Unified approach for structural behavior of RHS T jointsMarsel Garifullin, Kristo Mela, Markku Heinisuo

Tampere University of Technology, Tampere, Finland

METNET International Workshop

15-16 March 2017, Kemi and Rovaniemi, Finland

SCOPE OF RESEARCH 2 / 22

Goal: Cost optimization for tubular trusses with semi-rigid joints

Need: Unified approach for design resistance and initial stiffness of tubular joints under arbitrary loading

NOTATIONS & LOADING 3 / 22

Loading• axial force N• in-plane moment Mip

• out-of-plane moment Mop

Notationsb0, h0, t0 Chord dimensions b1, h1, t1 Brace dimensionsfy0, fu0 Chord material propertiesa Fillet weld size= b1 / b0

η= h1 / b0

CURRENT APPROACH 4 / 22

EN 1993-1-8:2005 - Failure modes approach

Possible failure modes:

• Chord face failure

• Chord side wall failure

• Chord shear failure

• Punching shear

• Brace failure

• Local buckling

CURRENT APPROACH 5 / 22

EN 1993-1-8:2005 - Failure modes approach

1. Geometry of the joint

2. Limiting failure mode

3. Resistance by simple equations

CURRENT APPROACH 6 / 22

EN 1993-1-8:2005 - Failure modes approach

• Simple & fast

Challenges

• Restricted by cases studied

• Additional checks for welds required

• No rules for initial stiffness

Possible solution

Component method

COMPONENT METHOD 7 / 22

Brief history

1974, Zoetemeijer, bolted connections

1987, Tschemmernegg et al.

1995, Wald, column bases

1998, Grotmann & Sedlacek, rotational stiffness

2001, Weynand & Jaspart, hollow section joints

2008, da Silva, 3D joints

2009, Heinisuo et al., end plate joints

2015, Weynand et al., general approach for all types of joints

Currently: EN 1993-1-8 for joints connecting H or I sections

This research

Component method for RHS T joints under arbitrary loading

COMPONENT METHOD 8 / 22

Major concept

1. Load is transferred through loading zones

2. Component model

a) chord face in bending

b) chord side walls in tension or compression

c) chord side walls in shear

d) chord face under punching shear

e) brace flange or webs in tension or compression

f) welds

COMPONENT METHOD 9 / 22

Major concept

3. Active components

4. Resistance and stiffness of active components

5. Design resistances and initial stiffnesses of joint

Simplified design model

Cj,ini,N axial longitudinal stiffness

Sj,ini,Mip rotational in-plane stiffness

Sj,ini,Mop rotational out-of-plane stiffness

RESISTANCE 10 / 22

1. Active components (Weynand et al., 2015)

Component Axial force In-plane moment Out-of-plane moment

aChord face in

bending

≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0

● – ● – ● –

b

Chord side wall(s) in

tension or

compression

≤ 0.85 0.85 < ≤ 1.0 = 1.0 ≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0

– ● ● – ● – ●

cChord side wall(s) in

shear– – – – – – –

dChord face under

punching shear

≤ 0.85 0.85 < ≤ (1–1/ ) > (1–1/ ) ≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0

– ● – – – – –

e

Brace flange and

web(s) in tension or

compression

≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0 ≤ 0.85 0.85 < ≤ 1.0

– ● – ● – ●

f Welds ● ● ● ● ● ●

RESISTANCE 11 / 22

2. Resistances of active components (Weynand et al., 2015)

3. Minimum resistances RdMopfRdMopeRdMopdRdMopcRdMopbRdMopaRdMop

RdMipfRdMipeRdMipdRdMipcRdMipbRdMipaRdMip

RdNfRdNeRdNdRdNcRdNbRdNaRdN

FFFFFFF

FFFFFFF

FFFFFFF

,,,,,,,,,,,,min,,

,,,,,,,,,,,,min,,

,,,,,,,,,,,,min,,

;;;;;min

;;;;;min

;;;;;min

RdMopfRdMopeRdMopdRdMopcRdMopbRdMopa

RdMipfRdMipeRdMipdRdMipcRdMipbRdMipa

RdNfRdNeRdNdRdNcRdNbRdNa

FFFFFF

FFFFFF

FFFFFF

,,,,,,,,,,,,

,,,,,,,,,,,,

,,,,,,,,,,,,

;;;;;

;;;;;

;;;;;

RESISTANCE 12 / 22

opRdMopRdop

ipRdMipRdip

RdNRd

zFM

zFM

FN

min,,,

min,,,

min,,

2

2

44. Design resistances of joint

5. Final resistance

1,

,

,

, Rdop

Edop

Rdip

Edip

Rd

Ed

M

M

M

M

N

N

INITIAL STIFFNESS 13 / 22

1. Component a (chord face in bending)

2

0

3

25.1

0

2

2

30

6.15.14.10

1

tan1

4.14

t

L

L

b

L

b

L

b

L

c

bt

L

L

tk

stiff

stiff

stiff

stiffstiffstiff

stiffa

16

2

1

1

2030

3,

30

b

ltk cfeff

a

(Weynand et al., 2015)

(Grotmann & Sedlacek, 1998)

INITIAL STIFFNESS 14 / 22

2. Component b (chord side wall in tension or compression)

(Weynand et al., 2015)

(Grotmann & Sedlacek, 1998)

0

0,,2

h

tbk wcceff

b

00

,,0

3

2

th

btk elcweff

b

3. Component c chord side wall in shear)

ip

VCc z

Ak 38.0 (Weynand et al., 2015)

INITIAL STIFFNESS 15 / 22

4. Component d (chord face under punching shear)

kd = ∞ (Weynand et al., 2015)

5. Component e (brace flange and web in tension or compression)

ke = ∞ (Weynand et al., 2015)

6. Component f (welds)

kf = ∞ (Weynand et al., 2015)

INITIAL STIFFNESS 16 / 22

Longitudinal stiffness

ba

NsnNinij

kk

EkC

21,

,,

Rotational out-of-plane stiffness

Rotational in-plane stiffness

cba

ipsnipinij

kkk

kEhS

122,

21

,,

ba

opsnopinij

kk

kEbS

22,

21

,,

EXAMPLES 17 / 22

In-plane bending

b0 [mm] 150.6

h0 [mm] 151.6

t0 [mm] 7.98

fy0 [N/mm2] 478

fu0 [N/mm2] 537

E [GPa] 185

b1 [mm] 100.33

h1 [mm] 100.85

t1 [mm] 7.94

Full penetration butt welds

EN 1993-1-8:2005

Failure mode: Chord face failure;

Reduction factor: 0.9;

Design resistance:

;85.067.0

.2.17,1, kNmM Rdip

Component method

Active components: a, f;

Reduction factor 0.9 for component a;

Resistances of the components:

Design resistance:

;85.067.0

;1.171;4.92 ,,,, kNFkNF RdMipfRdMipa .2.17, kNmM Rdip Experimental resistance:

Numerical resistance:

;5.18exp, kNmM ip .7.15, kNmM FEMip

EXAMPLES 18 / 22

In-plane bending

0

5

10

15

20

25

30

0,00 0,05 0,10 0,15 0,20 0,25

M[k

Nm

]

φ [rad]

Test

FEM

M_ip,Rd

M_ip,exp

M_ip,FEM

Initial rotational stiffness

Active components: a, b, c;

Stiffnesses of the components:

Design rotational stiffness:

Experimental rotational stiffness:

Numerical rotational stiffness:

;64.8;61.8;04.1 mmkmmkmmk cba ;/830,, radkNmS ipinij

;/977exp,,, radkNmS ipinij ./888,,, radkNmS FEMipinij

EXAMPLES 19 / 22

Out-of-plane bending

b0 [mm] 150.6

h0 [mm] 151.6

t0 [mm] 7.98

fy0 [N/mm2] 478

fu0 [N/mm2] 537

E [GPa] 185

b1 [mm] 100.33

h1 [mm] 100.85

t1 [mm] 7.94

Full penetration butt welds

EN 1993-1-8:2005

Failure mode: Chord face failure;

Reduction factor: 0.9;

Design resistance:

;85.067.0

.5.17,1, kNmM Rdop

Component method

Active components: a, f;

Reduction factor 0.9 for component a;

Resistances of the components:

Design resistance:

;85.067.0

;0.172;9.92 ,,,, kNFkNF RdMipfRdMipa .5.17,1, kNmM Rdop

EXAMPLES 20 / 22

Axial loading

b0 [mm] 140

h0 [mm] 80

t0 [mm] 4

fy0 [N/mm2] 361.9

fu0 [N/mm2] 418.6

E [GPa] 200

b1 [mm] 100

h1 [mm] 100

t1 [mm]a 3

a [mm] 5

EN 1993-1-8:2005

Failure mode: Chord face failure;

Design resistance without chord stress function:

Chord stress function:

Design resistance:

Component method

Active components: a, f;

Resistances of the components without chord stress function:

Chord stress function:

Resistances of the components:

Design resistance:

Experimental resistance:

Numerical resistance:

;85.071.0

;87.0nk

.8.62,1 kNN Rd

;3.72* ,1 kNN Rd

;5.84exp kNN .0.90 kNNFEM

;85.071.0

;6.144;1.18 ,,*

,, kNFkNF RdNfRdNa ;87.0nk

;6.144;7.15 ,,,, kNFkNF RdNfRdNa ;8.62 kNNRd

EXAMPLES 21 / 22

Axial loading

Initial longitudinal stiffness

Active components: a, b;

Stiffnesses of the components:

Design rotational stiffness:

Experimental rotational stiffness:

Numerical rotational stiffness:

;71.3;91.1 mmkmmk ba ;/189,, mmkNC Ninij

;/100exp,,, mmkNC Ninij ./133,,, mmkNC FEMNinij 0

10

20

30

40

50

60

70

80

90

100

0,0 1,0 2,0 3,0 4,0 5,0 6,0

N[k

N]

δ [mm]

Test

FEM

N_Rd

CONCLUSIONS 22 / 22

Discussions

1. Eurocode-based approach of component method -> safe design resistances

2. Larger amount of calculations

3. Unclear axial and in-plane stiffnesses, uncovered out-of-plane stiffness

4. Joints assumed to behave similarly in compressions and tension

Further investigations

1. Parametric studies for verification

2. Chord stress functions for stiffness

3. Interaction of loads

4. Reduction coefficients for HSS

5. Effect of fillet welds