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Clasification Society Rules and Regulations - Rules and Regulations for the Classification of Offshore Units, January 2016 - Part 10 SHIP UNITS - Chapter 1 General Requirements - Section 18 Buckling

Section 18 Buckling

Parent topic: Chapter 1 General Requirements

18.1 General

18.1.1  Symbols. The symbols used in this Chapter are defined as follows:

= allowable buckling utilisation factor, as defined in Pt 10, Ch 3, 1.5 Hull girder buckling strength 1.5.2
= actual compressive stresses for plates, in N/mm2
= compressive axial stress in the stiffener, in N/mm2, in way of the midspan of the stiffener
τ = actual shear stress, in N/mm2
= critical compressive stress, in N/mm2, as defined in Pt 10, Ch 1, 18.2 Buckling of plates 18.2.1
= critical shear stress, in N/mm2, as defined in Pt 10, Ch 1, 18.2 Buckling of plates 18.2.1
K = buckling factor, see Pt 10, Ch 1, 18.1 General 18.1.2
= reference stress, in N/mm2
= 0,9E
E = modulus of elasticity, 206 000 N/mm2
= net thickness of plate panel, in mm
= length of the side of the plate panel, as defined in Pt 10, Ch 1, 18.1 General 18.1.2, in mm
= specified minimum yield stress of the material, in N/mm2
= reduction factors, as given in Table 1.18.1
= bending stress at the midspan of the stiffener according to Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2, in N/mm2
s = stiffener spacing, in mm
= depth of web plate, in mm, as shown in Pt 10, Ch 1, 18.1 General 18.1.1
= net flange thickness, in mm
= net web thickness, in mm
= flange breadth, in mm
= Poisson’s ratio, 0,3.

Figure 1.18.1 Stiffener cross-sections

18.1.2  Scope
  1. This Section contains the methods for determination of the buckling capacity, definitions of buckling utilisation factors and other measures necessary to control buckling of plate panels, stiffeners and primary support members.
  2. The buckling utilisation factor is to satisfy the following criteria:

  3. For structural idealisation and definitions see also Pt 10, Ch 1, 8 Structural idealisation. The thickness and section properties of plates and stiffeners are to be taken as specified by the appropriate Rule requirements.

Table 1.18.1 Buckling factor and reduction factor for plane plate panels

Case Stress ratio ψ Aspect ratio α Buckling factor K Reduction factor C
1 ≥ ψ ≥ 0 α > 1 K = = 1 for λ ≤
= c () for λ >
0 > ψ > –1 K = 7,63 – ψ (6,26 – 10ψ) where
ψ ≤ –1 K = 5,975 (1 – ψ)2 c =(1,25 – 0,12ψ) ≤ 1,25
=(1 + )
1 ≥ ψ ≥ 0 α > 1 K = =
where
0 > ψ > –1 1 ≤ α ≤ 1,5 K = c =(1,25 – 0,12ψ) ≤ 1,25
R =λ (1 – λ/c) for λ <
R = 0,22 for λ ≥
α > 1,5 K = =0,5c
  F =
= – 0,5 and 1 ≤ ≤ 3
  =1 for due to direct loads (3)
ψ ≤ –1 1 ≤ α ≤ K = 5,975 =(1 – 1/α) ≥ 0 for due to bending (in general) (2)
=0 for σ due to bending in extreme load cases (e.g. w/t.bhds.)
α > K = H =
T=
1 ≥ ψ ≥ 0 α > 0 K = = 1 for λ ≤ 0,7
0 > ψ ≥ –1 K = = for λ > 0,7
1 ≥ ψ ≥ –1 α > 0 K =  
    K = = 1 for λ ≤ 0,84
α ≥ 1 = for λ > 0,84
0 < α < 1  
    K = K’ r  
K’ = K according to Case 5  
r = opening red. factor  
r =  
≤ 0,7 and ≤ 0,7  
where
ψ = the ratio between smallest and largest compressive stress, as shown for Cases 1 to 4
= length, in mm, of the shorter side of the plate panel for Cases 1 and 2
= length, in mm, of the side of the plate panel, as defined for Cases 3, 4, 5 and 6
α = aspect ratio of the plate panel
Edge boundary conditions:
- - - - - - - - - plate edge free
plate edge simply supported
NOTES
1. Cases listed are general cases. Each stress component () is to be understood in local coordinates.
2. due to bending (in general) corresponds to straight edges (uniform displacement) of a plate panel integrated in a large structure. This value is to be applied for hull girder buckling and buckling of web plate of primary support members in way of openings.
3. for direct loads corresponds to a plate panel with edges not restrained from pull-in which may result in non-straight edges.

18.2 Buckling of plates

18.2.1  Uni-axial buckling of plates.
  1. The buckling utilisation factor for uni-axial stress is to be taken as:

    for compressive stresses in x-direction

    for compressive stresses in y-direction

    for shear stress.

  2. Reference degree of slenderness, to be taken as:

  3. The critical stresses, or , of plate panels subject to compression or shear, respectively, is to be taken as:

18.3 Buckling of stiffeners

18.3.1 Critical compressive stress.
  1. The buckling utilisation factor of stiffeners is to be taken as the maximum of the column and torsional buckling mode as given in Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2 and Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.3
18.3.2 Column buckling mode.
  1. Stiffeners are to be verified against the column buckling mode as given in Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2 with the allowable buckling utilisation factor, , see Pt 10, Ch 1, 18.1 General 18.1.2. Stiffeners not subjected to lateral pressure and that have a net moment of inertia, , complying with Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2 have acceptable column buckling strength and need not be verified against Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2.
  2. The buckling utilisation factor for column buckling of stiffeners is to be taken as:

    where

    = bending stress at the midspan of the stiffener according to Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2, in N/mm2.
  3. The bending stress in the stiffener is equal to:

    where

    = net section modulus of stiffener, in cm3, including effective breadth of plating according to Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.4
    1. if lateral pressure is applied to the stiffener:
      = the section modulus calculated at flange if the lateral pressure is applied on the same side as the stiffener
      = the section modulus calculated at attached plate if the lateral pressure is applied on the side opposite to the stiffener
    2. if no lateral pressure is applied on the stiffener:
      = the minimum section modulus among those calculated at flange and attached plate
      = bending moment, in Nmm, due to the lateral load P
      =
      P = lateral load, in kN/m2
      = span of stiffener, in metres, equal to spacing between primary support members
      = bending moment, in Nmm, due to the lateral deformation w of stiffener
      =
      = ideal elastic buckling force of the stiffener, in N
      =
      = moment of inertia, in cm4, of the stiffener including effective width of attached plating according to Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.4. is to comply with the following requirement:
      =
      = net thickness of plate flange, to be taken as the mean thickness of the two attached plate panels, in mm
      = nominal lateral load, in N/mm2, acting on the stiffener due to membrane stresses, and , in the attached plate in way of the stiffener midspan:
      =
      = N/mm2
      =

      with and taken equal to

      = 1,47 = 0,49 for ≥ 2,0
      = 1,96 = 0,37 for ≥ 2,0
      = net sectional area of the stiffener without attached plating, in mm2
      = factor taking into account the membrane stresses in the attached plating acting perpendicular to the stiffener’s axis
      = 0,5 (1 + ψ) for 0 ≤ ψ ≤ 1
      = for ψ < 0
      ψ = edge stress ratio for Case 2 according to Pt 10, Ch 1, 18.1 General 18.1.2
      = membrane compressive stress in the attached plating acting perpendicular to the stiffener’s axis, in N/m2
      τ = shear membrane stress in the attached plating, in N/mm2
      w = deformation of stiffener, in mm
      =
      = assumed imperfection, in mm
      = min

      For stiffeners sniped at both ends is not to be taken less than the distance from the midpoint of attached plating to the neutral axis of the stiffener calculated with the effective width of the attached plating according to Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.4

      = deformation of stiffener at midpoint of stiffener span due to lateral load P, in mm. In case of uniformly distributed load is to be taken as:
      =
      = elastic support provided by the stiffener, in N/mm2
      =
      =
      = for
      = for
  4. Stiffeners not subjected to lateral pressure are considered as complying with the requirements of Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2 if their net moments of inertia, in cm4, satisfy the following requirement:

    where

    = distance from connection to plate (C as shown in Pt 10, Ch 1, 18.1 General 18.1.1) to centre of flange, in mm
    = () for bulb flats
    = () for angles and T bars

    NOTE

    Other parameters are as defined in Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.2.

18.3.3 Torsional buckling mode.
  1. The torsional buckling mode is to be verified against the allowable buckling utilisation factor, , see Pt 10, Ch 1, 18.1 General 18.1.2. The buckling utilisation factor for torsional buckling of stiffeners is to be taken as:

    where

    = compressive axial stress in the stiffener, in N/mm2, calculated at the attachment point of the stiffener to the plate, in way of the midspan of the stiffener measured along the global x-axis
    = torsional buckling coefficient
    = 1,0 for ≤ 0,2
    = for > 0,2
    Φ = 0,5 (1 + 0,21 ( – 0,2) + )
    = reference degree of slenderness for torsional buckling
    =
    = reference stress for torsional buckling, in N/mm2
    =
    = net polar moment of inertia of the stiffener about point C, in cm4, as shown in Pt 10, Ch 1, 18.1 General 18.1.1 and Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.3
    = net St.Venant’s moment of inertia of the stiffener, in cm, as shown in Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.3
    = net sectorial moment of inertia of the stiffener about point C, in cm6, as shown in Pt 10, Ch 1, 18.1 General 18.1.1 and Pt 10, Ch 1, 18.3 Buckling of stiffeners 18.3.3
    ∊ = degree of fixation
    = torsional buckling length to be taken equal the distance between tripping supports, in metres, distance from connection to plate (C in Pt 10, Ch 1, 18.1 General 18.1.1) to centre of flange, in mm
    = ( – 0,5) for bulb flats
    = ( + 0,5) for angles and T Bars net web area, in mm2
    = ( – 0,5) net flange area, in mm2
    =

    Table 1.18.2 Moments of inertia

    Section property Flat bars Bulb flats, angles and T bars
    for bulb flats and angles:
    for T bars:
18.3.4 Effective breadth of attached plating.
  1. The effective breadth of attached plating of ordinary stiffeners is to be taken as:

    = min ()

    where

    = 0,0035 — 0,0673 + 0,4422 – 0,0056 ≤ 1,0
    = average reduction factor for buckling of the two attached plate panels, according to Case 1 in Pt 10, Ch 1, 18.1 General 18.1.2
    = span of stiffener, in metres, equal to spacing between primary support members
    = effective span of stiffeners in metres
    = if simply supported at both ends
    = 0,6 if fixed at both ends.

18.4 Primary support members

18.4.1  Buckling of web plate of primary support members in way of openings.
  1. The web plate of primary support 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 Pt 10, Ch 1, 18.4 Primary support members 18.4.1. The buckling utilisation factor, η, is to be taken as:

    where

    = average compressive stress in the area of web plate being considered according to Case 1, 2 or 3 in Pt 10, Ch 1, 18.1 General 18.1.2, in N/mm2
    = average shear stress in the area of web plate being considered according to Case 5 or 6 in Pt 10, Ch 1, 18.1 General 18.1.2, in N/mm2
    e = 1 + exponent for compressive stress
    eτ = 1 + C exponent for shear stress
    C = reduction factor according to Case 1 or 3 in Pt 10, Ch 1, 18.1 General 18.1.2
    C = reduction factor according to Case 2 in Pt 10, Ch 1, 18.1 General 18.1.2
    = reduction factor according to Case 5 or 6 in Pt 10, Ch 1, 18.1 General 18.1.2.
  2. The reduction factors, or in combination with , of the plate panel(s) of the web adjacent to the opening is to be taken as shown in Pt 10, Ch 1, 18.1 General 18.1.2.

    Table 1.18.3 Reduction factors

    Mode

    Separate reduction factors are to be applied to areas P1 and P2 using Case 3 in Pt 10, Ch 1, 18.1 General 18.1.2, with edge stress ratio:

    ψ = 1,0

    		 A common reduction factor is to be applied to areas P1 and P2 using Case 6 in Pt 10, Ch 1, 18.1 General 18.1.2 for area marked:

    Separate reduction factors are to be applied for areas P1 and P2 using:

    for Case 1 or , for Case 2, see Pt 10, Ch 1, 18.1 General 18.1.2

    with stress ratio ψ = 1,0

    		Separate reduction factors are to be applied for areas P1 and P2 using Case 5 in Pt 10, Ch 1, 18.1 General 18.1.2

    Panels P1 and P2 are to be evaluated in accordance with (a).

    Panel P3 is to be evaluated in accordance with (b)

    NOTE
    Web panels to be considered for buckling in way of openings are shown shaded and numbered P1, P2, etc.

18.5 Other structures

18.5.1  Struts, pillars and cross ties.
  1. The critical buckling stress for axially compressed struts, pillars and cross ties is to be taken as the lesser of the column and torsional critical buckling stresses. The buckling utilisation factor, η, is to be taken as:

    where

    = average axial compressive stress in the member, in N/mm2
    = minimum critical buckling stress according to Pt 10, Ch 1, 18.5 Other structures 18.5.1, in N/mm2.
  2. The critical buckling stress in compression for each mode is to be taken as:

    = for

    = for

    where

    = elastic compressive buckling stress, in N/mm2, given for each buckling mode, see Pt 10, Ch 1, 18.5 Other structures 18.5.1 to Pt 10, Ch 1, 18.5 Other structures 18.5.1.
  3. The elastic compressive column buckling stress of pillars subject to axial compression is to be taken as:

    where

    = net moment of inertia about the weakest axis of the cross-section, in cm4
    = net cross-sectional area of the pillar, in cm2
    = end constraint factor:
    • 1,0 where both ends are pinned
    • 2,0 where one end is pinned and the other end is fixed
    • 4,0 where both ends are fixed
    • A pillar end may be considered fixed when effective brackets are fitted. These brackets are to be supported by structural members with greater bending stiffness than the pillar
    • Column buckling capacity for cross tie shall be calculated using equal to 2,0
    = unsupported length of the pillar, in metres.
  4. The elastic torsional buckling stress, , with respect to axial compression of pillars is to be taken as:

    = N/mm2

    where

    G = shear modulus
    =
    = net St.Venant’s moment of inertia, in cm4, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = net polar moment of inertia about the shear centre of cross-section
    = + + () cm4
    = end constraint factor:
    • 1,0 where both ends are pinned
    • 2,0 where one end is pinned and the other end is fixed
    • 4,0 where both ends are fixed
    • Elastic torsional buckling capacity for cross tie shall be calculated using equal to 2,0
    = warping constant, in cm6, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = unsupported length of the pillar, in metres
    = position of shear centre relative to the cross-sectional centroid, in cm, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = position of shear centre relative to the cross-sectional centroid, in cm, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = net cross-sectional area, in cm2
    = net moment of inertia about y-axis, in cm4
    = net moment of inertia about z-axis, in cm4
  5. For cross-sections where the centroid and the shear centre do not coincide, the interaction between the torsional and column buckling mode is to be examined. The elastic torsional/column buckling stress with respect to axial compression is to be taken as:

    =

    where

    = position of shear centre relative to the cross-sectional centroid, in cm, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = position of shear centre relative to the cross-sectional centroid, in cm, see Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = net cross-sectional area, in cm2
    = net polar moment of inertia about the shear centre of cross-section, as defined in Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = elastic torsional buckling stress, as defined in Pt 10, Ch 1, 18.5 Other structures 18.5.1
    = elastic column compressive buckling stress, as defined in Pt 10, Ch 1, 18.5 Other structures 18.5.1.

    Table 1.18.4 Cross-sectional properties

    Double symmetrical sections
    Single symmetrical sections
    NOTE
    All dimensions of thickness, breadth and depth are in mm.
    Cross-sectional properties not covered by this Table are to be obtained by direct calculation.
18.5.2  Corrugated bulkheads.
  1. Local buckling of a unit flange of corrugated bulkheads is to be controlled according to Pt 10, Ch 1, 18.2 Buckling of plates 18.2.1, for Case 1, as shown in Pt 10, Ch 1, 18.1 General 18.1.2, applying stress ratio ψ = 1,0.
  2. The overall buckling failure mode of corrugated bulkheads subjected to axial compression is to be checked for column buckling according to Pt 10, Ch 1, 18.5 Other structures 18.5.1 (e.g. horizontally corrugated longitudinal bulkheads, vertically corrugated bulkheads subject to localised vertical forces). End constraint factor corresponding to pinned ends is to be applied, except for fixed end support to be used in way of stool with width exceeding two times the depth of the corrugation.
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