Transcript 피로설계 예

6. Example of Fatigue Design
★
This was prepared to demonstrate how to apply “fatigue design” to real case.
A designer should consider all design condition.
Therefore please use this diagram or process as a reference.
Composite plate girder(I-3 girder)
: 3 span continuous bridge.
[Design condition]
• Design method
: Allowable Stress Design method
• Bridge Classification :
: 1 Grade(DB-24 or DL-24)
• Bridge Type
: 3 span continuous composite plate girder
(45.0+60.0+45.0=150.0m)
• Bridge width
: 13.2m
Figure1. Bridge profile
STEP 1 Selection the position of fatigue investigation
STEP 1.1 Selection Standard

This case shows fatigue design to girder.

Generally, it’s desirable to perform fatigue design of every section of member.





It is performed fatigue design for main girder in 0.4L(section 1) and the first middle supporting point.
Because, maximum moment by live load is occurs in position of 0.4L and
maximum negative bending moment is occurs in the first middle supporting point.
Maximum shear force is occurs in the first middle supporting point.
STEP 1 Selection the position of fatigue investigation
STEP 1.2 Position of Fatigue Investigation

It is performed fatigue design for section 1 and section 2 of inner side girder G2 .
Section 1 is section with gusset plate for connecting horizontal bracing.
section 1
section 1
① : Flange-to-Web welding part
② : end of welding of vertical stiffener
③ : end of welding of transverse stiffener
④ : end of welding of gusset plate for
connecting horizontal bracing
Figure 2. position of Fatigue Investigation
STEP 1 Selection the position of fatigue investigation STEP
1.2 Position of Fatigue Investigation
section 2
section 2
The others
① : Flange-to-Web welding part
• Splice part (Bolt splice) – Splice plate of
② : end of welding of supporting point stiffener
tensile flange.
③ : end of welding of transverse stiffener
• Groove welding joint of flange – tensile flange
④ : flange adjacent to stud
etc.
STEP 2 Decision of Allowable Fatigue Stress Range.
STEP 2.1 Decision of Stress Category
section 1
classification
Detail
Acting Stress
Stress Category
①
Flange-to-Web welding part
Tensile or Altering
B
②
end of welding of vertical stiffener
Tensile or Altering
C
③
end of welding of transverse stiffener
Tensile or Altering
E
④
end of welding of gusset plate
Tensile or Altering
E
Acting Stress
Stress Category
Tensile or Altering
B
Shear
F
remarks
section 2
classification
Detail
①
Flange-to-Web welding part
②
end of welding of vertical stiffener
Tensile or Altering
C
③
end of welding of transverse stiffener
Tensile or Altering
E
④
flange adjacent to stud
Tensile or Altering
E
remarks
The others
Detail
Acting Stress
Stress Category
Splice part
Tensile or Altering
B
Groove welding part of flange
Tensile or Altering
B
remarks
STEP 2 Decision of Allowable Fatigue Stress Range.
STEP 2.2 Number of Repeated Stress

Number of repeated stress is defined by Bridge design code.
• Kind of load : Main Load Transfer Member(longitudinal
direction member)
• Kind of Road : Freeway, national way and Arterial
Kind of load
Number of repeated stress
Truck load(DB-24)
2 million time
Lane load(DL-24)
500 thousand time
STEP 2 Decision of Allowable Fatigue Stress Range
STEP 2.3 Decision of Allowable Fatigue Stress Range
1. Judgement of Redundancy
This bridge is 3 girder bridge. In case that collapse of inner side girder G2 is
generating, load is redistributed to both outside girder . So, The probability of
fracture of whole bridge is small.
So, it can be judge as multi loading path structure.
2. Decision of Allowable stress range
(is defined by Bridge design code.)
section 1
Allowable stress range
Detail
Stress Category
500 thousand
time(DL-24)
2 million
time(DB-24)
①
Flange-to-Web welding part
B
20.3
12.6
②
end of welding of vertical stiffener
C
14.7
9.1
③
end of welding of transverse stiffener
E
9.1
5.6
④
end of welding of gusset plate
E
9.1
5.6
STEP 2 Decision of Allowable Fatigue Stress Range
STEP 2.3 Decision of Allowable Fatigue Stress Range
section 2
Allowable Stress Range
Detail
 sr (kg / mm2 )
Stress Category
500 thousand
time(DL-24)
2 million
time(DB-24)
B
20.3
12.6
F
8.4
6.3
①
Flange-to-Web welding part
②
end of welding of vertical stiffener
C
14.7
9.1
③
end of welding of transverse stiffener
E
9.1
5.6
④
flange adjacent to stud
E
14.7
9.1
The others
Allowable Stress Rang
 sr (kg / mm2 ),
Detail
Stress Category
500 thousand
time(DL-24)
2 million
time(DB-24)
Splice part
B
20.3
12.6
Groove welding part of flange
B
20.3
12.6
STEP 3 Calculation of fatigue design stress range
STEP 3.1 Selection of load
Member of fatigue investigation
Longitudinal direction member
(girder, stringer etc)
load
• Dead load
• Dead load + DB load
• Dead load + DL load
remarks
Impact consideration
Impact consideration
The position of fatigue investigation is main girder which longitudinal member.
Therefore live load is using by DB-24 and DL-24 each other and Impact is included at live load.
The position of live load is decided to generate maximum and minimum stress resultant
in considering of influence line of fatigue investigation section.
STEP 3 Calculation of fatigue design stress range
STEP 3.2 Calculation of structure(stress resultant)
The bridge is composite girder structure.
Bridge can be calculated to divide by dead load before composite and dead load after composite, DB24 and DL-24 load.
For it is the same with calculation of stress resultant to perform stress resultant design of main girder,
it is not necessary independent to calculate structure for fatigue design.
However, in stress resultant design, it is necessary to examine about DB load and DL load each other.
※ Tensile side flange splice plate of splice part and grove welding part of girder is passed the content
for the process of examination is the same with section 1 and 2.
STEP 3 Calculation of fatigue design stress range
STEP 3.2 Calculation of structure(stress resultant)
The result that calculated section 1 and section 2 of inner side girder G2 is summarized as follows.:
(when live load is loading, load is loading in 2 lane toward transverse direction. Impact consideration)
section 1
1. Stress resultant by dead load before composite (Wd1 = 3.75 t/m)
• Moment Md1 = 484.7 t • m
• Shear force Sd1 = 484.7 t • m
2. Stress resultant by dead load after composite (Wd2 = 1.23 t/m)
• Moment Md2 = 159 t • m
• Shear force Sd1 = -2.2 t • m
3. Moment by DB-24(2lane loading, impaction consideration)
• Maximum moment MMAX = 159 t • m
• Minimum moment MMIN = -146.5 t • m
4. Moment by DL-24(2lane loading, impaction consideration)
• Maximum moment MMAX = 602.1 t • m
• Minimum moment MMIN = -200 t • m
STEP 3 Calculation of fatigue design stress range
STEP 3.2 Calculation of structure(stress resultant)
Section 2
1. Stress resultant by dead load before composite (Wd1 = 3.75 t/m)
• Moment Md1 = -1066.4 t • m
• Shear force Sd1 = 112.5 t • m
2. Stress resultant by dead load after composite (Wd2 = 1.23 t/m)
• Moment Md2 = -349.8 t • m
• Shear force Sd1 = 36.9 t • m
3. Stress resultant by dead load after composite
4. Moment by DL-24(2lane loading, impaction consideration)
• Maximum moment MMAX = 79.9 t • m
• Maximum moment MMAX = 90.7 t • m
• Minimum moment MMIN = -366.7 t • m
• Minimum moment MMIN = -817.7 t • m
• Maximum Shear force SMAX = 66.5 t
• Maximum Shear force SMAX = 91.2 t
• Minimum Shear force SMIN = -6.0 t
• Minimum Shear force SMIN = -7.5 t
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
1. Calculation of moment of inertia of area
• section 1, Is calculation (before composition)
• section 1, Iv calculation (after composition)
n=8,
effective width of slab : 327.5cm,
Thickness of slab : 27cm,
haunch height : 8.5cm.
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
• Section 2, Is Calculation of moment of inertia of area
 Composite effect of section 2 not to be considered
(considering the simplicity of calculation and it being safety side.)
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
2. Calculation of fatigue design stress range
(In case of negative bending moment , composite effect of floor slab is not considered.)

Section 1 (+ : Tensile Stress , - : Compressive Stress)
fatigue investigation position ① : flange-to-web welded part
1) Stress by dead load before composition

2) Stress by dead load after composition


d1
d2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
4) Stress by DL – 24 load,
DB
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
 max
DL
 min
r, d
formula
r, d calculation
Result
= d1 +d 2+ max, DB 1843.7kg/cm2
= d1 + d 2+  min, DB 823.5kg/cm2
= max -  min
1020.2kg/cm2
= d1 + d 2 +  max, DL 1864kg/cm2
= d1 + d 2 +  min, DL 725.5kg/cm2
=  max -  min
1138.5kg/cm2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position② : end of welded of vertical stiffener
1) Stress by dead load before composition,
2) Stress by dead load after composition ,
d1

d2
d 2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
DB
4) Stress by DL – 24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
 max
DL
 min
r, d
r, d ,
formula
calculation
Result
= d1 +d 2+ max, DB 1799kg/cm2
= d1 + d 2+  min, DB 800.1kg/cm2
= max -  min
998.9kg/cm2
= d1 + d 2 +  max, DL 1818.9kg/cm2
= d1 + d 2 +  min, DL 705.2kg/cm2
=  max -  min
1113.7kg/cm2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position③ : end of welding of horizontal
1) Stress by dead load before composition,
2 ) Stress by dead load after composition,
d1
d 2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
DB
4) Stress by DL – 24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d ,
formula
calculation
Result
= d1 +d 2+  max, DB -442.6kg/cm2
= d1 +d 2+ min, DB -582.8kg/cm2
No need to do fatigue check due min.stress and max.stress are
compressed stress
 max
DL
 min
= d1 + d 2 +  max, DL -370.1kg/cm2
= d1+ d 2 +  min, DL -581.2kg/cm2
No need to do fatigue check due min.stress and max.stress are
compressed stress
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position ④: end of welding of gusset plate which
connecting horizontal
1) Stress by dead load before composition,
2) Stress by dead load after composition ,
d1
d 2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load, DB
4) Stress by DL – 24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
 max
DL
 min
r, d
r, d
formula
, calculation
Result
= d1 +d 2+ max, DB 1460.6kg/cm2
= d1 + d 2+  min, DB 623.5kg/cm2
= max -  min
837.1kg/cm2
= d1 + d 2 +  max, DL 1477.9kg/cm2
= d1 + d 2 +  min, DL 552.5kg/cm2
=  max -  min
925.4kg/cm2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
Section 2 (+ : Tensile Stress , - : Compressive Stress)

fatigue test position ①: flange-to-web welded part
(Examination on shear is done in step4(Design Propriety judgment)

1) Stress by dead load before composition,
2) Stress by dead load after composition,
d1

d2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
DB
4) Stress by DB -24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
formula
, calculation
Result
= d1+ d 2+  max, DB 1769.5kg/cm2
= d1+ d+2  min, DB 1326.3kg/cm2
=  max-  min
443.2kg/cm2
d 2+  max, DL 2217.1kg/cm2
d 2+  min, DL 1315.6kg/cm2
 min
= d1+
= d1+
r, d
=  max -  min
 max
DL
r, d
901.5kg/cm2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range

 Fatigue test position ②: end of welding of supporting point.
- Fatigue investigation position ② is same with ①
Fatigue test position ③ : end of welding of horizontal stiffener
1) Stress by died load force before composition,
2) Stress by died load force after composition ,
d1
d 2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
DB
4) Stress by DL – 24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
formula
, calculation
Result
= d1 +d 2+  max, DB -773.6kg/cm2
= d1 +d 2+ min, DB -1032.3kg/cm2
It is not need to investigate fatigue for minimum stress and maximum stress
are all compressed stress.
 max
DL
 min
= d1 + d 2 +  max, DL -767.4kg/cm2
= d1+ d 2 +  min, DL -1293.3kg/cm2
It is not need to investigate fatigue for minimum stress and maximum stress
are all compressed stress.
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position ④ : flange adjacent to stud
1) Stress by dead load before composition,
2) Stress by dead load before composition ,
d1
d 2
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
3) Stress by DB -24 load,
DB
4) Stress by DL – 24 load,
DL
STEP 3 Calculation of fatigue design stress range
STEP 3.3 Calculation of fatigue design stress range
5) Fatigue design stress range,
Classification or
Category
DB
 max
 min
r, d
 max
DL
 min
r, d
r, d
formula
, calculation
Result
= d1 +d 2+ max, DB 1875.7kg/cm2
= d1 + d 2+  min, DB 1405.8kg/cm2
= max -  min
469.9kg/cm2
= d1 + d 2 +  max, DL 2350.1kg/cm2
= d1 + d 2 +  min, DL 1394.5kg/cm2
=  max -  min
955.6kg/cm2
STEP 4 Design propriety judgment
Section 1
classification
Stress
category
Live load
Number of
repeated
stress
Allowable
stress
range(kg/c
m2)
Design
stress
range(kg/c
m2)
judgment
①
B
DB
2 million time
1260
1020.2
OK
DL
500 thousand
2030
1138.5
OK
DB
2 million time
910
998.9
NG
DL
500 thousand
1470
1113.7
OK
DB
2 million time
560
-
-
DL
500 thousand
910
-
-
DB
2 million time
560
837.1
NG
DL
500 thousand
910
925.4
NG
②
③
④
C
E
E
STEP 4 Design propriety judgment
Section 2
classification
Stress
category
Live load
Number of
repeated
stress
Allowable
stress
range
(kg/cm2)
Design
stress
range
(kg/cm2)
judgment
①
B
DB
2 million time
1260
443.2
OK
DL
500 thousand
2030
901.5
OK
DB
2 million time
910
443.2
OK
DL
500 thousand
1470
901.5
OK
DB
2 million time
560
-
-
DL
500 thousand
910
-
-
DB
2 million time
910
469.9
OK
DL
500 thousand
1470
955.6
OK
②
③
④
C
E
E
STEP 4 Design propriety judgment


Fatigue examination on shear of Section 2 fatigue investigation
position ①
1.Calculation of Allowable shear flow range

1) multi load path structure, stress category F
DB load : 2milion time, 630kg/cm2
DL load : 500 thousand time, 840 kg/cm2

2) If size of fillet welding of Flange-to-Web(S) is 13mm,







S
1 .3
Welding depth a= 2 =
= 0.919 cm
2
For Both welding, 2a = 1.838cm
3) Allowable shear flow range, Sa , calculation
DB load : 630 x 1.838 = 1157.9 kg/cm
DL load : 840 x 1.838 = 1543.9 kg/cm
STEP 4 Design propriety judgment

2. Calculation of Design shear flow range
1)DB load
shear force range , Sr = 66500kg – (-6000kg) = 72500kg
design shear flow range, Sd, calculation
Sd =
Sr  Q 72500  40046
=
= 240.1kg/cm
12091069
I
(where, Q= geometrical moment = 45 x 7.2 x (120+7.2/2) = 40046cm2
2) DL load
shear force range, Sr = 91200kg –(-7500kg) = 98700kg
design shear flow range, Sd calculation
Sd=
Sr  Q 98700  40046
=
=326.9kg/cm
12091069
I
STEP 4 Design propriety judgment

3. Design propriety judgment

DB load : 57.9kg/cm > 240.1kg/cm

DL load : 1543.9kg/cm > 326.9kg/cm
 OK
 OK
STEP 5 Design change
1. Fatigue investigation position ② of Section 1
Until now, example I mentioned is that
Fatigue strength is sufficient for DL load(500 thousand time).
But, fatigue strength is not sufficient for DB load(2 million time).
• Design change
In korea Bridge design code , it is prescribed that
net interval between end of vertical stiffener and tensile flange is about 35mm.
In AASHTO, net interval is about 4 ~ 6tw (this case is 64 ~ 96mm).
But, fatigue design stress range should be less than allowable fatigue stress range
In next calculation process, as you can see
It is need that net interval is 200mm.
So. It is considered that section should be redesigned.
STEP 5 Design change
※ Section is redesigned as net interval is 200mm
STEP 5 Design change
- Calculation of fatigue design stress range (DB load)
∴ fatigue design stress range :
- Design propriety judgment:
STEP 5 Design change
2. Fatigue investigation position ④ of section 1
This is case that fatigue strength is not sufficient for DB load and DL load.
• Design change
It is advisable to upward setting stress category and increase allowable fatigue stress range
rather change of welding detail of gusset plate than change the position of gusset plate
or redesign of section
- before change : length of gusset plate is 40cm, thickness is 1cm, width is 35cm .
groove welding without radius in joining part.(stress category E)
※ Adjoining base member at welding member that groove welding or welding length of
stress direction of fillet welding is more than 10cm or 12times of thickness
and thickness of plate of stiffener is less than 2.5cm (category E), is more than (category E’).
-After change : length of gusset plate is 70cm, thickness is 1cm, width is 35cm.
radius is 15cm and grinding at groove welding part.(category C)
※ independent length of welding joint , radius of welding part is more than 15cm , is less than 60cm
grinding and base member adjacent to joining member by complete penetrated groove welding and
partial penetrated welding.(category C)
STEP 5 Design change( Fatigue investigation )
복부판
After change
Before change
classification
Before
change
After
change
Stress
category
E
C
Allowable stress
range
Design stress range
judgment
DB
560
DB
837.1
NG
DL
910
DL
925.4
NG
DB
910
DB
837.1
OK
DL
1470
DL
925.4
OK
remarks
Thank you