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Offshore Standard DNV-OS-C501, November 2013 Sec.14 Calculation example: two pressure vessels – Page 204 6.14 Summary evaluation 6.14.1 Summarising as follows: — Impact resistance should be evaluated experimentally if the vessel may be exposed to impact loads. Experiments should show that possible impact loads will not cause fibre damage. — The water vessel passed all other requirements for service at 14.8 bar. — The matrix dominated ply strength is the design limiting factor for this vessel. — Component testing is recommended to establish the level of leakage instead of using the matrix cracking criterion. This approach would utilise the vessel much better. 7 Linear analysis of vessel for water without liner 7.1 General 7.1.1 This method uses a linear analysis with non-degraded properties instead of a non-linear failure analysis in [6]. 7.1.2 In the present section we assume that leakage will occur if matrix cracking is present in at least one of the plies. Therefore, in the context of the water vessel we can apply the linear failure analysis with nondegraded material properties (Sec.9 [2.4]). In this case we have to modify the criterion for fibre failure (see Sec.9 [3.2]) Guidance note: It is possible to apply a more realistic requirement for leakage, i.e. that leakage will not occur until matrix cracking is present in all the plies of the laminate. In this case, a (non-linear) progressive failure analysis must be performed as shown in [6]. ---e-n-d---of---G-u-i-d-a-n-c-e---n-o-t-e--- 7.1.3 Most parts of this analysis are identical to the one in [6]. Only the differences are shown here. 7.2 Analysis procedure (ref. Sec.9 [2]) 7.2.1 The elastic properties without matrix cracking are needed here and were calculated in [4.1.4]. The values are different at the beginning and the end of the life of the component. Table 14-28 Elastic properties Property New component After 25 years in water E 1 fibre 23.7 GPa 21.3 GPa E 2 matrix 7.6 GPa 6.8 GPa ν 12 0.29 0.29 G 12 linear 3.2 GPa 2.9 GPa 7.2.2 The following results are obtained from the stress and laminate theory analysis (without using a load factor): Table 14-29 Results for vessel for water without liner General: After 25 years in water, no matrix cracks Pressure MPa 1.48 Diameter mm 250 Thickness mm 6 Average axial stress MPa 15.8 Average hoop stress MPa 31.6 E axial GPa 11.02 E hoop GPa 16.34 ±15 o plies: ε 1 % 0.108 ε 2 % 0.168 ε 12 % 0.035 σ 1 MPa 27.0 σ 2 MPa 13.9 σ 12 MPa 1.01 DET NORSKE VERITAS AS
Offshore Standard DNV-OS-C501, November 2013 Sec.14 Calculation example: two pressure vessels – Page 205 Table 14-29 Results for vessel for water without liner (Continued) General: After 25 years in water, no matrix cracks ±85 o plies: ε 1 % 0.17 ε 2 % 0.10 ε 12 % 0.01 σ 1 MPa 39.9 σ 2 MPa 10.7 σ 12 MPa 0.35 The results are identical with the non-linear analysis (see [6.2.5]). 7.2.3 For each ply the local stress and strain components are applied in the design criteria. 7.3 Matrix cracking (short term) (ref. Sec.6 [4]) 7.3.1 The analysis for matrix cracking is the same as in [6.3]. Matrix cracking determines the design pressure for this component. 7.4 Matrix cracking under long-term static loads (ref. Sec.4 [3.4]) 7.4.1 The analysis for matrix cracking is the same as in [6.4]. 7.5 Matrix cracking under long-term cyclic fatigue loads (ref. Sec.4 [3.9]) 7.5.1 The analysis for matrix cracking is the same as in [6.4]. 7.6 Fibre failure – short-term (ref. Sec.6 [3]) 7.6.1 Fibre failure can be analysed the same way as in the progressive failure analysis in [6.7]. This method requires a stress analysis with degraded matrix properties. Since checking for matrix cracks in [7.3] requires an analysis with non-degraded properties the structure is analysed two times. This is easily done in this example, but may be time-consuming for more complicated structures. An alternative method is given here, where fibre failure is checked by the same analysis with non-degraded properties as is used for checking matrix cracking. 7.6.2 The short-term static design criterion for fibre failure on the ply level is given by: where, ε nk ˆ ε fibre k γ . γ ∧ fiber k characteristic value of the local response of the structure (strain) in the fibre direction n characteristic value of the axial strain to fibre failure. 7.6.3 The following values are selected for the water vessel without liner: F Sd . ε nk ε < γ . γ Table 14-30 Short term values used for vessel for water without liner Partial factor Value Explanation Characteristic fibre strain to failure ˆ ε fibre k 1.69% For the new vessel 0.87% For the vessel after 25 years See [4.1.4] and [4.4.5], [4.4.6] Partial load effect factor γ F x γ M 1.18 From Sec.8 [2.4]: Partial resistance factor Maximum load is known with 0 COV Strain to failure COV ≤ 5% Target reliability level E Load-model factor γ Sd 1.05 Due to simplifications in analytical model, see [5.2.5] Partial resistance-model factor γ Rd γ a Non-degraded properties are used in the analysis 7.6.4 To find the model factor γ a the procedure in Sec.9 [3.2] shall be used. The laminate's Young's modulus in each fibre direction shall be determined for non-degraded properties and for properties with matrix cracking. We use the ply properties for the laminate after 25 years in water as a basis for the laminate calculations (from [4.1.4]): M Rd DET NORSKE VERITAS AS
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OS-C501

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