Fatigue Limit of SPD.pdf

1
by
Muhammad Abrar Victoriawan (M2)
Supervisor
Professor Kazuo TATEISHI
TATEISHI – HANJI – SHIMIZU Laboratory of Steel Structures
Study on the Fatigue Limit State of
Shear Panel Dampers
Final presentation - 29 July 2021

2
Introduction
Great Hanshin Earthquake (1995)
Revisions of seismic design specifications have been done
extensively over the past decades
Source: ASSOCIATED PRESS

3
Multiple-steel-pipe column (MSPC)
Source: hanshin-exp.co.jp
Steel-pipe column
Superstructure
Shear panel damper (SPD)
Flange
Panel
Stiffener
SPD configuration

4
Main advantages
• Principal components of the bridge are preserved after earthquake
• Damaged SPD units will not obstruct the traffic
• Easy inspection (first damaged component limited to SPD)
• Damaged SPD units can be easily replaced
SPD
Steel-pipe column

5
Main advantages
• Principal components of the bridge are preserved after earthquake
• Damaged SPD units will not obstruct the traffic
• Easy inspection (first damaged component limited to SPD)
• Damaged SPD units can be easily replaced
Elastic deformation
Plastic deformation
Earthquake
SPD
Steel-pipe column
Low-yield point steel
LY225
Source: Hashimoto (2016)

Nishiumi (2006)
Average shear strain
Shear
stress
Stability limit of SPD → γ = 0.08
6
Shear Panel Damper performance
γ
Δℎ
γ = average shear strain
Δh= displacement
Avg. shear strain (dimensionless)
−50 −25 0 25 50
−2
−1
0
1
2
無次元化平均せん断応力
無次元化平均せん断ひずみ
無次元化平均せん断ひずみ
Avg.
shear
stress
(dimensionless)
Hanshin, Nagoya University (2017)
Hysteresis loop of SPD (experiment)
Unstable response
Clarifying other performance limits of the SPD is essential

7
Low-cycle fatigue
105
Low-cycle fatigue
High-cycle fatigue
Stress/strain
range
Number of Cycles
Low cycle fatigue damage is one of the primary failure modes for steel
structures during earthquake
Source: Hanbin (2013)
Ductile fracture in steel bridge
pier during Kobe earthquake
Fatigue cracks typically occur at welded joints due to low-cycle fatigue

8
Low-cycle fatigue of SPD
Applied cyclic amplitude
0 1 2 3 4 5 6 7 8 9 10
−1
−0.5
0
0.5
1
time (s)
displacement
Weld
Note: displacement >> yield displacement

9
0 1 2 3 4 5 6 7 8 9 10
−1
−0.5
0
0.5
1
time (s)
displacement

10
Fatigue crack will grow due to repeated loading, consequently reducing the load-
carrying capacity of the SPD
0 1 2 3 4 5 6 7 8 9 10
−1
−0.5
0
0.5
1
time (s)
Amplitude
Crack opening
Crack growth

11
In order to maintain its function, low-cycle fatigue durability is essential
0 1 2 3 4 5 6 7 8 9 10
−1
−0.5
0
0.5
1
time (s)
Amplitude
Crack opening
Crack growth

12
Research Objective
To evaluate the low-cycle fatigue durability of Shear Panel Dampers
(SPD) by considering the influence of its dimensional parameters
Crack initiation life
Investigation of critical crack length
Low-cycle fatigue evaluation
1
Crack propagation life
2
Low-cycle fatigue test
3

13
Research Objective
1
2
3

14
Crack initiation life based on local strain
k C
Base metal 0.587 0.392
Deposited metal 0.587 0.291
Heat affected zone 0.587 0.203
Empirical material constants
𝜀𝑙𝑁𝑘 = 𝐶
Where,
εl : Local strain amplitude at crack initiation point
N : Number of cycles
k, C : Empirical material constants
[Tateishi et al., 2006]

15
Assumption of crack initiation location
Location of maximum principle strain
Analysis assumption
Crack will initiate at mid-panel near the flange-to-panel weld area

16
SPD parameters
Cases considered
b
(mm)
h
(mm)
tw
(mm)
α Rt
480 600 13.2 0.8 0.34
540 600 14.4 0.9 0.34
600 600 15 1 0.34
12
12
Flange
Shear panel
45°
Fully penetrated weld
b = width
h
=
height
tw
tf
• Aspect-ratio (α) = b/h
• Width-to-thickness ratio parameter (Rt)
𝑅𝑡 =
ℎ
𝑡𝑤
12 1 − 𝜈2 𝜏𝑦
𝜋2𝑘𝑡𝐸
≤ 0.40

17
Loading scheme and boundary condition
→ Average shear strain range γr values considered are 2, 4, 6, 8%
Note: γr = 8% → stability limit of SPD
0 0.5 1 1.5 2 2.5 3 3.5
-1
-0.5
0
0.5
1
Amplitude
Step time
γr
γ
Fixed
h
b
γ
∆h
γ =
𝛥ℎ
𝑏
γ : average shear strain
Δh : displacement
b : SPD width
Where,

18
Zooming analysis
Global model Sub-model Local-model
Global model Sub-model Local model
Components all flange, weld, panel panel, weld
Element type C3D8R (8-node linear brick, reduced integration)
Min. element size 6 mm 1 mm 0.05 mm
The ABAQUS software was used to perform all analysis in this study

19
Effect of toe radius
Local model
Panel
Weld
Toe radius detail
r
Toe radius values considered (r) = 0.5, 2.0, 3.0 mm

20
Local strain range vs Average shear strain range
0 0.02 0.04 0.06 0.08 0.1
0
0.05
0.1
0.15
0.2
0.25
α = 0.8
r = 0.5
r = 2.0
r = 3.0
Average shear strain range
Local
strain
range
Local strain can be alleviated by
increasing weld toe radius
0 0.02 0.04 0.06 0.08 0.1
0
0.05
0.1
0.15
0.2
0.25
Average shear strain range
Local
strain
range
Effect of aspect ratio is
marginal
α = 1.0
α = 0.9
α = 0.8
r = 3.0
Effect of toe radius (r) Effect of aspect-ratio (α)

10
0
10
1
10
2
10
-2
10
-1
10
0
21
Fatigue strength curve
α = 0.8
Number of cycles
Average
shear
strain
range
Crack initiation life can be slightly
extended by increasing weld toe radius
10
0
10
1
10
2
10
−2
10
−1
10
0
Number of cycles
Average
shear
strain
range
Effect of toe radius (r) Effect of aspect-ratio (α)
Effect of aspect ratio on the
crack initiation life is marginal
r = 3.0
r = 0.5
r = 2.0
r = 3.0
α = 1.0
α = 0.9
α = 0.8

22
Research Objective
1
2
3

23
Fatigue cracks
Mid-panel crack
Lcr = crack length
b
h
Analysis - Crack cases considered
Crack propagation life: Number of cycles for crack to reach critical length

24
Modelling consideration
Modelled component Whole SPD
Meshing scheme Coarse
Element type C3D8R
Loading scheme Monotonic
Applied avg. shear strain (γ) 8%
Critical crack length criterion
10% loss of load
carrying capacity
Summary
SPD model
Fatigue crack

25
Parametric analysis
Modelling consideration – SPD cases
No
b
(mm)
h
(mm)
t
(mm)
h/t (30-50) α Rt
1 420 600 12 50.00 0.7 0.34
2 420 600 13.8 43.48 0.7 0.30
3 420 600 16.2 37.04 0.7 0.25
4 480 600 13.2 45.45 0.8 0.34
5 480 600 15 40.00 0.8 0.30
6 480 600 18 33.33 0.8 0.25
7 540 600 14.4 41.67 0.9 0.34
8 540 600 16.2 37.04 0.9 0.30
9 540 600 19.2 31.25 0.9 0.25
10 600 600 15 40.00 1 0.35
11 600 600 17.4 34.48 1 0.30
12 600 600 19.8 30.30 1 0.26
→ Investigate the influence of aspect-ratio (α) and width-to-thickness
ratio parameter (Rt) on critical crack length (Lcr crit)

26
Analysis results : force vs displacement
0 10 20 30 40 50
0
500000
1e+06
1.5e+06
Force
(N)
Displacement (mm)
Lcr = 0
Lcr = 144
Lcr = 288
Lcr = 432
Force reduction
α = 1.0, Rt = 0.35
α = aspect-ratio
Rt = width-to-thickness ratio parameter
Lcr = Crack length (mm)

27
Regression analysis
0.8 0.85 0.9 0.95 1
0.8
0.85
0.9
0.95
1
Pc/Ps (Analysis)
P
c
/P
s
(Estimated)
R2 = 0.997
𝑃𝑐
𝑃𝑠
= −0.28946 𝑅𝑡0.01
𝐿𝑐𝑟
𝑏
2
𝛼0.7
+ 1
Pc/Ps = Load carrying capacity ratio (Cracked / Sound) condition
Mid-panel crack
Set Pc/Ps to 0.9 to obtain critical crack length

28
Critical crack calculation
b
(mm)
h
(mm)
t
(mm)
α Rt
Lcr crit
(mm)
Lcr crit/b
420 600 12 0.7 0.34 281.2 0.67
420 600 13.8 0.7 0.30 281.4 0.67
420 600 16.2 0.7 0.25 281.6 0.67
480 600 13.2 0.8 0.34 306.7 0.64
480 600 15 0.8 0.30 306.9 0.64
480 600 18 0.8 0.25 307.2 0.64
540 600 14.4 0.9 0.34 331.1 0.61
540 600 16.2 0.9 0.30 331.3 0.61
540 600 19.2 0.9 0.25 331.6 0.61
600 600 15 1 0.35 354.5 0.59
600 600 17.4 1 0.30 354.8 0.59
600 600 19.8 1 0.26 355.0 0.59
Lcr crit = critical crack length (mm)
b = SPD width
Lcr crit/b = critical crack length-to-width ratio
Aspect-ratio (α) is influential while width-to-thickness ratio (Rt) has no effect on the
critical crack length

29
Research Objective
1
2
3

Fatigue growth prediction for welded joints
Δ𝐽 = ‫׬‬𝛤
𝑊′ ⅆ𝑦 − ∆𝑇
𝜕∆𝑢
𝜕𝑥
𝑑𝑠
𝑊′ = න
0
∆𝜀𝑖𝑗
∆𝜎𝑖𝑗𝑑∆𝜀𝑖𝑗
𝑑𝑎
𝑑𝑁
= 9.6𝑥10−6 ∆𝐽 1.67
ΔJ = cyclic J-integral range
N = number of cycles
a = crack length
da/dN = crack growth per cycle
x
y
T
Γ
[Hanji et al., 2017]
30

Flow of crack propagation life evaluation
31
Define SPD cases
Calculate critical crack length (Lcr crit)
Perform analysis with several crack lengths
Calculate ΔJ
Obtain relationship between ΔJ and crack length
Calculate crack growth rate
𝑑𝑎
𝑑𝑁
= 9.6𝑥10−6 ∆𝐽 1.67
Obtain crack propagation life
Update crack length
𝑎 > Lcr crit?
Yes
No
𝑎 = crack length
ΔJ = cyclic J-integral
𝑑𝑎
𝑑𝑁
= crack growth per cycle

32
Loading scheme and boundary condition
→ Average shear strain range γr value considered was 8%
Note: γr = 8% → stability limit of SPD
Fixed
h
b
γ
∆h
γ =
𝛥ℎ
𝑏
γ : average shear strain
Δh : displacement
b : SPD width
Where,
0 0.5 1 1.5 2 2.5
-1
-0.5
0
0.5
1
Amplitude
Step time
ΔJ calculation sequence

Modelling technique
Zooming analysis – Submodel
Crack surface
Panel portion
Weld portion
Modelled component Weld, Panel
Boundary Conditions
Disp. Data
(global model)
Element type C3D8R
Meshing scheme Uniform
Mesh size 1 mm
Summary
33
*Same SPD parameters for the crack-initiation
life evaluation were considered

0 500 1000 1500 2000
0
50
100
150
200
250
300
350
400
Crack Propagation Life
34
Despite applying large average shear strain (8%) the crack propagation
life of the SPD is considerably high (N >1000 cycles)
Number of cycles
Crack
length
(mm)
Mid-panel crack
* α = aspect-ratio
Lcr crit = critical crack length (mm)
α = 1.0
α = 0.9
α = 0.8
Lcr crit (α = 1.0)
Lcr crit (α = 0.9)
Lcr crit (α = 0.8)

35
Research Objective
1
2
3

General setup
36
500
500 600
2100
γ = average shear strain (1.6%)
D = length of the SPD in the
diagonal direction
ΔD = displacement along the diagonal
direction
b = SPD width
h = SPD height
ҧ
𝛾 =
𝐷 + ∆𝐷 2 − 𝑏2 − ℎ2
2𝑏ℎ
Load
*all units in mm

SPD specimen
Weld average measurements
37
Specimen-2
19.19
15.22
Shear panel
Flange
r = 0.86
Specimen-1
12.30
7.93
Shear panel
r = 1.83
Flange
22
22
600
150
150
600
600
SPD specimen
16
*all units in mm

Test outcome
38
Crack inspection
No cracks were detected despite applying more than 100 loading cycles
Conclusion: The SPD has significant low-cycle fatigue durability

Conclusion
• Influence of aspect-ratio on the crack initiation life is marginal.
• The crack initiation life can be slightly improved by increasing the toe radius
of the weld. The effects are more apparent in larger shear strain ranges.
• The aspect-ratio (α) has a considerable effect on the critical crack length whereas
the effect of width-to-thickness ratio (Rt) was insignificant.
• Crack propagation life is relatively large with N values of over 1000 cycles for all
cases.
• The low-cycle fatigue durability was confirmed by cyclic-loading test as no fatigue
cracks was detected even after applying more than 100 loading cycles.
39

Thank you for your attention
40

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