OS-C501

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Offshore Standard DNV-OS-C501, November 2013 Sec.14 Calculation example: two pressure vessels – Page 200 Table 14-24 Elastic ply properties Property New component After 25 years in water No matrix cracks No matrix cracks With matrix cracks in ±15 plies ±15 plies E 1 fibre 23.7 GPa 21.3 GPa 21.3 GPa 21.3 GPa E 2 matrix 7.6 GPa 6.8 GPa 0.08 GPa 0.08 GPa ν 12 0.29 0.29 0.003 0.003 G 12 linear 3.2 GPa 2.9 GPa 0.03 GPa 0.03 GPa ±85 plies E 1 fibre 23.7 GPa 21.3 GPa 21.3 GPa 21.3 GPa E 2 matrix 7.6 GPa 6.8 GPa 6.8 GPa 0.08 GPa ν 12 0.29 0.29 0.29 0.003 G 12 linear 3.2 GPa 2.9 GPa 2.9 GPa 0.03 GPa 6.2.3 Using properties of the laminate in water addresses possible diffusion of water into the laminate. 6.2.4 A load-model factor of 1.05 is chosen, for the same reasons as described in [5.2.4]-[5.2.5]. 6.2.5 The following results are obtained from the stress and laminate theory analysis (without using a load factor): Table 14-25 Results for vessel for water without liner Laminate na: not applicable, since the matrix is cracked. 6.2.6 The component is checked for the pressure of: 1.48 MPa. After 25 years in water, with no matrix cracks Pressure MPa 1.48 1.48 Diameter mm 250 250 Thickness mm 6 6 Average axial stress MPa 15.8 15.8 Average hoop stress MPa 31.6 31.6 E axial GPa 11.02 6.22 E hoop GPa 16.34 14.0 ±15 o plies: ε 1 % 0.108 0.233 ε 2 % 0.168 0.217 ε 12 % 0.035 0.009 σ 1 MPa 27.0 49.5 σ 2 MPa 13.9 NA σ 12 MPa 1.01 NA ±85 o plies: ε 1 % 0.17 0.216 ε 2 % 0.10 0.234 ε 12 % 0.01 0.003 σ 1 MPa 39.9 45.9 σ 2 MPa 10.7 NA σ 12 MPa 0.35 NA 6.2.7 For each ply the local stress and strain components are applied in the failure criteria. With matrix cracks in ±15 plies and ±85 plies matrix cracks DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.14 Calculation example: two pressure vessels – Page 201 6.3 Matrix cracking (short term) at 1.48 MPa pressure (ref. Sec.6 [4]) 6.3.1 The criterion of Sec.6 [4.2.2] is not fulfilled and stress combinations should be taken into account. max i ∧ σ σ ik matrix ik / nk ∑ ≤ 10 n ≠ i ∧ matrix σ nk 6.3.2 Since there is interaction the design criterion from Sec.6 [4.2.3] shall be used: σ 6.3.3 The following values are selected for the water vessel without liner: Table 14-26 Short term values used for vessel for water without liner Partial factor Value Explanation Characteristic value of the local load effect of σ nk the structure (stress) in the direction n Characteristic value of the stress components to matrix cracking in the direction 2 Characteristic value of the stress components to matrix cracking in the direction 12 Partial load effect factor Partial resistance factor 6.3.4 Checking the design criterion in [6.3.2] we find that stresses in the ±15 plies are just acceptable, while no matrix cracking is predicted for the ±85 plies: for ±15 plies: for ±85 plies: γ . γ F 13.9 MPa 1.01 MPa 10.7 MPa 0.35 MPa 26.3 MPa 23.7 MPa 17.0 MPa 15.3 MPa 6.3.5 First matrix cracking anywhere in the structure is usually used as the criterion for onset of leakage. Matrix cracking determines the design pressure for this component. A maximum pressure of 14.8 bar is acceptable. 6.4 Matrix cracking under long-term static loads (ref. Sec.4 [3.4]) Sd . γ M . γ Rd . ∧ matrix 2 σ ∧ matrix 12 σ ⎛ ∑ ∧ ⎟ ⎟ ⎞ ⎜ σ nk n ⎜ matrix ⎝ σ nk ⎠ Ply stresses in +15 and +85 ply. See [6.2.5] For the new vessel For the vessel after 25 years See [4.1.4] and [4.4.5], [4.4.6] For the new vessel For the vessel after 25 years See [4.1.4] and [4.4.5], [4.4.6] γ F × γ M 1.4 From Sec.8 [2.4]: Maximum load is known with 0 COV Strain to failure COV ≤ 10% Target reliability level C Load-model factor γ Sd 1.05 Due to simplifications in analytical model, see [5.2.5]. Partial resistance-model factor γ Rd 1.15 Given in Sec.6 [4.2.1] 1.05 ⋅1.4 ⋅1.15 1.05 ⋅1.4 ⋅1.15 ⎛ ⎜ ⎝ 13 .9 MPa 23 .7 MPa ⎛ 1.01 MPa + ⎜ ⎝ 15 .3MPa 6.4.1 Matrix cracking under long-term static loads can be ignored if the stresses are below the level to initiate matrix cracking, and if the vessel can carry the loads with a fully cracked matrix according to Sec.4 [3.3.10] and [3.4.4]. The first point was shown in [6.3]. The second point is shown in [6.6], where all loads can be carried by a laminate with a fully degraded matrix. 2 ⎞ ⎟ ⎠ ⎛ 10 .7MPa ⎞ ⎜ ⎟ ⎝ 23 .7MPa ⎠ 2 ⎛ 0.35 MPa + ⎜ ⎝ 15 .3MPa 2 < 1 2 ⎞ ⎟ ⎠ 2 ⎞ ⎟ ⎠ = 1.00 = 0.76 DET NORSKE VERITAS AS
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