Determination of Structural Capacity by Non-linear FE analysis Methods

Size: px
Start display at page:

Download "Determination of Structural Capacity by Non-linear FE analysis Methods"

Transcription

1 RECOMMENDED PRACTICE DNV-RP-C208 Determination of Structural Capacity by Non-linear FE analysis Methods JUNE 2013 The electronic pdf version of this document found through is the officially binding version

2 FOREWORD DNV is a global provider of knowledge for managing risk. Today, safe and responsible business conduct is both a license to operate and a competitive advantage. Our core competence is to identify, assess, and advise on risk management. From our leading position in certification, classification, verification, and training, we develop and apply standards and best practices. This helps our customers safely and responsibly improve their business performance. DNV is an independent organisation with dedicated risk professionals in more than 100 countries, with the purpose of safeguarding life, property and the environment. DNV service documents consist of among others the following types of documents: Service Specifications. Procedural requirements. Standards. Technical requirements. Recommended Practices. Guidance. The Standards and Recommended Practices are offered within the following areas: A) Qualification, Quality and Safety Methodology B) Materials Technology C) Structures D) Systems E) Special Facilities F) Pipelines and Risers G) Asset Operation H) Marine Operations J) Cleaner Energy O) Subsea Systems U) Unconventional Oil & Gas Det Norske Veritas AS June 2013 Any comments may be sent by to rules@dnv.com This service document has been prepared based on available knowledge, technology and/or information at the time of issuance of this document, and is believed to reflect the best of contemporary technology. The use of this document by others than DNV is at the user's sole risk. DNV does not accept any liability or responsibility for loss or damages resulting from any use of this document.

3 Changes Page 3 CHANGES CURRENT General This is a new document. Acknowledgement This Recommended Practice is developed in a Joint Industry Project that was initiated through a pre-project supported by Statoil and DNV. The Joint Industry Project was sponsored by the following companies and institutions (in alphabetic order): ConocoPhillips Skandinavia AS Det Norske Veritas AS Maersk Olie og Gas AS Petroleum Safety Authority Norway Statoil ASA Total E&P Norge AS In addition to their financial support the above companies are also acknowledged for their technical contributions through their participation in the project.

4 Contents Page 4 CONTENTS 1. Introduction Objective of the document Validity Definitions Symbols Basic Considerations Limit state safety format Characteristic resistance Type of failure modes Use of linear and non-linear analysis methods Empirical basis for the resistance Ductility Serviceability Limit State Permanent deformations General requirements Definition of failure Modelling Determination of characteristic resistance taking into account statistical variation Requirement to the software Requirement to the user Requirements to The FEM Analysis General Selection of FE software Selection of analysis method Selection of elements Mesh density Geometry modelling Material modelling Boundary conditions Load application Application of safety factors Execution of non-linear FE analyses, quality control Requirements to documentation of the FE analysis Representation of different failure modes Design against tensile failure Failure due to repeated yielding (low cycle fatigue) Accumulated strain ( Ratcheting ) Buckling Repeated buckling Bibliography Appendix A. Commentary Appendix B. Examples... 42

5 Sec.1 Introduction Page 5 1 Introduction 1.1 Objective of the document This document is intended to give guidance on how to establish the structural resistance by use of non-linear FE methods. It deals with determining the characteristic resistance of a structure or part of a structure in a way that fulfils the requirements to ultimate strength in DNV offshore standards. Non-linear effects that may be included in the analyses are e.g., material and geometrical non-linearity, contact problems etc. The characteristic resistance should represent a value that meets the requirement that there is less than 5% probability that the resistance is less than this value. This definition of the characteristic resistance is similar to what is required by many other structural standards using the limit state safety format and these recommendations are expected to be valid for determination of capacities to be used with such standards. The recommendations are foreseen to be used for cases where the characteristic resistance is not directly covered by codes or standards. The objective is that analyses carried out according to the recommendations given in this document will lead to a structure that meets the requirements to the minimum safety margin in the standard. This document is not intended to replace formulas for resistance in codes and standards for the cases where they are applicable and accurate, but to present methods that allows for using non-linear FE-methods to determine resistance for cases that is not covered by codes and standards or where accurate recommendations are lacking. 1.2 Validity The document is valid for marine structures made from structural steels meeting requirements to offshore structures with a yield strength of up to 500 MPa. The recommendations presented herein are adapted to typical offshore steels that fulfil the requirements specified in DNV-OS-C101 /14/ or an equivalent offshore design standard. The specified requirements are made under the assumption that the considered structure is operating under environmental conditions that are within the specifications of the applied offshore standard. If the offshore unit is operating outside these specifications, the failure criterion presented in this Recommended Practice can only be utilized if it can be documented that both the weld and parent material have sufficient toughness in the actual environmental conditions. This recommended practice is concerned only with failure associated with extreme loads, and failure due to repeated loading from moderate loads (fatigue) needs to be checked separately. See DNV-RP-C203 /17/. 1.3 Definitions This Recommended Practise uses terms as defined in DNV-OS-C101. Additional terms are defined below: characteristic resistance conservative load ductility engineering shear strain equivalent strain the resistance that for a particular failure mode is meeting the requirement of having a prescribed probability that the resistance falls below a specified value (usually 5% fractile) load that maintains its orientation when the structure deforms (e.g., gravity loads) the ability to deform beyond the proportionality limit without significant reduction in the capacity due to fracture or local buckling (originally ductility refers to the behaviour of the material, but is here also used for the behaviour of structures and structural details) =2 =2 =2 = follower load load that changes direction with the structure (e.g., hydrostatic pressure) gross yielding yielding across the entire structural component e.g., a flange low cycle fatigue the progressive and localised damage caused by repeated plastic strain in the material. Low cycle fatigue assessments are carried out by considering the cyclic strain level. net area area of a cross-section or part of a cross-section where the area of holes and openings are subtracted net section ratio the ratio between the net area and the gross area of the tension part of a cross-section redundant structure a structure may be characterized as redundant if loss of capacity in one of its structural elements will lead to little or no reduction in the overall load-carrying capacity due to load redistribution shake down shake down is a state in which a structure after being loaded into the elasto-plastic range will behave essentially linear for all subsequent cycles

6 Sec.1 Introduction Page Symbols b c C C FEM D E 1 2 K M N t! " # $ # % $ % u &' ε p_ult ε p_y1 ') Δ h" Δ, Δ ,1 2 1 # span of plate flange outstand damping matrix resistance knock down factor outer diameter of tubular sections modulus of elasticity stress-strain curve parameter stress-strain curve parameter external forces internal forces yield stress/yield strength Ramberg-Osgood parameter eigenvalue for governing buckling mode characteristic element size of smallest element mass matrix number of cycles to failure design resistance characteristic resistance design action effect characteristic action effect time, thickness displacement vector strain critical strain engineering (nominal) strain equivalent strain fatigue ductility coefficient stress-strain curve parameter stress-strain curve parameter true (logarithmic) strain fully reversible maximum principal hot spot strain range fully reversible local maximum principal strain range time step material factor partial factor for actions reduced slenderness Poisson s ratio = 0.5 for plastic strain density principal stresses representative stress

7 Sec.1 Introduction Page , 1 '2 1 ') 1 ), 1,$ 1,$2 engineering (nominal) stress fatigue strength coefficient critical buckling stress linearized buckling stress disregarding local buckling modes linearized local buckling stress stress-strain curve parameter true (Cauchy) stress stress-strain curve parameter stress-strain curve parameter stress-strain curve parameter

8 Sec.2 Basic Considerations Page 8 2 Basic Considerations 2.1 Limit state safety format A limit state can be defined as: A state beyond which the structure no longer satisfies the design performance requirements. See e.g. /1/. Limit states can be divided into the following groups: Ultimate limit states (ULS) corresponding to the ultimate resistance for carrying loads. Fatigue limit states (FLS) related to the possibility of failure due to the effect of cyclic loading. Accidental limit states (ALS) corresponding to failure due to an accidental event or operational failure. Serviceability limit states (SLS) corresponding to the criteria applicable to normal use or durability. This Recommended Practice deals with limit states that can be grouped to ULS and ALS. It also addresses failure modes from cyclic loading for cases that cannot adequately be checked according to the methods used in codes for check of FLS. This is relevant for situations where the structure is loaded by a cyclic load at a high load level but only for a limited number of cycles (low cycle fatigue). The safety format that is used in limit state codes is schematically illustrated in Figure 2-1. S d < R d Figure 2-1 Illustration of the limit state safety format The requirement can be written as: S d R d (1) S d = S k γ f Design action effect R d = R k / γ M Design resistance S k = Characteristic action effect γ f = Partial factor for actions R k = Characteristic resistance γ M = Material factor. It can be seen from this figure that it is important that the uncertainty in the resistance is adequately addressed when the characteristic resistance is determined.

9 Sec.2 Basic Considerations Page Characteristic resistance The characteristic resistance should represent a value which will imply that there is less than 5% probability that the resistance is less than this value. Often lack of experimental data prevents an adequate statistical evaluation so the 5% must be seen as a goal for the engineering judgments that in such cases are needed. The characteristic resistance given in design codes is determined also on the basis of consideration of other aspects than the maximum load carrying resistance. Aspects like post-peak behaviour, sensitivity to construction methods, statistical variation of governing parameters etc. are also taken into account. In certain cases these considerations are also reflected in the choice of the material factor that will be used to obtain the design resistance. It is necessary that all such factors are considered when the resistance is determined by nonlinear FE methods. 2.3 Type of failure modes When steel structures are loaded to their extreme limits they will either fail by some sort of instability (e.g., buckling) that prevents further loading or by tension failure or a combination of the two. For practical cases it is often necessary to define characteristic resistance at a lower limit in order to be able to conclude on structural integrity without excessive analysis. Examples of this can be limiting the plastic strain to avoid cyclic failure for dynamically loaded structures or deformation limit for structural details failing by plastic strain in compression. See Section [3.1]. The following types of failure modes are dealt with in this Recommended Practice: tensile failure failure due to repeated yielding (low cycle fatigue) accumulated plastic strain buckling repeated buckling. 2.4 Use of linear and non-linear analysis methods Traditionally, the ultimate strength of offshore structures are analysed by linear methods to determine the internal distribution of forces and moments, and the resistances of the cross-sections are checked according to design resistances found in design codes. These design resistance formulas often require deformations well into the inelastic range in order to mobilise the code defined resistances. However, no further checks are normally considered necessary as long as the internal forces and moments are determined by linear methods. When nonlinear analysis methods are used, additional checks of accumulated plastic deflections and repeated yielding will generally be needed. These checks are important in case of variable or cyclic loading e.g., wave loads. 2.5 Empirical basis for the resistance All engineering methods, regardless of level of sophistication, need to be calibrated against an empirical basis in the form of laboratory tests or full scale experience. This is the case for all design formulas in standards. In reality the form of the empirical basis vary for the various failure cases that are covered by the codes, from determined as a statistical evaluation from a large number of full scale representative tests to cases where the design formulas are validated based on extrapolations from known cases by means of analysis and engineering judgements. It is of paramount importance that capacities determined by non-linear FE methods build on knowledge that is empirically based. That can be achieved by calibration of the analysis methods to experimental data, to established practise as found in design codes or in full scale experience. 2.6 Ductility The integrity of a structure is also influenced by other factors than the value of the characteristic resistance. The ability of a structural detail to maintain its resistance in case of overload is highly influencing the resulting reliability of the structure. It is therefore necessary to consider not only the value of the resistance when determining the characteristic resistance, but also to judge how the load deflection relationship is for a particular failure mode. The check for ductility requires that all sections subjected to deformation into the inelastic range should deform without loss of the assumed load-bearing resistance. Such loss of resistance can be due to tensile failure, instability of cross-sectional parts or member buckling. The design codes give little explicit guidance on this issue, with exception for stability of cross-sectional parts in yield hinges, which normally are covered by requirement to cross-sectional class 1. See e.g. DNV OS-C101 /14/. Steel structures generally behave ductile when loaded to their limits. The established design practise is based on this behaviour, which is beneficial both with respect to simplifying the design process and improving the performance of the structure. For a ductile structure, significant deflections may occur before failure and thus give a collapse warning. Ductile structures also have larger energy absorption capabilities against impact loads. The possibility for the structure to redistribute stresses lessens the need for an accurate stress calculation during design as the structure may redistribute forces and moments to be in accordance with the assumed static model. This is the basis for use of linear analyses for ULS checks even for structures which behave significantly nonlinear when approaching their ultimate limit states.

10 Sec.2 Basic Considerations Page Serviceability Limit State Use of non-linear analysis methods may result in more structural elements being governed by the requirements to the Serviceability Limit State and additional SLS requirements may be needed compared with design using linear methods. E.g., when plate elements are used beyond their critical load, out of plane deflections may need to be considered from a practical or aesthetic point of view. 2.8 Permanent deformations All steel structures behave more or less non-linear when loaded to their ultimate limit. The formulas for design resistance in DNV Offshore Standard /14/ or similar codes and standards are therefore developed on the basis that permanent deformation may take place before the characteristic resistance is reached.

11 Sec.3 General requirements Page 11 3 General requirements 3.1 Definition of failure In all analyses a precise definition of failure should be formulated. The failure definition needs to correspond with the functional requirement to the structures. In certain cases like buckling failure it may be defined by the maximum load, while in other cases it need to be selected by limiting a suitable control parameter e.g., plastic strain. For Ultimate Limit States (ULS) and Accidental Limit States (ALS) the definition of failure needs to reflect the functional requirement that the structure should not loose is load-carrying resistance during the dimensioning event. That may e.g., imply that in an ULS check the failure is defined as the load level where the remaining cycles in the storm that includes the ULS loadcase, will not lead to a progressive or cyclic failure. Alternatively a specific check for these failure modes can be carried out. See also [5.2]. Another example is in case of an ALS check for blast pressure, where one may consider the failure criterion to be the limiting deflection for the passive fire protection. Care should be made to ascertain that all relevant failure modes are addressed either directly by the analysis or by additional checks. Examples are local buckling, out of plane buckling, weld failure etc. 3.2 Modelling It should be checked that the analysis tool and the modelling adopted represent the non-linear behaviour of all structural elements that may contribute to the failure mechanism with sufficient accuracy. The model should be suitable to represent all failure modes that are intended to be checked by the analysis. It should be made clear which failure modes the model will adequately represent and which failure modes that are excluded from the analysis and that are assumed to be checked by other methods. 3.3 Determination of characteristic resistance taking into account statistical variation When FE methods are used to determine the structural resistance it is necessary to take due account of the statistical variation of the various parameters such that the results will be equal to or represent an estimate to the safe side compared with what would be obtained if physical testing could be carried out. The model should aim to represent the resistance as the characteristic values according to the governing code. In general that means 5% fractile in case a low resistance is unfavourable and 95% fractile in case a high resistance is unfavourable. In cases where data of the statistical variation of the resistance is uncertain one needs to establish a selection of the governing parameters by engineering judgement. The parameters should be selected such that it can be justified that the characteristic resistance established meets the requirement that there is less than 5% probability that the capacity is below this value. All parameters that influence the variability of the resistance need to be considered when establishing the characteristic resistance. It is therefore necessary to validate the analysis procedure according to one of the following methods: a) Selection of all governing parameters to be characteristic or conservative values. In this method all parameters that influence the result (key parameters) are selected to give results to the safe side. E.g., element type, mesh size, material curve, imperfections, residual stresses etc. For structures or structural details where the resistance is dominated by the value of the yield stress, using the specified minimum yield stress according to offshore steel material standards will represent the requirements to the characteristic resistance. Other parameters with statistical variation that will influence the resistance e.g., plate thickness should be selected as a safe estimate of the expected value in order to meet the required statistical requirement for the resulting resistance. In cases of doubt a sensitivity assessment may be necessary. In some cases values are given in the codes for analysis of specific problems see e.g., [5.4.3]. b) Validation against code values In this method a selected code case is used for calibration (denoted code calibration case). The case should represent the same failure mode that is to be investigated. The key parameters e.g., element type, mesh size, material curve, imperfections, residual stresses etc. should be selected so the analysis provide the resistance predicted by the code for the code calibration case. The same parameters are then used when the resistance of the actual problem is determined. If the analysis is calibrated against ordinary code values that meet the requirements to characteristic resistance then the resistance of the analysed structure also will meet the requirement. c) Validation against tests In this method one or more physical tests that are judged to fail in a similar way as the problem to be analysed are selected for calibration (denoted test calibration case). First the key parameters e.g., element type, mesh size, material curve, imperfections, residual stresses etc. are varied so the analysis simulates the test calibration case satisfactorily. (Giving the same or less resistance.) Then the actual problem is analysed using the same key parameters. It should be ascertained that the statistical variation of the problem is duly

12 Sec.3 General requirements Page 12 covered such that the requirements for determination of resistance by use of FE methods correspond to the requirements for determination of resistance from testing as given in Annex D of Eurocode 1990 /3/ or in ISO /10/. 3.4 Requirement to the software The software used shall be documented and tested for the purpose. 3.5 Requirement to the user The user should be familiar with FE methods in general and non-linear methods in particular. The analyst needs to understand the structural behaviour of the problem in question. The user shall know the theory behind the methods applied as well as the features of the selected software. When documenting structures to meet a code described reliability level with use of non-linear methods for determination of the resistance it is necessary the engineers understand the inherent safety requirements of the governing code.

13 Sec.4 Requirements to The FEM Analysis Page 13 4 Requirements to The FEM Analysis 4.1 General The term non-linear FE analysis covers a large number of analysis types for different purposes and objects. The content of this section is written with analyses of steel structures in mind. The objective is to document structural capacity of the structure in a way that fulfils the requirements for determining characteristic resistance in accordance with DNV Offshore Standards and other similar standards, such as the Norsok N- series, /11/ to /13/, and the ISO suite of standards /9/. 4.2 Selection of FE software The software must be tested and documented suited for analysing the actual type of non-linear behaviour. This includes: non-linear material behaviour (yielding, plasticity) non-linear geometry (Stress stiffening, 2 nd order load effects). Other types of non-linearity that may need to be included are: contact temperature effects (e.g. material degradation, thermal expansion) non-linear load effects (e.g. follower loads). 4.3 Selection of analysis method Implicit versus explicit solver Both implicit and explicit equation solvers may be used to solve the general equation system: -)3+4)5+ = (2) Where M is the mass matrix C is the damping matrix u is the displacement vector F int is the internal forces F ext is the external forces. In dynamic analyses, explicit solvers are attractive for large equation systems, as the solution scheme does not require matrix inversion or iterations, and thus, are much more computational effective for solving one time step than solvers based on the implicit scheme. However, unlike the implicit solution scheme, which is unconditionally stable for large time steps, the explicit scheme is stable only if the time step size is sufficiently small. An estimate of the time step required to ensure stability for beam elements is: =! " 4 =! "7 0 (3) where L s is the characteristic element size of the smallest element and C is the speed of sound waves in the material. Similar expressions exist for shells and solids. This makes the explicit scheme well suited for shorter time transients as seen in for instance impact - or explosion response analyses. For longer time transients the number of time steps will, however, be much larger than needed for an implicit solution scheme. For moderately non-linear problems, implicit Newton Raphson methods are well suited, gradually incrementing the time and iterate to convergence for each time step Solution control for explicit analysis Most explicit FE codes calculate the governing size of the time step based on equations similar to Equation (3). For problems of longer duration, one often wants to save analysis time by reducing the number of time steps. This can be done by accelerating the event or mass scaling. Accelerating the event reduces the simulation time and thus computational time, the mass scaling increases the time step reducing the computational time, see Equation (3). The time saving methods are only useful if the inertia forces are small. Thus, it must be documented that the kinetic energy is small compared to the deformation energy (typically less than 1%) when explicit analyses are used to find quasi-static response. Due to the typically large number of time steps in explicit analyses, the numerical representation of decimal numbers is important for the stability of the solution. The software options to use high precision ( double precision ) float are generally preferred.

14 Sec.4 Requirements to The FEM Analysis Page Solution control for dynamic implicit analysis A large number of time integration procedures exists (e.g. The Newmark family of methods and the α-method). For non-linear analyses they should be used in combination with Newton iterations. As a rule of thumb the time step should not be larger than 1/10 of the lowest natural period of interest. The most commonly used integration procedures can be tuned by selection of the controlling parameters. The parameters should in most cases be selected to give an unconditionally stable solution. For the α-method (HHT method) ref. /27/ the parameters α, β and γ can be selected by the user. The method is unconditionally stable if: 8= :2, = 1 2 : and 1 3 : 0 (4) Selecting α less than 0 gives some numerical damping. In order to avoid noise from high frequency modes, parameters that give some numerical damping can be useful. Table 4-1 presents some combinations of parameters that give unconditional stability. Table 4-1 Combinations of α, β and γ for unconditional stability α β γ Comment Trapezoidal rule, no numerical damping Numerical damping Numerical damping Solution control for static implicit analysis In case the dynamic effects are not important, the equation system to solve may be reduced to: = (5) In such cases the implicit equation solvers are in general better suited, as the dynamic terms cannot be excluded in an explicit analysis. Instead of time, applied load or displacement boundary conditions are normally incremented in a static solution. The selection of a load control algorithm for the analysis should be based on the expected response and need for post peak-load results: A pure load control algorithm will not be able to pass limit points or bifurcation points when the inertia effects are not included. Using a displacement control algorithm, limit points and bifurcation points can be passed, but the analysis will stop at turning points. For snap-back problems (passing turning point), or limit/bifurcation point problems that cannot be analysed using displacement control, an arc length method is needed. Figure 4-1 Limit, Bifurcation and Turning points 4.4 Selection of elements The selection of element type and formulation is strongly problem dependent. Points to consider are: shell elements or solid elements elements based on constant, linear or higher order shape functions

15 Sec.4 Requirements to The FEM Analysis Page 15 full vs. reduced, vs. hybrid integration formulations number of through thickness integration points(shell) volumetric locking, membrane locking and transverse shear locking hourglass control/artificial strain energy (for reduced integration elements). In general higher order elements are preferred for accurate stress estimates; elements with simple shape functions (constant or linear) will require more elements to give the same stress accuracy as higher order elements. Constant stress elements are not recommended used in the area of interest. Some types of elements are intended as transition elements in order to make the generation of the element mesh easier and are known to perform poorly. Typically 3-noded plates/shells and 4-noded tetrahedrons are often used as transition elements. This type of elements should if possible be avoided in the area of interest. Proper continuity should be ensured between adjacent elements if elements of different orders are used in the same model. For large displacements and large rotation analyses, simple element formulations give a more robust numerical model and analysis than higher order elements. Care should be taken when selecting formulations and integration rules. Formulations with (selective) reduced integration rules are less prone to locking effects than full integrated simple elements; however the reduced integration elements may produce zero energy modes ( hourglassing ) and require hourglass control. When hourglass control is used, the hourglass energy should be monitored and shown to be small compared to the internal energy of the system (typically less than 5%). 4.5 Mesh density General The element mesh should be sufficiently detailed to capture the relevant failure modes: For ductility evaluations, preferably several elements should be present in the yield zone in order to have good strain estimates. For stability evaluations, sufficient number of elements and degrees of freedom to capture relevant buckling modes, typically minimum 3 to 6 elements dependent upon element type per expected half wave should be used. The element aspect ratio should be according to requirements for the selected element formulation in the areas of interest. Care is required in transitioning of mesh density. Abrupt transitioning introduces errors of a numerical nature. Load distribution and load type also have an influence on the mesh density. Nodes at which loads are applied need to be correctly located, and in this situation can drive the mesh design, at least locally Mesh refinement study Often it will be necessary to run mesh sensitivity studies in order to verify that the results from the analyses are sufficiently accurate. The analyst should make sure that the element mesh is adequate for representing all relevant failure modes. In the general case mesh refinement studies may be done by checking that convergence of the results are obtained e.g. by showing that the results are reasonably stable by rerunning the analysis with half the element size. See example in Appendix [B.2]. 4.6 Geometry modelling Geometry models for FE analyses often need to be simplified compared to drawings of the real structure. Typically small details need to be omitted as they interfere with the goal of having a good regular element mesh. The effect the simplifications may have on the result should be evaluated. Typical simplifications include: Cut-outs or local reinforcements are not included Eccentricities are not included for beam elements or in thickness transitions in shell models Weld material is not included Welded parts are modelled as two parts and joined using contact surfaces. For buckling analyses it is necessary to introduce equivalent geometric imperfections in order to predict the buckling capacity correctly, see Section [5.4]. A common way to include the imperfections is to use one or more of the structures eigenmodes and scale these such that the buckling capacity is predicted correctly for the calibration model. For problems where the geometry of the real structure deviates from the theoretical one, the analysis needs to reflect that possible geometrical tolerances may have impacts on the result. Example is fabrication tolerances of surfaces transferring loads by contact pressure.

16 Sec.4 Requirements to The FEM Analysis Page Material modelling General The selected material model should at least be able to represent the non-linear behaviour of the material both for increasing and decreasing loads (unloading). In some cases the material model also needs to be able to account for reversed loading. The material model selected needs to be calibrated against empirical data (see [3.3]). The basic principle is that the material model needs to represent the structural behaviour sufficiently for the analysis to be adequately calibrated against the empirical basis Material models for metallic materials For metallic materials time independent elasto-plastic models are often used. The main components in such models are: A yield surface, defining when plastic strains are generated. von Mises plasticity is commonly used for metals. The model assumes that the yield surface is unaffected by the level of hydrostatic stress. A hardening model defining how the yield surface changes for plastic strains Commonly used are isotropic hardening (expanding yield surface) and kinematic hardening (translating yield surface) or a combination of both. A flow rule (flow potential) defining the plastic strain increment a change in stress gives. The yield surface function is often used as a flow potential (associated flow). The von Mises yield function is considered suitable for most capacity analyses of steel structures. The hardening rule is important for analyses with reversed loading due to the Bauschinger effect. A material model with kinematic (or combined kinematic/isotropic) hardening rule should be used in such analyses. Figure 4-2 The von Mises yield surface shown in the σ 1 -σ 2 plane with isotropic (left) and kinematic (right) hardening models Figure 4-3 Isotropic vs Kinematic hardening

17 Sec.4 Requirements to The FEM Analysis Page Stress strain measures Stress and strain can be measured in several ways: From material testing the results are often given as Engineering stress-strain curves (calculated based on the initial cross section of the test specimen). FE software input is often given as True stress-strain (calculated based on updated geometry). Other definitions of strains are also used in FE formulations, e.g., the Green-Lagrange strain, and the Euler- Almansi strain. For small deformations/strains, all strain measures give similar results. For larger deformations/strains the strain measure is important, e.g. the Green-Lagrange measure is limited to small strains only. Figure 4-4 shows a comparison of some strain measures. Limitations in the formulations on the use of the selected element type should always be noted and evaluated for the intended analysis. Figure 4-4 Comparison of some strain measures The relationship between Engineering (Nominal) stress and True (Cauchy) stress (up to the point of necking) is: σ true =σ eng 1+ε eng The relationship between Engineering (Nominal) strain and True (Logarithmic) strain is: ε true =ln1+ε eng The stress-strain curve should always be given using the same measure as expected by the software/ element formulation Evaluation of strain results As element strain in FE- analyses is an averaged value dependent on the element type and element size, the reported strain will always depend on the computer model. It is often necessary to re-mesh and adjust the analysis model after the initial analyses are done in order to have a good model for strain estimates. Strain extracted from element integration points are the calculated strain based on element deformations. Most FE software presents nodal averaged strains graphically. At geometry intersections the nodal average value may be significantly lower than the element (nodal or integration point) strain if the intersecting parts are differently loaded. When evaluating strain results against ductility limits, the integration point strains or extrapolated strains from integration points should be used Stress - strain curves for ultimate capacity analyses When defining the material curve for the analysis, the following points should be considered: (6) (7) Characteristic material data should normally be used, see Section [3.3]. The predicted buckling capacity will depend on the curve shape selected, thus equivalent imperfection calibration analyses and final analyses should be performed using the same material curves.

18 Sec.4 Requirements to The FEM Analysis Page 18 The extension of the yield zones and predicted stress and strain levels depend on the curve shape selected. Acceptance criteria should thus be related to the selected material curve, the curve need not represent the actual material accurately as long as the produced results are to the safe side. The stiffness of most steels reduces slightly before the nominal yield stress is reached; in fact yield stress is often given as the stress corresponding to 0.2% plastic strain. Some steels have a clear yield plateau; this is more common for mild steels than for high strength steels. One should avoid using constant stress (or strain) sections in the material curves, due to possible numerical instability issues. Idealized material curves for steel according to European Standards EN /38/ and EN /39/ are proposed in Table 4-2 to Table 4-5. These properties are assumed to be used with the acceptance criteria given in this RP. Idealized material curves for steel materials delivered according to other codes e.g. DNV Offshore Standards can be established by comparison with these curves. Figure 4-5 shows the parameters. Figure 4-6 shows the resulting curves for thicknesses less than 16 mm. The stress-strain values are given using the engineering stress-strain measure. Table 4-6 to Table 4-9 and Figure 4-7 show the corresponding true stressstrain values. Alternative bi-linear curves may be used for buckling problems e.g. as shown in Figure 5-6. The curves should also be adjusted for temperature effects as appropriate. σ ult σ E p1 E p2 σ yield σ prop σ yield2 E ε p =0 ε p_y1 ε p_y2 ε p_ult ε,ε p Figure 4-5 Parameters to define stress strain curves

19 Sec.4 Requirements to The FEM Analysis Page 19 Table 4-2 Proposed non-linear properties for S235 steels (Engineering stress-strain) S235 Thickness [mm] t < t < t 63 E [MPa] σ prop /σ yield 0.9 E p1 /E σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult 0.2 E p2 /E Table 4-3 Proposed non-linear properties for S355 steels (Engineering stress-strain) S355 Thickness [mm] t 16 16< t < t 63 E [MPa] σ prop /σ yield 0.9 E p1 /E σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult 0.15 E p2 /E Table 4-4 Proposed non-linear properties for S420 steels (Engineering stress-strain) S420 Thickness [mm] t 16 16< t < t 63 E [MPa] σ prop /σ yield 0.9 E p1 /E σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult 0.12 E p2 /E

20 Sec.4 Requirements to The FEM Analysis Page 20 Table 4-5 Proposed non-linear properties for S460 steels (Engineering stress-strain) Thickness [mm] t 16 16< t 25 25< t 63 E [MPa] S460 σ prop /σ yield 0.9 E p1 /E σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult 0.1 E p2 /E Table 4-6 Proposed non-linear properties for S235 steels (True stress strain) S235 Thickness [mm] t 16 16< t < t 63 E [MPa] σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult Table 4-7 Proposed non-linear properties for S355 steels (True stress strain) S355 Thickness [mm] t 16 16< t < t 63 E [MPa] σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult

21 Sec.4 Requirements to The FEM Analysis Page 21 Table 4-8 Proposed non-linear properties for S420 steels (True stress strain) S420 Thickness [mm] t 16 16< t < t 63 E [MPa] σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult Table 4-9 Proposed non-linear properties for S460 steels (True stress strain) S460 Thickness t 16 16< t 25 25< t 63 E [MPa] σ prop [MPa] σ yield [MPa] σ yield2 [MPa] σ ult [MPa] ε p_y ε p_y ε p_ult Figure 4-6 Material curves according to Table 4-2 to Table 4-5 (Engineering stress-strain) (t< 16 mm)

22 Sec.4 Requirements to The FEM Analysis Page 22 Figure 4-7 Material curves according to Table 4-6 to Table 4-9 (True stress-strain) (t< 16 mm) Strain rate effects The proposed material curves in Section [4.7.5] can be used for strain rates up to 0.1 s -1. For impact loads higher strain rates may be experienced, and the increased strength and reduced ductility may be considered. The Cowper-Symonds (CS) model is one model often used to simulate strain rate effects: 1 $IJ& =1 "I& K1+L M N (8) As seen, the relative effect will be the same for all static stress (strain) levels. Thus the model must be calibrated for the expected maximum stress (strain), otherwise the effect may be overestimated for large strains. The constants C and p should be based on experiments and the maximum strain level expected. In lack of data, C = 4000 [s -1 ] and p = 5 is proposed for common offshore steel materials. 4.8 Boundary conditions The selected model boundary condition needs to represent the real condition in a way that will lead to results that are accurate or to the safe side. Often it is difficult to decide what the most correct or a conservative boundary condition is. In such cases sensitivity studies should be performed. 4.9 Load application Unlike linear elastic analyses, where results from basic load cases can be scaled and added together, the sequence of load application is important in non-linear analyses. Changing the sequence of load application may change the end response. The loads should be applied in the same sequence as they are expected to occur in the condition/event to be simulated. E.g. for an offshore structure subjected to both permanent loads (such as gravity and buoyancy) and environmental loads (such as wind, waves and current); the permanent loads should be incrementally applied first to the desired load level, then the environmental load should be incremented to the target level or collapse. In some cases the initial load cases (e.g. permanent loads) may contribute positively to the load carrying capacity for the final load case, in such cases a sensitivity study on the effect of reduced initial load should be performed. The analyst needs to evaluate if the loads are conservative (independent of structure deformation) or nonconservative (follow structure deformation) and model the loads correspondingly. The number of time/load increments used to reach the target load level may also influence the end predicted response. Increment sensitivity studies should be performed to ensure that all failure modes are captured.

23 Sec.4 Requirements to The FEM Analysis Page Application of safety factors Applying load and resistance safety factors in a non-linear analysis can be challenging as application of safety factors on the capacity model side for one failure mode may influence the capacity of another failure model. One example of this is yielding vs. column buckling capacity. In general it is more practical to prepare one capacity model representing the desired characteristic capacity for all failure modes to be analysed for, and then apply all the safety on the load side, defining a target load level that accounts for both load and resistance safety. Using this approach, the same model may be used for both ULS and ALS type of analysis without recalibration of the model: # >%!2I$ -I'I, where R k is the characteristic resistance found from the analysis, and S k is the characteristic load effect Execution of non-linear FE analyses, quality control The following points should be considered in a quality control of non-linear FE analyses: boundary conditions calibration against known values. inertia effects in dynamic analyses element formulation/ integration rule suited for the purpose material model suited for the purpose mesh quality suited for the purpose, mesh convergence studies performed for stress strain results. equivalent imperfections calibrated for stability analyses time/load increments sufficient small, convergence studies performed numerical stability reaction corresponds to input convergence obtained for equilibrium iterations hourglass control for reduced integration, hourglass energy remains small sensitivity analysis both from idealisation and numerical points of views could be provided in particular around singularities, for boundary conditions, etc. reference recommendations in Standards, Codes or Rules that are applicable directly to the studied system, or to a similar system with different dimensions reference similar analyses for systems or subsystems that are validated from analytical or experimental sources evaluation of analysis accuracy based on performed sensitivity studies Requirements to documentation of the FE analysis The analysis should be documented sufficiently detailed to allow for independent verification by a third party, either based on review of the documentation, or using independent analyses. The documentation should include description of: purpose of the analysis failure criteria geometry model and reference to drawings used to create the model boundary conditions element types element mesh material models and properties loads and load sequence analysis approach application of safety factors results discussion of results conclusions. (9) Sensitivity studies and other quality control activities performed in connection with the analyses should also be documented.

24 Sec.5 Representation of different failure modes Page 24 5 Representation of different failure modes 5.1 Design against tensile failure General An accurate analysis of tensile failure is demanding as numerous factors affect the problem and determination of the results from the analysis is highly influenced on how the analysis is carried out. The recommendations given in this document are not valid for failure that is related to unstable fracture due to either insufficient material toughness, defects outside fabrication specifications or cracks. In such cases fracture mechanics methods need to be used. In general accurate prediction of tensile failure needs to be made by analyses that are calibrated against tests or a known solution where the conditions for tensile failure are similar as in the structural detail being investigated. This method is described in [5.1.2]. Simplified tensile failure criteria for the base material are presented in [5.1.3]. Welds are assumed to be made with overmatching material that ensures that plastic straining and eventual failure takes place in the base material. Welds should therefore be checked according to ordinary code methods based on the forces carried by the welds. See [5.1.4] Tensile failure resistance from non-linear analysis calibrated against a known solution The most accurate method to check a structure against tensile failure is by calibrating the non-linear FE analysis against a known solution. In this method the following steps should be followed. i) Select a test or a problem with known capacity (e.g. from a design code) as the reference object. The reference object should have the similar conditions for tensile failure as the actual problem such as the type of stress (axial, bending or shear) and the degree of triaxial stress state. ii) Model and analyse the reference object following recommended modelling and analysis technique. iii) Determine the selected strain parameter that is judged to best describe the problem (e.g. principal strain) at failure for the reference object. iv) Model the actual object using the same analysis technique as for the reference object i.e. mesh density, element type, material properties, etc. v) Determine the capacity against tensile failure for the structure as the load corresponding to the load level when the failure strain as determined in iii) is reached Tensile failure in base material. Simplified approach for plane plates General Tensile failure can be assessed by the following simplified procedure for some selected situations if a calibrated solution as given in is not attainable. The simplified check of tensile failure is a two-step check: i) tensile failure due to gross yielding along the failure line (see [ ]) ii) tensile failure due to cracks starting from local strain concentrations (see [ ]). Tensile failure in structures modelled by beam elements is best checked on the basis of the total deflection e.g. as given in DNV-RP-C204 /18/. This method is valid for structures made with typical offshore steel that will meet requirements to ductility and toughness. The structural details need to meet fabrication requirements for offshore steel structures. The safety factors that should be used for tensile fracture according to this procedure should apply an additional safety factor γ tf = 1.2 compared with standard material factor of the code. The analyses should apply stress-strain relationship according to [4.7.2]. As the calculated plastic strain in the non-linear FE analysis will always involve inaccuracies depending upon mesh density, element type, material model etc., the analyst must assure that any deviation from a correct result is to the safe side. A mesh convergence study can be used to check that satisfactory accuracy is obtained. If it is found impractical to perform the analysis with the required mesh density, larger elements can be used as long as the calculated capacity is reduced by e.g. applying a resistance knock down factor C FEM or by reducing the material key parameters. Such factors should be determined for the actual problem by means of a mesh convergence study Strain limits for tensile failure due to gross yielding of plates This method assumes that a failure line across the plate being analysed can be identified. Along this failure line the plastic strain can be calculated as an averaged linear strain (gross yield strain) that can be compared with critical values given in Table 5-1. With the gross yield strain is understood a plastic strain that is averaged over a length in the direction of the largest principal strain and is linearized (axial and a bending components) in the transverse directions.

25 Sec.5 Representation of different failure modes Page 25 The strain shall be calculated as the maximum principal plastic strain along the likely failure line. The failure line should be assumed as a straight line. Local cut outs or holes need to be included in the model if the ratio of the net area to the gross area of the tension part is less than specified in Table 5-1. Local strains caused by non-loaded attachments like doubler plates or brackets do not need to be considered. The strains caused by tension stresses both due to axial tension, in-plane and out-of-plane bending and in-plane shear should be extrapolated based on the linearized distributed maximum principal stress to the plate edge corners both transverse to the plate as well as through thickness. The strain can be taken as the average value over a length l avg given in Equation (10) in the direction of the maximum principal strain., IP = 16 3 R 3 Where: S), IP 2 (10) t p = plate thickness w p = plate width Shear strain due to out-of-plane bending should be checked separately as averaged engineering shear across the failure line. The critical engineering shear strains can be taken as equal to the maximum principal strains given in Table 5-1. The linearized averaged plastic strain can be found by curve fitting a straight line using the method of least squares. In cases where the direction of the maximum principal plastic strain significantly varies along the failure line it is recommended to consider different failure line directions. Table 5-1 Critical strain and net area ratio for uniaxial stress state 1), 2) Maximum principal plastic linearized strain 1) S235 S355 S420 S460 Critical gross yield strain Net section ratio ) The strain can be calculated as average values over a length (in the direction of the principal strain) equal to the thickness for in-plane bending and up to 5 times the thickness for pure membrane strains. 2) Any strain due to cold-forming should be added to the calculated plastic strain considering the direction of the plastic strain due to cold forming Strain limits for tensile failure due to local yielding in plane plates The danger of cracks developing in ductile materials due to local concentrated yielding can be checked by the following simplified procedure. The local gross yielding can be checked by averaging the strain over a rectangular prismatic volume at the location with the largest strain. The volume should be taken through the thickness (t) of the plate and should extend from t to 5*t in the other directions. Where strain gradients are present due to changes in the cross section or holes the length of the averaging volume should not be larger than a 25% of the length or width of a notch or 20% of the diameter of a hole for problems dominated by in-plain strains. In case of out-of-plane bending the length and width of the averaging volume should be taken equal to the thickness. See Figure 5-1.

26 Sec.5 Representation of different failure modes Page 26 t Figure 5-1 Example of rectangular prism for check of local strains The strain can be calculated as the average value in the direction of the maximum principal strain and should be linearized (axial and bending component) in the other two directions. The corner with the largest strain should be compared with the critical strains given in Table 5-2. For cases with out-of-plane bending the engineering shear strain in the direction normal to the plate should be checked against the critical values in Table 5-2. The engineering shear strain can be taken as the average engineering shear strain across the thickness for all cross-sections within the prismatic volume. Table 5-2 Critical local maximum principal plastic strain for uniaxial stress states 1) Maximum principal plastic critical strain S235 S355 S420 S460 Critical local yield strain ) Any strain due to cold-forming should be added to the calculated plastic strain considering the direction of the plastic strain due to cold forming Failure of welds The welds may or may not be represented with separate elements. For cases where the welds are not modelled the check of the strength of welds should be based on stress resultants determined by integration of stresses from the closest elements and checked against ordinary code requirements e.g. EN /7/ or the relevant code for the problem at hand. If welds are modelled the linearized stress components (axial, bending, shear) should be determined from integration of the stresses in the elements representing the welds and checked against ordinary code requirements e.g. EN /7/ or the relevant code for the problem at hand. Normally it is required that in welded connections the welds are stronger than the base material (overmatch). See also Section [2.6]. 5.2 Failure due to repeated yielding (low cycle fatigue) General Non-linear FE-analyses may imply that the structure is assumed to be loaded beyond proportionality limits. This means that the structure may be weakened against subsequent load cycles by repeated yielding leading to a possible cyclic failure. This is called low cycle fatigue and need to be treated different from how high cycle fatigue checks are carried out. The fatigue damage due to loads that leads to repeated yielding, i.e. cyclic plastic strains, will be underestimated if conventional linear elastic methods, such as those presented in DNV-RP-C203 ref. /17/, are applied. The methodology presented in the following must therefore be applied if repeated yielding occurs. The low cycle fatigue strength will be reduced for details that may include damage from high cycle fatigue. For such cases the damage from high cycle fatigue should be added to the damage from low cycle fatigue. See [5.2.2].

27 Sec.5 Representation of different failure modes Page Fatigue damage accumulation The fatigue life may be calculated under the assumption of linear cumulative damage, i.e. U=V, W =1 (11) where D is the accumulated fatigue damage. n i is the number of cycles in block i and N i the number of cycles to failure at constant strain range ε. In cases where the fatigue damage from high cycle fatigue (HCF) is considerable the total damage is obtained by summation, i.e. D(tot) = D(LCF) + D(HCF) Determination of cyclic loads Failure due to repeated yielding is associated with Ultimate Limit States (ULS) or Accidental Limit States (ALS). The cyclic loads should meet the same requirements as for a single extreme load when it comes to partial safety factors and selection of return periods. Depending on the nature of the actual loads it may be necessary to carry out a check against failure due to repeated plastic straining. This check is necessary as non-linear analysis allows parts of the structure to undergo significant plastic straining and the ability to sustain the defined loads may be reduced by the repeated loading. For offshore structures this is evident for environmental loads like waves and wind. When cyclic loads are present it is necessary to define a load history that will imply a probability of failure that is similar or less than intended for static loads. See also [3.1]. The load-history for the remaining waves in a 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 /26/. All the remaining cycles in the storm of the maximum wave action may be assumed to come from the same direction as the dimensioning wave Cyclic stress strain curves It is required that the cyclic stress-strain curve of the material is applied. The use of monotonic stress-strain curve must be avoided since it may provide non-conservative fatigue life estimates, especially for high strength steels. It is required that the welds are produced with overmatching material. Consequently the cyclic stressstrain properties of the base material should be used when assessing welded joints. Unless the actual cyclic behaviour of the material is known the true cyclic stress strain curves presented in Figure 5-2 can be applied. Kinematic hardening, as illustrated in Figure 4-3 should be assumed. The curves are described according to the Ramberg-Osgood relation: = 1 +X1 Y Z 10. (12) The value of the coefficient K is given in Table 5-3. Table 5-3 Ramberg-Osgood parameters for base material Grade K (MPa) S S S S

28 Sec.5 Representation of different failure modes Page 28 Figure 5-2 The true cyclic stress-strain curve for common offshore steel grades Low cycle fatigue of welded joints Accumulated damage criterion The number of cycles to failure, N, for welded joints due to repeated yielding is estimated by solving the following equation h" Where: 2 =1 2W W 0.5 The parameters in Equation (13) are given in Table 5-4 for air and seawater with cathodic protection. (13) ε hs is the fully reversible maximum principal hot spot strain range E is the modulus of elasticity (material constant) σ f ' is the fatigue strength coefficient (material constant) ε f ' is the fatigue ductility coefficient (material constant) Table 5-4 Data for low cycle fatigue analysis of welded joints Environment σ ' f (MPa) ε ' f Air Seawater with cathodic protection

29 Sec.5 Representation of different failure modes Page 29 Figure 5-3 ε-n curves for welded tubular joints in seawater with cathodic protection and in air Derivation of hot spot strain for plated structures It is recommended to derive the hot spot strain by applying the principles of the procedure given in Section 4 of DNV-RP-C203 ref. /17/. The procedure in ref. /17/ is originally developed for assessing the hot spot stress of a linear elastic material in relation to high cycle fatigue assessments. However, by substituting maximum principal stresses with maximum principal strains it may also be applied for determining hot spot strains. It is recommended to mesh with elements of size t*t in the hot spot region. The strain gradient towards the hot spot may be steep because the cyclic plastic strains often will be localised in a limited area near the hot spot. In order to reflect steep strain gradient in a good manner it is recommended to use finite elements with mid side nodes, such as 8-noded shell elements or 20-noded brick elements. For modelling with shell elements without any weld included in the model a linear extrapolation of the strains to the intersection line from the read out points at 0.5t and 1.5t from the intersection line can be performed to derive hot spot strain. For modelling with three-dimensional elements with the weld included in the model a linear extrapolation of the strains to the weld toe from the read out points at 0.5t and 1.5t from the weld toe can be performed to derive hot spot strain Derivation of hot spot strain for tubular joints Reference is made to section on stress concentration factors in DNV-RP-C203 ref. /17/ Low cycle fatigue of base material Accumulated damage criterion Despite the fact that the fatigue capacity of structures very often is governed by welded joints there are situations where the origin of a fatigue crack is in the base material. This is often due to geometrical details, such as notches, that cause rise in the cyclic stress-strain level. A low cycle fatigue check of the base material may therefore be necessary. As opposed to assessments of welded joints where the fatigue damage is determined by means of the cyclic hot spot strain, low cycle fatigue analysis of base material is based on the maximum principal strain range. The strain range is obtained from the local maxima of the considered detail. The number of cycles to failure, N, for base material due to repeated yielding is estimated by solving the following equation, 2 =1 2W W 0.43 (14)

30 Sec.5 Representation of different failure modes Page 30 where ε l is the fully reversible maximum principal hot spot strain range E is the modulus of elasticity (material constant) σ f ' is the fatigue strength coefficient (material constant) ε f ' is the fatigue ductility coefficient (material constant) Values of the parameters in Equation (14) are given in Table 5-5 for air and seawater with cathodic protection. Table 5-5 Data for low cycle fatigue analysis of base material Environment σ ' f (MPa) ε ' f Air Seawater with cathodic protection Figure 5-4 ε-n curve for low cycle fatigue of base material for tubular joint in seawater with cathodic protection and in air Derivation of local maximum principal strain The maximum principal strain is obtained from the local maxima of the considered detail. The local strain state will be underestimated if the finite element mesh is too coarse. A mesh sensitivity study should therefore be carried out to ensure that the applied strain is not underestimated. Reference is made to [4.5.2] regarding mesh refinement Shake down check Structures loaded beyond the elastic range may alter their response behaviour for later cycles. However, if a structure is behaving essentially linear for all cyclic loads after the first few cycles following the dimensioning load, it will be said to achieve shake down and further checks of failure due to repeated yielding or buckling is not necessary. In the general case it is necessary to define a characteristic cyclic load and to use this load with appropriate partial safety factors. It should be checked that yielding only takes place in the first few loading cycles and that later load repetitions only cause responses in the linear range. This may then serve as an alternative to a low cycle fatigue check as described in [5.2.5]. It is necessary to show that the structure behaves essentially linear for all possible load situations and load cycles. 5.3 Accumulated strain ( Ratcheting ) For cases where the structure will be loaded by cyclic loads in a way that incremental plasticity may accumulate and in the end lead to tensile failure or excessive deformations the maximum accumulated strain needs to be checked against the strain values in Section [5.1]. The criteria for excessive deformations may alternatively be determined on a case by case basis due to

31 Sec.5 Representation of different failure modes Page 31 requirements to the structural use or performance. Cases where accumulated strain may need to be checked can be structures that are repeatedly loaded by impacts in the same direction or functional loads that change position or angle of attack. Examples of the first are protection structures that are hit by swinging loads and the latter may be wheel loads on stiffened plate decks. 5.4 Buckling General The buckling resistance of a structure or structural part is a function of the structural geometry, the material properties, the imperfections and the residual stresses present. When the buckling resistance is determined by use of non-linear methods it is important that all these factors are accounted for in a way so that the resulting resistance meets the requirement to the characteristic resistance or is based on assumptions to the safe side. Three different methods for carrying out the analysis are proposed in the following: a) Linearized approach: Apply the FE method for assessing the buckling eigenvalues (linear bifurcation analysis) and determine the ultimate capacity using empirical formulas, b) Full non-linear analysis using code defined equivalent tolerances and/or residual stresses and c) Non-linear analysis that is calibrated against code formulations or tests. Either of these methods can be used to determine the resistance of a structure or part of a structure and recommendations for their use are given in the following sections. The proposed methods are valid for ordinary buckling problems that are realistically described by the FE analysis. Care should be exercised when analysing complex buckling cases or cases that involve phenomena like snap through, non-conservative loads, interaction of local and global stability problems etc Determination of buckling resistance by use of linearized buckling values General In order to establish the buckling resistance of a structure or part of the structure using linearized buckling values (eigenvalues) the buckling resistance can be determined by following the steps: i) Build the model. The element model selected for analysis need to represent the structure so that any simplifications are leading to results to the safe side. If certain buckling failure modes are not seen as appropriate to be represented by the model their influence on the resulting resistance can be established according to [ ]. ii) Perform a linear analysis for the selected representative load case S Rep showing maximum compressive and von-mises stresses. iii) Determine the buckling eigenvalues and the eigenmodes (buckling modes) by the FE analysis iv) Select the governing buckling mode (usually the lowest buckling mode) and the point for determining the buckling representative stress. The point for reading the representative stress is the point in the model that will first reach yield stress when the structure is loaded to its buckling resistance. v) Determine the von-mises stress at the point for the representative stress σ Rep from step ii). vi) Determine the critical buckling stress as the eigenvalue for the governing buckling mode times the representative stress: σ ki = k g σ Rep (15) Determine the reduced slenderness as:.= 1 (16)

32 Sec.5 Representation of different failure modes Page 32 vii) Select empirically based buckling curve to be used based on the sensitivity of the problem with respect to imperfections, residual stresses and post buckling behaviour. Relevant buckling curves can be selected from codes, but if not available the following may be used: Table 5-6 Buckling curves Type of buckling Column and stiffened plate and plate without redistribution possibilities Plate with redistribution possibilities Shell buckling κ 1 ]+7] =1.0 for for.>0.673 Curves to be selected from specific shell buckling codes such as DNV-RP-C202 /16/ or Eurocode EN /6/ ]=0.5 1+: (17) α = 0.15 for strict tolerances and low residual stresses 0.3 for strict tolerances and moderate residual stresses 0.5 for moderate tolerances and moderate residual stresses 0.75 for large tolerances and severe residual stresses viii)determine the buckling resistance R d as: # $ = a % # - 1 # (18) 1,4 1,2 buckling factor κ 1 0,8 0,6 Critical stress (Euler) Plate Column Shell 0,4 0,2 0 reduced slenderness Figure 5-5 Examples of buckling curves showing sensitivity for imperfections etc. for different buckling forms Empirical buckling curves are needed to account for the buckling resistance reduction effects from imperfections, residual stresses and material non-linearity. The effect is illustrated in Figure 5-5. For all buckling forms the usable buckling resistance is less than the critical stress for reduced slenderness less than 1.2. Above this value, plates with possibility of redistributing stresses to longitudinal edges may reach buckling

33 Sec.5 Representation of different failure modes Page 33 capacities above the critical value, column buckling problems will be less than the critical value, but approach the critical value for large slenderness. Shell buckling is more sensitive to imperfections and the difference between the buckling capacities that may be exploited in real shell structures are considerably less than the critical value also for large slenderness. Members will buckle as columns for cross-section classes 1, 2 and 3 with exception of tubular sections exposed to external hydrostatic pressure. For definition of cross-sectional classes see DNV-OS-C101 Appendix A /14/ Correction for local buckling effects There may be cases where a reliable FE representation of local buckling phenomena is not feasible. This may for instance be torsional buckling of stiffener or local stability of stiffener flange and web. For such cases the eigenvalue analysis should be carried out without the local buckling modes represented and the interaction of local and global buckling may be accounted for in a conservative manner by linear interaction as shown in Equation (19). 1 σ ki 1 = σ kig 1 + σ kil (19) σ kig is the linearized buckling stress when local buckling modes are disregarded and σ kil is the linearized local buckling stress Buckling resistance from non-linear analysis using code defined equivalent tolerances The buckling resistance of a structure or part of a structure can be determined by performing non-linear analyses where the effects of imperfections, residual stresses and material non-linearity is accounted for by use of a defined material stress-strain relationship and the use of empirically determined equivalent imperfections. The defined equivalent imperfections will include effects from real life imperfections, but will in general be different in shape and size. This method is only valid for buckling problem similar to the cases where the equivalent imperfections are given in Table 5-7. For other cases see [5.4.4]. The material model to be used with the equivalent imperfections is shown in Figure 5-6 or with the models proposed in [4.7.5]. 1 E/100 Stress 1 E Strain Figure 5-6 Material model for analysis with prescribed equivalent imperfections

34 Sec.5 Representation of different failure modes Page 34 Table 5-7 Equivalent imperfections Component Shape Magnitude Member bow L/300 for strict tolerances and low residual stresses L/250 for strict tolerances and moderate residual stresses L/200 for moderate tolerances and moderate residual stresses L/150 for large tolerances and severe residual stresses Longitudinal stiffener girder webs bow L/400 Plane plate between stiffeners Longitudinal stiffener or flange outstand buckling eigenmode bow twist s/ rad It is required that an eigenvalue analysis is carried out to determine the relevant buckling modes. Usually the pattern from the buckling can be used as the selected pattern for the imperfections, but in certain cases e.g. when the shape of the buckling load differ from the deflected shape from the actual loads it may be necessary to investigate also other imperfection patterns. It may be useful to divide the imperfections into local and global imperfections as shown in Figure 5-7. The values in Table 5-7 apply to the total imperfection from local and global imperfection patterns. Sensitivity analyses may be required for cases that are particularly imperfection sensitive.

35 Sec.5 Representation of different failure modes Page 35 Figure 5-7 Example of local (left) and global (right) imperfections for stiffened panel Buckling resistance from non-linear analysis that are calibrated against code formulations or tests Buckling resistance can be found by non-linear methods where the effect of imperfections, residual stresses and material non-linearity is accounted for by use of equivalent imperfections and/or residual stresses by calibrating the magnitude of the imperfections (and, or the residual stresses) to the resistance of a known case that with regard to the stability resistance resembles the buckling problem at hand. The following procedure assumes that an equivalent imperfection is accounting for all effects necessary to obtain realistic capacities: i) Prepare a model that is intended to be used for the analysis. ii) Perform an eigenvalue analysis to determine relevant buckling modes. iii) Select the object for calibration and prepare a model using the same element type and mesh density as intended for the model to be analysed. iv) Perform eigenvalue analysis of the calibration object and determine the appropriate buckling mode for the calibration object. v) Determine the magnitude of the equivalent imperfection that will give the correct resistance for the calibration object. vi) Define an equivalent imperfection for the most relevant failure mode for the problem under investigation based on the results from the calibration case. The definition of the equivalent imperfection may in certain cases not be obvious and it will then be required to check alternative patterns for the equivalent imperfections. Usually an imperfection pattern according to the most likely buckling eigenmode will be suitable for use. Exceptions may be cases where the pattern of the deflected shape due to the loads differ from the shape of the buckling eigenmodes. In cases of doubt several patterns may be needed. Example of the use of this procedure is included in the Appendix [B.3] Strain limits to avoid accurate check of local stability for plates and tubular sections yielding in compression General For cases where compressed parts of the cross-section (as a flange) are experiencing plastic strain in compression, but one wants to avoid an accurate stability analysis of the local buckling effects the stability can be assumed to be satisfactory if the plastic strain are limited to the values given below. The requirements are valid for plates that are loaded in the longitudinal direction and supported on one or both of their longitudinal edges, and for tubular sections. Plates supported on both longitudinal edges: &' L2.7L S M M 355 S) 0< &' <0.10 (20) Where b is distance between longitudinal supports and t is plate thickness

36 Sec.5 Representation of different failure modes Page 36 Plates supported on one edge (flange outstand) &' =c0.29l & M e 355 S) 0< &' <0.10 Where c is the plate outstand and t is plate thickness Tubular sections without hydrostatic pressure: (21) &' =c8.5l U M e 355 S) 0< &' <0.10 The strain shall be calculated as plastic strain and may be taken as the average value through a cross-section of the compressed plated for element length no less than 2 times the plate thickness. Material properties should be according to [4.7]. For structural parts meeting requirements to cross-sectional class 3 or 4 no plastic strain due to compressive stresses can be allowed without an accurate buckling analysis. For definition of cross-sectional classes see DNV-OS-C101 /14/. 5.5 Repeated buckling For cases where buckling of parts of the structure may occur before the total capacity of the entire structure is reached, it is necessary to investigate if the buckling may cause reduced capacity against cyclic loads. When significant cyclic loads are present one should limit the capacity to the load level that corresponds to the first incident of buckling or a cyclic check needs to be carried out. See [5.2.3] for determination of cyclic loads. For cyclic loads following an extreme wave or wind load, it is considered acceptable to disregard failure due to repeated buckling of the following cases: Buckling of the individual plates in a stiffened plate structure if the plate span to thickness ratio is less than 120. Member buckling if all parts of the cross-section meet requirements to cross-sectional Class 1 and the reduced member slenderness as a column is above 0.5. Failure due to low cycle fatigue according to [5.2] needs to be checked also for these cases. It should be noted that structural parts that are yielding in tension may buckle when unloaded. If cyclic loads leads to yielding in tension one must check against buckling through the entire dimensioning load cycle. In certain cases sufficient capacity may be proved by disregarding the structural part that suffer buckling in the cyclic capacity checks. (22)

37 Sec.6 Bibliography Page 37 6 Bibliography /1/ ISO 2394, General principles on reliability for structures, Second edition /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 Eurocode 3 Design of steel structures. Part 1-1 General rules and rules for buildings /5/ EN , Eurocode 3 - Design of steel structures - Part 1-5: Plated structural elements, October 2006 /6/ EN , Eurocode 3 - Design of steel structures - Part 1-6: Strength and Stability of Shell Structures, February 2007 /7/ EN , Eurocode 3 - Design of steel structures - Part 1-8: Design of Joints, 2005/AC:2009 /8/ AISC , Specification for Structural Steel Buildings, March /9/ ISO Petroleum and natural gas industries General requirements for offshore structures. First edition /10/ ISO Petroleum and natural gas industries Fixed steel offshore structures, First edition /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, 5 th 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 /22/ Skallerud, Amdahl: Nonlinear analyses of offshore structures, Research studies press ltd., 2002 (ISBN ) /23/ Corrocean ASA: Design of offshore facilities to resists gas explosion hazards. Engineering handbook. Oslo /24/ ASME Boiler & Pressure Vessel Code 2013 Edition July 1, 2010 VIII Division 2, Alternative Rules /25/ EN :2012 Unfired pressure vessels Part 3 /26/ Hagen, Ø, Solland, G. Mathisen, J. Extreme storm wave histories for cyclic check of offshore structures OMAE /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 /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 , /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 /30/ Boge, Helland, Berge: Proceedings of the International Conference on Offshore Mechanics and Arctic Engineering - OMAE, v 4, p , 2007.

38 Sec.6 Bibliography Page 38 /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 , 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) /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) /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. 9 th Symposium on Practical Design of Ships and Other Floating Structures. Germany /38/ EN Hot rolled products of structural steels. Part 2, 3, 4 and 6 /39/ EN Weldable structural steels for fixed offshore structures - Technical delivery conditions

39 App.A Commentary Page 39 A.1 Comments to [4.1] General APPENDIX A COMMENTARY 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 /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.

40 App.A Commentary Page 40 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 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 when the stress has approached the monotonic stress level of 235MPa. A.8 Comment to [ ] 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 , 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 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.

41 App.A Commentary Page 41 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/.

42 App.B Examples Page 42 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 [ ] is applied for assessing the beam A M 500 N Section A A P 40 Figure B-1 Geometry and boundary conditions for cantilever beam 300 According to the criterion presented in Section [ ], 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 3 rd 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

43 App.B Examples Page 43 Chosen failure line 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 [ ], the local tensile failure criterion presented in [ ] must be applied when assessing the beam.

44 App.B Examples Page A Section A M N A P 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 In addition, the local strain, according to [ ], must not exceed the critical strain value of 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

45 App.B Examples Page 45 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 4 - = 305kN 315kN =0.968 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

46 App.B Examples Page 46 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 = 0.01 m. Three different mesh densities and two element types are included in a convergence study, to ensure a sufficiently refined mesh. See Figure B-11. The element types used are 4 node rectangular shell elements and 8 node rectangular shell elements. The analyses are performed using the FEM-software ABAQUS A a 2000 b = 500 R = 1500 A 4000 Section A Figure B-9 Geometry of test example

47 App.B Examples Page 47 Figure B-10 Displacement/boundary conditions

48 App.B Examples Page 48 Figure B-11 Top: coarse mesh. Middle: fine mesh. Bottom: very fine mesh

49 App.B Examples Page 49 For the eigenvalue analyses and the linear analyses elastic material properties were used and for the buckling capacity analyses non-linear material properties were used. Details are shown in Table B-3. Table B-3 Material properties Density, ρ 7850 kg/m 3 Young s modulus, E 210 GPa Poisson s ratio, ν 0.3 The loading is applied as displacement on the web at one end of the frame, as shown in Figure B-10. Hence, the eigenvalue defines the displacement corresponding to linearized buckling. A convergence study is performed by analysing 6 cases and the resulting buckling displacements are listed in Table B-4. From these results all combinations of mesh size and element type except the coarse 4 node combination, seems to be sufficiently refined. However, the stress results wanted are also highly dependent on the mesh refinement, and a fine mesh in the area where high stress values are reached is preferable. An analysis using the very fine mesh is time consuming, hence the mesh size and element type combination chosen is the 4 node elements with fine meshing. Table B-4 Convergence study of frame Case number Mesh size Element type Linearized buckling displacement [m] 1 Coarse 4-node Fine 4-node Very fine 4-node Coarse 8-node Fine 8-node Very fine 8-node In summary the convergence test has shown that case number 2 and case 4 will produce sufficiently accurate results of the linearized buckling value. Case 2 is preferred as the analysis is more efficient compared to case 4. The increased mesh refinement of case 3, 5 and 6 will not significantly improve the accuracy for the actual problem solution. B.3 Example: Determination of buckling resistance by use of linearized buckling values B.3.1 Step i) Build model The same problem as shown in Figure B-9 will be used in this example and the boundary conditions are as in Figure B-10. The material properties are shown in Table B-5. Table B-5 Material properties Density, ρ 7850 kg/m 3 Young s modulus, E 210 GPa Poisson s ratio, ν 0.3 Yield strength, σ Y 355 MPa The analysis follows the steps as given in [5.4.2]. Step i) is completed as the model from the example in [B.2]. B.3.2 Step ii) Linear analysis of the frame The results from a linear analysis are shown in Figure B-12 and Figure B-13 for the von-mises and membrane compression stresses respectively. The linear analysis is performed with the same applied displacement as in the eigenvalue analysis u 2,applied = 0.01m, equivalent to an applied load i y-direction S Rep = 75.7 kn.

50 App.B Examples Page 50 Figure B-12 Distribution of von-mises stress from linear analysis

51 App.B Examples Page 51 Figure B-13 Distribution of compressive stress from linear analysis (minimum in-plane principal stress) B.3.3 Step iii) Determine the buckling eigenvalues Eigenvalue analysis is performed to find the buckling modes and eigenvalues of the frame. The first eigenvalue is k g = 6.24, and the corresponding buckling mode shape is shown in Figure B-14.

52 App.B Examples Page 52 Figure B-14 First buckling mode B.3.4 Step iv) Select the governing buckling mode and the point for reading the representative stress The lowest buckling mode is judged to be a realistic buckling shape for this case and is selected. The reference stress is taken as the maximum von-mises stress in the structural part subjected to buckling. B.3.5 Step v) Determine the von-mises stress at the point for the representative stress σ Rep from step ii) Stress from linear analysis: σ Rep = 97.4 MPa B.3.6 Step vi) Determine the critical buckling stress The critical buckling stress for the governing buckling mode is determined as: 1 = 1 # =608 MPa The reduced slenderness is determined as: B.3.7 Step vii) Select empirically based buckling curve The buckling curve used here is taken from Table 5-6. The curve selected is the one for column and stiffened plate and plate without redistribution possibilities as it is judged that the corner plate cannot redistribute stresses in a way so the plate curve could be used. a=. = i 1 = ]+j]

53 App.B Examples Page 53 α is set to 0.3 for the following calculations. B.3.8 Step viii) Determine the buckling resistance R d With. =0.76 then the buckling factor is a=0.767 ]=0.5 [1+: ] # $ = a % # - 1 # Assuming a material factor - =1.15, the buckling resistance is B.4 Example: Determination of buckling resistance from non-linear analysis using code defined equivalent tolerances B.4.1 Description of model # $ = = MN The same problem as shown in Figure B-9 will be used in this example and the boundary conditions are as in Figure B-10. The material properties are shown in Table B-5 and the material model is shown in Figure B-15. Figure B-15 Material model for analysis with material non-linearity A non-linear analysis (using the arc-length method) is performed, where the effects of imperfections, residual stresses and material non-linearity is accounted for by use of a defined material stress-strain relationship and the use of empirically determined equivalent imperfections. The shape of the governing buckling mode is taken as the lowest buckling mode as shown in Figure B-14, and is used as the pattern for the equivalent imperfection. The magnitude of the equivalent imperfection δ is calculated using the tolerances given in Table 5-7. The analysed frame can be considered equivalent to a component of longitudinal stiffener or flange outstand, hence the magnitude is given as n=0.02 rad =0.02& where c is half the width of the flange. Two values of c are analysed, the largest c; & I =I, where I=0.975 J is the distance between where the webs cross in the corner of the frame and the midpoint of the flange curvature, and an average c; & IP = I+S 2, where S=0.5 J is the width of the flange outside the curved area. See Figure B-9 2

54 App.B Examples Page 54 n I = n IP = Figure B-16 Stress distribution for non-linear analysis with initial imperfection o p at maximum applied force B.4.2 Results The stress distribution for the non-linear analysis with initial imperfection is shown in Figure B-16. Figure B- 17 displays the force-displacement curves for the displaced end of the frame for the linear analysis and the forcedisplacement corresponding to the critical buckling stress where imperfections are taken into consideration as calculated in Section [B.3], and from the non-linear analyses.

55 App.B Examples Page 55 Figure B-17 Force-displacement from non-linear analyses, linear analysis and the calculated critical value B.5 Example: Determination of buckling resistance from non-linear analysis that are calibrated against code formulations or tests B.5.1 Step i): Prepare model A conical transition subjected to external hydrostatic pressure and axial tension is chosen for this analysis. The geometry of the conical transition and the calibration object is shown in Figure B-18. The applied loading is defined as a hydrostatic pressure =1.01MPa and an axial tension W =58.4MN. The boundary conditions are modelled using constraints with kinematic coupling between a reference point in the cross-section centre and the nodes on the circumference of the conical transition ends. At the bottom all translations and rotations of the reference point are constrained and the top reference point is constrained in the horizontal plane (x- and z-direction). Load and boundary conditions and element mesh are shown in Figure B-19. The conical transition is modelled using 4-noded shell elements (S4R). Material properties are listed in Table B-6. Figure B-18 Geometry of conical transition (on top) and calibration object (bottom), dimensions in mm

56 App.B Examples Page 56 Figure B-19 Left: Load and boundary conditions. Right: Element mesh Table B-6 Material properties Density, ρ 7850 kg/m 3 Young s modulus, E 210 GPa Poisson s ratio, ν 0.3 Yield strength, σ Y 420 MPa Density water, ρ w 1030kg/m 3

57 App.B Examples Page 57 B.5.2 Step ii): Determine relevant buckling modes Eigenvalue analysis is performed to find the buckling modes for the conical transition. The first relevant buckling mode (with positive eigenvalue) is mode 3, shown in Figure B-20. Figure B-20 Buckling mode shape for conical transition

58 App.B Examples Page 58 B.5.3 Step iii): Select object for calibration and prepare model The calibration object is selected as a cylinder. The diameter and wall thickness are equal to the lower cylindrical part of the conical transition, while the length is chosen as 2/3 of the conical transition length (lower part, conical part and a part of the top part). The load and boundary conditions, element type and mesh density used is the same as for the model of the conical transition, see Figure B-21. Figure B-21 Left: Load and boundary conditions. Right: Element mesh

59 App.B Examples Page 59 B.5.4 Step iv): Determine the appropriate buckling mode for the calibration object Eigenvalue analysis is performed to find the buckling modes for the calibration object. These buckling modes are compared to the buckling modes found for the conical transition and a mode with similar pattern is selected. Figure B-22 shows the first cylinder buckling mode. This shows a similar pattern to the buckling mode of the conical transition Figure B-20, hence this is determined to be an appropriate buckling mode. Figure B-22 Buckling mode shape for cylinder B.5.5 Step v): Determine magnitude of the equivalent imperfection To determine the magnitude of the equivalent imperfection a non-linear analysis of the cylinder with imperfections is performed. The imperfection shape from the chosen buckling mode was transferred to the nonlinear analysis, and the same load and boundary conditions as for the eigenvalue analysis were applied. The material model shown in Figure 5-6 is used for the non-linear analysis. The imperfection is scaled so the buckling capacity of the cylinder is equal to the buckling capacity for cylinders given in N-004 /12/. To obtain this capacity the magnitude of the imperfection was found to be 40 mm. B.5.6 Step vi): Perform non-linear analysis of the model with imperfections A non-linear analysis of the conical transition with imperfections is performed. The load and boundary conditions remain the same, and the material model and magnitude of the calibrated imperfection from Step v is used. The load proportionality factor for this case is shown in Figure B-23. The maximum load proportionality factor is!r JI = Thus the buckling capacity of the conical transition subjected to the given load combination is; hydrostatic pressure =0.95MPa and an axial tension W =54.7MN. Figure B-24 shows the von Mises stress at maximum load on the deformed conical transition.

60 App.B Examples Page 60 Figure B-23 Load proportionality factor for conical transition with initial imperfection Figure B-24 Deflected shape showing von Mises stress at maximum load deformations scaled with a factor of 10

61 App.B Examples Page 61 B.6 Example: Low cycle fatigue analysis of tubular joint subjected to out of plane loading. This example presents a low cycle fatigue analysis of a tubular T-joint subjected to an out-of-plane fully reversible load of ± 60 kn. The objective of the analysis is to estimate the design life based on the recommendations in Section [5.2.5]. The assumed geometry and dimensions are given in Table B-7 and Figure B-25. Table B-7 Dimensions [mm] Chord diameter D = 300 Chord thickness T = 15.9 Chord length L = 1800 Brace diameter d = 160 Brace thickness t = 11.5 Brace length l = 500 Figure B-25 Geometry of test example, dimensions in mm It is assumed that the cyclic stress-strain behaviour is well described by the Ramberg-Osgood relationship: The values for the Ramberg-Osgood parameters are presented in Table B-8 for the chord and the brace. Table B-8 Ramberg-Osgood parameters K [MPa] n Chord Brace = 1 +X1 Y Z 1 In order to obtain the cyclic strains a finite element analysis was carried out using the FEM-software ABAQUS. An 8-noded shell element (S8R) model was established with load and support conditions as shown in Figure B-26. The chord was constrained at each end for all translational and rotational degrees of freedom. The out-of-plane load was applied by means of a reference point located at the cross-section centre of the brace end. This reference point is connected to the circumference of the brace end by means of kinematic coupling. The load was applied using three steps as illustrated in Figure B-27.

62 App.B Examples Page 62 Figure B-26 Boundary and loading conditions for tubular joint Figure B-27 Load steps Figure B-28 (a) shows an overview of the finite element mesh. Figure B-28 (b) shows a close-up of the bracechord intersection area. The finite element mesh in the hot spot region is in accordance with the recommended practice DNV-RP-C203 for tubular joints. In this example the element nodes coincide with the specified extrapolation points (a and b). Hence, nodal values are applied in the extrapolation procedure for calculating the hot spot strain range. The distance from the hot spot to the first extrapolation point, a is obtained by means of Equation (23). The distance to the second extrapolation point, b is obtained by Equation (24). I=0.2 ' = 6.1mm S= t# 36 =13.1mm (23) (24)

63 App.B Examples Page 63 Figure B-28 Left: (a) Meshed model, Right: (b) Close-up of brace-chord intersection area Figure B-29 shows the principal strain range due to the out-of-plane cyclic loading. Figure B-29 Maximum principal strain range The hotspot strain range is obtained according to the following procedure: i) Establish the total strain ranges ( Δ,Δ,Δ etc.) by subtracting the minimum strain values of load step 2 by the maximum values of load step 3. In ABAQUS this is done by using the Create Field Output option. ii) Extract the principal strain ranges at the two extrapolation points, i.e, at distances a and b. iii) The hotspot strain range is calculated by means of the following equation: Δ h" Δ h" =Δ I X I S I ZΔ S Δ I The hot spot strain range along with values at distances a and b are presented in Table B-9. Table B-9 Hotspot strain range (25) vw p vw x vw yz Nodal value saddle

64 App.B Examples Page 64 Air environment is assumed. Hence, the characteristic design life due to the cyclic loading is obtained by solving the following equation, ref. Section [5.2.5]: ε hs 2 =σ f E 2N 0.1 +ε f 2N 0.5 W=1270 cycles B.7 Example: Low cycle fatigue analysis of plate with circular hole. In this example a low cycle fatigue analysis of a plate with a circular hole subjected to cyclic displacement of 1.0mm is presented. The objective of the analysis is to estimate the design life based on recommendations in Section [5.2.6]. The dimensions of the plate are presented in Figure B-30. The plate material is of grade S355 and the cyclic stress-strain curve is obtained from Table 5-3. Figure B-30 Geometry of considered specimen The maximum principal strain range is obtained by performing a finite element analysis with the FEM-software ABAQUS. The finite element analysis was performed with 8-noded shell elements with reduced integration (S8R). The material modelling is according to specifications in Section [4.7.5]. The boundary conditions and cyclic displacement is applied as illustrated in Figure B-32. Note that a total of 6 complete load cycles is specified in the analysis in order to see how the stress strain hysteresis curve developed. Figure B-31 Geometry and loading

65 App.B Examples Page 65 Figure B-32 Load steps The maximum principal strain range is obtained according to the following procedure: i) Perform a strain convergence study. The mesh around the hole is refined until the strain value in the relevant nodal point converges. Based on the convergence study it was found sufficient to use 48 elements around the hole. ii) Establish the strain component ranges ( Δ,Δ,Δ, etc.) by subtracting the strain component values of load step 12 from the values of load step 13. Hence, the stress/strain output from the last cycle is used as basis for calculating the design fatigue life. In ABAQUS the strain range is obtained by using the Create Field Output option. iii) Calculate the maximum principal strain range based on the strain component ranges. iv) Calculate the design fatigue life based on the seawater with cathodic protection curve. Figure B-33 shows the maximum principal strain range due to the specified cyclic loading of the plate. The hysteresis loop in the location adjacent to the hole with the highest cyclic strain is plotted in Figure B-34. The maximum principal strain range of ε l = obtained from the last cycle in the finite element analysis is used as basis for calculating the design fatigue life. Hence, by solving Equation (13) in Section a design fatigue life of N = 139 is obtained. Figure B-33 Equivalent strain range

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials.

Objectives. Experimentally determine the yield strength, tensile strength, and modules of elasticity and ductility of given materials. Lab 3 Tension Test Objectives Concepts Background Experimental Procedure Report Requirements Discussion Objectives Experimentally determine the yield strength, tensile strength, and modules of elasticity

More information

Nonlinear Analysis Using Femap with NX Nastran

Nonlinear Analysis Using Femap with NX Nastran Nonlinear Analysis Using Femap with NX Nastran Chip Fricke, Principal Applications Engineer, Agenda Nonlinear Analysis Using Femap with NX Nastran Who am I? Overview of Nonlinear Analysis Comparison of

More information

Optimising plate girder design

Optimising plate girder design Optimising plate girder design NSCC29 R. Abspoel 1 1 Division of structural engineering, Delft University of Technology, Delft, The Netherlands ABSTRACT: In the design of steel plate girders a high degree

More information

Abaqus Technology Brief. Automobile Roof Crush Analysis with Abaqus

Abaqus Technology Brief. Automobile Roof Crush Analysis with Abaqus Abaqus Technology Brief Automobile Roof Crush Analysis with Abaqus TB-06-RCA-1 Revised: April 2007. Summary The National Highway Traffic Safety Administration (NHTSA) mandates the use of certain test procedures

More information

Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1

Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1 Introduction to Solid Modeling Using SolidWorks 2012 SolidWorks Simulation Tutorial Page 1 In this tutorial, we will use the SolidWorks Simulation finite element analysis (FEA) program to analyze the response

More information

The elements used in commercial codes can be classified in two basic categories:

The elements used in commercial codes can be classified in two basic categories: CHAPTER 3 Truss Element 3.1 Introduction The single most important concept in understanding FEA, is the basic understanding of various finite elements that we employ in an analysis. Elements are used for

More information

Deflection Calculation of RC Beams: Finite Element Software Versus Design Code Methods

Deflection Calculation of RC Beams: Finite Element Software Versus Design Code Methods Deflection Calculation of RC Beams: Finite Element Software Versus Design Code Methods G. Kaklauskas, Vilnius Gediminas Technical University, 1223 Vilnius, Lithuania (gintaris.kaklauskas@st.vtu.lt) V.

More information

Back to Elements - Tetrahedra vs. Hexahedra

Back to Elements - Tetrahedra vs. Hexahedra Back to Elements - Tetrahedra vs. Hexahedra Erke Wang, Thomas Nelson, Rainer Rauch CAD-FEM GmbH, Munich, Germany Abstract This paper presents some analytical results and some test results for different

More information

Technology of EHIS (stamping) applied to the automotive parts production

Technology of EHIS (stamping) applied to the automotive parts production Laboratory of Applied Mathematics and Mechanics Technology of EHIS (stamping) applied to the automotive parts production Churilova Maria, Saint-Petersburg State Polytechnical University Department of Applied

More information

Lap Fillet Weld Calculations and FEA Techniques

Lap Fillet Weld Calculations and FEA Techniques Lap Fillet Weld Calculations and FEA Techniques By: MS.ME Ahmad A. Abbas Sr. Analysis Engineer Ahmad.Abbas@AdvancedCAE.com www.advancedcae.com Sunday, July 11, 2010 Advanced CAE All contents Copyright

More information

Chapter Outline. Mechanical Properties of Metals How do metals respond to external loads?

Chapter Outline. Mechanical Properties of Metals How do metals respond to external loads? Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain Tension Compression Shear Torsion Elastic deformation Plastic Deformation Yield Strength Tensile Strength Ductility

More information

ANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET

ANALYTICAL AND EXPERIMENTAL EVALUATION OF SPRING BACK EFFECTS IN A TYPICAL COLD ROLLED SHEET International Journal of Mechanical Engineering and Technology (IJMET) Volume 7, Issue 1, Jan-Feb 2016, pp. 119-130, Article ID: IJMET_07_01_013 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=7&itype=1

More information

Solved with COMSOL Multiphysics 4.3

Solved with COMSOL Multiphysics 4.3 Vibrating String Introduction In the following example you compute the natural frequencies of a pre-tensioned string using the 2D Truss interface. This is an example of stress stiffening ; in fact the

More information

Course in. Nonlinear FEM

Course in. Nonlinear FEM Course in Introduction Outline Lecture 1 Introduction Lecture 2 Geometric nonlinearity Lecture 3 Material nonlinearity Lecture 4 Material nonlinearity continued Lecture 5 Geometric nonlinearity revisited

More information

Numerical Analysis of Independent Wire Strand Core (IWSC) Wire Rope

Numerical Analysis of Independent Wire Strand Core (IWSC) Wire Rope Numerical Analysis of Independent Wire Strand Core (IWSC) Wire Rope Rakesh Sidharthan 1 Gnanavel B K 2 Assistant professor Mechanical, Department Professor, Mechanical Department, Gojan engineering college,

More information

CH 6: Fatigue Failure Resulting from Variable Loading

CH 6: Fatigue Failure Resulting from Variable Loading CH 6: Fatigue Failure Resulting from Variable Loading Some machine elements are subjected to static loads and for such elements static failure theories are used to predict failure (yielding or fracture).

More information

Finite Element Formulation for Plates - Handout 3 -

Finite Element Formulation for Plates - Handout 3 - Finite Element Formulation for Plates - Handout 3 - Dr Fehmi Cirak (fc286@) Completed Version Definitions A plate is a three dimensional solid body with one of the plate dimensions much smaller than the

More information

Tensile Testing Laboratory

Tensile Testing Laboratory Tensile Testing Laboratory By Stephan Favilla 0723668 ME 354 AC Date of Lab Report Submission: February 11 th 2010 Date of Lab Exercise: January 28 th 2010 1 Executive Summary Tensile tests are fundamental

More information

Nonlinear analysis and form-finding in GSA Training Course

Nonlinear analysis and form-finding in GSA Training Course Nonlinear analysis and form-finding in GSA Training Course Non-linear analysis and form-finding in GSA 1 of 47 Oasys Ltd Non-linear analysis and form-finding in GSA 2 of 47 Using the GSA GsRelax Solver

More information

Shell Elements in ABAQUS/Explicit

Shell Elements in ABAQUS/Explicit ABAQUS/Explicit: Advanced Topics Appendix 2 Shell Elements in ABAQUS/Explicit ABAQUS/Explicit: Advanced Topics A2.2 Overview ABAQUS/Explicit: Advanced Topics ABAQUS/Explicit: Advanced Topics A2.4 Triangular

More information

The Basics of FEA Procedure

The Basics of FEA Procedure CHAPTER 2 The Basics of FEA Procedure 2.1 Introduction This chapter discusses the spring element, especially for the purpose of introducing various concepts involved in use of the FEA technique. A spring

More information

New approaches in Eurocode 3 efficient global structural design

New approaches in Eurocode 3 efficient global structural design New approaches in Eurocode 3 efficient global structural design Part 1: 3D model based analysis using general beam-column FEM Ferenc Papp* and József Szalai ** * Associate Professor, Department of Structural

More information

1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 1 Introduction / Design Criteria for Reinforced Concrete Structures

1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 1 Introduction / Design Criteria for Reinforced Concrete Structures Prof. Oral Buyukozturk Massachusetts Institute of Technology Outline 1 1.054/1.541 Mechanics and Design of Concrete Structures (3-0-9) Outline 1 Introduction / Design Criteria for Reinforced Concrete Structures

More information

Technical Report Example (1) Chartered (CEng) Membership

Technical Report Example (1) Chartered (CEng) Membership Technical Report Example (1) Chartered (CEng) Membership A TECHNICAL REPORT IN SUPPORT OF APPLICATION FOR CHARTERED MEMBERSHIP OF IGEM DESIGN OF 600 (103 BAR) 820MM SELF SEALING REPAIR CLAMP AND VERIFICATION

More information

NOTCHES AND THEIR EFFECTS. Ali Fatemi - University of Toledo All Rights Reserved Chapter 7 Notches and Their Effects 1

NOTCHES AND THEIR EFFECTS. Ali Fatemi - University of Toledo All Rights Reserved Chapter 7 Notches and Their Effects 1 NOTCHES AND THEIR EFFECTS Ali Fatemi - University of Toledo All Rights Reserved Chapter 7 Notches and Their Effects 1 CHAPTER OUTLINE Background Stress/Strain Concentrations S-N Approach for Notched Members

More information

Fatigue Performance Evaluation of Forged Steel versus Ductile Cast Iron Crankshaft: A Comparative Study (EXECUTIVE SUMMARY)

Fatigue Performance Evaluation of Forged Steel versus Ductile Cast Iron Crankshaft: A Comparative Study (EXECUTIVE SUMMARY) Fatigue Performance Evaluation of Forged Steel versus Ductile Cast Iron Crankshaft: A Comparative Study (EXECUTIVE SUMMARY) Ali Fatemi, Jonathan Williams and Farzin Montazersadgh Professor and Graduate

More information

Local buckling of plates made of high strength steel

Local buckling of plates made of high strength steel Local buckling of plates made of high strength steel Tapani Halmea, Lauri Huusko b,a, Gary Marquis a, Timo Björk a a Lappeenranta University of Technology, Faculty of Technology Engineering, Lappeenranta,

More information

STRAIN-LIFE (e -N) APPROACH

STRAIN-LIFE (e -N) APPROACH CYCLIC DEFORMATION & STRAIN-LIFE (e -N) APPROACH MONOTONIC TENSION TEST AND STRESS-STRAIN BEHAVIOR STRAIN-CONTROLLED TEST METHODS CYCLIC DEFORMATION AND STRESS-STRAIN BEHAVIOR STRAIN-BASED APPROACH TO

More information

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS

COMPUTATIONAL ENGINEERING OF FINITE ELEMENT MODELLING FOR AUTOMOTIVE APPLICATION USING ABAQUS International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 7, Issue 2, March-April 2016, pp. 30 52, Article ID: IJARET_07_02_004 Available online at http://www.iaeme.com/ijaret/issues.asp?jtype=ijaret&vtype=7&itype=2

More information

Lecture 12: Fundamental Concepts in Structural Plasticity

Lecture 12: Fundamental Concepts in Structural Plasticity Lecture 12: Fundamental Concepts in Structural Plasticity Plastic properties of the material were already introduced briefly earlier in the present notes. The critical slenderness ratio of column is controlled

More information

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied

Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Mechanical Properties of Metals Mechanical Properties refers to the behavior of material when external forces are applied Stress and strain fracture or engineering point of view: allows to predict the

More information

TENSILE TESTING PRACTICAL

TENSILE TESTING PRACTICAL TENSILE TESTING PRACTICAL MTK 2B- Science Of Materials Ts epo Mputsoe 215024596 Summary Material have different properties all varying form mechanical to chemical properties. Taking special interest in

More information

CRITERIA FOR PRELOADED BOLTS

CRITERIA FOR PRELOADED BOLTS National Aeronautics and Space Administration Lyndon B. Johnson Space Center Houston, Texas 77058 REVISION A JULY 6, 1998 REPLACES BASELINE SPACE SHUTTLE CRITERIA FOR PRELOADED BOLTS CONTENTS 1.0 INTRODUCTION..............................................

More information

A NEW DESIGN METHOD FOR INDUSTRIAL PORTAL FRAMES IN FIRE

A NEW DESIGN METHOD FOR INDUSTRIAL PORTAL FRAMES IN FIRE Application of Structural Fire Engineering, 9-2 February 29, Prague, Czech Republic A NEW DESIGN METHOD FOR INDUSTRIAL PORTAL FRAMES IN FIRE Yuanyuan Song a, Zhaohui Huang b, Ian Burgess c, Roger Plank

More information

Approximate Analysis of Statically Indeterminate Structures

Approximate Analysis of Statically Indeterminate Structures Approximate Analysis of Statically Indeterminate Structures Every successful structure must be capable of reaching stable equilibrium under its applied loads, regardless of structural behavior. Exact analysis

More information

The Suitability of CRA Lined Pipes for Flowlines Susceptible to Lateral Buckling SUT Global Pipeline Buckling Symposium, 23 24 February 2011

The Suitability of CRA Lined Pipes for Flowlines Susceptible to Lateral Buckling SUT Global Pipeline Buckling Symposium, 23 24 February 2011 The Suitability of CRA Lined Pipes for Flowlines Susceptible to Lateral Buckling SUT Global Pipeline Buckling Symposium, 23 24 February 2011 Duncan Wilmot, Technical Manager, Cladtek International, Australia

More information

bi directional loading). Prototype ten story

bi directional loading). Prototype ten story NEESR SG: Behavior, Analysis and Design of Complex Wall Systems The laboratory testing presented here was conducted as part of a larger effort that employed laboratory testing and numerical simulation

More information

State of Stress at Point

State of Stress at Point State of Stress at Point Einstein Notation The basic idea of Einstein notation is that a covector and a vector can form a scalar: This is typically written as an explicit sum: According to this convention,

More information

An Overview of the Finite Element Analysis

An Overview of the Finite Element Analysis CHAPTER 1 An Overview of the Finite Element Analysis 1.1 Introduction Finite element analysis (FEA) involves solution of engineering problems using computers. Engineering structures that have complex geometry

More information

INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES. Interpretations of the FTP

INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES. Interpretations of the FTP INTERNATIONAL ASSOCIATION OF CLASSIFICATION SOCIETIES Interpretations of the FTP CONTENTS FTP1 Adhesives used in A or B class divisions (FTP Code 3.1, Res A.754 para. 3.2.3) June 2000 FTP2 Pipe and duct

More information

INTRODUCTION TO LIMIT STATES

INTRODUCTION TO LIMIT STATES 4 INTRODUCTION TO LIMIT STATES 1.0 INTRODUCTION A Civil Engineering Designer has to ensure that the structures and facilities he designs are (i) fit for their purpose (ii) safe and (iii) economical and

More information

ANALYSIS OF A LAP JOINT FRICTION CONNECTION USING HIGH STRENGTH BOLTS

ANALYSIS OF A LAP JOINT FRICTION CONNECTION USING HIGH STRENGTH BOLTS Nordic Steel Construction Conference 212 Hotel Bristol, Oslo, Norway 5-7 September 212 ANALYSIS OF A LAP JOINT FRICTION CONNECTION USING HIGH STRENGTH BOLTS Marouene Limam a, Christine Heistermann a and

More information

BUCKLING OF BARS, PLATES, AND SHELLS. Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219

BUCKLING OF BARS, PLATES, AND SHELLS. Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219 BUCKLING OF BARS, PLATES, AND SHELLS ROBERT M. JONES Science and Mechanics Professor Emeritus of Engineering Virginia Polytechnic Institute and State University Biacksburg, Virginia 24061-0219 Bull Ridge

More information

A Study of Durability Analysis Methodology for Engine Valve Considering Head Thermal Deformation and Dynamic Behavior

A Study of Durability Analysis Methodology for Engine Valve Considering Head Thermal Deformation and Dynamic Behavior A Study of Durability Analysis Methodology for Engine Valve Considering Head Thermal Deformation and Dynamic Behavior Kum-Chul, Oh 1, Sang-Woo Cha 1 and Ji-Ho Kim 1 1 R&D Center, Hyundai Motor Company

More information

Loads Tools Checks Reports

Loads Tools Checks Reports Loads Tools Checks Reports SDC Verifier or the Structural Design Code Verifier is a powerful postprocessor program with an advanced calculation core which works seamlessly with Siemens multi-solver, FEA

More information

Tensile Testing of Steel

Tensile Testing of Steel C 265 Lab No. 2: Tensile Testing of Steel See web for typical report format including: TITL PAG, ABSTRACT, TABL OF CONTNTS, LIST OF TABL, LIST OF FIGURS 1.0 - INTRODUCTION See General Lab Report Format

More information

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS

EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME 2 ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS ENGINEERING COMPONENTS EDEXCEL NATIONAL CERTIFICATE/DIPLOMA MECHANICAL PRINCIPLES OUTCOME ENGINEERING COMPONENTS TUTORIAL 1 STRUCTURAL MEMBERS Structural members: struts and ties; direct stress and strain,

More information

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014

Finite Element Method (ENGC 6321) Syllabus. Second Semester 2013-2014 Finite Element Method Finite Element Method (ENGC 6321) Syllabus Second Semester 2013-2014 Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered

More information

Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions

Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions Mesh Discretization Error and Criteria for Accuracy of Finite Element Solutions Chandresh Shah Cummins, Inc. Abstract Any finite element analysis performed by an engineer is subject to several types of

More information

CHAPTER 4 4 NUMERICAL ANALYSIS

CHAPTER 4 4 NUMERICAL ANALYSIS 41 CHAPTER 4 4 NUMERICAL ANALYSIS Simulation is a powerful tool that engineers use to predict the result of a phenomenon or to simulate the working situation in which a part or machine will perform in

More information

Uniaxial Tension and Compression Testing of Materials. Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng

Uniaxial Tension and Compression Testing of Materials. Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng Uniaxial Tension and Compression Testing of Materials Nikita Khlystov Daniel Lizardo Keisuke Matsushita Jennie Zheng 3.032 Lab Report September 25, 2013 I. Introduction Understanding material mechanics

More information

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES

EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES EFFECTS ON NUMBER OF CABLES FOR MODAL ANALYSIS OF CABLE-STAYED BRIDGES Yang-Cheng Wang Associate Professor & Chairman Department of Civil Engineering Chinese Military Academy Feng-Shan 83000,Taiwan Republic

More information

Stress Strain Relationships

Stress Strain Relationships Stress Strain Relationships Tensile Testing One basic ingredient in the study of the mechanics of deformable bodies is the resistive properties of materials. These properties relate the stresses to the

More information

METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING

METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING METU DEPARTMENT OF METALLURGICAL AND MATERIALS ENGINEERING Met E 206 MATERIALS LABORATORY EXPERIMENT 1 Prof. Dr. Rıza GÜRBÜZ Res. Assist. Gül ÇEVİK (Room: B-306) INTRODUCTION TENSION TEST Mechanical testing

More information

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading:

SEISMIC DESIGN. Various building codes consider the following categories for the analysis and design for earthquake loading: SEISMIC DESIGN Various building codes consider the following categories for the analysis and design for earthquake loading: 1. Seismic Performance Category (SPC), varies from A to E, depending on how the

More information

Finite Element Formulation for Beams - Handout 2 -

Finite Element Formulation for Beams - Handout 2 - Finite Element Formulation for Beams - Handout 2 - Dr Fehmi Cirak (fc286@) Completed Version Review of Euler-Bernoulli Beam Physical beam model midline Beam domain in three-dimensions Midline, also called

More information

Design rules for bridges in Eurocode 3

Design rules for bridges in Eurocode 3 Design rules for bridges in Eurocode 3 Gerhard Sedlacek Christian üller Survey of the Eurocodes EN 1991 EN 1990 Eurocode: Basis of Design EN 1992 to EN 1996 Eurocode 1: Actions on Structures Eurocode 2:

More information

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems:

SLAB DESIGN. Introduction ACI318 Code provides two design procedures for slab systems: Reading Assignment SLAB DESIGN Chapter 9 of Text and, Chapter 13 of ACI318-02 Introduction ACI318 Code provides two design procedures for slab systems: 13.6.1 Direct Design Method (DDM) For slab systems

More information

Hybrid simulation evaluation of the suspended zipper braced frame

Hybrid simulation evaluation of the suspended zipper braced frame Hybrid simulation evaluation of the suspended zipper braced frame Tony Yang Post-doctoral scholar University of California, Berkeley Acknowledgements: Andreas Schellenberg, Bozidar Stojadinovic, Jack Moehle

More information

Introduction to Mechanical Behavior of Biological Materials

Introduction to Mechanical Behavior of Biological Materials Introduction to Mechanical Behavior of Biological Materials Ozkaya and Nordin Chapter 7, pages 127-151 Chapter 8, pages 173-194 Outline Modes of loading Internal forces and moments Stiffness of a structure

More information

Strip Flatness Prediction in a 4 High Tandem Mill Using a Dynamic Model.

Strip Flatness Prediction in a 4 High Tandem Mill Using a Dynamic Model. Strip Flatness Prediction in a 4 High Tandem Mill Using a Dynamic Model. M. A. Bello-Gomez 1, M. P. Guerrero-Mata 1, L. A. Leduc Lezama 1, T. P. Berber- Solano 1, L. Nieves 2, F. Gonzalez 2, H. R. Siller

More information

Mechanical Properties - Stresses & Strains

Mechanical Properties - Stresses & Strains Mechanical Properties - Stresses & Strains Types of Deformation : Elasic Plastic Anelastic Elastic deformation is defined as instantaneous recoverable deformation Hooke's law : For tensile loading, σ =

More information

Hardened Concrete. Lecture No. 14

Hardened Concrete. Lecture No. 14 Hardened Concrete Lecture No. 14 Strength of Concrete Strength of concrete is commonly considered its most valuable property, although in many practical cases, other characteristics, such as durability

More information

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.)

III. Compression Members. Design of Steel Structures. Introduction. Compression Members (cont.) ENCE 455 Design of Steel Structures III. Compression Members C. C. Fu, Ph.D., P.E. Civil and Environmental Engineering Department University it of Maryland Compression Members Following subjects are covered:

More information

Burst Pressure Prediction of Pressure Vessel using FEA

Burst Pressure Prediction of Pressure Vessel using FEA Burst Pressure Prediction of Pressure Vessel using FEA Nidhi Dwivedi, Research Scholar (G.E.C, Jabalpur, M.P), Veerendra Kumar Principal (G.E.C, Jabalpur, M.P) Abstract The main objective of this paper

More information

AN EXPLANATION OF JOINT DIAGRAMS

AN EXPLANATION OF JOINT DIAGRAMS AN EXPLANATION OF JOINT DIAGRAMS When bolted joints are subjected to external tensile loads, what forces and elastic deformation really exist? The majority of engineers in both the fastener manufacturing

More information

Linear Static Analysis of a Cantilever Beam Using Beam Library (SI Units)

Linear Static Analysis of a Cantilever Beam Using Beam Library (SI Units) APPENDIX A Linear Static Analysis of a Cantilever Beam Using Beam Library (SI Units) Objectives: Create a geometric representation of a cantilever beam. Use the geometry model to define an MSC.Nastran

More information

Damage due to fatigue occurs when loading is markedly varying in time. R decreases with time S T. MSÚ F max

Damage due to fatigue occurs when loading is markedly varying in time. R decreases with time S T. MSÚ F max 5. Fatigue of steel structures Fatigue loading, Wöhler s approach and fracture mechanics, fatigue strength, influence of notches, damage accumulation, Eurocode approach. Damage due to fatigue occurs when

More information

Application of LS-DYNA Implicit for the Design of Plastic Components

Application of LS-DYNA Implicit for the Design of Plastic Components 9. LS-DYNA Forum, Bamberg 2010 Application of LS-DYNA Implicit for the Design of Plastic Components Thomas Wimmer, Martin Fritz 4a engineering GmbH, Traboch - A Abstract: LS-Dyna is a common code in explicit

More information

Long term performance of polymers

Long term performance of polymers 1.0 Introduction Long term performance of polymers Polymer materials exhibit time dependent behavior. The stress and strain induced when a load is applied are a function of time. In the most general form

More information

Preliminary steel concrete composite bridge design charts for Eurocodes

Preliminary steel concrete composite bridge design charts for Eurocodes Preliminary steel concrete composite bridge 90 Rachel Jones Senior Engineer Highways & Transportation Atkins David A Smith Regional Head of Bridge Engineering Highways & Transportation Atkins Abstract

More information

different levels, also called repeated, alternating, or fluctuating stresses.

different levels, also called repeated, alternating, or fluctuating stresses. Fatigue and Dynamic Loading 1 Fti Fatigue fil failure: 2 Static ti conditions : loads are applied gradually, to give sufficient i time for the strain to fully develop. Variable conditions : stresses vary

More information

Design of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column

Design of reinforced concrete columns. Type of columns. Failure of reinforced concrete columns. Short column. Long column Design of reinforced concrete columns Type of columns Failure of reinforced concrete columns Short column Column fails in concrete crushed and bursting. Outward pressure break horizontal ties and bend

More information

SOUTH AFRICAN NATIONAL INSTITUTE OF ROCK MECHANICS CHAMBER OF MINES OF SOUTH AFRICA CERTIFICATE IN ROCK MECHANICS PART 1 ROCK MECHANICS THEORY

SOUTH AFRICAN NATIONAL INSTITUTE OF ROCK MECHANICS CHAMBER OF MINES OF SOUTH AFRICA CERTIFICATE IN ROCK MECHANICS PART 1 ROCK MECHANICS THEORY SOUTH AFRICAN NATIONAL INSTITUTE OF ROCK MECHANICS CHAMBER OF MINES OF SOUTH AFRICA CERTIFICATE IN ROCK MECHANICS PART 1 ROCK MECHANICS THEORY SYLLABUS Copyright 2006 SANIRE CONTENTS PREAMBLE... 3 TOPICS

More information

Force measurement. Forces VECTORIAL ISSUES ACTION ET RÉACTION ISOSTATISM

Force measurement. Forces VECTORIAL ISSUES ACTION ET RÉACTION ISOSTATISM Force measurement Forces VECTORIAL ISSUES In classical mechanics, a force is defined as "an action capable of modifying the quantity of movement of a material point". Therefore, a force has the attributes

More information

The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM

The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM 1 The simulation of machine tools can be divided into two stages. In the first stage the mechanical behavior of a machine tool is simulated with FEM tools. The approach to this simulation is different

More information

Objective To conduct Charpy V-notch impact test and determine the ductile-brittle transition temperature of steels.

Objective To conduct Charpy V-notch impact test and determine the ductile-brittle transition temperature of steels. IMPACT TESTING Objective To conduct Charpy V-notch impact test and determine the ductile-brittle transition temperature of steels. Equipment Coolants Standard Charpy V-Notched Test specimens Impact tester

More information

COMPARISON OF STRESS BETWEEN WINKLER-BACH THEORY AND ANSYS FINITE ELEMENT METHOD FOR CRANE HOOK WITH A TRAPEZOIDAL CROSS-SECTION

COMPARISON OF STRESS BETWEEN WINKLER-BACH THEORY AND ANSYS FINITE ELEMENT METHOD FOR CRANE HOOK WITH A TRAPEZOIDAL CROSS-SECTION COMPARISON OF STRESS BETWEEN WINKLER-BACH THEORY AND ANSYS FINITE ELEMENT METHOD FOR CRANE HOOK WITH A TRAPEZOIDAL CROSS-SECTION Yogesh Tripathi 1, U.K Joshi 2 1 Postgraduate Student, 2 Associate Professor,

More information

RP-C203: Fatigue design of offshore steel structures

RP-C203: Fatigue design of offshore steel structures RECOMMENDED PRCTICE DNVGL-RP-0005:04-06 RP-C03: Fatigue design of offshore steel structures The electronic pdf version of this document found through http://www.dnvgl.com is the officially binding version.

More information

NAPA/MAESTRO Interface. Reducing the Level of Effort for Ship Structural Design

NAPA/MAESTRO Interface. Reducing the Level of Effort for Ship Structural Design NAPA/MAESTRO Interface Reducing the Level of Effort for Ship Structural Design 12/3/2010 Table of Contents Introduction... 1 Why Create a NAPA/MAESTRO Interface... 1 Level of Effort Comparison for Two

More information

MECHANICS OF MATERIALS

MECHANICS OF MATERIALS T dition CHTR MCHNICS OF MTRIS Ferdinand. Beer. Russell Johnston, Jr. John T. DeWolf ecture Notes: J. Walt Oler Texas Tech University Stress and Strain xial oading - Contents Stress & Strain: xial oading

More information

FATIGUE CONSIDERATION IN DESIGN

FATIGUE CONSIDERATION IN DESIGN FATIGUE CONSIDERATION IN DESIGN OBJECTIVES AND SCOPE In this module we will be discussing on design aspects related to fatigue failure, an important mode of failure in engineering components. Fatigue failure

More information

Pancake-type collapse energy absorption mechanisms and their influence on the final outcome (complete version)

Pancake-type collapse energy absorption mechanisms and their influence on the final outcome (complete version) Report, Structural Analysis and Steel Structures Institute, Hamburg University of Technology, Hamburg, June, 2013 Pancake-type collapse energy absorption mechanisms and their influence on the final outcome

More information

EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST

EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST EVALUATION OF SEISMIC RESPONSE - FACULTY OF LAND RECLAMATION AND ENVIRONMENTAL ENGINEERING -BUCHAREST Abstract Camelia SLAVE University of Agronomic Sciences and Veterinary Medicine of Bucharest, 59 Marasti

More information

Numerical modelling of shear connection between concrete slab and sheeting deck

Numerical modelling of shear connection between concrete slab and sheeting deck 7th fib International PhD Symposium in Civil Engineering 2008 September 10-13, Universität Stuttgart, Germany Numerical modelling of shear connection between concrete slab and sheeting deck Noémi Seres

More information

Three dimensional thermoset composite curing simulations involving heat conduction, cure kinetics, and viscoelastic stress strain response

Three dimensional thermoset composite curing simulations involving heat conduction, cure kinetics, and viscoelastic stress strain response Three dimensional thermoset composite curing simulations involving heat conduction, cure kinetics, and viscoelastic stress strain response Harrison Poon, Seid Koric, M. Fouad Ahmad National Center for

More information

Reliable FE-Modeling with ANSYS

Reliable FE-Modeling with ANSYS Reliable FE-Modeling with ANSYS Thomas Nelson, Erke Wang CADFEM GmbH, Munich, Germany Abstract ANSYS is one of the leading commercial finite element programs in the world and can be applied to a large

More information

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE

DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE DYNAMIC ANALYSIS OF THICK PLATES SUBJECTED TO EARTQUAKE ÖZDEMİR Y. I, AYVAZ Y. Posta Adresi: Department of Civil Engineering, Karadeniz Technical University, 68 Trabzon, TURKEY E-posta: yaprakozdemir@hotmail.com

More information

DS/EN 1990 DK NA:2013

DS/EN 1990 DK NA:2013 National Annex to Eurocode: Basis of structural design Foreword This National Annex (NA) is a consolidation and revision of DS/EN 1990 DK NA 2010 and DS/EN 1990 DK NA Addendum 1:2010 and supersedes these

More information

Solution for Homework #1

Solution for Homework #1 Solution for Homework #1 Chapter 2: Multiple Choice Questions (2.5, 2.6, 2.8, 2.11) 2.5 Which of the following bond types are classified as primary bonds (more than one)? (a) covalent bonding, (b) hydrogen

More information

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab,

DESIGN OF SLABS. 3) Based on support or boundary condition: Simply supported, Cantilever slab, DESIGN OF SLABS Dr. G. P. Chandradhara Professor of Civil Engineering S. J. College of Engineering Mysore 1. GENERAL A slab is a flat two dimensional planar structural element having thickness small compared

More information

P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures

P4 Stress and Strain Dr. A.B. Zavatsky MT07 Lecture 3 Statically Indeterminate Structures 4 Stress and Strain Dr... Zavatsky MT07 ecture 3 Statically Indeterminate Structures Statically determinate structures. Statically indeterminate structures (equations of equilibrium, compatibility, and

More information

EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE COLLAR PRODUCTION ON THE PIERCED FLAT SHEET METAL USING LASER FORMING PROCESS

EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE COLLAR PRODUCTION ON THE PIERCED FLAT SHEET METAL USING LASER FORMING PROCESS JOURNAL OF CURRENT RESEARCH IN SCIENCE (ISSN 2322-5009) CODEN (USA): JCRSDJ 2014, Vol. 2, No. 2, pp:277-284 Available at www.jcrs010.com ORIGINAL ARTICLE EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE COLLAR

More information

STIFFENING OF THIN CYLINDRICAL SILO SHELL AGAINST BUCKLING LOADS

STIFFENING OF THIN CYLINDRICAL SILO SHELL AGAINST BUCKLING LOADS STIFFENING OF THIN CYLINDRICAL SILO SHELL AGAINST BUCKLING LOADS Fuat TİNİŞ, tinis@gama.com.tr GAMA Industrial Plants Manufacturing & Erection Corp., 06791, Ankara, Turkey Fatih BAZMAN, fbazman@gama.com.tr

More information

CE591 Fall 2013 Lecture 26: Moment Connections

CE591 Fall 2013 Lecture 26: Moment Connections CE591 Fall 2013 Lecture 26: Moment Connections Explain basic design procedure for moment (FR) connections Explain considerations for connections in momentresisting frames for seismic demands Describe problems

More information

جامعة البلقاء التطبيقية

جامعة البلقاء التطبيقية AlBalqa Applied University تا سست عام 997 The curriculum of associate degree in Air Conditioning, Refrigeration and Heating Systems consists of (7 credit hours) as follows: Serial No. Requirements First

More information

Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak (fc286@) Office: Inglis building mezzanine level (INO 31)

Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak (fc286@) Office: Inglis building mezzanine level (INO 31) Plates and Shells: Theory and Computation - 4D9 - Dr Fehmi Cirak (fc286@) Office: Inglis building mezzanine level (INO 31) Outline -1-! This part of the module consists of seven lectures and will focus

More information

Reinforced Concrete Design

Reinforced Concrete Design FALL 2013 C C Reinforced Concrete Design CIVL 4135 ii 1 Chapter 1. Introduction 1.1. Reading Assignment Chapter 1 Sections 1.1 through 1.8 of text. 1.2. Introduction In the design and analysis of reinforced

More information

FATIGUE DESIGN OF OFFSHORE STEEL STRUCTURES

FATIGUE DESIGN OF OFFSHORE STEEL STRUCTURES RECOMMENDED PRCTICE DNV-RP-C03 FTIGUE DESIGN OF OFFSHORE STEEL STRUCTURES PRIL 00 FOREWORD (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, property and the environment,

More information