tubular joint api rp 2a design

Offshore Structures – Tubular Connections

ContentsContents• Tubular Joints

• Behaviour of Tubular connections

Fail e modes• Failure modes

• API RP 2A Design Method

16 July 2007 Dr. S. NallayarasuDepartment of Ocean Engineering

Indian Institute of Technology Madras-361





T b l C tiTubular Connections

• The cross sections of one or more tubes serving asbraces are joined by fusion welding to theundisturbed surface of another tube serving as achord member

• Also called Tubular Joints loosely




Source : API RP 2A




Simple Tubular JointsSimple Tubular Joints

• The branch members (braces) are welded individually toth i b ( h d)the main member (chord)

• The chord then transfers loads from one branch memberto another

• This create sever localized shell bending stresses in theThis create sever localized shell bending stresses in thechord

A short length of joint can with increase thickness may• A short length of joint can with increase thickness maybe used




Localized Shell BendingLocalized Shell Bending

• The braces deliver their reactions to the chord in theThe braces deliver their reactions to the chord in theform of line loads

The e act distrib tion depends on the relati e• The exact distribution depends on the relativeflexibilities

• The localized shell bending in the chord reaches apeak at these line loads with steep local gradients

• Contains punching shear, shell bending, membranestresses




Stresses in Tubular Joints




Gl b l St A l iGlobal Stress Analysis

• Global stress analysis to find the nominal axial and• Global stress analysis to find the nominal axial andbending stresses in the members

• Typical 20ksi (140 N/mm2) in a jacket bracing for aone-time extreme wave load

• What are the stresses in the tubular connection?

• The local stress distributions are extremely complex• The local stress distributions are extremely complex




Local Scale Stress AnalysisLocal Scale Stress Analysis

• No closed-form solutions exist for practical cases of• No closed-form solutions exist for practical cases ofinterest

C b i ti t d b FEM i t l t• Can be investigated by FEM, experimental stressanalysis, analytical shell theory

• Stresses near the weld intersection can be severaltimes higher than nominal, often exceeding yield

• For routine design, empirical formulas based on thepunching shear concept are proposed




Punching Shear

• To formulate design criteria, the complex stressdistribution in chord is represented by a simplepunching shearp g

• The average punching shear stress acting at theperimeter of the brace to chord intersection is defined

pV

perimeter of the brace-to-chord intersection is definedas

acting )(sin bap ffV += θτ

Punching component normal to the chord wall

g )( bap ff




Punching Stress ConceptsPunching Stress Concepts

acting

=

+=

Tt

ffV bap

τ

θτ

/

)(sin

l b t b=+

=ffa

θ angle between members

nominal axial and bendingStress in brace




Elastic Stresses inC li d S bj dCylinders Subjected to

Punching ShearPunching Shear




Shell Theory

Closed form solutions exist for very simple load• Closed-form solutions exist for very simple loadcases

• Punching shear capacity at first yield depends on(=D/(2T)), (=d/D) and Fγ β y

• The line load capacity is proportional to the 1.5- 2.0power of cylinder thick T




Closed-Form Solutions For Axi-symmetric Line LoadClosed Form Solutions For Axi symmetric Line Load




Closed-form Solutions for Parallel Line LoadsClosed-form Solutions for Parallel Line Loads




St i T J i tStresses in a T-Joint

• Due to the differences in relative flexibility of braceand chord, the line load transferred across the weldat their intersection is far from uniform

• It is also more efficient to carry loads in the plane ofthe material than in carrying punching loads







Dundrova:Brace: MembraneChord: Shell

Theoretical Elastic Stresses Axially Loaded T Joint



T-Joint


Peak Hot Spot StressPeak Hot Spot Stress

• The results have confirmed experimentally (in terms• The results have confirmed experimentally (in termsof measured strains where stress are above yield)

Th k h t t t i th h d i 7 3 ti th• The peak hot spot stress in the chord is 7.3 times thenominal stress in the brace

• First yielding occurs with 2.5 ksi in the brace for 36ksi chord material




Thin-Shell Finite Element Models

• The cylindrical shells are subdivided into a mesh ofl t hi h i t th b d t felements which approximate the membrane and out-of-

plane (punching shear and localized shell bending)behavior of the actual tubes

• Steep gradients adjacent to the brace-to- chordintersectionintersection

• Hot spot stress = 2.5 - 2.7 times the nominal bracet f K j i tstress for K joints







Three-Dimensional Iso-parametric FiniteElements

• Use of solid elements to model the finite thickness of theshell and the weld geometry at their intersectionshell and the weld geometry at their intersection

• Avoid the paradoxical results that are sometimesbt i d f " f ” t t th id lobtained for "surface” stresses at the mid-plane

intersection using thin-shell element




Thick Shell Finite Element Model of K-jointj




P t i E tiParametric Equations

Ro tine design of simple joints can se empirical• Routine design of simple joints can use empiricalformulas obtained from prior stress analyses ofsimilar configurations

• The general form is based on static strengthconsiderationconsideration

• Specific coefficients are derived from thedetailed finite element or experimental stressdetailed finite element or experimental stressanalysis




Behaviourofof

Tubular Connections




Reserve StrengthReserve Strength

• The theoretical and experimental stress analyses areuseful in understanding the behavior of tubular jointsand indispensable in fatigue analysis

Th d id i l f l i• They do not provide a practical measure of ultimatestrength

• Most tubular joints have a tremendous reserve• Most tubular joints have a tremendous reservestrength beyond first yield

• Considerable reserve strength beyond theoretical• Considerable reserve strength beyond theoreticalyielding due to triaxiality, plasticity, large deflectioneffects, and load redistribution




Load Deflection Curve




Load Deflection BehaviorLoad Deflection Behavior

• For small load elastic⇒

• Beyond yield plastic deformation ⇒

• At a load 2.5 – 8 times that at first yield, theconnection fails

• By pullout failure • By localized collapse of the chord for compression loads




Early Test Resultsy




Observations (1)

• For stocky chords with (=d/(2T)) Less than 7,theγFor stocky chords with ( d/(2T)) Less than 7,thematerial shear strength would govern (i.e. allowable

)• Using the punching shear concept the axial load capacity

γ

yp FV 4.0=• Using the punching shear concept, the axial load capacityis proportional to the brace perimeter and chord thicknessto the 1.7 power

• This result is qualitatively consistent with shell theory




Observations (2)Observations (2)The overall strength level is due to

•The difference between elastic and plastic bending section moduliThe difference between elastic and plastic bending section moduli

• plastic load redistribution

i l i fl d i i l• restraint to plastic flow due to tri-axial stresses

• strain hardening

• Require extraordinary demands on the ductility of the chordmaterial

F• Due to the dependence on the strain hardening, should notexceed 2/3 of the tensile strength

yF




Factors Affecting the Ultimate StrengthFactors Affecting the Ultimate Strength

• and (=D/(2T)) (as mentioned before) yF γ

• Type of loading: axial (Ten/Comp), IPB,OPB

• Load pattern: K, T/Y ,X

• Geometric parameters: (=d/D) g/dβGeometric parameters: ( d/D), g/d

• Chord’s own load

β




F il M dFailure Modes




Failure Criteria

• Reaching the elastic limit of the material

• Reaching the material yield strength

• Detection of first cracking in a tension jointsDetection of first cracking in a tension joints

• Maximum load a joint will sustain in compression b f d f tibefore gross deformation occurs




Distortion Patterns and Yield RegionsDistortion Patterns and Yield Regions




Failure patternFailure pattern

• For tubular connection with < 0.3, failure occurs bypunching in or pulling out the plug from the side of the

βpunching in or pulling out the plug from the side of thechord (punching shear failure)

• When > 0.8, the chord fails by collapse

• In the range in between, must estimate the interaction of

β

In the range in between, must estimate the interaction ofpunching shear and general chord collapse




General Collapse

• Gross flattening or distortion of aglarge part of the chord

• Intersection between punching• Intersection between punchingshear and general bending ofchord wall




Failure Modes

• Local failure of the chord• Local failure of the chord

• General collapse of the chord

• Unzipping or progress weld failure

• Material problems• Fracture and delaminating

• Fatigue




Local Failure of the ChordLocal Failure of the Chord

In the vicinity of the brace member

• Plastic failure of chord face at radial line loadsPlastic failure of chord face at radial line loads

• Punching shear at the material strength




General Collapse of the Chord

Involves more of collapse with

p

a) Ovalisation

b) Beam bendingb) Beam bending

c) Beam shear

d) Sidewall web bucking

e) Longitudinal distress




Modes of General Collapsep







Unzipping or Progress Failure

• Uneven distribution of loadacross the weld

pp g g

• Peak load can be a factor oftwo higher than the nominaltwo higher than the nominalload

L l i ldi f• Local yielding may occur forload distribution

• If the weld is a weak, it may‘’unzip’’ before redistribution




Reserve Strength in Weld

• Design rules are intended to prevent this unzipping, t ki d t f th hi h t th i

Reserve Strength in Weld

taking advantage of the higher reserve strength in weld allowable stresses than is normally else where in the jointj




Material Problems

• Need plastic deformation to reach designcapacityp y

• Fracture and fatigue• Lamellar tearing• Weldability (HAZ)• Weldability (HAZ)




Static Strength Designg gof Tubular Connections




Compact Connections

• A connection can develop the full static capacity of• A connection can develop the full static capacity ofthe members jointed if

• The main member is compact (D/T less than 15 or 20)p ( )

• The branch member thickness is limited to 50 or 60% of themain member thickness

• A pre-qualified weld detail is used

• Need more detailed consideration if theNeed more detailed consideration if theabove conditions are not met




R l t D i C dRelevant Design Codes

• API RP 2A WSD

• API RP 2A LRFD

• AWS D1.1 Structural Welding Code

ISO 19902 (DIS only)• ISO 19902 (DIS only)

Marshall, P.W., Design of welded Tubular Connections: Basis and Use of AWS Code Provisions, Elsevier: Amsterdam, New York, 1992.




Local Failure

• In terms of punching shear (AWS & WSD)

• The main member acts as a cylindrical shell inresisting the concentrated radial line loads deliveredt it t th b h b f t i tto it at the branch member footprint

• Simplified localized shell stressesp• Acting punching shear

• is the nominal stress at the end of the bracef

θτ sinnp fV =

is the nominal stress at the end of the brace

• Axial and bending are treated separately

nf







Nominal Punching Shear Stress

• Actual localized stress: Shell: bending, member stressg,and shear stresses

• Conservative representation of the average shear• Conservative representation of the average shearstress at failure

• Safety factors

• AWS D1.1: 1.8• API RP2A WSD: 1 7• API RP2A WSD: 1.7

• Independent of the footprint length etc!




API RP2A WSD21ST Edition (2000)21 Edition (2000)

Section 4C iConnections




Definitions




Validity RangeValidity RangeThe validity range for application of the practice defined is as follows:

0.2 ≤ β ≤ 1.0

10 ≤ γ ≤ 50

30˚ ≤ θ ≤ 90˚

F ≤ 72 k i (500 MP )Fy ≤ 72 ksi (500 MPa)

g/D > -0.6 (for K joints)

The commentary discusses approaches that may be adopted for joints that fall outside the above range.




API Recommendations

St th f ti• Strength of connections• Larger than the design load• Not less than 50% of the effective memberstrength (buckling load or yield load)strength (buckling load or yield load)

• Simplified conditionYield stress of brace member,Not brace stub

0.1)5.1

11(

)sin(≤

+

θγτ

yc

yb

F

F

Chord yield stress or 2/3 of the tensile strength if less

)(βyc




Simple Joints

• Without overlap no gussets diaphragms or stiffeners• Without overlap, no gussets, diaphragms or stiffeners

• Classifications as K, T&Y, or X based on load pattern

• K-joints : the punching load in a brace should be essentially balanced byloads on other braces in the same plane on the same side of the joint

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

• X-joints: the punching load is carried through the chord to braces on theopposite side




K- Connections

• For balanced K-connections• the inward radial loads from

one branch member iscompensated by outwardcompensated by outwardloads on the other

• Ovalizing is minimized, and capacityapproaches the local punching shearapproaches the local punching shear




T or Y Connections

• For T and Y connections •• the radial load from the

single branch member isreacted by beam shear inreacted by beam shear inthe main member or chord

• The resulting ovalizing leadsto tower capacityto tower capacity




X C tiX Connections

• For cross or X connections, the load from onebranch is reacted by the opposite branch

• The resulting double dose of ovalizing in themain member leads to still further reductionsmain member leads to still further reductionsin capacity




Examplesp







Design Criteria• Based on punching shear

Design Criteria

• Although failure mechanisms and strength properties may bedifferent when approaching 1.0

• At present, insufficient experimental evidence exists to preciselytif th d f i d t thquantify the degree of increased strength

• Nominal loads

• Equivalent results




Based On Punching ShearBased On Punching Shear

θτ sinfVp =

• f = nominal axial, in-plane bending or out -of- plane bending stress in the brace

• Allowable punching shear stressF

• are different for different load cases

ycyc

fqp FF

QQV 4.06.0

≤=γ

V• are different for different load cases

• Qq, and Qf are empirical constants

paV



Offshore Structures – Tubular ConnectionsFactor Qq

Type Axial T i

AxialC

In-planeB di

Out-of- PlaneB di

Influence of connection type, geometry and load pattern

Tension Compression

Bending Bending

K (1.10-0.20/ ) β gQ

TT & Y (1.10-0.20/β3.72-0.67/β (1.37-0.67/ )Qβ β

X (1.10- (0.75-0.20/ 0.20/ )Qβ β β

30 20/1081 ≤−= TforgQ γ

6.00.1

6.0)833.01(

3.0

≤=

>−

=

β

βββ

β

β

forQ

forQ

0.1

20/48.1

20/1.08.1

≥

>−=

≤=

g

g

g

Q

DforgQ

TforgQ

γ

γ




Factor QfFactor Qf

• To account for the presence of nominall it di l t i th h dlongitudinal stress in the chord

• Qf = 1.0 - 2Aλγ= 1.0 of all extreme are in tension

•Where = 0.030 for brace axial stress0.045 for brace IPB 0.021 for brace OPB

A=222

OPBIPBAX fff ++


Indian Institute of Technology Madras-3665 YCF6.0


Interaction EquationsInteraction Equations

2 2V V⎛ ⎞ ⎛ ⎞

1.0p p

pa paIPB OPB

V V

V V

⎛ ⎞ ⎛ ⎞+ ≤⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

2 2

2arcsin 1 0p p pV V V⎛ ⎞ ⎛ ⎞

+ + ≤⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟arcsin 1.0pa pa paAX IPB OPB

V V Vπ+ + ≤⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠




Based On Nominal Loads (API RP 2A – 2003) Supplement 2( ) pp

θsin

2

FS

TFQQP yc

fua=Allowable Axial Load θsinFS

2dTFQQM yc=Allowable Moment

θsinFSQQM

fua=Allowable Moment

(Inplane or Out-of plane)

WhereWherePa = allowable capacity for brace axial loadMa = allowable capacity for brace bending moment,F = the yield stress of the chord member at the joint for 0 8 of the Fy = the yield stress of the chord member at the joint for 0.8 of the

tensile strength, if less), ksi (MPa)FS = safety factor = 1.60







Qf is a factor to account for the presence of nominal

21 2 31 c c

f

FSP FSMQ C C C A

⎡ ⎤⎛ ⎞ ⎛ ⎞= + − −⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟

f ploads in the chord.

1 2 31fy p

Q C C C AP M

+⎢ ⎥⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎝ ⎠ ⎝ ⎠⎣ ⎦

The parameter A is defined as follows:50

⎤⎡5.022

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟

⎟⎠

⎞⎜⎜⎝

⎛=

p

c

y

c

M

FSM

P

FSPA

Wh P d M h i l i l l d d b di lWhere Pc and Mc are the nominal axial load and bending resultant

(i.e. M2c = M2

ipb + M2opb

Py is the yield axial capacity of the chordPy is the yield axial capacity of the chord

Mp is the plastic moment capacity of the chord, and

C1, C2 and C3 are coefficients depending on joint and load type







Interaction EquationsInteraction Equations

22

⎟⎞

⎜⎛

⎟⎞

⎜⎛ MMP

0.1≤⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+

OPBa

p

IPBaAXaM

M

M

M

P

P

Where

• P and M are applied axial load and moment in brace member

• Pa and Ma are allowable axial load and bending moment in brace member




Calculate the interaction ratio for a balanced K joint with the chord and brace details shown belowjsubjected to axial, inplane and out-off plane bending moments. Neglect the stresses in the chordmember. Yield strength of the connection shall be taken as 345 MPa. Compare the results whenthe calculation is carried out using Y joint empirical coefficients.

Joint DataJoint Data

d1 508 mm⋅:= t1 15.88 mm⋅:= θ1 45 deg⋅:=Brace 1 Data

Brace 2 Data d2 406 mm⋅:= t2 12.7 mm⋅:= θ2 30 deg⋅:=2 2 2 g

Chord DataD 762 mm⋅:= Tc 15.88 mm⋅:=

Yield Strength F 345 MPa⋅:=Yield Strength Fy 345 MPa⋅:=

Loads on brace 1 P1 900 kN⋅:= M1IP 275 kN⋅ m⋅:= M1OP 125 kN⋅ m⋅:=

Loads on brace 2 P2 1275 kN⋅:= M2IP 225 kN⋅ m⋅:= M2OP 145 kN⋅ m⋅:=

Chord Load factor Qf 1:=




Joint Geometry parameters

Gap between braces gap 50 mm⋅:=

Geometric parameters β1d1

D:= β1 0.667= β2

d2

D:= β2 0.533=

γD

2 Tc⋅:=

γ 23.992=

gap

D0.066=

⎛ ⎞3

Qg for K joint Qg 1 0.2 1 2.8gap

D⋅−⎛⎜

⎝⎞⎟⎠

3

⋅+:= Qg 1.109=




Brace 1 - Joint Strength calculation (K Joint Method)

Qu for axial load Quax1 16 1.2 γ⋅+( ) β 11.2

⋅ Qg⋅:= Quax1 30.53=

Qulim1 40 β 11.2

⋅ Qg⋅:= Qulim1 27.264=

Pa1 Quax1 Qf⋅Fy Tc

2⋅

1.6 sin θ1( )⋅⋅:=Allowable axial load Pa1 2347.7 kN⋅=

1 2Quip1 5 0.7 γ⋅+( ) β 1

1.2⋅:= Quip1 13.398=

Quop1 2.5 4.5 0.2 γ⋅+( ) β 12.6

⋅+:= Quop1 5.74=

Allowable inplane bending moment

Ma1IP Quip1 Qf⋅Fy Tc

2⋅ d1⋅

1.6 sin θ1( )⋅⋅:=

Ma1IP 523.4 m kN⋅=

Allowable out-off plane bending M 1OP Q 1 Qf⋅Fy Tc

2⋅ d1⋅

⋅:=Allowable out off plane bending moment

Ma1OP Quop1 Qf⋅1.6 sin θ1( )⋅⋅:=

Ma1OP 224.2 m kN⋅=

Unity check ratio UC1P1

Pa1

M 1IP

M a1IP

⎛⎜⎝

⎞⎟⎠

2

+M1OP

Ma1OP

⎛⎜⎝

⎞⎟⎠

2

+:=UC1 0.97=




Brace 2 - Joint Strength calculation (K Joint Method)Brace 2 Joint Strength calculation (K Joint Method)

Qu for axial load Quax2 16 1.2 γ⋅+( ) β21.2

⋅ Qg⋅:= Quax2 23.33=

Qulim2 40 β21.2

⋅ Qg⋅:= Qulim2 20.835=


2⋅


Q 5 0 7+( ) β1.2

: Q 10 239Quip2 5 0.7 γ⋅+( ) β2⋅:= Quip2 10.239=

Quop2 2.5 4.5 0.2 γ⋅+( ) β21.2

⋅+:= Quop2 6.868=

F T2

⋅ d2⋅Ma2IP Quip2 Qf⋅

Fy Tc d2

1.6 sin θ2( )⋅⋅:=Allowable inplane bending

momentMa2IP 452.1 m kN⋅=

Allowable out-off plane bending t

Ma2OP Quop2 Qf⋅Fy Tc

2⋅ d2⋅

1 6 sin θ( )⋅:=M 2OP 303 2 m kN⋅=moment

p 1.6 sin θ2( )⋅ Ma2OP 303.2 m kN

UC2P2

Pa2

M2IP

Ma2IP

⎛⎜⎝

⎞⎟⎠

2

+M2OP

Ma2OP

⎛⎜⎝

⎞⎟⎠

2

+:=Unity check ratio UC2 0.979=




Brace 1 - Joint Strength calculation (Y Joint Method)Brace 1 Joint Strength calculation (Y Joint Method)

Qu for axial load Quax1 16 1.2 γ⋅+( ) β11.2

⋅:=Quax1 27.535=

Qulim1 30 β1⋅:=Qulim1 20=


2⋅


Q 5 0 7( ) β1.2

Quip1 5 0.7 γ⋅+( ) β11.2

⋅:=Quip1 13.398=

Quop1 2.5 4.5 0.2 γ⋅+( ) β12.6

⋅+:=Quop1 5.74=

2

Allowable inplane bending moment

Ma1IP Quip1 Qf⋅Fy Tc

2⋅ d1⋅

1.6 sin θ1( )⋅⋅:=

Ma1IP 523.4 m kN⋅=

Allowable out-off plane bending Ma1OP Quop1 Qf⋅Fy Tc

2⋅ d1⋅

( )⋅:=M 224 2 kNmoment

a1OP Quop1 Qf 1.6 sin θ1( )⋅ Ma1OP 224.2 m kN⋅=

Unity check ratio UC1P1

Pa1

M1IP

Ma1IP

⎛⎜⎝

⎞⎟⎠

2

+M1OP

Ma1OP

⎛⎜⎝

⎞⎟⎠

2

+:=UC1 1.012=




Brace 2 - Joint Strength calculation (Y Joint Method)

Qu for axial load Quax2 2.8 20 0.8 γ⋅+( ) β 21.6

⋅+:=Quax2 17.113=

Qulim2 2.8 36 β 21.6

⋅+:=Qulim2 15.947=


2⋅

1.6 sin θ2( )⋅⋅:=Allowable axial load Pa2 1861 kN⋅=

Q 0( ) β1.2

Quip2 5 0.7 γ⋅+( ) β 21.2

⋅:=Quip2 10.239=

Quop2 2.5 4.5 0.2 γ⋅+( ) β 21.2

⋅+:=Quop2 6.868=

2

M a2IP Quip2 Qf⋅Fy Tc

2⋅ d2⋅

1.6 sin θ2( )⋅⋅:=Allowable inplane bending

momentMa2IP 452.1 m kN⋅=

Allowable out-off plane bending moment

Ma2OP Quop2 Qf⋅Fy Tc

2⋅ d2⋅

1 6 sin θ2( )⋅⋅:=

Ma2OP 303.2 m kN⋅=moment 1.6 sin θ2( ) a2OP

UC2P2

Pa2

M2IP

Ma2IP

⎛⎜⎝

⎞⎟⎠

2

+M2OP

Ma2OP

⎛⎜⎝

⎞⎟⎠

2

+:=Unity check ratio UC2 1.161=




Design of Tubular Joint to API RP 2ADesign of Tubular Joint to API RP 2ACheck the tubular connection between a jacket leg (1976mm x 38mm) and horizontal brace(762mm x 32mm) subjected to loads listed below. The jacket is designed with a grouted mainpile (1824mm x 50mm) The yield strength of jacket leg brace and pile is 345 MPa Use APIpile (1824mm x 50mm). The yield strength of jacket leg, brace and pile is 345 MPa. Use APIRP 2A guidelines using nominal loads method.

Brace Loads P 8000 kN⋅:= MIP 200 kN⋅ m⋅:= MOP 600 kN⋅ m⋅:=

Chord Loads Pc 3000 kN⋅:= McIP 600 kN⋅ m⋅:= McOP 0 kN⋅ m⋅:=

Brace data d 762 mm⋅:= t 32 mm⋅:= θ 90 deg⋅:=d 762 mm:= t 32 mm:= θ 90 deg:=

Yield Strength Fy 345 MPa⋅:=

Leg Diameter and thickness D 1976 mm⋅:= TL 50 mm⋅:=

Pile Diameter and thickness DP 1976 mm⋅:= TP 50 mm⋅:=




Estimation of Qu for axial inplane and out-off plane bending momentEstimation of Qu for axial, inplane and out-off plane bending moment

Since the brace to chord angle is given as 90 degrees, the joint is classified as T joint andappropriate formula for the computation of Qu shall be selected.

Equivalent chord thickness 2 2Equivalent chord thickness for grouted (leg + pile) Tc TP

2TL2

+:= Tc 70.7 mm⋅=

γD

2 Tc⋅:=

βd

D:= β 0.386= γ 13.972=Geometric Parameters cDGeometric Parameters

Qu Factor for axial load Quax 2.8 20 0.8 γ⋅+( ) β1.6

⋅+:=Quax 9.588=

Quaxmax 2.8 36 β1.6

⋅+:= Quaxmax 10.637=Qu limit for axial load

Qu for inplane bending Quip 5 0.7 γ⋅+( ) β1.2

⋅:=Q 4 711

p gmoment

Quip 5 0.7 γ( ) β:Quip 4.711=

Qu for out-off plane bending moment Quop 2.5 4.5 0.2 γ⋅+( ) β

2.6⋅+:=

Quop 3.112=




Ultimate capacity of chord

C1ax 0.3:= C2ax 0.0:= C3ax 0.8:=Chord Coefficients

C1b 0.20:= C2b 0.0:= C3b 0.40:=

Equivalent MomentMc McIP

2McOP

2+:=

Yield Axial Capacity of chordPy π D⋅ Tc⋅ Fy⋅:= Py 1.514 10

5× kN⋅=y c y y

Plastic moment capacity of chord Mp D

2Tc⋅ Fy⋅:= Mp 9.525 10

4× kN m⋅⋅=

Factor of Safety against chord yielding FSC 1.2:=




Estimation of Qf for axial, inplane and out-off plane bending momentEstimation of Qf for axial, inplane and out off plane bending moment

Applied Load effect AA FSCPc

Py⋅

⎛⎜⎝

⎞⎟⎠

2

FSCM c

M p⋅

⎛⎜⎝

⎞⎟⎠

2

+:= AA 0.025=

Qf for axial loadQfax 1 C1ax

FSC Pc⋅

Py

⎛⎜⎝

⎞⎟⎠

⋅+ C2ax

FSC M c⋅

Mp

⎛⎜⎝

⎞⎟⎠

⋅− C3ax AA2

⋅−:=

Qfax 1=

Qf for inplane bending momentQfip 1 C1b

FSC Pc⋅

Py

⎛⎜⎝

⎞⎟⎠

⋅+ C2b

FSC M c⋅

Mp

⎛⎜⎝

⎞⎟⎠

⋅− C3b AA2

⋅−:=

Qfip 1=

Qf for out-off plane bending moment Qfop 1 C1b

FSC Pc⋅

P

⎛⎜⎝

⎞⎟⎠

⋅+ C2b

FSC M c⋅

M

⎛⎜⎝

⎞⎟⎠

⋅− C3b AA2

⋅−:=op b Py⎝ ⎠b M p⎝ ⎠

3b

Qfop 1=




E ti ti f ll bl i l i l d t ff l b diEstimation of allowable axial, inplane and out-off plane bendingmoment capacity

Factor of Safety joint capacity FS 1.6:=

Allowable Axial load Pa Quax Qfax⋅Fy Tc

2⋅

FS sin θ( )⋅⋅:=

Pa 10405.2 kN⋅=

2Allowable inplane bending moment MaIP Quip Qfip⋅

Fy Tc2

⋅ d⋅

FS sin θ( )⋅⋅:=

MaIP 3887.5 m kN⋅=

2Allowable out-off plane bending moment MaOP Quop Qfop⋅

Fy Tc2

⋅ d⋅

1.6 sin θ( )⋅⋅:=

MaOP 2568.4 m kN⋅=

Interaction between axial inplane and out-off plane bending momentInteraction between axial, inplane and out-off plane bending moment

Combined interaction ratio of axial and bending effects UC

P

Pa

MIP

MaIP

⎛⎜⎝

⎞⎟⎠

2

+MOP

MaOP

⎛⎜⎝

⎞⎟⎠

2

+:=UC 0.826=




Design Practices

• Design Based on Actual Loads

Design Practices

• Design based on Planer connections

Design for minim m 50% brace strength• Design for minimum 50% brace strength

• Can length (minimum requirements)

• Brace stub

• Offset or Eccentricities







Load Transfer Across Chord

• When load is transferred across the chord, it shouldb d i d i t l ll

Load Transfer Across Chord

be designed against general collapse

• For d < 0. 9 DP= P(1) + L/2.5D (P)2) – P(1)) if L < 2.5DP= P(2) if L > 2.5D

• P (1) uses nominal chord thickness

P (2) h d i d thi k• P (2) uses chord can increased thickness



Offshore Structures – Tubular ConnectionsFor More Complex Joints

• Crushing Load = iii P θsin∑

• Approximate closed ring analysis

• Any reinforcement within the effective chord length• Any reinforcement within the effective chord lengthcan be included

• Alternatively , compute the ovalizingparameter as in AWS D1.1




Eff ti Ch d L thEffective Chord Length




Adverse Load Patterns




GROUTED LEG JOINTSGROUTED LEG JOINTSMain piles along the leg with grouted annulus will give additional strength to the tubular connections The pile wall additional strength to the tubular connections. The pile wall and the leg wall will act together for compressive loads as well as for small tensile loads and can be taken as equivalent thickness as per the following formulathickness as per the following formula

2 2C P LT T T= +C P L




Multi-planar Joints

• Many tubular space frames have bracing in multiple planes

p

• For some loading conditions, these different planes interact

• In AWS, an “ovalizing parameter”(α) may be used to estimatethe beneficial or deleterious effect of various branch member loading combinations on main member ovalizingloading combinations on main member ovalizing



Offshore Structures – Tubular ConnectionsComputation of Ovalizing Parametersα




Ovalizing Parameter AlphaOvalizing Parameter Alpha

• To be evaluated separately for each branch and for each load caseeach load case

• Influence of braces• Cosine term and exponential decay term

• Compatible with values for strength designα = 1 0 Kα = 1.0 Kα = 1.7 T&Yα = 2.4 x

→→

→




Ovalizing Parameter Alpha

A t ti ll t k f l d tt f ll i b t th• Automatically take care of load pattern falls in between thestandard cases

• no need to use interpolated values

• When > 2 4 or a low value of α results from interactionαWhen > 2.4 or a low value of α results from interactionother than the classical K-joint action, alternative designmethods should be used for investigation

α




Ring Stiffened jointsRing Stiffened joints




Equivalent chord wall thickness calculation for Ring Stiffened jointsq g j




Equivalent area methodq

Internal diameter, di = D-2t = 1219-2*50=1119e a d a e e , di 9 50 9

Stiffener plate width = bs

Effective Chord Length, Le = 1.1(Dt)1/2= 272

Area, A = (Le*t)+(bs*ts)+(bf*tf )

Equivalent thickness, Te = A/Le

Note: Te: Not greater than 2t

Bs/ts is limited to 18 or less




Equivalent moment of inertia methodq

Internal diameter, di = D-2t

Stiffener plate width = bs

)2/(*)*())2/(*)*(()2/**( tfbsttfbfbsttsbsttLe +++++

Effective Chord Length, Le = 1.1(Dt)1/2

Centroidal distance, y =

)*()*()*(

)2/(*)*())2/(*)*(()2/**(

tfbftsbstLe

tfbsttfbfbsttsbsttLe

+++++++

Equivalent moment of Inertia =

2

3

233

)2

(**12

)2

(12

2)2

(**12

yt

bttbtbb

tytbbtt

ytLtL s

sffffs

ssss

ee −++++−−++−+

E i l t thi k T312

Le

ITEquivalent thickness, Te =

Note: Te Not greater than 2t

Bs/ts is limited to 18 or less



tubular joint api rp 2a design

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