SCF equations in multi-planar welded tubular DT-joints including bending effects

Marine Structures 15 (2002) 157173

SCF equations in multi-planar welded tubularDT-joints including bending effects

Spyros A. Karamanosa,*, Arie Romeijnb, Jaap Wardenierb

aDepartment of Mechanical & Industrial Engineering, University of Thessaly, Pedion Areos,

38334 Volos, GreecebFaculty of Civil Engineering and Geosciences, Delft University of Technology, CN 2628 Delft, Netherlands

Received 4 December 2000; received in revised form 15 June 2001; accepted 25 June 2001

Abstract

Welded tubular connections exhibit significant stress concentrations at the weld vicinity,which may result in fatigue failure. Stress concentration factors (SCFs) in DT-joint arecomputed, based on an extensive finite element study. The present paper develops amethodology for the calculation of the maximum local stress, referred to as hot-spot stress,

in a multi-planar DT-joint, with particular emphasis on the effects of bending moments on thebraces and the chord. Special attention is focussed on the location where critical stressconcentration occurs, as well as on the so-called carry-over phenomenon and its

implications on the hot-spot stress value. Simplified design equations for fatigue design areproposed to determine SCF values due to bending in order to improve predictions with respectto existing design tools. r 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Fatigue design; Hot spot stress; Multi-planar effects; Bending effects; Tubular joint

1. Introduction

Welded joints from circular hollow section (CHS) members are widely used intubular lattice structures, for offshore and onshore applications (cranes, masts ortowers). The fatigue design of such joints constitutes a critical factors towardssafeguarding the integrity of tubular structures. The complex joint geometry causessignificant stress concentrations at the vicinity of the welds. Under repeated loadingsthey result in the formation of cracks, which can grow to a size sufficient to cause

*Corresponding author. Tel.: +30-421-74-086; fax: +30-421-74-009.

E-mail address: [email protected] (S.A. Karamanos).

0951-8339/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved.

PII: S 0 9 5 1 - 8 3 3 9 ( 0 1 ) 0 0 0 2 0 - X

joint failure. The location of maximum stress concentration is called hot-spot andthe corresponding local stress is referred to as hot-spot stress.

For fatigue design purposes, the hot-spot stress method has been quite efficientand popular. According to this method, the nominal stress range Dsnom at the jointmembers is multiplied by an appropriate stress concentration factor (SCF) toprovide the so-called geometric stress S0 at a certain location. When the membersof a joint are subjected to a combination of axial and bending loads on all members,the geometric stress at a specific location around the weld is calculated bysuperimposing the contributions of the nominal stresses from each loading type (k)considering the corresponding SCF values:

S0 Xk

SCFkDsknom: 1

The SCF value depends on joint geometry, loading type, weld size and type, and thelocation around the weld under consideration. Geometric stresses S0 are calculated atvarious locations around the welds and the maximum geometric stress is the hot-spotstress S: The fatigue life of the joint is estimated through an appropriate SN fatiguecurve, N being the number of load cycles.

There exists considerable information regarding the fatigue behavior and design ofuni-planar joints, i.e. joints where the axes of all members lay on a single plane.However, many joints used in practical applications are multi-planar, and littleinformation has been reported concerning their fatigue capacity.

SCF design equations for multi-planar joints were proposed by Marshall andLuyties [1], who introduced the computed alpha parameter a [also adopted by theAmerican Petroleum Institute [2], and by Efthymiou [3] in terms of the so-calledinfluence functions. Both methodologies refer to axial loads only and neglectmulti-planar bending effects. Thus, SCFs due to bending are computed from thecorresponding uni-planar joint equations, neglecting any multi-planar effects. Amore recent work by Chiew et al. [4] on XT (triple T)-joints, based on finite elementresults, proposed parametric equations to calculate stress concentrations due to axialloads only.

To investigate stress concentrations in multiplanar joints under variousloading conditions, an extensive FE analysis has been conducted by the authors,and a large finite element (FE) SCF database [5] has been developed, over a widerange of joint parameters, SCFs due to axial and bending loads are computed at asufficient number of locations around the welds, on the brace and the chord side. In arecent paper [6], the authors presented the SCF design equations for multi-planarDT-joints (Fig. 1) under axial loads, based on the FE database. The present paperextends the aforementioned SCF equations in DT-joints subjected to bendingmoments.

The so-called carry-over effect is examined in detail. It is defined as the stressconcentration at a certain location at the weld toe, due to a load (axial or bending)on another brace. Referring to the joint of Fig. 1, the local stress at a weld locationof brace (a) due to a load on brace (b) is a carry-over effect. In such a case, braces(a) and (b) are called the reference and the carry-over brace respectively. In

S.A. Karamanos et al. / Marine Structures 15 (2002) 157173158

other words, SCFs due to reference load means that SCFs at the weld of theloaded brace are examined, and SCFs due to carry-over load means that SCFs atthe weld of the non-loaded brace are examined.

2. Joint geometry, loading and modeling

The geometry of a DT-joint (Fig. 1), is described by the four dimensionlessparameters, bd1=d0; gd0=2t0; tt1=t0 and j (out-of-plane brace angle). The DT-joints considered in the present work are assumed to have braces of equal size(diameter and thickness), concentric (i.e. no eccentricity), gap joints (no overlap) andperpendicular to the chord (in-plane angle y between the chord and the brace axes isequal to 901for all braces).

In the present study, 12 combinations (pairs) of b and j values are considered(Table 1). For each pair of b and j; there exist 12(4 3) combinations of g and t: 4values of g (12, 18, 24, and 30) and 3 values of t (0.25. 0.50, and 1.0). Therefore, thepresent study comprises a total of 12 12=144 combinations of joint parameters,i.e. a total of 144 DT-joint cases are analyzed, which cover a wide range of practicalapplications.

Moreover, the following loading conditions are considered: (a) in-plane bracebending (reference and carry-over), (b) out-of-plane brace bending (reference andcarry-over) and (c) chord loads (axial and bending). SCF values due to axial loads(on the brace and the chord) have been presented extensively in a recent publication[6]. The present paper focuses on the effects of bending moments.

Finally, stress concentrations are measured at specific locations around the weld atboth the chord and the brace points. More specifically, three locations areconsidered: (1) saddle. (2) in-between location and (3) crown. These locations areshown around the weld of brace (a) of the DT-joint depicted in Fig. 1.

Fig. 1. Configuration of a DT-joint, joint parameters and locations around the welds.

S.A. Karamanos et al. / Marine Structures 15 (2002) 157173 159

2.1. Numerical modeling

The aforementioned 144 DT-joint cases are analyzed using a finite elementmodeling (Fig. 2). The finite element analysis is conducted with the software packageI-DEAS, whereas the preprocessing (mesh generation) of the tubular joint model isperformed with the PRETUBE module of the tubular joint modeling packageSESAM. Before conducting the parametric study, a few preliminary finite elementanalyses have been performed to determine specific numerical issues. Furthermore,experience from previous analyses is also used [7].

In the present study, 20-node solid (brick) elements are employed, instead of thinor thick shell elements. It would be possible to employ a combination of solidelements (near the weld) and shell elements (elsewhere). However, to avoid the use ofspecial transition elements [8] 20-node solid elements are exclusively employed.Reduced integration (2 2 2) is assumed, but no differences have been detectedwhen a full integration scheme (3 3 3) was employed.

Initial numerical results have shown that the computed value of geometric stress issensitive to the weld profile, as well as to the mesh near the weld (Fig. 2). A densemesh is used near the weld, where stress concentrations are to be computed. The sizeof an element at the vicinity of the weld is selected equal to 1/32 and 1/70 of the totalweld length in the circumferential and the axial direction respectively (Fig. 2).Moreover, the weld is also modeled with 20-node solid elements and its profile(shape and size) is considered according to the AWS [12] provisions.

Regarding the value of the stress concentration at the weld vicinity, anextrapolation of stresses up to the weld toe from a specific region near the weld iscarried out. The region is called extrapolation region. The extrapolation method isintroduced by the ECSC WG III [13] recommendations and has been used inexperimental works [14]. More specifically, a parabolic interpolation using five stressdata points within this region is assumed. Then, using the parabolic curve points at

Table 1

Values of b; j; g and t and corresponding combinations examined in the parametric studya

Out-of-plane angle j

b 451 701 901 1351 1801

0.30 0.50 0.65 0.70 0.90

g 12 18 24 30t 0.25 0.50 1.0

aFor each pair of b and j; all possible combinations of g and t are used.


the two ends of the region, a linear extrapolation is performed up to the weld toe todetermine the geometric stress. The procedure is described in a recent publication ofthe authors [9].

To remain consistent with previously reported SCF measurements [610] the so-called primary stress is considered. This is the stress normal to the weld (for thechord side) or the stress in the direction of the brace axis (for the brace side). Therehas been a certain concern among researchers and engineers regarding the use ofprimary stress instead of the maximum principal stress. In the present work, thechoice of the primary stress is based on the experimental observation that thedeveloped cracks are normal to the primary stresses, whereas the direction of themaximum principal stress may be different. Nevertheless, it should be noted thatin tubular joints with braces normal to the chord (y 901), the difference betweenthe primary stress and the maximum principal stress is very small, whereas, thisdifference becomes more important in joints with inclined braces. In Fig. 1, thearrows at the vicinity of the weld of brace (a) indicate the direction of the primarystress at the saddle, crown and in-between location.

Fig. 2. Finite element modeling of welded tubular DT connections showing the FE mesh around the weld;

out-of-plane angle is 901 for the depicted joint.


Finally, bending moments, referred to as compensating moments, are applied atthe chord ends, at appropriate directions in order to eliminate the effects ofboundary conditions of the chord, which may produce undesired stresses at thewelds. These moments, are applied so that the obtained SCF values are independentof the chord boundary conditions, and can be superimposed directly undercombined loads [Eq. (2)]. More details regarding joint modeling can be found in[57,9].

3. Finite element results

Due to lack of symmetry (when jo1801), the two saddle locations of a braceexhibit different responses. Therefore, it is necessary to distinguish between the farand the near saddle of the brace under consideration, according to their positionwith respect to the other brace (see Fig. 1). The near saddle of a brace is the bracenearest to the other brace. For the particular case of j 1801; near and farsaddle coincide. In this particular case, the DT-joint is actually a uni-planar X-joint.

For each joint analyzed, SCFs are computed at saddle, crown, and in-betweenpoints. The results of a pilot study, as well as results from previous investigations[5,6,8], indicate that the in-between point of a brace perpendicular to the chord doesnot exhibit the maximum SCF value under any load condition. Therefore, thenumerical results at in-between locations of DT-joints are neglected for the purposeof developing simplified SCF equations and only results from saddle and crownlocations are considered.

3.1. Bending moment on the reference brace

Previous attempts to describe the behavior of multi-planar joints (e.g. [3,11]),assumed that the SCF at the reference brace (i.e. the loaded brace) of a multi-planarjoint is equal to the SCF of the corresponding uni-planar joint (i.e. the one with thesame values of b; g and t). Following the above argument, SCFs at the referencebrace of a DT-joint can be computed from SCF equations of a uni-planar T-jointwith the same joint parameters (Fig. 3). This argument was also adopted byWordsworth and Smedley [11] and Efthymiou [3].

There is a certain concern regarding the above argument, because of the presenceof an unloaded member, which may affect the stress field at the joint. However,evidence from the numerical analysis indicates that in DT-joints, subjected to in-plane and out-of-plane reference bending, this effect is negligible for design purposesat both brace and chord locations. In conclusion, DT-joint SCFs due to referencebrace bending can be computed from the corresponding T-joint SCF equations.

3.2. Bending moment on the chord

The effects of axial and bending chord loads in tubular joints have been examinedextensively elsewhere [10]. It was shown that, chord crown locations exhibit


significant stress concentrations, whereas SCF values at all other locations arenegligible. It was also reported that the chord moment effect on the chord crown ismaximized when the chord bending moment vector becomes normal to the axis ofthe brace under consideration. More specifically, consider a DT-joint with j 901;loaded with two moments in the direction of the brace axes x2 and x3 (Fig. 4). Forthis particular joint geometry and moment orientation, moment M2 affects the weldcrown of brace (a) only, whereas moment M3 affects the weld crown of brace(b) only, i.e. crown points A and B respectively. These observations are verified bythe present FE results. Finally, it should be noted that DT-joints with y 901;exhibit relatively small SCFs (values usually range between 1 and 1.5).

3.3. Bending moment on the carry-over brace

The numerical results indicate that the multi-planar carry-over effects due to in-plane bending loads are non-significant in both crown and saddle locations. In otherwords, these effects due to in-plane loading can be disregarded for design purposes.On the other hand, out-of-plane bending may have a significant carry-over effecton saddle locations, because out-of-plane bending causes significant distortion(ovalization) of the chord cross-section.

Another indication that carry-over effects due to out-of-plane bending may besignificant, stems from the observation that the particular case of a DT-joint with anout-of-plane angle j value equal to 1801 is a uni-planar X-joint, investigatedextensively elsewhere under out-of-plane bending conditions (e.g. [11]. Fig. 5 depicts

Fig. 3. DT-joint and T-joint under reference out-of-plane bending loads. Hot-spot location is the chord

saddle for both joints under this loading condition.


the SCF value of a X-joint under balanced out-of-plane moment conditionscompared with that of a corresponding T-joint subjected to an out-of-plane moment.The comparison shows that for relatively large values of b there is a significantdifference in the SCF value and this is due to the presence of the out-of-planemoment on the carry-over brace.

Herein, carry-over effects due to out-of-plane bending for the general case of aDT-joint (values of j other than 1801) are investigated. Fig. 6 shows the variation of

Fig. 5. Comparison between T-joint and X-joint SCFs for out-of-plane bending. T-joint is subjected to

out-of-plane bending, X-joint is subjected to balanced out-of-plane bending (g 12; t 0:5); FE results.

Fig. 4. Bending moments is chord member for a DT-joint with an out-of-plane angle j equal to 901.Moment M2 causes stress concentration at the chord crown location of (a) point A, and moment M3causes stress concentration at the chord crown location of (b) point B.


carry-over SCF value at the far saddle in terms of j and b and Fig. 7 for thenear saddle. Comparison of Figs. 6 and 7 shows that there exists a certainsimilarity between the chord and the brace side, which is used for the developmentof the design formulae (see next section).

4. SCF design formulae for bending moments in DT-joints

4.1. Reference brace bending

SCFs for reference bending loads (in-plane and out-of-plane) can be calculatedfrom existing design equations for T-joints [3,11]. Adopting the format introducedby IIW [15] and assuming y=901, the proposed SCF equations for reference loads atchord saddle and crown locations have the following form:

SCFchordref b; g; t g12

X1 t0:5

X2SCF0b; 2

where SCF0 is either constant or a function of b reflecting the SCF value for g 12and t 0:5; and X1; X2 are constant exponents. The values of SCF0, X1 and X2 aredepicted in Table 2 and Fig. 8, in terms of the load condition and the location underconsideration. For the particular location of brace saddle, the SCF due to out-of-plane reference bending can be calculated from the corresponding SCF value at thechord saddle by the following equation (see also [6,9]):

SCFbraceref 2

1 4t

SCFchordref : 3

Fig. 6. Variation of SCFcov due to carry-over out-of-plane bending in terms of the out-of-plane angle j(chord and brace far saddle locations).


4.2. Chord bending

Chord bending affects only chord crown locations, and a constant SCF value of1.4 is suggested (Table 2). The chord moment should be analyzed in twocomponents, one along the axis of the brace under consideration and oneperpendicular to this direction. The SCF should multiply the nominal stress fromthe latter component (Fig. 4).

4.3. Carry-over brace bending

Carry-over effects due to in-plane bending are small and may be neglected fordesign purposes. On the other hand, the carry-over effects because of out-of-planebending are significant and should be considered at saddle locations. Based on the

Table 2

Values of SCF0 and exponents X1, X2 to be used in Eq. (2), for reference brace bending and chord bending

Type of load SCF location X1 X2 SCF0

In-plane bending

(reference)

Chord crown 0.6 0.8 2.2

Brace crown 0 0 1.85

Out-of-plane bending

(reference)

Chord saddle 1.0 1.0 Fig. 8

Brace saddle Eq. (3)

Chord bending Chord crown 0 0 1.4

Fig. 7. Variation of SCFcov due to carry-over out-of-plane bending in terms of the out-of-plane angle j(chord and brace near saddle locations).


FE data, a simple and efficient methodology is suggested for calculating carry-overSCFs under out-of-plane bending at saddle locations. The corresponding parametricequation for SCFs at chord saddle locations has the following form:

SCFchordcov b; g; t; j z1b z2g z3twj; 4

where z1b; z2g; z3t and wj are functions of b; g; t and j respectively.Motivated by the SCF results of Figs. 6 and 7, two functions wij are proposed

for the near (i 1) and for the far saddle (i 2) as shown in Fig. 9. In this Figurepositive SCFs denote tensile stress and the depicted SCF values correspond to themoment direction shown in the same figure. To describe the effects of b; g and t; thefollowing power equations are suggested:

z1b b0:5

A1; z2g

g12

A2; z3t

t0:5

A3: 5

The normalizing values of b; g and t are chosen equal to 0.5, 12 and 0.5respectively [for consistency with Eq. (2)] and using a standard regression analysis,the values of the exponents A1, A2 and A3 are computed equal to 3.3, 0.90 and 1.20respectively.

The SCF at the brace saddle locations due to out-of-plane carry-over bending maybe calculated by the corresponding SCF at the chord location, by the following

Fig. 8. Values of function SCF0 in terms of b for reference out-of-plane bending of DT-joints; the SCF0value is the SCF value for g 12 and t 0:5:


simple equation:

SCFbracecov 2

1 4t

SCFchordcov ; 6

which is the same as Eq. (3) for reference out-of-plane bending. This equation ismotivated by the similarity between the SCF values at the chord and the bracesaddle locations (see Figs. 6 and 7).

5. Discussion

The proposed SCF equations for out-of-plane bending carry-over effects at DT-joint saddle locations are

SCFchordcov b; g; t; j b0:5

3:3 g12

0:90 t0:5

1:2wij 7

and

SCFbracecov b; g; t; j 2

1 4t

SCFchordcov b; g; t; j; 8

Fig. 9. Functions wj which show the variation of SCFchordcov due to out-of-plane carry-over bendingmoment in terms of the out-of-plane angle j: Positive stresses denote tensile stresses; sign convention forcarry-over bending moment; direction of carry-over moment corresponding to the values of the wffunctions.


where functions wij are depicted in Fig. 9. The equations concern concentric, non-overlap joints and for the following range of joint parameters:

0:30pbp0:90; 0:25ptp1:00;12:0pgp30:0; 451pjp1801: 9

The above indicate that the SCF values in the brace are smaller than those in thechord. The comparison for the entire range of joint parameters for the saddlelocations is shown in Fig. 10a and b. There is a very good correlation for the farsaddle, whereas the comparison for the near saddle is generally acceptable. Morespecifically, there exist some differences between FE data and formulae predictionsfor cases where b 0:65 and j 901 (the gap angle c is less or equal to 101).Excluding these cases, the correlation becomes very good. In any case, the overallcorrelation is considered to be satisfactory for the purposes of the present study,taking into account the simplicity of the proposed equations.

Figs. 11 and 12 depict DT-joint SCFs under balanced out-of-plane bending interms of the out-of-plane brace angle j: Joint parameter values for b; g and t areassumed equal to 0.50, 12 and 0.50 respectively (z1 z2 z3 1). The bendingSCFs are calculated from the equations proposed herein and the axial load SCFs arecalculated from the corresponding SCF design equations proposed by Karamanoset al. [6], summarized in the appendix. The SCF value from the T-joint equation isalso plotted. The comparison between the T-joint SCF value and the DT-joint SCFvalue indicates that the carry-over influence may be significant for out-of-planebending moments and that SCF predictions based on the reference loads only (i.e.T-joint consideration) may not be accurate. Note also the significant difference inthe SCF values at the near and far saddle.

Fig. 10. DT-joints under out-of-plane carry-over bending; simplified equation for far and near chord

saddle locations; comparison with numerical (FE) results.


It should be noted that typical joint configurations in practical offshoreapplications are usually more complex than the simple configurations examined inthe present work. In such cases, a more detailed FE analysis is required or, at least,strongly recommended for detailed design, instead of using simplified designequations. However, it is the authors opinion that the proposed equations can beused for preliminary fatigue design, because they provide a first good estimateregarding the influence of joint parameters on the fatigue design life of the joint. Inonshore applications (e.g. lattice masts or towers) tubular joint configurations aresignificantly simpler and, therefore, the proposed SCF equations can be used directlyfor definitive design purposes.

6. Conclusions

Bending moments may cause significant stress concentrations at the weld toe ofwelded tubular DT-joints. Based on an extensive SCF database obtained throughfinite element analyses, the various parameters affecting the SCF value are discussedand special attention is devoted to the location where significant SCF values occur,resulting in simple and efficient design equations for calculating SCFs due toreference and carry-over bending moments. Distinction between far and nearsaddle locations is made.

For reference bending, the corresponding equations for uni-planar T-joints maybe used for design purposes, neglecting the presence of the unloaded brace. It wasshown that out-of-plane bending is more critical and that the highest SCF valuesoccur in saddle locations. Carry-over effects due to in-plane bending in DT-jointscan also be neglected at both crown and saddle locations.

On the other hand, carry-over effects due to out-of-plane bending can be neglectedat crown locations but should be considered at saddle locations. To take into

Fig. 11. DT-joints under balanced out-of-plane bending moments.


account these effects, SCF design equations are proposed, which contain the jointparameters b; g; t and j in an uncoupled form, allowing the designer to estimate theeffects of every joint parameter on the hot spot stress in a simple and efficientmanner. These equations extend the SCF equations for axial loads from a previouspaper [6].

The proposed equations cover a wide range of DT-joints, their correlation withfinite element results is satisfactory and can be used for preliminary design ofoffshore joints. Furthermore, they are aimed at improving the understanding onstress concentrations in DT-joints, and can be extended to more complex multi-planar joint configurations.

Fig. 12. Carry-over effects in a DT-joint due to balanced out-of-plane bending moments (see Fig. 11).

SCF at chord saddle locations [(a) far and (b) near] are compared with the corresponding SCF due to

reference out-of-plane bending moment only (i.e. T-joint conditions).


Acknowledgements

The present study was partially supported by a research fellowship from DelftUniversity of Technology. The authors would also like to thank Prof. Dr. R.S. Puthli(Univ. of Karlsruhe), Dr. S. Herion (Univ. of Karlsruhe), Dr. O.D. Dijkstra (TNO-Bouw) and Dr. A.M. van Wingerde (TU Delft) for their comments and suggestions.

Appendix

The stress concentration factors for DT-joints due to carry-over axial loads [6]:chord

SCFchordcov 2:95b1:5 0:88b6

2:4g 712

0:65 t0:5

1:2hif:

Functions hij are shown in Fig. 13 for the near and the far chord saddle. brace

SCFbracecov 2

1 4t

SCFchordcov :

Fig. 13. Values of hij functions, for the calculation of SCF due to carry-over axial brace load (chordsaddle locationsFnear and far).


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SCF equations in multi-planar welded tubular DT-joints including bending effects