1 Structural Idealisation of Stiffeners and Primary Supporting Members

1.1 Effective spans

1.1.1 General

Where arrangements differ from those defined in this article, span definition may be specially considered.

1.1.2 Effective bending span of stiffeners

The effective bending span ℓ_bdg of stiffeners is to be measured as shown in Figure 1 for single skin structures and Figure 2 for double skin structures.

If the web stiffener is sniped at the end or not attached to the stiffener under consideration, the effective bending span is to be taken as the full length between PSMs unless a backing bracket is fitted, see Figure 1.

The effective bending span may be reduced where brackets are fitted to the flange or free edge of the stiffener. Brackets fitted on the side opposite to that of the stiffener with respect to attached plating are not to be considered as effective in reducing the effective bending span.

In single skin structures, the effective bending span of a stiffener supported by a bracket or by a web stiffener on one side only of the primary supporting member web, is to be taken as the total span between primary supporting members as shown in item (a) of Figure 1. If brackets are fitted on both sides of the primary supporting member, the effective bending span is to be taken as in items (b), (c) and (d) of Figure 1.

Figure 1 : Effective bending span of stiffeners supported by web stiffeners (single skin construction)

Figure 2 : Effective bending span of stiffeners supported by web stiffeners (double skin construction)

Where the face plate of the stiffener is continuous along the edge of the bracket, the effective bending span is to be taken to the position where the depth of the bracket is equal to one quarter of the depth of the stiffener, see Figure 3.

Figure 3 : Effective bending span for local support members with continuous face plate along bracket edge

1.1.3 Effective shear span of stiffeners

The effective shear span, _shr in m, of stiffeners is to be measured as shown in Figure 4 for single skin structures and Figure 5 for double skin structures.

Figure 4 : Effective shear span of stiffeners supported by web stiffeners (single skin construction)

The effective shear span may be reduced for brackets fitted on either the flange or the free edge of the stiffener, or for brackets fitted to the attached plating on the side opposite to that of the stiffener.

If brackets are fitted at both the flange or free edge of the stiffener, and to the attached plating on the side opposite to the stiffener the effective shear span may be reduced using the longer effective bracket arm.

Regardless of support detail, the full length of the stiffener may be reduced by a minimum of s/4000 m at each end of the member, hence the effective shear span _shr, is not to be taken greater than:

Figure 5 : Effective shear span of stiffeners supported by web stiffeners (double skin construction)

For curved and/or long brackets (high length/height ratio), the effective bracket length is to be taken as the maximum inscribed 1:1.5 right angled triangle as shown in item (c) of both Figure 4 and Figure 5.

Where the face plate of the stiffener is continuous along the curved edge of the bracket, the bracket length to be considered for determination of the span point location is not to be taken greater than 1.5 times the length of the bracket arm as shown in Figure 6.

Figure 6 : Effective shear span for local support members with continuous face plate along bracket edge

1.1.4 Effect of hull form shape on span of stiffeners

For curved stiffeners, the span is defined as the chord length between span points to be measured at the flange for stiffeners with a flange, and at the free edge for flat bar stiffeners. The calculation of the effective span is to be in accordance with requirements given in [1.1.2] and [1.1.3].

1.1.5 Effective span of stiffeners supported by struts

The arrangement of stiffeners supported by struts is not allowed for ships over 120 m in length.

The span, of stiffeners supported by one strut fitted at mid distance of the primary supporting members is to be taken as 0.7₂.

In case where two struts are fitted at 1/3 and 2/3 length between primary supporting members, the span, of stiffeners is to be taken as 0.7₂.

₁ and ₂ are the spans defined in Figure 7 and Figure 8.

Figure 7 : Span of stiffeners with one strut

Figure 8 : Span of stiffeners with two struts

Figure 9 : Effective bending span of primary supporting member

Figure 10 : Effective shear span of primary supporting member

1.1.6 Effective bending span of primary supporting members

The effective bending span, _bdg, in m, of a primary supporting member without end bracket is to be taken as the length of the member between supports.

The effective bending span, _bdg, of a primary supporting member may be taken as less than the full length of the member between supports provided that suitable end brackets are fitted.

The effective bending span _bdg, in m, of a primary supporting member with end brackets is taken between points where the depth of the bracket is equal to half the web height of the primary supporting member as shown in item (b) of Figure 9. The effective bracket used to define these span points is to be taken as given in [1.1.8].

In case of brackets where the face plate of the member is continuous along the face of the bracket, as shown in items (a), (c) and (d) of Figure 9, the effective bending span _bdg, in m, is taken between points where the depth of the bracket is equal to one quarter the web height of the primary supporting member. The effective bracket used to define these span points is to be taken as given in [1.1.8].

For straight brackets with a length to height ratio greater than 1.5, the span point is to be taken to the effective bracket; otherwise the span point is to be taken to the fitted bracket.

For curved brackets, for span positions above the tangent point between fitted bracket and effective bracket, the span point is to be taken to the fitted bracket; otherwise, the span point is to be taken to the effective bracket.

For arrangements where the primary supporting member face plate is carried on to the bracket and backing brackets are fitted; the span point need not be taken greater than to the position where the total depth reaches twice the depth of the primary supporting member. Arrangements with small and large backing brackets are shown in items (e) and (f) of Figure 9.

For arrangements where the height of the primary supporting member is maintained and the face plate width is increased towards the support; the effective bending span may be taken to a position where the face plate breadth reaches twice the nominal breadth.

1.1.7 Effective shear span of primary supporting members

The effective shear span of the primary supporting member may be reduced compared to effective bending span, and taken between the toes of the effective brackets supporting the member, where the toes of effective brackets are as shown in Figure 10. The effective bracket used to define the toe point is given in [1.1.8].

For arrangements where the effective backing bracket is larger than the effective bracket in way of face plate, the shear span is to be taken as the mean distance between toes of the effective brackets as shown in item (f) of Figure 10.

1.1.8 Effective bracket definition

The effective bracket is defined as the maximum size of right angled triangular bracket with a length to height ratio of 1.5 that fits inside the fitted bracket. See Figure 9 for examples.

1.2 Spacing and load supporting breadth

1.2.1 Stiffeners

Stiffeners spacing, s, in mm, for the calculation of the effective attached plating of stiffeners is to be taken as the mean spacing between stiffeners and taken equal to, see Figure 11.

where:

b₁, b₂, b₃, b₄: Spacings between stiffeners at ends, in mm.

In general, the loading breadth supported by stiffener is to be taken equal to s.

1.2.2 Primary supporting member

Primary supporting member spacing, S, for the calculation of the effective attached plating of primary supporting members is to be taken as the mean spacing between adjacent primary supporting members, and taken equal to, see Figure 11.

where:

b₁, b₂, b₃, b₄ : Spacings between primary supporting members at ends.

In general, the loading breadth supported by a primary supporting member is to be taken equal to S.

1.2.3 Spacing of curved plating

For curved plating, the stiffener spacing, s or the primary supporting member spacing, S is to be measured on the mean chord between members.

Figure 11 : Spacing of plating

1.3 Effective breadth

1.3.1 Stiffeners

The effective breadth, b_eff, in mm, of the attached plating to be considered in the actual net section modulus for the yielding check of stiffeners is to be obtained from the following formulae:

• Where the plating extends on both sides of the stiffener:

  b_eff = 200ℓ, or

  b_eff = s

  whichever is lesser.

• Where the plating extends on one side of the stiffener (i.e. stiffeners bounding openings):

  b_eff = 100, or

  b_eff = 0.5 s

  whichever is lesser.

However, where the attached plate net thickness is less than 8 mm, the effective breadth is not to be taken greater than 600 mm.

The effective breadth, b_eff, in mm, of the attached plating to be considered for the buckling check of stiffeners is given in Ch 8, Sec 5, [2.3.5].

1.3.2 Primary supporting members

The effective breadth of attached plating, b_eff, in m, for calculating the section modulus and/or moment of inertia of a primary supporting member is to be taken as:

1.3.3 Effective area of curved face plate and attached plating of primary supporting members

The effective net area given in a) and b) is only applicable to curved face plates and curved attached plating of primary supporting members. This is not applicable for the area of web stiffeners parallel to the face plate.

The effective net area is applicable to primary supporting members for the following calculations:

• Actual net section modulus used for comparison with the scantling requirements in Ch 6.
• Actual effective net area of curved face plates, modelled by beam elements, used in Ch 7.
  • a) The effective net area, A_eff-n50, in mm², is to be taken as:
  • where:
  • A_eff-n50 = C_f t_f-n50 b_f
  • C_f : Flange efficiency coefficient taken equal to:
  • 
  • C_f1 : Coefficient taken equal to:

  • For symmetrical and unsymmetrical face plates,

    

  • For attached plating of box girders with two webs,

    C_f1 =

  • For attached plating of box girders with multiple webs,

    C_f1 =

  • β : Coefficient calculated as:
  • 
  • b₁ : Breadth, in mm, to be taken equal to:
  • For symmetrical face plates, b₁ = 0.5 (b_f – t_w-n50)
  • For unsymmetrical face plates, b₁ = b_f
  • For attached plating of box girders, b₁ = s_w – t_w-n50
  • s_w : Spacing of supporting webs for box girders, in mm.
  • t_f-n50 : Net flange thickness, in mm. For calculation of C_f and β of unsymmetrical face plates, t_f-n50 is not to be taken greater than t_w-n50.
  • t_w-n50 : Net web plate thickness, in mm.
  • r _f: Radius of curved face plate or attached plating, in mm, see Figure 12 at mid thickness.
  • b_f : Breadth of face plate or attached plating, in mm, see Figure 12.
  • b) The effective net area, in mm², of curved face plates supported by radial brackets, or attached plating supported by cylindrical stiffeners, is given by:
  • 
  • where:
  • s_r : Spacing of tripping brackets or web stiffeners or stiffeners normal to the web plating, in mm, see Figure 12.

Figure 12 : Curved shell panel and face plate

1.4 Geometrical properties of stiffeners and primary supporting members

1.4.1 Stiffener profile with a bulb section

The properties of bulb profile sections are to be determined by direct calculations.

Where direct calculation of properties is not possible, a bulb section may be taken equivalent to a built-up section. The net dimensions of the equivalent built-up section are to be obtained, in mm, from the following formulae.

t_w = t′_w

where:

h’_w, t’_w : Net height and thickness of a bulb section, in mm, as shown in Figure 13.

α : Coefficient equal to:

• 
• α = 1.0 for h′_w > 120

Figure 13 : Dimensions of stiffeners

1.4.2 Net elastic shear area of stiffeners

The net elastic shear area, A_shr, in cm², of stiffeners is to be taken as:

A_shr = d_shr t_w 10^–2

d_shr : Effective shear depth of stiffener, in mm, as defined in [1.4.3].

t_w : Net web thickness of the stiffener, in mm, as defined in Ch 3, Sec 2, Figure 2.

1.4.3 Effective shear depth of stiffeners

The effective shear depth of stiffeners, d_shr, in mm, is to be taken as:

d_shr = (h_stf − 0.5t_c-stf + t_p + 0.5t_c-pl) sinϕ_w

where:

h_stf : Height of stiffener, in mm, as defined in Ch 3, Sec 2, Figure 2.

t_p : Net thickness of the stiffener attached plating, in mm, as defined in Ch 3, Sec 2, Figure 2.

t_c-stf : Corrosion addition, in mm, of considered stiffener as given in Ch 3, Sec 3.

t_c-pl : Corrosion addition, in mm, of attached plate of the stiffener considered as given in Ch 3, Sec 3.

ϕ_w : Angle, in deg, as defined in Figure 14. ϕ_w is to be taken as 90 degrees if the angle is greater than or equal to 75 degrees.

1.4.4 Elastic net section modulus and net moment of inertia of stiffeners

The elastic net section modulus, Z, in cm³ and the net moment of inertia, I, in cm⁴ of stiffeners, is to be taken as:

Z = Z_stf sin ϕ_w

I = I_st sin² ϕ_w

where:

Z_stf : Net section modulus of the stiffener, in cm³, considered perpendicular to its attached plate, i.e. with ϕ_w = 90 deg.

I_st : Net moment of inertia of the stiffener, in cm⁴ , considered perpendicular to its attached plate, i.e. with ϕ_w = 90 deg.

ϕ_w : Angle, in deg, as defined in Figure 14. ϕ_w is to be taken as 90 degrees if the angle is greater than or equal to 75 degrees.

Figure 14 : Angle between stiffener web and attached plating

1.4.5 Effective net plastic shear area of stiffeners

The net plastic shear area, A_shr-pl, of stiffeners, in cm², which is used for assessment against impact loads is to be taken as:

A_shr-pl = A_shr

where:

A_shr : Net elastic shear area, in cm², as defined in [1.4.2].

1.4.6 Effective net plastic section modulus of stiffeners

The effective net plastic section modulus, Z_pl, of stiffeners, in cm³, which is used for assessment against impact loads, is to be taken as:

where:

f_w : Web shear stress factor, taken equal to:

• For flanged profile cross sections with n = 1 or 2, f_w = 0.75.
• For flanged profile cross sections with n = 0, f_w = 1.0.
• For flat bar stiffeners, f_w = 1.0.

n : Number of plastic hinges at end supports of each member, taken equal to: 0, 1 or 2.

A plastic hinge at end support may be considered where:

• The stiffener is continuous at the support.
• The stiffener passes through the support plate while it is connected at its termination point by a carling (or equivalent) to adjacent stiffeners.
• The stiffener is attached to an abutting stiffener effective in bending (not a buckling stiffener).
• The stiffener is attached to a bracket effective in bending. The bracket is assumed to be effective in bending when it is attached to another stiffener (not a buckling stiffener).

h_w : Depth of stiffener web, in mm, taken equal to:

• For T, L (rolled and built-up) profiles and flat bar, as defined in Ch 3, Sec 2, Figure 2.
• For L2 and L3 profiles as defined in Ch 3, Sec 2, Figure 3.
• For bulb profiles, to be taken as defined in [1.4.1].

β : Coefficient equal to:

• β=for L profiles without a mid-span tripping bracket,

  but not to be taken greater than 0.5.

• β = 0.5 for other cases.

A_f : Net cross sectional area of flange, in mm²:

• A_f = 0 for flat bar stiffeners.
• A_f = b_f t_f for other stiffeners.

b_f-ctr : Distance from mid thickness of stiffener web to the centre of the flange area:

• b_f-ctr = 0.5 (b_f − t_w) for rolled angle profiles and bulb profiles..
• b_f-ctr = 0 for T profiles.

h_f-ctr : Height of stiffener measured to the mid thickness of the flange:

• h_f-ctr = h_fw + 0.5 t_f for profiles with flange of rectangular shape except for L3 profiles.

  and for bulb profiles

• h_f-ctr = h_stf – d_e – 0.5 t_f for L3 profiles as defined in Ch 3, Sec 2, Figure 3.

d_e : Distance from upper edge of web to the top of the flange, in mm, for L3 profiles, see Ch 3, Sec 2, Figure 3.

f_b : Coefficient taken equal to:

• f_b = 0.8 for flanges continuous through the primary supporting member, with end bracket(s).
• f_b = 0.7 for flanges sniped at the primary supporting member or terminated at the support without aligned structure on the other side of the support, and with end bracket(s).
• f_b = 1.0 for other stiffeners.

t_f : Net flange thickness, in mm.

• t_f = 0 for flat bar stiffeners.
• For bulb profiles t_f is defined in [1.4.1].

1.4.7 Primary supporting member web not perpendicular to attached plating

Where the primary supporting member web is not perpendicular to the attached plating, the actual net shear area, in cm², and the actual net section modulus, in cm³, can be obtained from the following formulae:

• Actual net shear area:

  A_sh–n50 = A_sh–0–n50 sin ϕ_w for ϕ_w < 75°

  A_sh–n50 = A_sh–0–n50 for 75° ≤ ϕ_w ≤ 90°

• Actual net section modulus:

  Z_n50 = Z_perp–n50 sin ϕ_w for ϕ_w< 75°

  Z_n50 = Z_perp–n50 for 75° ≤ ϕ_w ≤ 90°

where:

Z_perp–n50 : Actual section modulus, in cm³, with its attached plating of the primary supporting member assumed to be perpendicular to the attached plating.

1.4.8 Shear area of primary supporting members with web openings

The effective web height, h_eff, in mm, to be considered for calculating the effective net shear area, A_sh-n50 is to be taken as the lesser of:

h_eff = h_w

h_eff = h_w3 + h_w4

h_eff = h_w1 + h_w2 + h_w4

where:

h_w : Web height of primary supporting member, in mm.

h_w1, h_w2, h_w3, h_w4 : Dimensions as shown in Figure 16.

Where an opening is located at a distance less than h_w/3 from the cross-section considered, h_eff is to be taken as the smaller of the net height and the net distance through the opening. See Figure 16.

Figure 16 : Effective shear area in way of web openings