experimental and numerical investigation of geometric scfs...

1

* E-mail: [email protected]

Experimental and Numerical Investigation of Geometric SCFs in Internally Ring-Stiffened

Tubular KT-Joints of Offshore Structures

Ahmadi, Hamid*; Lotfollahi-Yaghin, Mohammad Ali

Faculty of Civil Engineering, University of Tabriz, Tabriz, IR Iran

Received: July 2012 Accepted: November 2012

© 2013 Journal of the Persian Gulf. All rights reserved.

Abstract Tubular KT-joints are quite common in offshore structural design and despite the crucial role of stress

concentration factors (SCFs) in evaluating the fatigue performance of tubular joints. However, the SCF

distribution in internally ring-stiffened KT-joints have not been investigated and no design equation is

currently available to determine the SCFs for this type of joint. In the present paper, results of

experimental and numerical investigations of the SCF distribution in internally ring-stiffened tubular KT-

joints are presented. In this research, experimental study has been followed by a set of parametric stress

analyses for 118 steel ring-stiffened KT-joints subjected to balanced axial loads. The analysis results are

used to present the general remarks on the effect of geometrical parameters on the SCF distribution along

the weld toe and to establish a new set of SCF parametric equations for the fatigue design of internally

ring-stiffened KT-joints.

Keywords: Fatigue, Stress concentration factor (SCF), Tubular KT-joint, Internal ring-stiffener, Parametric

design equation

1. Introduction

Offshore jacket-type platforms are mainly

fabricated from tubular members by welding one end

of the branch member (brace) to the undisturbed

surface of the main member (chord), resulting in

what are known as tubular joints. The static and

fatigue strengths of tubular joints are the governing

factors in the design of offshore steel structures.

Significant stress concentrations at the vicinity of

the welds are considerably detrimental to the fatigue

performance of the joints. Since, offshore structures

are subjected to cyclic wave loading, it is imperative

that these structures be designed for long fatigue life.

Hence, it is important to accurately determine the

magnitude of stress concentration and to reduce it to

a reasonable level. In the design practice, a parameter

called the stress concentration factor (SCF) is used to

evaluate the magnitude of the stress concentration.

The SCF is the ratio of the local surface stress to the

nominal direct stress in the brace and its value

depends on the joint geometry, loading type, weld size

and type and the considered location around the weld.

If the capacity of a joint is found to be inadequate

during the design stage proper method for its

Journal of the Persian Gulf

(Marine Science)/Vol. 4/No. 12/June 2013/12/1-12

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. For exampl

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ened tubula

meters (τ, γ,

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Although, the

ractice and

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ation is curre

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erimental an

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yses for 11

ts subject to b

alanced axial loa

gation of Geom

ar KT-joint

η, β, ζ, α,

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despite the

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wed by a s

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present pape

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set of param

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geometrical

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iffened KT-

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Journal of the Persian Gulf (Marine Science)/Vol .4/No. 12/June 2013/12/1-12

3

The analysis results were used to present general

remarks on the effect of geometrical parameters

including τ (brace-to-chord thickness ratio), γ (chord

wall slenderness ratio), η (ring-to-chord width ratio), β

(brace-to-chord diameter ratio), and θ (outer brace

inclination angle) on the SCF distribution along the

weld toe. Since the vertical (central) brace SCFs are

generally much bigger than the inclined (outer) brace

SCFs, the present study was focused only on the SCF

distribution along the weld toe of the intersection

between the central brace and the chord. Based on the

results of ring-stiffened KT-joint finite element (FE)

models which were verified against experimental

measurements, a comprehensive SCF database was

constructed and a new set of SCF parametric equations

was established, through nonlinear regression analysis,

for the fatigue design of internally ring-stiffened KT-

joints. An assessment study of these equations was

conducted based on the acceptance criteria proposed by

the UK DoE (1983). Significant effort has been devoted over the past

four decades to the study of SCFs in various unstiffened joints. Nevertheless, very few investigations have been reported for stiffened joints due mainly to the geometrical complexity and the vast variety of possible stiffening arrangements.

Dharmavasan and Aaghaakouchak (1988) showed

that in the case of axial and Out-of-Plane Bending (OPB)

loadings, careful positioning of the stiffeners greatly

reduced the stress concentrations and gave a more

uniform stress distribution around the intersection.

Various stiffener sizes and configurations were analyzed

and recommendations made on the optimum design.

Aaghaakouchak and Dharmavasan (1990) presented an

improved FE technique consisting of 3-D brick and

semi-loof shell elements. Ramachandra et al. (1992)

investigated the effect of geometrical parameters on the

SCFs in ring-stiffened tubular T- and Y-joints. They

proposed a set of parametric equations for the prediction

of maximum SCFs under axial, In-Plane Bendeing

(IPB), and OPB loadings. Using degenerate shell

elements, Nwosu et al. (1995) studied the stress

distribution along the intersection of internally ring-

stiffened tubular T-joints, under the action of axial,

IPB, and OPB loads. The effects of stiffener size,

location and number have been investigated in this

study. Ramachandra et al. (2000) investigated the effect

of internal ring stiffeners on the fatigue strength of

tubular T- and Y-joints. Hoon et al. (2001) studied the

SCF distributions along the intersections of a doubler-

plate reinforced T-joint subjected to combined

loadings. Myers et al. (2001) investigated the effects of

three different longitudinal stiffeners on the stress

concentration factors in jack-up chords. The constant

thickness continuous stiffener returned the best

performance when compared to the dual thickness

stiffener (rack/rib plate) and the non-continuous

stiffener. Woghiren and Brennan (2009) proposed a set

of parametric equations to predict the SCFs in multi-

planar tubular KK-joints stiffened by rack plates.

2. Experimental Investigation of the SCF Distribution in Ring-Stiffened KT-Joints

2.1. Details of Specimens

Two steel KT-joint specimens were fabricated for

the purpose of experimental tests in order to

investigate the effect of internal ring-stiffeners on the

SCF distribution along the weld toe of tubular KT-

joints. Fabricated specimens were of the same size

with identical geometrical characteristics. The only

difference between the two specimens was the

presence of internal ring-stiffeners in the second

specimen. Geometrical details of the internally ring-

stiffened specimen are presented in Figure 2. As

shown in this figure, three ring-stiffeners were used

in the present study for each brace. One of them was

placed at the saddle position and the other two were

welded at the crown positions.

2.2. Test Setup and Loading Scheme

The two fabricated specimens were tested using a

hydraulically controlled test rig. Both ends of the

chord and upper ends of the outer (inclined) braces

we

two

loa

bra

Fig

Fig

ere welded on

o standing su

ading was ap

ace. In ord

g. 2: Geometrica

g. 3: Test setup

nto the flat p

upports as sh

pplied at the e

der to guar

al details of the

Table 1:

N

A

Ahmadi et al

plates and bo

hown in Figur

end of the ce

rantee the

e internally ring

: Axial loads ap

Nominal stress,

Applied load, F

l. / Experimen

lted directly

re 3. The stat

entral (vertica

accuracy an

-stiffened KT-j

pplied on the ce

σn (MPa) ±5

Fa (kN) 11

ntal and Nume

4

to

tic

al)

nd

reliab

were

for e

were

oint specimen

entral brace in s

5 ±10 ±

.95 23.9 3

erical Investig

bility of rec

e chosen for

each applicat

e recorded 10

tiffened and un

±15 ±20 ±

5.85 47.8 5

gation of Geom

corded data,

the applied

tion, output

0 times in 5 se

nstiffened specim

±25 ±30

59.75 71.7

metric SCFs in

6 different

axial load (T

data from s

ec intervals.

mens

n Internally…

magnitudes

Table 1) and

strain gauges

s

d

s

2.3. Strain

Procedure

In the pre

around the

intervals. A

were used

components

arrangemen

linear extrap

XV-E (199

distance of

point lies a

4b). The ho

extrapolatio

gauges to th

two crowns

gauges wer

along the d

measure the

extrapolatio

of the strain

extrapolatio

results to

sufficiently

avoid avera

of steep gra

After rec

strain conce

using the foSNCF =

Where from the m

are glued on

midpoint.

For the f

SCFs were

SCF = SNC

Where along the w

SCF/SNCF

Gauge Loc

esent study,

entire brac

As shown in

at each loc

s perpendicu

nt of the two

polation proc

99). The firs

0.4T from t

at 1.0T furth

ot-spot strain

on of the re

he weld toe.

s and two sa

re glued on

direction pa

e parallel co

on points. Ag

n at the wel

on of these

the weld t

small strain

aging high a

adients.

cording the

entration fact

ollowing equ

/ n

n is the no

measurement

nto the surfa

four typical

calculated us

CF ×⁄

is Poisson

weld toe, SC

ratio which

cations and

the strain ga

ce/chord int

Figure 4a, t

cation to m

ular to the

o strain gau

cedure recom

st extrapolat

the weld toe

her from the

n ( ) was o

esults from

At four typi

addles, anoth

nto the surfa

arallel with

omponents of

gain, parallel

ld toe was o

e two paral

toe. It mus

n gauges sh

and low strai

data from s

tors (SNCFs

ation:

ominal strain

of four stra

ace of the lo

positions alo

sing the follo

n’s ratio. Fo

CFs were d

h was obtain

Journal

SCF Extra

auges were p

tersection at

two strain ga

easure the s

weld toe.

uges followe

mmended by

ion point is

e, and the se

e first point

obtained by l

these two s

ical position

her pair of s

ace of the c

the weld to

f the strain a

l component

obtained by l

llel strain g

t be noted

hould be use

ins in the re

strain gauges

s) were calcu

n that is obt

ain gauges w

oaded brace a

ong the weld

owing equati

or other posi

derived using

ned by avera

of the Persian

5

action

placed

t 30˚

auges

strain

The

d the

IIW-

s at a

econd

(Fig.

linear

strain

ns, i.e.

strain

chord

oe to

at the

t ( n )

linear

gauge

that

ed to

gions

s, the

ulated

(1)

tained

which

at the

d toe,

ion:

(2)

itions

g the

aging

th

th

fo

F

2

w

st

ex

co

g

w

w

cr

co

n Gulf (Marin

he SCF/SNC

he present st

or unstiffene

Fig. 4: (a) Plan vi(b) Extrapolatio

.4. Results a

Figure 5 il

weld toe on t

tiffened KT

xperimental

ompared. D

eometry and

weld toe is s

whole 360˚

rown and

onsidered. A

ne Science)/Vo

CF ratios at th

tudy, average

d and stiffen

iew of the strain on procedure rec

and Discussi

lustrates the

he chord sur

T-joint spe

data and

Due to the

d loading, the

symmetric a

brace/chord

saddle posi

As shown in

ol .4/No. 12/Ju

he four typic

e ratios were

ned specimen

n gauge locationscommended by I

ion

e SCF distrib

rface of the

ecimens. In

FE resul

e symmetry

e SCF distrib

and only one

intersection

itions, is r

n Figure 5, t

une 2013/12/1

cal positions

e 1.20 and 1

ns, respective

s along the weld IIW-XV-E (199

bution along

unstiffened a

n this figu

ts have b

in the jo

bution along

e fourth of

n, between

required to

there is a go

1-12

. In

1.25

ely.

d toe, 99)

the

and

ure,

een

oint

the

the

the

be

ood

Ahmadi et al. / Experimental and Numerical Investigation of Geometric SCFs in Internally…

6

agreement between the test results and FE predictions

in both unstiffened and stiffened joints (Fig. 5).

Hence, generated FE models could be considered to

be accurate enough to produce valid results. Details of

FE analysis are discussed in Section 4. It can be

clearly concluded from comparing the SCF

distributions in stiffened and unstiffened joints that,

internal ring-stiffeners can effectively reduce the

stress concentration along the brace/chord intersection

and consequently, improve the fatigue performance

of the tubular joint. It can also be seen that the

presence of stiffeners have resulted in the change of

peak SCF location from the saddle position to φ =

60˚. This result means that the position from which

the fatigue cracks initiate could be different in

stiffened and unstiffened KT-joints subjected to

axial loading. As depicted in Figure 5, the SCF

distribution along the weld toe of the stiffened joint

is much more uniform than the distribution in the

unstiffened joint. This observation is a result of

using the stiffeners at both saddle and crown

positions and means that the applied load on the

brace transfers to the chord in nearly equal

proportions through the intersection. The difference

between the SCFs in stiffened and unstiffened joints

is larger at locations adjacent to the saddle position.

This result implies that the stiffener located at the

saddle position is more effective than the stiffeners

welded at the crown positions in reducing the SCFs

along the weld toe.

Fig. 5: SCF distribution along the weld toe on the chord surface of the unstiffened and internally ring-stiffened KT-joint: comparison of the experimental data and FE results

3. SCF Numerical Analysis of Ring-Stiffened KT-Joints

3.1. Important Modeling Considerations

In the present study, the multi-purpose FEM-

based software package, ANSYS was used for the

numerical modeling and analysis of internally ring-

stiffened tubular KT-joints, subjected to balanced

axial loading (Fig. 1a), in order to investigate the

SCF distribution along the weld toe. During the FE

modeling of an internally ring-stiffened tubular joint,

there were two subjects that needed careful attention:

(a) accurate simulation of the weld profile and (b)

correct modeling of the interaction between the

chord and the stiffener, when direct merging should

be avoided in order to provide high-quality mesh

along the brace/chord intersection.

In this study, the welding size along the

brace/chord intersection satisfied the AWS D 1.1

specifications (2002). Modeling of the weld profile

according to AWS D 1.1 (2002) has been extensively

discussed by Lotfollahi-Yaghin and Ahmadi (2010).

The chord and stiffener were meshed separately

and then the ANSYS contact capability was used to

define the interaction between them.

Due to the XY-plane symmetry in the joint geometry

and loading, only half of the entire ring-stiffened KT-

joint is required to be modeled (Fig. 6a).

3.2. Mesh Generation

In the present study, ANSYS element type

SOLID95 was used to model the chord, brace,

stiffener, and the weld profile. The element is

defined by 20 nodes having three degrees of

freedom per node and may have any spatial

orientation. In order to guarantee the mesh quality,

a sub-zone mesh generation method was used

during the FE modeling. The mesh generated by

this method for an internally ring-stiffened tubular

KT-joint is shown in Figure 6.

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90

Polar Angle φ (measure from crown position)

Str

ess

Con

cent

rati

on F

acto

r

Unstiffened Joint (EXP)Unstiffened Joint (FEA)Internally Ring-Stiffened Joint (EXP)Internally Ring-Stiffened Joint (FEA)

Fig. 6: The me

4. Effects oDistributio

4.1. Parame

In order

internally

models wer

purpose FE

objective w

geometrical

along the w

subjected t

Different v

parameter w

0.4, 0.5, 0.6

45˚, 60˚. Th

the normali

esh generated fo

of Geometricon

etric Study

to investiga

ring-stiffene

re generated

EM-based sof

was to study t

l parameter

weld toe of t

to balanced

values assig

were as follo

6; γ = 12, 18,

hese values

ized parame

for a ring-stiffen

cal Paramet

ate the stress

ed tubular

and analyzed

ftware packa

the effect of

s on the S

the central b

d axial loa

gned to eac

ows: η = 0.

, 24; τ = 0.4,

cover the pr

eters typicall

Journal

ned tubular KT-

ters on the S

s concentrati

KT-joints,

d using the m

age, ANSYS

f non-dimens

SCF distrib

brace in the j

ading (Fig.

ch dimensio

1, 0.15, 0.2

0.7, 1.0; θ =

ractical rang

ly found in

of the Persian

7

-joint using the

SCF

on in

118

multi-

S. The

sional

bution

joints

1a).

onless

; β =

= 30˚,

ges of

ring-

st

st

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th

ra

0

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1

0

3

4

stco3

n Gulf (Marin

sub-zone meth

tiffened tub

tructures. Th

race in all m

he other two

The 118 ge

anges of the

.1 ≤ η ≤ 0.2

.4 ≤ β ≤ 0.6

2 ≤ γ ≤ 24

.4 ≤ τ ≤ 1.0

0˚ ≤ θ ≤ 60˚

.2. Effect of

The SCF dtiffened andompared in F60˚ curve o

ne Science)/Vo

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bular joints

hree ring-stif

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at the crown

enerated mo

geometric pa

internal ring

distribution d unstiffeneFigure 7a. Thf the weld p

ol .4/No. 12/Ju

of offsho

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along the wed tubular he polar angpath is mea

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dle position a

d the follow

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weld toe in tKT-joints

gle (φ) along asured from

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crocroobis stifalsstifThinvthecrounat stifdesjoistifanddevstifdifuntheagr

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ffened joint so clear thatffened and u

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ffened joint.sign equatioints were uffened jointsd highly convelop SCF fffened tubulafference betstiffened joine saddle preement with

3. Effect of th

eld Toe

Since the pickness of thodels havingads to the decThe increaseall positionsthe τ (say τ =the saddle po

ut for interme7, 1.0), changak SCF posit

4. Effect of th

eld Toe

The parameord thicknes

n. Hence, val90˚/270˚ at in the unstif

the saddleit is located t the shapesunstiffened j

bservations hhe SCF distripical positio

hown in FigT-joint is 4.5 position in This result

ons developesed for thes, obtained nservative. Hformulae spar KT-joints.tween the nts was largposition. Thh the experim

he γ on the S

parameter γ he chord, thg fixed valucrease of thee of the γ leas along the w= 0.4), the position regarediate and bge of the γ ction.

he τ on the S

ter τ is the rss and the γ

Ahmadi et al

lues of φ arethe saddles

ffened joint, e position, at the crowns of SCF dijoints are q

highlight theibution inste

ons, such as tgure 7b, thetimes biggerthe corresp

indicated thed for the une SCF calcu

SCFs ould Hence, it waecially desig It can also bSCFs in

ger at locatiohis observa

mental results

SCF Distribu

is the ratioe increase o

ue of the ch chord thicknads to an incweld toe. Fopeak SCF is ardless of the big values of can result in

SCF Distribut

ratio of bracγ is the ratio

l. / Experimen

0˚/180˚ at th. It could bthe peak SCwhile in th

n position. It istributions

quite differene necessity ad of studyinthe saddle ane SCF in ar than the SCponding rin

hat, if the SCnstiffened KTulation in thbe unrealists necessary gned for rinbe seen that thstiffened an

ons adjacent ation was

(Section 3.4

ution along th

o of radius of the γ in thhord diametness. crease in SCFr small valualways locatevalue of the

f the τ (say τdisplacing th

tion along th

ce thickness o of radius

ntal and Nume

8

he be

CF he is in

nt. of ng nd an

CF ng-CF T-he tic to

ng-he nd to in

4).

he

to he ter

Fs ues ed γ. = he

he

to to

thickthe mincre

That allthe iτ is geomτ connot hSCF

Fig. 7and sproperSCF positio

4.5. E

Weld

R

SCF

the p

erical Investig

kness of the cmodels havinease of the brhe increase ol positions ancrease in Shighly rema

metrical paransiderably afhave remarkdistribution

7: (a) SCF distristiffened tubularties (η = 0.15, βin the consideron in the corresp

Effect of the

d Toe

esults of inv

distribution

present secti

gation of Geom

chord. Henceng fixed valrace thicknesof the τ leadlong the welCF values drkable in cometers. Althffects the makable influen

along the we

ibutions along thar KT-joints hβ = 0.4, γ = 12, τred unstiffened ponding stiffened

e η on the SC

vestigating th

along the w

on. In this s

metric SCFs in

e, the increaslue of the γ ss.

ds to an increld toe. The m

due to the incomparison whough, the incagnitude of Snce on the s

weld toe.

the weld toe in having the samτ = 1.0, θ = 45˚),joint to the SCd joint

CF Distributio

he effect of

weld toe are

study, the in

n Internally…

se of the τ inleads to the

ease in SCFsmagnitude ofcrease of theith the othercrease of the

SCFs, it doesshape of the

two unstiffenedme geometrical, (b) The ratio ofCF at the same

on along the

the η on the

discussed in

nteraction of

n e

s f e r e s e

d l f e

e

n

f

the η with t

investigated

stiffener wi

providing t

remains unc

increase of

presented in

distribution

analyzed m

the η and i

Figure 8 s

different va

the paramet

presented c

0.4, 0.7, and

For smal

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regardless o

η, from 0.1

positions alo

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Fig. 8: Effects o

the other geo

d. The para

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that the va

changed, the

f the stiffen

n Figure 8,

of SCFs alo

models. These

its interactio

shows the

alues of η (0

ters β, γ, an

harts and th

d 1.0, respec

ll values of

lways locat

of the value

to 0.2, lead

ong the weld

es of the o

he increase of

of the η on the S

ometrical par

meter η is

to the chord

alue of the

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ner width. T

as an exam

ong the weld

e charts illus

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e value of τ

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SCF distribution

Journal

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Three charts

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in Figure 8a

τ = 0.4), the

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ase in SCFs

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along the weld

of the Persian

9

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.6. Effect of

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Since the iameter to thn a model weads to an in6 comparativf the β. Theake of brevit

The increahe increase ooe. This conche other geomhe γ (say γemarkable iistribution and big valueCF distribu

oints having

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ly does not h

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the β on the

parameter βhe chord diamwith fixed vancrease in theve charts wese charts arety. se of the β, of SCFs at aclusion was metrical para= 12), incre

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have remarka

bution along

SCF Distrib

β is the ratiameter, the inalue of the e brace diamere used to se not present

from 0.4 to all positions independent

ameters. For ease of the βn the shapeld toe. But fay γ = 18, 24

be quite dlues of the β.

une 2013/12/1

able influence

the weld toe.

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io of the brncrease of thchord diame

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0.6, resultedalong the w

t from valuessmall valuesβ did not he of the Sfor intermedi4), the shapesdifferent in .

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SCF iate s of the


10

4.7. Effect of the θ on the SCF Distribution along the

Weld Toe

It can be concluded by investigating the effect of

the outer brace inclination angle (θ) on the SCF

distribution that, as it was expected, this parameter did

not have remarkable influence on either the magnitude

or the distribution pattern of SCFs along the weld toe

of the central brace. This conclusion was independent

from values of the other geometrical parameters.

5. Parametric Design Equations

After performing a large number of nonlinear

regression analyses by the statistical software

package SPSS, following geometrically parametric

equations are proposed for predicting the SCF

distribution along the weld toe and the peak weld-toe

SCF in internally ring-stiffened tubular KT-joints

subjected to balanced axial loading:

SCF distribution along the weld toe:

(4)

where functions ξ1 – ξ6 are expressed as follows:

1( , ) 0.198 0.009 0.310 0.920 (5.1)

(5.2)

(5.3)

(5.4)

(5.5)

(5.6)

Peak SCF along the weld toe:

(6)

In Eqs. (4) and (6), R2 denotes the coefficient of

correlation and its value is considered to be

acceptable for both equations regarding the complex

nature of the problem. The parameter φ (0˚ ≤ φ ≤

180˚) in Eq. (5.4) and the parameter θ in Eqs. (5.5)

and (6) should be inserted in radians. The validity

ranges of dimensionless parameters for the proposed

equations have been given in Eq. (3).

The UK Department of Energy (UK DoE) (1983)

recommended the following assessment criteria

regarding the applicability of the commonly used

SCF parametric equations (P/R stands for the ratio of

the predicted SCF from a given equation to the

recorded SCF from test or analysis):

For a given dataset, if % SCFs under-predicting

25%, i.e. [%P/R < 1.0] 25%, and if % SCFs

considerably under-predicting 5%, i.e. [%P/R <

0.8] 5%, then accept the equation. If, in

addition, the percentage SCFs considerably over-

predicting 50%, i.e. [%P/R > 1.5] 50%, then

the equation is to be regarded as generally

conservative.

If the acceptance criteria were nearly met i.e. 25%

< [%P/R < 1.0] 30%, and/or 5% < [%P/R < 0.8] 7.5%, then the equation was regarded as

borderline and engineering judgment must be used

to determine acceptance or rejection.

Otherwise reject the equation as it is too optimistic.

In view of the fact that for a mean fit equation,

there is always a large percentage of under-prediction,

the requirement for joint under-prediction, i.e. P/R <

1.0, can be completely removed in the assessment of

parametric equations (Bomel Consulting Engineers,

1994). Assessment results according to the UK DoE

criteria [1] are presented in Table 2.

Table 2: Results of equation assessment according to UK DoE (1983) acceptance criteria

Equation Conditions Decision

%P/R < 0.8 %P/R > 1.5

Eq. (4) 17.4% > 5 % 2.5% < 50 % OK. Revise

Eq. (6) 2.8% < 5 % OK 0% < 50 % OK. Accept

= 1 , + 2 , 3 4 5 6 , , , 2 = 0.915

2 , = 1.203 0.001 − 1.202 ∙ 1.146 1.426 − 61.095

3 = 1.416 0.450 + 1.784 ∙ 2.892 2 + 2.874 + 1.904 4 = −0.260 + 0.397 1.218 − 4.302 0.180 + 4.577

5 = 1 + 6.559 −0.303 + 2.402 +8.022 6 , , , = 1 + 0.841 14.616 − 1.493 −0.049 + 0.320 − 0.291

max = 0.304 0.768 0.994 0.244 −0.307 −0.060 1 − 0.954 − 0.096 + 2.447 + 0.025 ∙ 2 = 0.909


11

As can be seen in Table 2, Eq. (6) satisfied the UK

DoE criteria, but Eq. (4) required revision. In order

to revise the Eq. (4), SCF values obtained from this

equation were multiplied by a coefficient in such a

way that resulted SCF set would satisfy the UK DoE

acceptance criteria. This idea could be expressed as

follows:

Design factor = SCFDesign / SCFEq. (4) (7)

where values of SCFEq. (4) were calculated from

the proposed equation and the values of SCF Design

were expected to satisfy the UK DoE criteria.

Multiple comparative analyses were carried out to

determine the optimum value of design factor.

Following equations should be used for design

purposes:

SCFDesign = 1.32 × SCFEq. (4) (8)

SCFDesign = 1.00 × SCFEq. (6) (9)

6. Conclusions

Results of experimental and numerical investigations

of the SCF distribution in internally ring-stiffened

tubular KT-joints were presented in this paper.

Numerical results from analyzing 118 FE models were

used to present general remarks on the effect of

geometrical parameters on the SCF distribution along

the weld toe of the central brace and to establish

parametric SCF equations for the fatigue design. Main

conclusions are summarized as follows:

The presence of internal ring-stiffeners, depending

on the values of geometrical parameters, might lead to

the disposition of the peak SCF along the weld toe.

The shapes of SCF distributions in stiffened and

unstiffened joints could also be quite different. The

SCF distribution along the weld toe of a stiffened joint

was usually much more uniform than the distribution

in its corresponding unstiffened joint. This behavior

was a result of using the stiffeners at both saddle and

crown positions. These results highlighted the

necessity of investigating the SCF distribution instead

of studying the SCFs at typical positions such as the

saddle and crown. SCFs in an unstiffened KT-joint are

generally much bigger than the SCFs at the same

positions in the corresponding ring-stiffened joint.

This observation implied that the use of SCF design

equations which were developed for the unstiffened

KT-joints generally led to over-predicting and highly

conservative SCFs for stiffened joints. Hence, it was

necessary to develop SCF formulae specially designed

for ring-stiffened tubular KT-joints.

The increase in the γ and/or τ and also the increase

of the β led to the increase of SCFs at all positions

along the weld toe. The magnitude of the increase in

SCF values due to the increase of the τ was highly

remarkable in comparison with the other geometrical

parameters. For small values of the τ, the peak SCF

was always located at the saddle position regardless

of the value of the γ. But for intermediate and big

values of the τ, change of the γ could result in

displacing the peak SCF position. For small values of

the γ, increase of the β did not have remarkable

influence on the shape of the SCF distribution along

the weld toe. But for intermediate and big values of

the γ, the shapes of SCF distributions could be quite

different in the joints having different values of the β.

The increase of the η led to a decrease in SCFs at all

positions along the weld toe. The parameter θ did not

have remarkable influence on either the magnitude or

the distribution pattern of SCFs along the weld toe of

the central brace.

Relatively high coefficients of correlation and the

satisfaction of acceptance criteria recommended by

UK DoE guaranteed the accuracy of the proposed

equations. Hence, the developed formulae could

reliably be used for the fatigue design of offshore

jacket-type structures.

References

Aaghaakouchak, A.A. and Dharmavasan, S., 1990.

Stress analysis of unstiffened and stiffened tubular

joints using improved finite element model of


12

intersection. Proceedings of the 9th OMAE

Conference, Houston, USA, 321–328.

American Welding Society, 2002. Structural Welding

Code: AWS D 1.1, Miami, USA.

Bomel Consulting Engineers, 1994. Assessment of

SCF equations using shell/KSEPL finite element

data. C5970R02.01 REV C.

Dharmavasan, S. and Aaghaakouchak, A.A., 1988.

Stress concentrations in tubular joints stiffened by

internal ring stiffeners. Proceedings of the 7th

OMAE Conference, Houston, USA, 141–148.

Hoona, K.H., Wong, L.K. and Soh, A.K., 2001.

Experimental investigation of a doubler-plate

reinforced tubular T-joint subjected to combined

loadings. Journal of Constructional Steel Research.

57: 1015–1039.

IIW-XV-E, 1999. Recommended Fatigue Design

Procedure for Welded Hollow Section Joints. IIW

Docs, XV-1035-99/XIII-1804-99, International

Institute of Welding, France.

Lotfollahi-Yaghin, M.A. and Ahmadi, H., 2010.

Effect of geometrical parameters on SCF

distribution along the weld toe of tubular KT-

joints under balanced axial loads. International

Journal of Fatigue. 32: 703–719.

Myers, P.T., Brennan, F.P. and Dover, W.D., 2001.

The effect of rack/rib plate on the stress

concentration factors in jack-up chords. Marine

Structures. 14: 485–505.

N’Diaye, A., Hariri, S., Pluvinage, G. and Azari, Z.,

2007. Stress concentration factor analysis for

notched welded tubular T-joints. International

Journal of Fatigue. 29: 1554–1570.

Nwosu, D.I., Swamidas, A.S.J. and Munaswamy, K.,

1995. Numerical stress analysis of internal ring-

stiffened tubular T-joints. Journal of Offshore

Mechanics and Arctic Engineering. 117: 113–125.

Ramachandra, D.S., Gandhi, P., Raghava, G. and

Madhava Rao, A.G., 2000. Fatigue crack growth in

stiffened steel tubular joints in seawater environment.

Engineering Structures. 22: 1390–1401.

Ramachandra, D.S., Madhava Rao, A.G., Ghandi, P.

and Pant, P.K., 1992. Structural efficiency of

internally ring stiffened steel tubular joints.

Structural Engineering. 118: 3016–3035.

UK Department of Energy, 1983. Background Notes

to the Fatigue Guidance of Offshore Tubular

Joints. UK DOE, London, UK.

Woghiren, C.O. and Brennan, F.P., 2009. Weld toe

stress concentrations in multi planar stiffened

tubular KK joints. International Journal of Fatigue.

31: 164–172.



Journal of the Persian Gulf

(Marine Science)/Vol. 4/No. 12/June 2013/12/1-12

experimental and numerical investigation of geometric scfs...

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