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April 2009/ John Wægter

Note 3.1

Stress concentrations in simple tubular joints

Introduction......................................................................................................................................2 Types of joints..................................................................................................................................4

General .........................................................................................................................................4 Definitions and symbols ..............................................................................................................4 Stress concentration factors .........................................................................................................6

Classification of simple joints........................................................................................................10 General .......................................................................................................................................10 Influence from force flow ..........................................................................................................10

Tubular joints and members according to DNV-RP-C203............................................................12 Introduction................................................................................................................................12 Tubular joints (2.3.4) .................................................................................................................12 Stress concentration factors for simple tubular joints (3.3.1) ....................................................12 Superposition of stresses in tubular joints (3.3.2)......................................................................12 Tubular joints welded from one side (3.3.3)..............................................................................14 DNV Appendix B.......................................................................................................................15

References......................................................................................................................................25

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Stress concentrations in simple tubular joints

Introduction Typical offshore structures are composed of three dimensional frames fabricated from steel tubulars. The connections between the different tubular members are denoted tubular joints. A tubular joint is made up of a chord (element of largest diameter) and one or more braces.

Figure 1 Tubular joints Both the structural members (elements) and the tubular joints must be designed to sustain the ultimate design load (e.g. the 100-year design condition), and the long term cyclic stresses due to environmental action. This lecture focuses on the fatigue aspect by demonstrating how the hot spot stress approach is used. The design process consists of a global analysis and a local analysis. The global analysis determines the sectional forces and the nominal (beam) stresses in the various elements of the structure.

Figure 2 Global and local analysis

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These sectional forces establish the boundary conditions for local stress analyses of the joints, see Figure 3.

Figure 3 Tubular joint for local analysis A local linear stress analysis will show that the stresses near the welded intersections are several times higher than the nominal stresses, sometimes even higher than the formal yield stress. We typically find very concentrated stresses and they depend highly on the detailing of the joint. Stresses of the order 2-10 times the nominal stresses are not unusual, and even higher values are sometimes found. The locations of the highest stresses are called hot spots. They are practically always found in the joints, and not in the members. The problem therefore boils down to a detailed stress determination of a tubular connection with known geometry and boundary condition in the shape of known forces. A detailed investigation of such a joint will show that we have two places where the stresses are extra high:

• one is at the weld toe at the brace side, • the other at the weld toe at the chord side.

These points are the hot spots.

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Types of joints

General Tubular joints come in many shapes such as obviously complicated joints exemplified by the stiffened joint shown to the right, and apparently simple planar joints like those shown to the left, see Figure 4.

Simple joints

Complex joint

Figure 4 Types of joints The term simple joint is deceptive, because even the simplest tubular joint has a complex stress pattern for the most basic loads. Therefore, an in depth stress analysis of a tubular joint always requires a finite element analysis, or alternatively, stress determination by experimental methods. Although real structures often are composed of multiplanar joints, the basic understanding of simple uniplanar joints such as T-joints, Y-joints, K-joints and X-joints plays an important role in the fatigue design of tubular joints. Present state of the art allows the design of not too complicated tubular joints to be based on the approach for uniplanar joints. The joint is then considered as uniplanar in relevant planes, and the effect of braces outside the considered plane is disregarded. - However, more advanced methods to be covered in a later lecture may also be used to consider the true interaction effects in multiplanar joints.

Definitions and symbols The most important loads in a tubular joint are the axial load, the in-plane bending moment and the out-of-plane bending moment. The corresponding three basic load cases are shown in Figure 5.

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Figure 5 Basic tubular joint load cases The geometric parameters used to define a tubular joint vary with the specific type of the joint, but the parameters given below for a Y-joint are fundamental, and these parameters are shared by most joint types.

• Chord outside diameter D • Brace outside diameter d • Chord wall thickness T • Brace wall thickness t • Brace inclination angle θ • Chord length L

More detailed definitions for other types of joints are given later.

Figure 6 Definitions for Y-joint

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In the design of tubular joints one generally considers each brace in turn in association with the chord. However, for the Y-joints there is only one brace to consider. The following non-dimensional parameters are used:

Diameter ratio dD

β = (1)

Chord stiffness 2DT

γ = (2)

Wall thickness ratio tT

τ = (3)

Chord length parameter 2LD

α = (4)

Generally, γ gives a measure of the chord radial stiffness, and it is a very important parameter in many SCF formulae.

Stress concentration factors Figure 7 illustrates the fundamental problem in tubular joints which is transferring in-plane forces (axial load) from the brace to bending and transverse loads in the chord. The mechanism is in principle quite similar to loading a cylindrical shell (the chord) with a concentrated load (from the brace).

Figure 7 Stress concentrations for axial load in T-joint

1 ksi = 6.9 MPa

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The local stresses near the welded connection between the chord and the brace are several times the nominal stresses and the load transferred across the weld is far from even, which is the result of the differences in relative stiffness of the brace and the chord. The thin chord wall is inefficient in carrying loads normal to the chord surface, as opposed to in-plane loads, and large bending stresses occur due to the ovalisation of the chord. As a result the peak hot spot stress in the chord reaches 160 ksi. We are now ready for a precise definition of the stress concentration factor which is defined as the local stress relative to the nominal brace stress. Since the chord stress is 7.3 times the 22 ksi nominal stress in the brace, we say that the stress concentration factor for the chord is 7.3 for axial load. It should be observed that what is shown in Figure 5 is only one load case, namely axial load. Other relevant load cases would be in-plane bending and out-of-plane bending. For this T-joint we would therefore determine 3 different SCFs, namely one for axial load, one for in plane bending and one for out-of-plane bending. When we talk about stress concentration factors in tubular joints we always relate the local stress to the nominal stress in the brace. This is true whether we consider the stress in the chord or the brace, and whether the stress comes from moments or axial loads. Further, we find high stresses in both the brace and in the chord, and therefore talk about the SCF on the brace side, and the SCF on the chord side. The SCF for axial load has already been determined to 7.3 on the chord side in this example, and if we had known the value of the peak stress in the brace we could have determined the brace SCF as the ratio between this stress and the 22 ksi nominal stress. Quite similar concentrated stressed can be found if we study the hot spot stresses in a Y-joint, see Figure 8. In this example the chord SCF can be seen to be 5.24.

Figure 8 Structural stresses in Y-joint

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Because the Y-connection has part of its axial load in the brace transferred into the chord as membrane loads and not as punching load normal to the chord shell surface (as for the T-joint) it makes sense that the SCF for the Y-joints is lower than the value (7.3) determined in the previous example. It is generally assumed that fatigue cracks will develop where the peak stresses occur i.e. normally at the weld toe. Therefore, ideally, the fatigue life should be based on these peak stresses. But unfortunately research with tubular joints over the last two decades has shown that these peak stresses are strongly influenced by weld shape irregularities (notches and discontinuities). And because the weld shape effects are highly localized and difficult to quantify the offshore industry does not use these notch stresses. Instead, the industry early decided to use structural hot spot stresses as the basis for fatigue life calculations. The hot spot stresses are defined as the stresses at the weld toe locations taking into consideration all geometrical influences except the local weld notch effect. If we examine the stresses close to the weld we can see that they increase rather smoothly in areas that are not too close to the weld. This increase is due to the geometric influence of the joint. Very closely to the weld we find a rapid increase in stresses due to the weld geometry. This effect is often called the local weld notch effect and results in what is often called the notch stresses, see Figure 9, which shows a detail from the Y-joint in Figure 8.

Figure 9 Extrapolation for hot spot stresses We can see that the hot spot stresses can be determined by linear extrapolation of the structural stresses from points which are located just outside the influence zone from the notch. More details in relation to the definition of extrapolation procedures can be found in Figure 10.

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Figure 10 Determination of hot spot stress Most research today recommends the use of linearly extrapolated structural hot spot stresses. When the stress concentration factors are determined experimentally the extrapolation is done with stresses measured by two strain gauges (A and B on the figure) located in the region of stress linearity. The same extrapolation points would also be suitable for analyzing stresses obtained by finite element analysis. However, for simple joints the offshore industry has developed simplified methods that can be used to determine stress concentration factors for routine design based on experimental and numerical analysis. This has resulted in a set of so-called parametric stress concentration formulas that can be used for simple, planar joints such as K-joints, T-joints, Y-joints and X-joints. The stress ranges determined using this approach are then used together with an S-N curve that have been bases on welded specimens. The local weld notch effect is included in this S-N curve. The relation between the nominal stress and the hot spot stress is given by

hotspot nomSCFσ σ= ⋅ (5) where nomσ is the nominal brace stress.

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Classification of simple joints

General SCF values are basically an expression of the degree of ovalisation or local bending of the chord section under the action of the brace load. Therefore, in X-joints the vertical forces acting at each side of the cross section produce a greater ovalisation than the single load in a T-joint, see the examples in Figure 11. Consequently, SCFX is greater than SCFT.

Figure 11 Joint classification In a Y-joint only the normal component of the brace force contributes to the ovalisation and we find that the SCFT is greater than the SCFY. In the K-joint the load transfer is mainly through the braces, and the chord is only slightly affected. We can therefore state a general relationship between stress concentration factors for the different types of joints with equal geometrical parameters

X T Y KSCF SCF SCF SCF> > > (6) For a specific set of parametric stress concentration factors the values in the table shown in Figure 11 confirms the general trend of Equation 6.

Influence from force flow The classification of simple joints is not solely determined by the geometry, but also by the axial force flow. The following general rules apply in order to determine the appropriate joint classification in dependence of the force flow.

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• To be considered a K-joint the punching load (component normal to the chord surface) should essentially be balanced by loads from other braces in the same plane on the same side of the joint.

• In T- and Y-joints the punching load is reacted as beam shear in the chord.

• In X-joints the punching load is carried through the chord to braces on the opposite side.

Figure 12 The effect of force flow on classification Figure 12 demonstrates the effect of the force flow on the classification of a tubular joint. In (a) the joint is an X-joint if P1 is balanced by P2. If P2 is small as in (b), then P1 is largely reacted as beam shear in the chord, and the joint is a T-joint. In (c) the P1 component normal to the brace is balanced by the normal component from P2, and the joint is then a K-joint. However, if P2 is small the normal component of P1 is reacted by beam shear, and the joint is a Y-joint. Such classification schemes are widely used in practical design work where the loading is split up into components to fit the described basic load patterns, see DNV Appendix B (later in the document). The result may become a joint where each brace carries part of the load as e.g. a K-joint and part of the load as a Y-joint. The joint is then classified accordingly. If e.g. a joint is classified as 40 % K-joint and 60 % Y-joint, the SCF values to be used in the design are found as 40 % of the K-joint values plus 60 % of the Y-joint values.

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Tubular joints and members according to DNV-RP-C203

Introduction In the following the stress concentration factors and procedures as recommended in Ref. /3/ are used as they reflect state of the art approaches in the offshore industry. In this section the original references to figures and tables (in Ref. /3/) have been maintained for easy cross reference.

Tubular joints (2.3.4) For a tubular joint, i. e. brace to chord connection, the stress to be used for design purpose is the range of idealised hot spot stress defined by: the greatest value of the extrapolation of the maximum principal stress distribution immediately outside the region effected by the geometry of the weld. The hot spot stress to be used in combination with the T-curve is calculated as

Stress concentration factors for simple tubular joints (3.3.1) Stress concentration factors for simple tubular joints are given in Appendix B.

Superposition of stresses in tubular joints (3.3.2) The stresses are calculated at the crown and the saddle points, see Figure 3-6. Then the hot spot stress at these points is derived by summation of the single stress components from axial, in-plane and out of plane action. The hot spot stress may be higher for the intermediate points between the saddle and the crown. The hot spot stress at these points is derived by a linear interpolation of the stress due to the axial action at the crown and saddle and a sinusoidal variation of the bending stress resulting from in-plane and out of plane bending. Thus the hot spot stress should be evaluated at 8 spots around the circumference of the intersection, ref. Figure 3-7.

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Influence functions may be used as an alternative to the procedure given here to calculate hot spot stress. See e.g. “Combined Hot-Spot Stress Procedures for Tubular Joints”, ref. /24/

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and “Development of SCF Formulae and Generalised Influence Functions for use in Fatigue Analysis” ref. /2/.

Tubular joints welded from one side (3.3.3) The root area of single-sided welded tubular joints may be more critical with respect to fatigue cracks than the outside region connecting the brace to the chord. In such cases, it is recommended that stubs are provided for tubular joints where high fatigue strength is required, such that welding from the backside can be performed. Failure from the root has been observed at the saddle position of tubular joints where the brace diameter is equal the chord diameter, both in laboratory tests and in service. It is likely that fatigue cracking from the root might occur for rather low stress concentrations. Thus, special attention should be given to joints other than simple joints, such as ring-stiffened joints and joints where weld profiling or grinding on the surface is required to achieve sufficient fatigue life. It should be remembered that surface improvement does not increase the fatigue life at the root. Based on experience it is not likely that fatigue cracking from the inside will occur earlier than from the outside for simple T and Y joints and K type tubular joints. The same consideration may be made for X-joints with diameter ratio ≤β 0.90. For other joints and for simple tubular X-joints with >β 0.90 it is recommended that a fatigue assessment of the root area is performed. Some guidance on such an assessment can be found in Appendix D, Commentary. Due to limited accessibility for in service inspection a higher design fatigue factor should be used for the weld root than for the outside weld toe hot spot. Reference is also made to Appendix D, Commentary

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DNV Appendix B

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References Ref. /1/ McClelland et al.: Planning and Design of Fixed Offshore Platforms. 1986. Van

Nostrand Reinhold Company Inc. Ref. /2/ Almar-Næss et al.: Fatigue Handbook – Offshore Steel Structures. 1985. Tapir,

Norway. Ref. /3/ DNV-RP-C203: Fatigue Design of Offshore Steel Structures. October 2008. Det

Norske Veritas.