Longitudinal Strength
D. Design Stresses 1. General
Design stresses for the purpose of this rule are global load stresses, which are acting:
– as normal stresses FL in ship's longitudinal direction : – for plates as membrane stresses
– for longitudinal profiles and longitudinal girders in the bar axis – shear stresses JL in the plate level
The stresses FL and JL are to be considered in the formulas for dimensioning of plate thicknesses (Section 6, B.1. and C.1.
and Section 12, B.1.), longitudinals (Section 9, B.2.) and grillage systems (Section 8, B.8. and Section 10, E.2.).
The calculation of the stresses can be carried out by an analysis of the complete hull. If no complete hull analysis is carried out, the most unfavourable values of the stress combinations according to Table 5.3 are to be taken for FL and JL respectively.
The formulae in Table 5.3 contain FSW, FWV, FWH, FST and FWT according to 2. and JSW, JWV, JWH, JST and JWT according to 3. as well as:
fF = weighting factor for the simultaneousness of global and local loads
= 0,8 for dimensioning of longitudinal structures according to Sections 3 and 6 to 12
=
for fatigue strength calculations according to Section 20 fQ = probability factor according to Table 4.2
fQmin= 0,75 for Q = 10-6 Note
fQ is a function of the planned lifetime. For a lifetime of n > 20 years, fQ may be determined by the following formulae for a straight-line spectrum of seaway induced stress ranges :
fQ =
For greatest vertical wave bending moment:
F’WV= J’WV=
For smallest vertical wave bending moment : F’WV=
J’WV=
C =
Note
For the preliminary determination of the scantlings, it is generally sufficient to consider load case 1, assuming the simultaneous presence of FL1a and JL1b, but disregarding stresses due to torsion.
The stress components (with the proper signs: tension positive, compression negative) are to be added such, that for FL and JL extreme values are resulting.
1.1 Buckling strength
For structures loaded by compression or shear forces, sufficient buckling strength according to Section 3, F. is to be proved.
1.2 Permissible stresses
The equivalent stress from FLand JLis not to exceed the following value :
FV = [N/mm2]
L1a,b = Load caused by vertical bending and static torsional moment.
L2a,b = Load caused by vertical and horizontal bending moment as well as static torsional moment.
L3a,b = Load caused by vertical and horizontal bending moment as well as static and wave induced torsional moment 1.3 Structural design
1.3.1 In general, longitudinal structures are to be designed such, that they run through transverse structures continuously.
Major discontinuities have to be avoided.
If longitudinal structures are to be staggered, sufficient shifting elements shall be provided.
1.3.2 The required welding details and classifying of notches result from the fatigue strength analysis according to Section 20.
Within the upper and lower hull girder flange, the detail categories for the welded joints (see Table 20.3) shall not be less than
)FR min = [N/mm2]
MWVhog, MWVsag = vertical wave bending moment for hogging and sagging according to B.3.1 n = design lifetime of the ship
20 [years]
≥
2. Normal stresses in the ship's longitudinal direction 2.1 Normal stresses from vertical bending moments 2.1.1 statical from MSW :
FSW = [N/mm2]
MSW = still water bending moment according to A.5. at the position x/L 2.1.2 dynamical from MWV :
FWV = [N/mm2]
2.2 Normal stresses due to horizontal bending moments dynamical from MWH :
FWH = ! [N/mm2]
MWH = horizontal wave bending moment according to B.3.3 at the position x/L
Iz = moment of inertia[m4] of the transverse ship section considered around the vertical axis at the position x/L
ey = horizontal distance of the structure considered from the vertical, neutral axis [m]
ey is positive at the port side, negative at the starboard side 2.3 Normal stresses from torsion of the ship's hull
When assessing the cross sectional properties the effect of wide deck strips between hatches constraining the torsion may be considered, e.g. by equivalent plates at the deck level having the same shear deformation as the relevant deck strips.
2.3.1 statical from MSTmax:
For a distribution of the torsional moments according to B.2.2.2, the stresses can be calculated as follows :
FST = [N/mm2]
MSTmax = max. static torsional moment according to B.2.2.2 see 2.3.2.
For other distributions the stresses have to be determined by direct calculations.
2.3.2 dynamical from MWTmax:
FWT = [N/mm2]
MWTmax = according to B.3.5
= for 0 # < 0,25
C
Tor= for 0,25 # # 0,65
= for 0,65 # # 1
IT = sectorial inertia moment [m6] of the ship's transverse section at the position X/L
Ti = sectorial coordinate [m2] of the structure considered
8 = warping value
= [l/m]
IT = torsional moment of inertia [m4] of the ship's transverse section at the position x/L e = Euler number (e = 2,718...)
a =
Rc = characteristical torsion length [m]
= for < 5,284
= for > 5,284
Cc = for 0 # # 0,4 and 0 # # 0,4
= 1 for 0,4 # # 0,55
= for 0,55 < # 1
xA = 0 for ships without cargo hatches
= distance [m] between the aft end of the length L and the aft edge of the hatch forward of the engine room front bulkhead on ships with cargo hatches, see also Fig. 5.13
3. Shear stresses
Shear stress distribution shall be calculated by calculation procedures approved by BKI. For ships with multi-cell transverse cross sections (e.g. double hull ships), the use of such a calculation procedure, especially with non-uniform distribution of the load over the ship's transverse section, may be stipulated.
3.1 Shear stresses due to vertical shear forces
For ships without longitudinal bulkheads or with two longitudinal bulkheads,the distribution of the shear stress in the shell and in the longitudinal bulkheads can be calculated with the following formulae:
statical from QSW : JSW =
dynamical from QWV : JWV =
Sy(z) = first moment of the sectional area considered [m3], above or below, respectively, the level z considered, and related to the horizontal, neutral axis
t = thickness of side shell or longitudinal bulkhead plating[mm] at the section considered
" = 0 for ships having no longitudinal bulkhead If 2 (two) longitudinal bulkheads are arranged :
" = 0,16 + 0,08 for the longitudinal bulkheads
= 0,34 - 0,08 for the side shell
As = sectional area of side shell plating [m2] within the depth H
AL = sectional area of longitudinal bulkhead plating [m2] within the depth H.
For ships of normal shape and construction, the ratio S/Iy determined for the midship section can be used for all sections.
3.2 Shear stresses due to horizontal shear forces 3. is to be applied to correspondingly.
3.3 Shear stresses due to torsional moments statical from MSTmax :
For a distribution of torsional moments according to B.2.2.2, the stresses can be calculated as follows:
[N/mm2]
CTor = according to D.2.3.1 MSTmax = according to B.2.2.2 MWTmax = according to B.3.5 IT = according to D.2.3.1
STi = statical sector moment [m4] of the structure considered ti = thickness[mm] of the plate considered
For other distributions the stresses have to be determined by direct calculations.
dynamical from MWTmax:
The permissible still water bending moments for any section within the length L are to be determined by the following formulae:
MSW= MT S MWV [kNm]
MWV see B.3.1
For harbour- and offshore terminal conditions the wave loads may be multiplied with the following factors:
— harbour conditions (normally) : 0,1
WD(a), WB(a) = actual section modulus in the deck or bottom, respectively
FD, F’D = longitudinal bending stress [N/mm2] for the ship’s upper hull girder flange