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 ( =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. Figure 2. position of Fatigue Investigation 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

STEP 1 Selection the position of fatigue investigation STEP 1.2 Position of Fatigue Investigation section 2 ① : Flange-to-Web welding part ② : end of welding of supporting point stiffener ③ : end of welding of transverse stiffener ④ : flange adjacent to stud The others Splice part (Bolt splice) – Splice plate of tensile flange. Groove welding joint of flange – tensile flange etc. section 2

STEP 2 Decision of Allowable Fatigue Stress Range. STEP 2.1 Decision of Stress Category classification DetailActing Stress Stress Category remarks ① Flange-to-Web welding part Tensile or AlteringB ② end of welding of vertical stiffener Tensile or AlteringC ③ end of welding of transverse stiffener Tensile or AlteringE ④ end of welding of gusset plate Tensile or AlteringE classification DetailActing StressStress Categoryremarks ① Flange-to-Web welding part Tensile or Altering B ShearF ② end of welding of vertical stiffenerTensile or Altering C ③ end of welding of transverse stiffenerTensile or Altering E ④ flange adjacent to stud Tensile or Altering E DetailActing StressStress Categoryremarks Splice part Tensile or Altering B Groove welding part of flange Tensile or Altering B section 1 section 2 The others

STEP 2 Decision of Allowable Fatigue Stress Range. STEP 2.2 Number of Repeated Stress Kind of loadNumber of repeated stress Truck load(DB-24)2 million time Lane load(DL-24)500 thousand time 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

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.) DetailStress Category Allowable stress range 500 thousand time(DL-24) 2 million time(DB- 24) ① Flange-to-Web welding part B ② end of welding of vertical stiffener C ③ end of welding of transverse stiffener E ④ end of welding of gusset plate E section 1

DetailStress Category Allowable Stress Range 500 thousand time(DL-24) 2 million time(DB- 24) ① Flange-to-Web welding part B F ② end of welding of vertical stiffener C ③ end of welding of transverse stiffener E ④ flange adjacent to stud E section 2 STEP 2 Decision of Allowable Fatigue Stress Range STEP 2.3 Decision of Allowable Fatigue Stress Range DetailStress Category Allowable Stress Rang, 500 thousand time(DL-24) 2 million time(DB-24) Splice partB Groove welding part of flangeB The others

STEP 3 Calculation of fatigue design stress range STEP 3.1 Selection of load Member of fatigue investigationloadremarks Longitudinal direction member (girder, stringer etc) Dead load Dead load + DB load Dead load + DL load 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, DB- 24 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) section 1 1. Stress resultant by dead load before composite (Wd1 = 3.75 t/m) Moment Md1 = t m Shear force Sd1 = t m 2. Stress resultant by dead load after composite (W d2 = 1.23 t/m) Moment M d2 = 159 t m Shear force S d1 = -2.2 t m 3. Moment by DB-24(2lane loading, impaction consideration) Maximum moment M MAX = 159 t m Minimum moment M MIN = t m 4. Moment by DL-24(2lane loading, impaction consideration) Maximum moment M MAX = t m Minimum moment M MIN = -200 t m 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)

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 (W d1 = 3.75 t/m) Moment M d1 = t m Shear force S d1 = t m 2. Stress resultant by dead load after composite (W d2 = 1.23 t/m) Moment M d2 = t m Shear force S d1 = 36.9 t m 3. Stress resultant by dead load after composite Maximum moment M MAX = 79.9 t m Minimum moment M MIN = t m Maximum Shear force S MAX = 66.5 t Minimum Shear force S MIN = -6.0 t 4. Moment by DL-24(2lane loading, impaction consideration) Maximum moment M MAX = 90.7 t m Minimum moment M MIN = t m Maximum Shear force S MAX = 91.2 t Minimum Shear force S MIN = -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, I s calculation (before composition) section 1, I v 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, I s 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.)

2. Calculation of fatigue design stress range ( In case of negative bending moment, composite effect of floor slab is not considered.) fatigue investigation position ① : flange-to-web welded part 2 ) Stress by dead load after composition 1) Stress by dead load before composition Section 1 (+ : Tensile Stress, - : Compressive Stress) STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

4) Stress by DL – 24 load, 3) Stress by DB -24 load, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

5) Fatigue design stress range, calculation Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 = kg/cm 2 DL = kg/cm 2 = kg/cm 2 = kg/cm 2 STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position ② : end of welded of vertical stiffener 2) Stress by dead load after composition, 1 ) Stress by dead load before composition, 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, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

5) Fatigue design stress range,, calculation Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 = kg/cm 2 DL = kg/cm 2 = kg/cm 2 = kg/cm 2 STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

fatigue investigation position ③ : end of welding of horizontal 2 ) Stress by dead load after composition, 1) Stress by dead load before composition, 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, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 No need to do fatigue check due min.stress and max.stress are compressed stress DL = kg/cm 2 = kg/cm 2 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 5) Fatigue design stress range,, calculation

1) Stress by dead load before composition, 2) Stress by dead load after composition, fatigue investigation position ④ : end of welding of gusset plate which connecting horizontal 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, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 = kg/cm 2 DL = kg/cm 2 = kg/cm 2 = kg/cm 2 STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range,, calculation

fatigue test position ① : flange-to-web welded part 2) Stress by dead load after composition, 1) Stress by dead load before composition, Section 2 (+ : Tensile Stress, - : Compressive Stress) (Examination on shear is done in step4(Design Propriety judgment) STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

4) Stress by DB -24 load, 3) Stress by DB -24 load, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 = kg/cm 2 DL = kg/cm 2 = kg/cm 2 = kg/cm 2 STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range,, calculation

Fatigue test position ② : end of welding of supporting point. -  Fatigue investigation position ② is same with ① 2) Stress by died load force after composition, 1) Stress by died load force before composition, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range Fatigue test position ③ : end of welding of horizontal stiffener

4) Stress by DL – 24 load, 3) Stress by DB -24 load, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 It is not need to investigate fatigue for minimum stress and maximum stress are all compressed stress. DL = kg/cm 2 = kg/cm 2 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 5) Fatigue design stress range,, calculation

fatigue investigation position ④ : flange adjacent to stud 2) Stress by dead load before composition, 1) Stress by dead load before composition, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

4) Stress by DL – 24 load, 3) Stress by DB -24 load, STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range

Classification or Category formulaResult DB = kg/cm 2 = kg/cm 2 = kg/cm 2 DL = kg/cm 2 = kg/cm 2 = kg/cm 2 STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range,, calculation

STEP 4 Design propriety judgment Section 1 classificationStress category Live loadNumber of repeated stress Allowable stress range(kg/c m 2 ) Design stress range(kg/c m 2 ) judgment ① B DB2 million time OK DL500 thousand OK ② C DB2 million time NG DL500 thousand OK ③ E DB2 million time560-- DL500 thousand910-- ④ E DB2 million time NG DL500 thousand NG

classificationStress category Live loadNumber of repeated stress Allowable stress range (kg/cm 2 ) Design stress range (kg/cm 2 ) judgment ① B DB2 million time OK DL500 thousand OK ② C DB2 million time OK DL500 thousand OK ③ E DB2 million time560-- DL500 thousand910-- ④ E DB2 million time OK DL500 thousand OK STEP 4 Design propriety judgment Section 2

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/cm 2 DL load : 500 thousand time, 840 kg/cm 2 2) If size of fillet welding of Flange-to-Web(S) is 13mm, Welding depth a= = = cm For Both welding, 2a = 1.838cm 3) Allowable shear flow range, Sa, calculation DB load : 630 x = kg/cm DL load : 840 x = 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 = = = 240.1kg/cm (where, Q= geometrical moment = 45 x 7.2 x ( /2) = 40046cm 2 2) DL load shear force range, Sr = 91200kg –(-7500kg) = 98700kg design shear flow range, Sd calculation Sd= = =326.9kg/cm STEP 4 Design propriety judgment

3. Design propriety judgment DB load : 57.9kg/cm > 240.1kg/cm OK DL load : kg/cm > 326.9kg/cm OK STEP 4 Design propriety judgment

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.

※ Section is redesigned as net interval is 200mm STEP 5 Design change

∴ fatigue design stress range : - Calculation of fatigue design stress range (DB load) - 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

Before change After change 복부판 classification Stress category Allowable stress range Design stress rangejudgmentremarks Before change E DB560DB837.1NG DL910DL925.4NG After change C DB910DB837.1OK DL1470DL925.4OK STEP 5 Design change( Fatigue investigation )

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