OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 106 3.1.8 Regardless of the analysis method used, these laminates should always be analysed with non-degraded matrix dominated elastic constants, i.e., E 2 , G 12 , n 12 . 3.2 Fibre failure at the ply level 3.2.1 For single loads, the maximum strain design criterion is given as: where: ε nk ̂ γ F γ Sd, γ M γ Rd, Characteristic value of the local response of the structure (strain) in the fibre direction n Characteristic value of the axial strain to fibre failure Partial load effect factor Partial load-model factor Partial resistance factor Partial resistance-model factor, given in [3.2.2] (below). 3.2.2 The selection of the resistance model factor γ Rd depends on the choice of structural analysis method: — if a linear analysis with non-degraded properties is chosen according to Sec.9 [2.4], then γ Rd = γ A , as described in Sec.9 [3.2.2] — in all other cases γ Rd = 1.0. 3.2.3 The maximum strain criterion shall be checked in all n directions parallel to the fibres, and for tensile and compressive strains. 3.2.4 εˆ k fibre is the time dependent characteristic strength of the ply in fibre direction. It shall be determined according to Sec.4 [3]. One value for one fibre and weave type. 3.2.5 For N combined loads, with combination j being the worst combination (see Sec.3 [11.2]) the maximum strain design criterion is given by: where, e i nk γ Sd ⎡ j . ⎢γ F . ε ⎣ γ . γ ∧ fiber k Characteristic value of the local response of the structure (strain) in the fibre direction - n - due to load - i - ˆ ε fibre k Characteristic value of the axial strain to fibre failure γ i F Partial load effect factor for load - i - Ψ i Combination factor for load - i - γ j F , Partial load effect and resistance factors for load - j - γ M Partial resistance factor γ Rd Partial resistance-model factor, given in [3.2.2] 3.2.6 The partial resistance factor γ M shall be the largest value for all load strength combinations - j -. Guidance note: In the equation above, it is important to see that the partial resistance factor γ j M , corresponding to the load j alone, is used as the common partial resistance factor. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 3.3 Fibre failure check using a modified Tsai-Wu criterion j nk F Sd +∑ i≠ j . ε nk i F ε < γ . γ 3.3.1 In many cases the maximum fibre strain criterion is not available in commercial software packages. As an alternative the Tsai-Wu criterion may be used with modified input parameters as described here. This approach was developed by FiReCo AS. 3.3.2 If [3.1.5] is relevant, this criterion may be used to check simultaneously for fibre failure and laminate failure due to high shear in the plies. i nk M γ . ε . Ψ i Rd ∧ fiber k ⎤ ε ⎥ < ⎦ γ M . γ Rd DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.6 Failure mechanisms and design criteria – Page 107 3.3.3 The Tsai-Wu criterion is described in 3-D as: in 2-D: with R = γ F · γ Sd · γ m · γ Rd R 2 + R + R R 2 2 2 2 2 2 2 ( F11σ 1 + F22σ 2 + F33σ 3 + F12σ 12 + F13σ 13 + F23σ 23 ) 2 ( 2H12σ 1σ 2 + 2H13σ 1σ 3 + 2H 23σ 2σ 3 ) ( Fσ + F σ + F σ ) < 1 1 1 2 2 3 3 2 2 2 ( F σ + F σ + F σ + H σ σ ) + R ( Fσ + F σ ) < 1 11 1 22 2 12 12 2 12 1 2 1 1 2 2 F 11 = ∧ σ 1t 1 ∧ σ 1c , F 22 = ∧ σ 2t 1 ∧ σ 2c , F 33 = ∧ σ 3t 1 ∧ σ 3c 1 1 F 12 = , F ∧ 13 = , ∧ 2 2 σ 12 σ 13 F 23 = 1 ∧ 2 23 σ F 1 = ∧ σ 1 1t 1 − ∧ σ 1c , F 2 = ∧ σ 1 2t − ∧ σ 1 2c , F 3 = ∧ σ 1 3t − ∧ σ 1 3c * H12 * H13 H 12 = , H 13 = , F F F F 11 22 11 33 H = * 23 H F 22 23 F 33 where, n σ∧ n σ nt ∧ σ nc ∧ the co-ordinate system is the ply co-ordinate system, where n refers to the directions 1, 2, 3, 12, 13 and 23 characteristic value of the local load effect of the structure (stress) in the direction n characteristic tensile strength in the direction n characteristic compressive strength in the direction n σ nk characteristic shear strength in the direction nk γ F partial load effect factor γ Sd, partial load-model factor γ M partial resistance factor γ Rd partial resistance-model factor, for values see [3.3.4]. H 12 H 13 H 23 * * * 3.3.4 The interaction parameters , , should be determined experimentally for each material. In that case γ Rd = 1.0. Alternatively values between 0 and -0.5 may be chosen as a default, in that case γ Rd = 1.15. 3.3.5 Since Tsai-Wu criterion is here only used to check for fracture of the laminate (see [3.1.5]) and small matrix cracks are acceptable, strength properties should be taken as described below. Characteristic strengths as described in Sec.4 [2.4] should always be used. ∧ σ ∧ σ 1t 1c ∧ σ ∧ σ ∧ σ 2t 2c 3t ∧ σ 3c E ∧ 2 = σ E 1 E ∧ 2 = σ E 1 1t 1c tensile ply strength in fibre direction, as defined in Sec.4. compressive ply strength in fibre direction, as defined in Sec.4. modified in-plane tensile ply strength transverse to the fibres. modified in-plane compressive ply strength transverse to the fibres. tensile through thickness ply strength in fibre direction, as defined in Sec.4. compressive through thickness ply strength in fibre direction, as defined in Sec.4. DET NORSKE VERITAS AS
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