Stress Concentration Factors of Cold-Formed Stainless ... · PDF fileHSSN perpendicular to weld toe Nominal strain Strain component parallel to weld toe. Determination of SCF Hot spot

Ran FENG1 and Ben YOUNG2

1 School of Civil Engineering, Hefei University of Technology, P.R. China

2 Department of Civil Engineering, The University of Hong Kong, Hong Kong

Stress Concentration Factors of Cold-Formed

Stainless Steel Tubular X-Joints

Stainless Steel In Structures: Fourth International Experts Seminar

6th-7th December 2012, Ascot, UK

Outline

Introduction

Hot Spot Stress Method

Experimental Investigation

Finite Element Analysis

Design Guidelines

Conclusions

Outline

Introduction




Design Guidelines

Conclusions

Introduction

Weld

Brace

Chord

Geometric stress distribution in an

axially loaded CHS tubular X-joint

Nominal stress in brace

Peak stress in brace

Peak stress in chord

t0d 0

t1d 1

Stress Concentration

Outline

Introduction




Design Guidelines

Conclusions


SCF FEA

Test

Weld

Brace

Chord

Geometric stress distribution in an

axially loaded CHS tubular X-joint

Nominal stress in brace

Peak stress in brace

Peak stress in chord

t0d 0

t1d 1

HSS

Hot Spot Location

t0

h0

b0

h1

b1

t1

Brace

Chord

45¡ã

A

BCD

EFH

I

G

Extrapolation Method SNCF

Distance from Weld Toe

Weld Toe

but ¡ Ý 4mm0.4t

Linear

Extrapolation

0.6t

SNCF Linear

Quadratic Extrapolation

1.0t

Measuring points

SNCF Quadratic

Outline

Introduction




Design Guidelines

Conclusions

Test Specimens

/2/2

Welds

Seam weld

Welds

Brace

Brace

Chord

L 0

L 1

h1

w

w

h1

h1

t 1 b1

h0

r1

Seam weld

Weld

Brace

Brace

Chord

wt 0

b0 h0

b1

w

r0

Test Specimens

w

Specimen

Chord Brace Weld

(mm) (mm) (mm)

h0 b0 t0 r0 L0 h1 b1 t1 r1 L1 w β

XD-C140×3-B40×2 140.2 80.2 3.33 6.5 737 39.9 40.3 1.96 2.0 99 6.6 –– 0.50

XD-C140×3-B140×3 140.0 80.1 3.09 6.5 851 140.1 80.1 3.10 6.5 346 6.6 8.5 1.00

XH-C150×6-B150×6 150.3 150.5 5.75 6.0 902 150.3 150.3 5.84 6.0 368 9.2 15.5 1.00

XH-C110×4-B150×6 110.3 196.3 3.98 8.5 698 150.3 150.4 5.82 6.0 365 9.6 –– 0.77

XN-C40×4-B40×2 40.1 40.0 3.79 4.0 240 40.2 40.1 1.97 2.0 98 6.5 11.9 1.00

HSSN Measurement

Stress Concentration Measurement

Location of Strain Gauges h1

b0 b1

t 0

h0

b0

Brace

Chord

: Single element strain gauge for nominal strain at mid-length of brace member

: Strip strain gauges for hot spot strain (HSSN) at chord member

: Strip strain gauges for hot spot strain (HSSN) at brace member

28

28

2

8

Weld Toe Weld Toe

Brace

Chord

28

Test Rig and Procedure

Determination of SCF

nSNCF /

SNCFSCF2

//

1

1

HSSN perpendicular to weld toe

Nominal strain

Strain component parallel to weld toe


Hot spot

location

Axial compression force (kN)

Average

S/N

ratio

19.9 40.1 59.8 80.3 99.5

ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N

A -40.2 26.6 0.88 -121.6 53.4 0.95 -204.0 80.4 0.97 -295.6 113.6 0.97 -388.6 148.4 0.97 0.948

B 20.1 44.0 1.82 -20.5 83.2 -0.24 -76.6 112.6 0.61 -155.0 139.2 0.80 -245.9 167.0 0.87 1.025

C 41.4 37.6 1.40 51.8 67.6 1.53 59.2 92.2 1.61 60.8 105.8 1.67 67.8 121.0 1.69 1.580

D 58.4 12.0 1.17 77.6 -20.4 1.01 95.8 -61.0 0.89 105.6 -108.8 0.76 115.2 -164.0 0.63 0.892

E -46.2 17.3 0.98 -150.8 22.7 1.05 -247.4 25.1 1.07 -353.6 34.3 1.07 -465.4 38.5 1.07 1.048

Average S/N ratio for all hot spot locations 1.10

SCF/SNCF ratios for stainless steel tubular X-joint of specimen XD-C140×3-B140×3 (β=1.00, τ=1.00, 2γ=25.92)


Hot spot

location

Axial compression force (kN)

Average

S/N

ratio

16.1 32.1 47.9 64.0 79.8

ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N ξ┴ ξ// S/N

A -160.4 26.4 1.04 -289.4 59.8 1.03 -366.8 102.8 1.01 -418.0 154.8 0.98 -456.0 213.6 0.94 1.000

B -324.6 -18.0 1.12 -709.0 -36.2 1.12 -1100.2 -49.0 1.11 -1476.6 -71.0 1.11 -1848.6 -101.6 1.12 1.116

C -207.8 -87.0 1.24 -494.2 -202.8 1.23 -809.2 -336.0 1.24 -1136.6 -476.6 1.24 -1496.6 -646.2 1.24 1.238

D -65.6 -79.8 1.50 -172.6 -187.4 1.46 -295.4 -307.6 1.44 -441.0 -437.6 1.43 -615.0 -593.6 1.42 1.450

E -4.4 23.8 -0.68 -24.0 60.2 0.27 -55.4 108.6 0.45 -99.8 162.6 0.56 -153.4 228.4 0.61 0.473

Average S/N ratio for all hot spot locations 1.06

SCF/SNCF ratios for stainless steel tubular X-joint of specimen XH-C110×4-B150×6 (β=0.77, τ=1.46, 2γ=49.32)


nSNCF /

SNCFSCF2

//

1

1

1.08

Outline

Introduction




Design Guidelines

Conclusions

Finite Element Model

A

B C

D

E

F

G

H

I

Verification of FEM

Specimen Comparison

Strain concentration factor (SNCF)

A B C D E F G H I

XD-C140×3-B40×2

Experiment –– 15.03 9.52 4.39 1.27 -0.79 –– 4.26 12.27

FE model –– 15.38 8.82 3.74 0.86 -1.33 –– 4.26 9.04

SNCFEXP/SNCFFE –– 0.98 1.08 1.17 1.48 0.59 –– 1.00 1.36

XH-C150×6-B150×6

Experiment 2.11 1.91 0.91 –– 1.52 0.35 0.09 2.49 1.69

FE model 2.27 2.13 1.01 –– 2.16 0.27 0.06 1.55 1.37

SNCFEXP/SNCFFE 0.93 0.90 0.90 –– 0.70 1.30 1.50 1.61 1.23

XN-C40×4-B40×2

Experiment 1.07 0.52 0.08 -0.04 0.75 1.19 0.04 1.63 0.72

FE model 1.19 0.67 0.16 -0.03 1.20 0.74 0.04 1.14 0.65

SNCFEXP/SNCFFE 0.90 0.78 0.50 1.33 0.63 1.61 1.00 1.43 1.11

Parametric Study

Geometric parameter β=b1/b0 τ=t1/t0 2γ=b0/t0

CIDECT [0.35-1.0] [0.25-1.0] [12.5-25.0]

Laboratory tests [0.5-1.0] [0.5-1.5] [10.0-50.0]

Parametric study [0.2-1.0] [0.25-2.0] [10.0-50.0]

Outline

Introduction




Design Guidelines

Conclusions

Current Design Rules hgfe

dcbaSCF

2

222

Hot spot location Coefficient

a b c d e f g h

Brace

A/E 0.013 0.693 -0.278 0 0.790 1.898 -2.109 0

Joints with fillet

welds

SCFA and SCFE are multiplied by a factor of 1.40

for brace side of weld.

Chord

B 0.143 -0.204 0.064 0 1.377 1.715 -1.103 0.75

C 0.077 -0.129 0.061 -0.0003 1.565 1.874 -1.028 0.75

D 0.208 -0.387 0.209 0 0.925 2.389 -1.881 0.75

X-joints

(β=1.0)

SCFC is multiplied by a factor of 0.65;

SCFD is multiplied by a factor of 0.50.

Comparison

Specimen β=b1/b0 τ=t1/t0 2γ=b0/t0 Comparison Stress concentration factor (SCF)

A B C D E

XD-C140×3-B40×2 0.50 0.59 24.08

Experiment 2.19 16.23 10.28 4.74 1.37

CIDECT 19.21 19.46 17.42 8.50 19.21

SCFEXP/SCFCIDECT 0.11 0.83 0.59 0.56 0.07

XD-C140×3-B140×3 1.00 1.00 25.92

Experiment 2.49 0.15 0.73 -0.55 1.39

CIDECT 3.95 1.95 2.04 1.60 3.95

SCFEXP/SCFCIDECT 0.63 0.08 0.36 -0.34 0.35

XH-C150×6-B150×6 1.00 1.02 26.17

Experiment 2.28 2.06 0.98 -0.11 1.64

CIDECT 4.01 2.08 2.00 1.64 4.01


XH-C110×4-B150×6 0.77 1.46 49.32

Experiment 5.62 16.51 12.14 4.47 0.84

CIDECT 26.93 93.02 -12.55 28.38 26.93

SCFEXP/SCFCIDECT 0.21 0.18 -0.97 0.16 0.03

XN-C40×4-B40×2 1.00 0.52 10.55

Experiment 1.16 0.56 0.09 -0.04 0.81

CIDECT 2.31 0.19 0.68 0.27 2.31


Proposed Design Rules

hgfedcbaSCF

2

222

Hot spot location Coefficient

a b c d e f g h

Brace

A/E/F 0.725 -2.000 2.000 -0.0025 0.270 4.350 -4.200 0.250

H 1.700 -5.000 5.000 -0.0015 -0.250 4.480 -4.200 0.500

Chord

B/I 0.191 -1.276 1.856 -0.0002 4.288 -3.800 -0.155 0.800

C 0.015 0.250 -0.250 -0.0002 1.500 0.778 -0.950 0.500

D/G 0.075 -0.300 0.540 0.0003 1.200 1.800 -2.700 0.300

Comparison

A total of 115 X-joints

Comparison

SCFFE/SCFCIDECT SCFFE/SCFProposed

A B C D A B C D H

Mean 0.80 0.99 0.17 0.54 1.00 1.00 1.00 1.00 1.00

COV 0.350 1.069 3.071 0.932 0.281 0.177 0.316 0.279 0.211

Outline

Introduction




Design Guidelines

Conclusions

Conclusions

The highest SCFs are usually found for stainless steel tubular

X-joints with medium β values.

The highest SCFs may occur at the center of brace and chord

intersection edges as well as the traditional hot spot locations

for stainless steel tubular X-joints.

The lower the 2γ ratio, the lower the SCF.

Conclusions

The design rules specified in the current design guideline are

generally quite unconservative for the SCFs of cold-formed

stainless steel tubular X-joints.

The values obtained from the proposed unified design

equation for the SCFs of cold-formed stainless steel tubular X-

joints are generally much more accurate than those calculated

using the current design formulae.

The limit of the geometric parameters (β, τ and 2γ) and the

thickness of the tubular sections in the proposed unified design

equation are beyond the limit in the CIDECT design formulae.

Hefei University of Technology The University of Hong Kong

Q & A

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Stress Concentration Factors of Cold-Formed Stainless ... · PDF fileHSSN perpendicular to weld toe Nominal strain Strain component parallel to weld toe. Determination of SCF Hot spot