OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 118 For orthotropic materials the directions shall be the material axes. For isotropic materials the directions shall be along either the principal normal stresses or the principal shear stresses. This is a conservative design criterion. It has been chosen due to a lack of data and experience with ultimate failure under multiple stress conditions. Other design criteria may be used if experimental evidence for their validity can be given (see under [19]). Guidance note: A resistance-model factor γ Rd = 1.25 should be used with this design rule. The modelling factor shall ensure a conservative result with respect to the simplifications made regarding the treatment of combined loads. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 7.1.6 The characteristic strength σ nk for each of the stress components σ nk and the corresponding coefficients of variation COV n are defined as specified in Sec.4 [1.6] andSec.5 [1.6]. 7.1.7 The combined COV comb is defined according to one of the following alternatives. The second alternative is conservative with respect to the first. or where, COV comb = max n (COV n ) n refers to the directions 11, 22, 33, 12, 13, 23 COV n COV for stress component n COV for the combined stress components. COV comb 7.1.8 When two or several loads are combined, each characteristic stress component σ nk in direction n can be the result of several combined loads. In that case each stress component σ j nk , local load effect of the structure in direction n due to load j, shall be considered separately as an individual stress component to determine the COV. ⎛ j ⎞ ⎛ j ⎞ COVcomb = ⎜∑σ . COVn ⎟ / ⎜ ⎟ nk ∑σ nk ⎝ n ⎠ ⎝ n ⎠ or COV comb. = max n (COV n ) The design criterion has then the form: 7.1.9 The choice of the partial safety factors shall be based on the most conservative partial safety factors obtained when treating each stress component σ nk j , local response of the structure in direction n due to load j, as a single load. 7.1.10 The partial safety factors γ F and γ M shall be chosen as described in Sec.8 with a resistance COV equal to COV comb. 8 Buckling 8.1 Concepts and definitions ∧ COV γ . γ F comb Sd ⎛ ⎞ ⎛ = ⎜∑ σ nk . COVn ⎟ / ⎜∑ σ ⎝ n ⎠ ⎝ n 8.1.1 Elastic buckling phenomena are commonly considered in two main categories: . γ M . γ Rd . ∑ n ⎛ ∑ ⎜ σ j ⎜ ∧ ⎝ σ nk — Bifurcation buckling: Increasing the applied loading induces at first deformations that are entirely (or predominantly) axial or in-plane deformations. At a critical value of applied load (elastic critical load) a new mode of deformation involving bending is initiated. This may develop in an unstable, uncontrolled fashion without further increase of load (unstable post-buckling behaviour, brittle type of failure), or grow to large values with little or no increase of load (neutral post-buckling behaviour, plastic type of failure) or develop gradually in a stable manner as the load is increased further (stable post-buckling behaviour, ductile type of failure). — Limit point buckling: As the applied load is increased the structure becomes less stiff until the relationship between load and deflection reaches a smooth maximum (elastic critical load) at which the deformations increase in an uncontrolled way (brittle type of failure). j nk ⎞ ⎟ ⎟ ⎠ 2 nk ⎞ ⎟ ⎠ < 1 DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 119 8.1.2 Determination of the elastic critical load of a structure or member that experiences bifurcation buckling corresponds to the solution of an 'eigenvalue' problem in which the elastic buckling load is an 'eigenvalue' and the corresponding mode of buckling deformation is described by the corresponding 'eigenvector'. 8.1.3 Elastic buckling may occur at different levels: — global level for the structure; this involves deformation of the structure as a whole. — global level for a structural member; this is confined mainly to one structural member or element but involves the whole of that member or element. — local level for a structural member; only a part of a structural member or element is involved (e.g. local buckling of the flange of an I-beam or of a plate zone between stiffeners in a stiffened plate). 8.1.4 Resistance of a structural member to elastic buckling is normally expressed as a critical value of load (applied force, or stress resultant induced in a member) or as a critical value of a nominal average stress (e.g. axial or shear force divided by area of cross-section). However, such resistance may also be expressed as a critical value of mean strain induced at a cross-section in a member. 8.1.5 Initial geometrical imperfections (out-of-straightness, out-of-roundness, or eccentricity of applied loading) that lead to a situation where compressive forces in a structural part are not coincident with the neutral axis of that part may influence significantly the buckling behaviour. An idealised structure without such imperfections is referred to as “geometrically perfect”. 8.1.6 Bifurcation buckling is essentially a feature of geometrically perfect structures. Geometrical imperfections generally destroy the bifurcation and lead to a situation where bending deformations begin to grow as the load is increased from zero. An elastic critical load may still be associated with the structure, and may provide a good indication of the load level at which the deformations become large. However, some structures with unstable post-buckling behaviour are highly sensitive to geometric imperfections. In the presence of imperfections, such structures may experience limit point buckling at loads that are significantly lower than the elastic critical load of the geometrically perfect structure. 8.1.7 Elastic buckling deformation of a geometrically perfect or imperfect structure may trigger other failure mechanisms such as fibre failure (compressive or tensile) or matrix cracking. 8.1.8 The presence of failure mechanisms such as matrix cracking or delamination may influence significantly the buckling behaviour of structures and structural members. 8.2 General requirements 8.2.1 Resistance of structures or structural members in the presence of buckling may be determined by means of testing or analysis. 8.2.2 The effects of initial geometrical imperfections shall always be evaluated for structures or structural members being checked for buckling. 8.2.3 Assumptions regarding geometrical imperfections shall wherever possible be based on — knowledge of production methods and corresponding production tolerances — knowledge of how imperfections of given shape and magnitude influence the structural behaviour, and — experience from previous measurements and tests. If an adequate knowledge base does not exist, a programme of measurement and/or testing shall be agreed to demonstrate that the design assumptions are justified. 8.3 Requirements when buckling resistance is determined by testing 8.3.1 If the resistance of a structure or structural member is determined by testing, the requirements in 302 to 306 shall be satisfied. Testing shall be done as described in Sec.10 'Component Testing'. 8.3.2 Sufficient tests shall be performed to provide statistical data so that both the mean resistance and the COV may be determined. 8.3.3 The structures or members tested shall incorporate the least favourable geometrical imperfections that are possible within the specified production tolerances. Alternatively, the structures or structural members tested may incorporate a representative range of geometrical imperfections that may arise in the intended production process; however, in such a case it must be demonstrated that the imperfections considered are representative in terms of their distributions of shape and amplitude. 8.3.4 The design criterion shall normally be applied at the level of overall load for a structure, or either force (stress resultant) or nominal stress or strain (averaged over the member cross-section) for a structural member. DET NORSKE VERITAS AS
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