** Direct Strength Analysis**

**7.4 Analysis Criteria**

7.3.2.3 Three load cases each corresponding to a dominant load parameter are to be considered for the strength assessment. The dominant load parameters are given below:

i. Wave Bending Moment (Hogging) – Head Sea ii. Wave Bending Moment (Sagging) – Head Sea iii. Pressure at Waterline – Beam Sea

For each load case the most probable extreme value of the dominant load component should be calculated considering the 3 hours exposure. The other load components are to be calculated using equivalent design wave concept given in section 7.3.2.5.

7.3.2.4 The extreme values for each dominant load parameter is evaluated using the spectral analysis based approach. In this approach the response amplitude operators (RAO’s) should be calculated for the range of frequencies corresponding to a wavelength of LR/5 to 5LR, where LR is the rule length. Care should be taken to include the possible peak in the RAO.

7.3.2.5 Equivalent Design Wave (EDW) for each load case is the sinusoidal wave of such amplitude and frequency that produces the most probable extreme value of the dominant load component corresponding to the load case (see 7.3.2.3).

The amplitude,

### ζ

_{W}, of the each EDW is given by:

### Most Probable Extreme Value Maximum magnitude of RAO ζ =

*W*

The frequency of the each EDW is the frequency at which the peak of the corresponding dominant load component RAO occurs.

7.3.2.6 Values of other load components, i.e. other than the dominant load component, are to be obtained by a hydrodynamic analysis carried out using a sinosidal wave of the amplitude and frequency of the equivalent design wave determined as per 7.3.2.5. The snapshot values that occur at the wave position when the dominant load reaches its peak value are to be used to define the load set for each load case.

**7.3.3 Structural weight **

7.3.3.1 Effect of the hull structure weight due to gravity is to be included. The dynamic load
components due to various acceleration from self-weight are to be ignored. Standard density of steel
will be taken as 7.85 t/m^{3}.

The results of the structural analysis are to satisfy the criterion for yielding strength, buckling strength and deflection, as given in 7.4.2 to 7.4.4 below.

**7.4.2 Yielding strength assessment **
7.4.2.1 Reference stresses

Based on the results of the FE analyses, the Reference stress for various structural elements is to be taken as :

− Von Mises equivalent stress at centre of a plane element in case of shell or membrane elements

− Combined axial + bending stress in case of a beam element, and

− Axial stress in case of a bar element

Where, Von Mises equivalent stress,

### σ

_{eq}, is given by :

2 2

2 _{x} _{y} _{y} 3 _{xy}

*x*

*eq* σ σ σ σ τ

σ = − + +

σ_{x}, σ_{y}: Element normal stresses,
τxy: Element shear stress
7.4.2.2 Allowable stress

The Reference stresses for steel structures are not to exceed 235/*k *N/mm^{2}, where *k *is the material
factor as per Chapter 2, Cl. 2.2.

For aluminum structures, the Reference stresses are not to exceed 200/*k**a** *N/mm^{2}, where *k**a** *is the
material factor as per Chapter 2, Cl. 3.2. * *

**7.4.3 Local buckling strength assessment **

7.4.3.1 The requirements in respect of buckling strength assessment described in this Section are independent of that given in 1.1.3, which relate to determination of the scantlings as per prescriptive Rules.

Buckling strength assessment is to be carried out for the plating and stiffened panels in areas where high compressive stresses are developed. The assessment is to be carried out for such panels in longitudinal hull girder structural members, primary supporting structural members and transverse bulkheads – i.e. deck, bottom & side shell, double bottom, double side, transverse and longitudinal bulkhead structures and transverse and vertical web frames, floors, girders, stringers, etc.

The buckling assessment is to be based on the net thickness obtained by deducting the full corrosion addition thickness from the gross scantlings provided.

The method used for buckling analysis is to be based on non-linear analysis techniques, or equivalent, which predict the complex behaviour of stiffened and un-stiffened panels subjected to simultaneous application of bi-axial compression/tension, shear and lateral pressure. The method is also to be capable of taking into account the following to satisfaction of IRS :

(a) non- linear geometrical behaviour (b) inelastic material behaviour

(c) initial deflections - geometrical imperfections/out-of flatness (d) welding residual stresses

(e) interactions between buckling modes and structural elements; plates, stiffeners, girders etc.

(f) boundary conditions as per section 7.4.3.3

The utilisation factor,

### η

, is used as a measure of safety margin available against buckling failure.For combined loads, the utilisation factor,

### η

, is defined as the ratio between the applied equivalent load and the equivalent membrane loads which would result in reaching the maximum buckling capacity of the panel.A structure is considered to have an acceptable buckling strength when

### η ≤ 1.0

.7.4.3.2 Panel stresses to be considered

The buckling assessment is to be based on membrane stress evaluated at the centroid of the plate elements. Where shell elements are used, stresses at the mid plane of the element are to be used for the buckling assessment.

For the purpose of buckling analyses, the relevant stress components in each panel are to be obtained according to the following procedure :

1) When the mesh model differs from the elementary plate panel geometry, the stresses σ*x*

, σ*y* and τ acting on an elementary plate panel are to be evaluated by extrapolation
and/or interpolation using the element stresses in the surrounding meshes.

2) Where the membrane the stresses σx

* and σy

* are both compressive stresses, they may be reduced for the purpose of buckling assessment to take account of the Poisson effect, the reduced stresses

### σ

_{x}and

### σ

_{y}, are given by :

### (

^{*}

^{.}

^{*}

### ) ^{/ (1}

^{2}

^{)}

*x* *x* *y*

### σ = σ − µ σ − µ

### (

^{*}

^{.}

^{*}

### ) ^{/ (1}

^{2}

^{)}

*y* *y* *x*

### σ = σ − µ σ − µ

Where, µ is the P ois on’s ratio for the material3) determine stress distributions along edges of the considered buckling panel by introducing proper linear approximation as shown in Fig 7.4.3.1

4) calculate edge factor Ψ

**Figure 7.4.3.1 : Stresses of Panel for buckling assessment **

7.4.3.3 Boundary conditions

Buckling load cases are to be applied suitably to the buckling panel under evaluation, depending on the stress distribution and geometry. In general simply supported boundary conditions of all edges will be applied.

**7.4.4 Deflection of primary girders **

The maximum relative deflection of primary girders is not to exceed the following criteria:

max

### 325

*l*

*i*

### δ =

where:

δmax: Maximum relative deflection [mm]

*l**i** *: Span of primary girder [mm]