OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 120 8.3.5 The design criterion for buckling when the resistance is determined by testing is as follows: where, F F ∧ buckling γ F γ Sd γ Mbuckle γ . γ . F < characteristic value of the load, or induced stress resultant, or nominal stress or strain characteristic value of the test load when the component buckles partial load or load effect factor partial load or load effect model factor partial resistance factor γ Rdbuckle partial resistance-model factor. 8.3.6 The partial factors shall be determined according to Sec.10 [2] 'Component Testing'. 8.4 Requirements when buckling is assessed by analysis F Sd Rdbuckle 8.4.1 If the resistance of a structure or structural member is determined by analysis, the requirements under [8.4.2] to [8.4.15] shall be satisfied. 8.4.2 Buckling analysis may be carried out by analytical or numerical methods as described in Sec.9 [11]. Such analyses may be applied to either geometrically perfect or imperfect structures. Analytical methods are mainly confined to geometrically perfect structures, except for some simple structural members with imperfections of simple shape. 8.4.3 When performing a buckling analysis the boundary conditions shall be evaluated carefully. γ 8.4.4 If in any buckling analysis the applied load is higher than the load that would introduce partial damage in the structure, e.g. matrix cracking or delaminations, the buckling calculations shall take this partial damage into account. 8.4.5 For structures or structural elements that are expected to exhibit bifurcation buckling, an analysis to determine the elastic critical load (or critical stress or strain) shall normally be carried out as described in Sec.9 [11.2.2] or Sec.9 [11.3.2], before more complex non-linear analysis is performed. The purpose of this is to establish: — whether it may be acceptable to perform only geometrically linear analysis as described in Sec.9 [11.2.5] (see also [8.4.11] below) — whether the structure is clearly under-dimensioned against buckling (if the applied load clearly exceeds, or is close to, the elastic critical load) — in the case of finite element analysis, the required fineness of mesh for a more complex buckling analysis. 8.4.6 Analytical formulae for elastic buckling shall be checked carefully if they contain empirical safety factors or not and if they are based on structures with or without imperfections. Without this knowledge analytical formulas should not be used. 8.4.7 Except in the case of analysis for elastic critical loads (or elastic critical stresses or strains), the analysis model shall incorporate the least favourable geometrical imperfections that are possible within the specified production tolerances. Alternatively, a series of analyses may be performed incorporating a representative range of geometrical imperfections that may arise in the intended production process, these may then be combined with statistical information about the imperfections that arise in practical production, in terms of their distributions of shape and amplitude. 8.4.8 If imperfections are not directly included in the buckling analysis as described in [8.4.7], their effects shall be evaluated by other means such as supplementary analysis or testing. However, if it is demonstrated that the eccentricities or local bending moments induced by the least favourable geometrical imperfections are less than 10% of the corresponding quantities resulting from other features inherent in the structure or its loading, such as out-of-plane loads, the geometrical imperfections may be neglected. 8.4.9 In assessing buckling-induced failure, the design criteria shall normally be applied at the level of local stress or strain state, considered at all points in the structure. The criteria related to fibre failure, matrix cracking, delamination, yield and ultimate failure given under [3], [4], [5], [6] and [7] shall be applied as appropriate. For sandwich structures the special criteria given under [16] shall be applied in addition. Additionally the displacement criterion given under [9] shall be applied both globally and locally to ensure that there are no excessive buckling displacements. Mbuckle buckling 8.4.10 To obtain the resistance quantities required for the checks in [8.4.9], geometrically non-linear analysis ∧ F . γ DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 121 shall be performed as described in Sec.9 [11]. Reduction of mechanical properties due to local failure such as matrix cracking or delamination shall be taken into account. 8.4.11 If the condition described in Sec.9 [11.2.5] is satisfied, the analysis may be performed without geometric non-linearity provided the load effect modelling factor is increased as specified. In such a case the geometrical imperfections must still be included. 8.4.12 Sec.9 [11.2.4] provides an approximate way of estimating the combined influence of imperfections and in-plane or axial loading, based on the use of linear analysis. 8.4.13 The calculated resistance is to be considered as a mean strength from a probabilistic point of view. 8.4.14 Variability to the mean strength is introduced by: — uncertainties in the stiffness parameters that are used in the buckling calculations — uncertainties in geometric parameters — uncertainties in size of imperfections and how imperfections are considered. 8.4.15 To reflect the uncertainty introduced by geometrical imperfections, the partial load effect model factor for checks on failure mechanisms referred to in [8.4.8] shall be based on a COV of 15% unless lower values can be justified. 9 Displacements 9.1 General 9.1.1 Maximum displacements shall be defined as extreme values with a small probability of being exceeded and without uncertainties or tolerances associated with them. The following design criterion shall be fulfilled: where, d n d spec γ F γ Sd, γ .γ characteristic value of the local response of the structure (here displacement) specified requirement on maximum displacement partial load effect factor load model factor Displacements may also be defined as maximum strains, curvatures etc. d F Sd . < n 9.1.2 Displacements shall be calculated as described in Sec.9 or shall be measured directly. A reduction of stiffness of the structure due to material non-linearity or due to time dependent effects on the elastic constants shall be considered. Plastic deformations due to permanent static or fatigue loads shall also be considered. 9.1.3 The failure type (Sec.2 [3.4]) associated with a displacement requirement shall be decided on an individual basis. Guidance note: If the displacement requirement requires that: - the structure should never touch the neighbouring structure locally, the failure type would be brittle - the structure can touch the neighbouring structure locally at low loads, the failure type would be plastic - the structure can touch the neighbouring structure locally at loads that may cause some permanent damage the failure type would be ductile. If the structures may touch each other slightly, the corresponding loads and possible damage effects shall be analysed. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 9.1.4 If the criterion is used in combination with a linear non-degraded analysis according to Sec.9 [2.4], all strains and stresses in fibre direction above the level to initiate matrix cracking shall be multiplied by the analysis factor γ a from Sec.9 [3.2]. d spec DET NORSKE VERITAS AS
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