factors, C_x or C_y in combination with, C_τ of the plate panel(s) of the web adjacent to the opening is to be taken as shown in Table 6.

2.4.3 The equivalent plate panel of web plate of primary supporting members crossed by perpendicular stiffeners is to be idealised as shown in Figure 2.

Figure 2 : Web plate idealisation

The correction of panel breadth is applicable also for other slot configurations provided that the web or collar plate is attached to at least one side of the passing stiffener.