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/1/ ISO 2394, General principles on reliability for structures, Second edition 1998-06-01

/2/ API RP 2A Recommended Practice for Planning, Designing and Constructing Fixed Offshore Platforms – Working Stress Design, Errata and supplement 3 October 2007

/3/ EN 1990, Eurocode - Basis of structural design, April 2002

/4/ EN 1993-1-1 Eurocode 3 Design of steel structures. Part 1-1 General rules and rules for buildings /5/ EN 1993-1-5, Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements, October

2006

/6/ EN 1993-1-6, Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell Structures, February 2007

/7/ EN 1993-1-8, Eurocode 3 - Design of steel structures - Part 1-8: Design of Joints, 2005/AC:2009 /8/ AISC 360-05, Specification for Structural Steel Buildings, March 9 2005

/9/ ISO 19900 Petroleum and natural gas industries – General requirements for offshore structures. First edition 2002-12-01

/10/ ISO 19902 Petroleum and natural gas industries – Fixed steel offshore structures, First edition 2007-12-01

/11/ Norsok Standard N-001, Integrity of offshore structures, Edition 7, June 2010 /12/ Norsok Standard N-004, Design of steel structures, Revision 4, February 2004

/13/ Norsok Standard N-006, Assessment of structural integrity for existing offshore load-bearing structures, Edition 1, March 2009

/14/ DNV-OS-C101, Design of Offshore Steel Structures, General (LRFD Method), April 2011 /15/ DNV-RP-C201 Buckling Strength of Plated Structures, October 2010

/16/ DNV-RP-C202 Buckling Strength of Shells

/17/ DNV-RP-C203 Fatigue Design of Offshore Steel Structures October 2012 /18/ DNV-RP-C204 Design against Accidental Loads, October 2010

/19/ ECCS publication No. 125, Buckling of Steel Shells. European Design Recommendations, 5th Edition, J.M. Rotter and H. Smith Editors.

/20/ DNV-RP-F110 Global Buckling of Submarine Pipelines Structural Design due to High Temperature/ High Pressure, October 2007

/21/ DNV-SINTEF-BOMEL: Ultiguide, Best practice for use of non-linear analysis methods in documentation of ultimate limit state for jacket type offshore structures, April 1999.

/22/ Skallerud, Amdahl: Nonlinear analyses of offshore structures, Research studies press ltd., 2002 (ISBN 0-86380-258—3)

/23/ Corrocean ASA: Design of offshore facilities to resists gas explosion hazards. Engineering handbook. Oslo 2001.

/24/ ASME Boiler & Pressure Vessel Code 2013 Edition July 1, 2010 VIII Division 2, Alternative Rules /25/ EN 13445-3:2012 Unfired pressure vessels Part 3

/26/ Hagen, Ø, Solland, G. Mathisen, J. Extreme storm wave histories for cyclic check of offshore structures OMAE 2010-20941

/27/ H. M. Hilber, T. J. R. Hughes and R. L. Taylor: Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake engineering and structural dynamics, 5 (1977), page 283-292.

/28/ Skallerud, Eide, Amdahl, Johansen: On the capacity of tubular T-joints subjected to severe cyclic loading. Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, v 1, n Part B, p 133-142, 1995.

/29/ Weignad, Berman: Behaviour of butt-welds and treatments using low-carbon steel under cyclic inelastic strains, Journal of Constructional Steel Research, v 75, p 45-54, August 2012.

/30/ Boge, Helland, Berge: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, v 4, p 107-115, 2007.

/31/ Scavuzzo, Srivatsan, Lam: Fatigue of butt welded steel pipes. American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, v 374, p 113-143, 1998, Fatigue, Environmental Factors, and New Materials.

/32/ Belytschko, Liu, Moran, Nonlinear Finite Elements and Continua and Structures, John Wiley&Sons, Ltd., November 2009

/33/ Maresca, Milella, Pino: A critical review of triaxiality based failure criteria, IGF 13 Cassino 27 e 28 Maggio, 1997

/34/ Kuhlmann: Definition of Flange Slenderness Limits on the Basis of Rotation Capacity Values, Journal of Constructional Steel Research, 14 (1989) 21-40

/35/ Gardner, Wang, Liew: Influence of strain hardening on the behavior and design of steel structures, International Journal of Structural Stability and Dynamics Vol. 11. No. 5 (2011) 855-875

/36/ DNV-OS-F101 Submarine Pipeline Systems, August 2012

/37/ Heo, Kang, Kim, Yoo, Kim, Urm: A Study on the Design Guidance for Low Cycle Fatigue in Ship Structures. 9th _{Symposium on Practical Design of Ships and Other Floating Structures. Germany. 2004.}

/38/ EN-10025 Hot rolled products of structural steels. Part 2, 3, 4 and 6

APPENDIX A COMMENTARY

A.1 Comments to [4.1] General

The element model selected for analysis needs to represent the structure so that any simplifications are leading to results to the safe side. This is especially important for the selection of boundary conditions and the representation of the load. The analyst needs to assess the possibility that simplification may lead to an overrepresentation of the resistance. An example may be the representation of neighbouring elements that also are subjected to buckling. In the case that the stiffness of the adjoining structure is uncertain it is recommended to use boundary condition corresponding to simple support. If there are uncertainties with respect to simplification in load it is recommended to vary the load pattern and perform alternative analyses to check the effect.

The requirements to characteristic resistance in other codes for offshore structures like ISO 19902 /10/ are similar and the analysis carried out according to the recommendations in this RP is expected to fulfil the requirements also in this code.

A.2 Comments to [4.4] Selection of elements

Guidance on selection of suitable elements for non-linear analysis can be found in text books e.g. /32/.

A.3 Comments to [4.7.5] Stress - strain curves for ultimate capacity analyses

The proposed stress-strain curves are based on steel according to /38/ and /39/. The curve is also applicable to materials according to DNV Offshore Standard /14/.

A.4 Comments to [5.1.1] General

There is not a universal method available that can be used for predicting tensile failure for practical engineering applications by FE methods.

The value of the acceptable strain will be governed by: — stress triaxiality

— load history — cold deformation. — material properties — material inhomogeneity

— different material properties of materials being joined. (Even material with the same strength specification may differ due to statistical variance if not from same batch)

— presence of defects.

The calculated strain values will be a function of: — element type

— element density — material properties — flow rules

— sequence of load modelling.

The acceptable strain values can therefore not be given with large accuracy without consideration of the conditions of the actual problem. This RP proposes to either use a simplified tensile failure criterion or to calibrate a problem specific criterion according to a specified procedure.

There are several models describing the local phenomenon of tensile failure. Common for most of these is that the strain and stress state during the entire loading sequence until failure is considered important for describing the damage process properly. Unfortunately, a high degree of complexity is a common feature of many of the models, and the theoretical and practical knowledge required to perform a FE analysis based on these criteria is judged not to be suited for engineering purposes.

Base material has in general better toughness properties than weld material. It is therefore regarded as good design practice to ensure that large plastic deformation occurs in the parent material and not in the weld. This is normally the case for full penetration welds where the overmatching material ensures limited plastic deformation in the weld. Weld material may however contain defects of considerable size. In such cases a fracture mechanics assessment is necessary in order to determine if fracture in the weld may be the governing failure mode.

A.5 Comments to [5.1.3] Tensile failure in base material. Simplified approach for plane plates

Dominant structural steel design codes like Eurocode 3 /7/ and AISC /8/ apply a larger material factor for tensile failure when the capacity is based on the tensile strength. In order to determine a resistance by use of non-linear FE methods a similar increase in the material factor should be included since the material curve used is including the strain hardening.

A.6 Comment to [5.2.3] Determination of cyclic loads

The check against cyclic failure should be carried out with the use of a dimensioning load history that has the prescribed probability of occurrence as required for a single extreme load. For environmental loads like wave and wind it should be established a dimensioning storm that the structure is required to survive. It would be in line with check for other failure modes to check the structure for one single storm from each of the critical directions, but without adding the calculated damage from different directions.

The load history for the remaining waves in a 10 000 year dimensioning storm investigated for southern North Sea conditions have been found to have a maximum value equal to 0.93 of the dimensioning wave, a duration of 6 h and a Weibull shape parameter of 2.0. This applies for check of failure modes where the entire storm will be relevant, such as crack growth.

When checking failure modes where only the remaining waves after the dimensioning wave (e.g. buckling) need to be accounted for, a value of 0.9 of the dimensioning wave may be used ref. /26/.

The load history for the remaining waves in a 100 year dimensioning storm investigated for southern North Sea conditions have been found to have a maximum value equal to 0.95 of the dimensioning wave, a duration of 6 h and a Weibull shape parameter of 2.0. The largest remaining waves after the dimensioning wave (e.g. for cases like buckling) the largest wave is found as 0.92 of the dimensioning wave.

A.7 Comment to [5.2.4] Cyclic stress strain curves

The cyclic stress-strain curves are only intended for low cycle fatigue analysis. The use of monotonic stress strain curve in low cycle fatigue analysis may provide non-conservative results and must therefore be avoided. The cyclic stress strain curves presented in Table 5-3 are based on cyclic behaviour of similar steels reported in reference /37/. In order to account for uncertainties in material behaviour the curves are based on conservative assumptions. A steel grade similar to S235 was not reported in /37/. Here, the same exponent of 10 in the Ramberg-Osgood relation was assumed. K was assessed by assuming a strain value of approximately 0.005 when the stress has approached the monotonic stress level of 235MPa.

A.8 Comment to [5.2.5.1] Accumulated damage criterion

Laboratory test results presented in references /28/ to /31/ make up the basis for the established ε-N curve for welded joints. The proposed mean and design curve for air along with the laboratory test data is presented in

Figure A-1 . Note that some of the results presented in the figure are not obtained directly from the referred articles. In some cases further analysis and interpretation was needed to obtain the data on a proper format. The mean curve is established based on judgement. The results reported by Weigans and Berman ref. /29/ are obtained from testing of dog-bone specimens cut out from a butt welded plate. These results have therefore been weighted less than results from ref. /28/ and ref. /30/ which is based on full scale testing of tubular joints. The fatigue test results presented in ref. /31/ are from pipes with wall thickness of less than 10 mm. The fatigue strength of welded joints is to some extent dependent on the wall thickness and since the thickness of structural elements normally is significantly larger than this the results have been weighted less.

Because the fatigue test data come from several different sources it was not found reasonable to establish the standard deviation from a regression analysis. Instead, a standard deviation of 0.2 in log N scale is assumed for constructing the design curve in air. A standard deviation of 0.2 is identical to what is used in high cycle fatigue (DNV-RP-C203 ref. /17/). It is a general opinion within the body of fatigue expertise that the statistical deviation in fatigue test results, decreases with decreasing fatigue life. Hence, assuming a standard deviation value of 0.2 should be conservative.

The high cycle fatigue design curve in DNV-RP-C203 is defined as the mean curve minus two standard deviations. In order to account for limited test data, the design curve has been established by subtracting three standard deviations. Three standard deviations on log N corresponds to a factor of 103·0.2 ≈ 4, i.e the design curve is below the mean curve by a factor of approximately four on fatigue life.

The design curve for seawater with cathodic protection is constructed by reducing the fatigue life by a factor of 2.5. This is identical to the reduction used in DNV-RP-C203 for fatigue lives less than 106_.

Due to limited test data the proposed model does not take into account that the fatigue strength decreases with increasing thickness. It is however believed that this effect is less pronounced in low cycle fatigue compared to high cycle fatigue, ref. DNV-RP-C203. In order to avoid non-conservative results it is recommended not to apply the proposed curves for thicknesses above 60 mm. For larger thicknesses it is recommended to multiply the strain amplitude (∆ε/2) with the thickness correction factor used in DNV-RP-C203. The reference thickness is set equal to 60 mm. In case that low-cycle fatigue is to be considered together with high cycle fatigue it may be more practical to use the same reference thickness in both checks.

Figure A-1

Mean and design curve for welded joints along with laboratory test results.

A.9 Comments to [5.2.7] Shake down check

When a structure is loaded beyond linear limits the response for subsequent cycles will be changed. It is therefore necessary to investigate the behaviour through the full cycles also for the next cycles. See e.g. /22/

for more guidance.

A.10 Comments to [5.4.1] General

The modelling of geometrical imperfections, out-of-straightness etc. is crucial for achieving a credible and safe estimate of the buckling and ultimate strength limits. The less redundant the structure is the more important it will be to model the geometrical deviations from perfect shape in a consistent way using the eigenmode, postbuckling shapes, combinations thereof or similar. For redundant structures the sensitivity of the ultimate load bearing capacity to the size of the geometrical imperfections will be negligible. In such cases the triggering of the governing modes rather than accounting for actual tolerance size will be most important for the analyses. Guidance on analysis of stability problems may be found in e.g. /19/.

A.11 Comments to [5.4.5] Strain limits to avoid accurate check of local stability for plates and

tubular sections yielding in compression.

The strain limits for plates are established from analysis of flanges meeting rotational capacities according to cross-section class 1 and 2 and by comparison with tests. See /34/ and /35/. Strain limits are also compared with recommendations given in the DNV Offshore Standard for submarine pipelines /36/.

APPENDIX B EXAMPLES

B.1 Example: Strain limits for tensile failure due to gross yielding of plane plates (uniaxial

stress state)

B.1.1 T-section cantilever beam

Gross yielding check of a T-section cantilever beam, subjected to axial and shear force and moment loading, is presented in this example. The finite element software ABAQUS is used to perform the analyses.

The geometry and boundary conditions of the beam are shown in Figure B-1 . Loading is applied to a reference point coinciding with the neutral axis of the beam cross section, using kinematic coupling between cross section and reference point. The beam is modelled using 4-noded shell elements with reduced integration (S4R) with mesh size of 16 mm x 16 mm. Material grade is S355, modelled according to Section [4.7.5].

The magnitude of the applied forces and moments are given by axial force N_x, shear force P_y = − 0.15N_x and bending moment M_z =− 0.45N_x.

The loading and boundary conditions result in a stress state dominated by uniaxial stress. Hence, the criterion presented in Section [5.1.3.2] is applied for assessing the beam.

Figure B-1

Geometry and boundary conditions for cantilever beam

According to the criterion presented in Section [5.1.3.2], the strain should be calculated as the linearized maximum principal plastic strain along the likely failure line and checked against the limit for the critical strain. The limit is a critical gross yield strain of 0.04 for this example.

Figure B-2 shows a contour plot of the maximum principal plastic strain and the chosen failure line, the 3rd element column from the clamped end. For the chosen failure line the maximum principal plastic strain is obtained from integration points and linearized using the method of least squares.

Based on the finite element analysis results and the linearization the critical load is determined to be between N_x= 489 kN and N_x= 500 kN. The maximum principal plastic strain distribution and corresponding linearized distribution for load level N_x=489 kN are shown in Figure B-3 and analysis results are shown in Table B-1 .

Table B-1 Analysis results

N_x Maximum linearized [kN] principal plastic strain

489 3.9·10-2 500 4.2·10-2 3000

A

A

460 300

Section A

500

M

_N

P

40 8

Figure B-2

Maximum principal plastic strain contour plot, with chosen failure line highlighted

Figure B-3

Maximum principal plastic strain and linearized maximum principal plastic strain distributions for web

The design resistance will be found as the characteristic resistance divided by the appropriate material factors. The selected element mesh is tested to be accurate meaning that a FEM knock down factor C_FEM can be taken as 1.0 in this case.

B.1.2 T-section cantilever beam with notch

Check for tensile failure of a T-section cantilever beam with a notch in the free edge of the web is presented in this example. The geometry and boundary conditions are shown in Figure B-4 . The model, loading and analysis setup and procedure are the same as in [B.1.1], except the size of the mesh which in this case is 25% of the notch height, i.e. 25 mm x 25 mm.

In addition to the gross yielding criterion presented in [5.1.3.2], the local tensile failure criterion presented in

[5.1.3.3] must be applied when assessing the beam. Chosen failure line

Figure B-4

Geometry and boundary conditions for cantilever beam with notch

For the gross yielding two likely failure lines were chosen; one at mid-notch and one at the notch corner displaying the highest strain values, see Figure B-5 . The maximum principal plastic strain is obtained from integration points and linearized using the method of least squares. Both failure lines must comply with the criterion of an allowable maximum principal plastic linearized strain of 0.04. In addition, the local strain, according to [5.1.3.3], must not exceed the critical strain value of 0.12. In this case the mesh size falls within the defined volume criteria. Hence, the local strain value is taken as the maximum principal plastic strain in the element with the largest strain.

Figure B-5

Maximum principal plastic strain contour plot, with chosen failure lines highlighted

Based on the finite element analysis results the linearization line 1 is found to be the critical failure line, with critical load determined to be between N_x = 310 kN and N_x = 315 kN. The maximum principal plastic strain distributions and corresponding linearized distributions for both failure lines at load level N_x = 310 kN are shown in Figure B-6 and analysis results are shown in Table B-2 .

Table B-2 Analysis results

N_x[kN] Maximum linearized principal plastic strain

Line 1 Line 2 Largest element strain

310 3.8·10-2 _3.0·10-2 _7.6·10-2 315 4.1·10-2 3.3·10-2 8.1·10-2 100 200 3000

A

A

500 500 460 300

Section A

40 8 N M P

Figure B-6

Maximum principal plastic strain and linearized maximum principal plastic strain distributions for web

A convergence study is used to ensure that satisfactory accuracy is obtained. When convergence is reached the critical load is determined between N_x = 305 kN and N_x = 310kN, resulting in a FEM knock down factor

The calculations in the convergence study are performed for a fixed volume, i.e. the volume used in the presented mesh. For the local strain criteria this is illustrated in Figure B-7 and Figure B-8 .

The design resistance will be found as the characteristic resistance divided with the appropriate material factors.

Figure B-7

Element mesh used for convergence study. Elements used in local strain check circled in red

Figure B-8

Maximum principal plastic strain for three mesh densities, the left mesh is presented in this example

B.2 Example: Convergence test of linearized buckling of frame corner

A symmetric frame of beams with I-section is analysed. The frame with boundary conditions is shown in Figure B-9 and Figure B-10 . The loading is applied as a displacement of the web at one end of the frame, u_2,applied =

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