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6. Example of Fatigue Design

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.

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6. Example of Fatigue Design

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  1. 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.

  2. 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

  3. STEP 1 Selection the position of fatigue investigationSTEP 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(section1) 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.

  4. 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. section1 Figure 2. position of Fatigue Investigation

  5. STEP 1 Selection the position of fatigue investigation STEP 1.2 Position of Fatigue Investigation section2

  6. STEP 2 Decision of Allowable Fatigue Stress Range.STEP 2.1 Decision of Stress Category section1 section2 The others

  7. 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

  8. 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.) section1

  9. STEP 2 Decision of Allowable Fatigue Stress Range STEP 2.3 Decision of Allowable Fatigue Stress Range section2 The others

  10. STEP 3 Calculation of fatigue design stress rangeSTEP 3.1 Selection of load 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.

  11. 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 bydead 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.

  12. 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) 1. Stress resultant by dead load before composite(Wd1 = 3.75 t/m) • MomentMd1 = 484.7 t • m • Shear forceSd1 = 484.7 t • m section1 2. Stress resultant by dead load after composite(Wd2= 1.23 t/m) • MomentMd2= 159 t • m • Shear forceSd1= -2.2 t • m 3. Moment by DB-24(2lane loading, impaction consideration) • Maximum momentMMAX = 159 t • m • Minimum momentMMIN= -146.5 t • m 4. Moment by DL-24(2lane loading, impaction consideration) • Maximum momentMMAX = 602.1 t • m • Minimum momentMMIN= -200 t • m

  13. 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) • MomentMd1= -1066.4 t • m • Shear forceSd1= 112.5 t • m 2. Stress resultant by dead load after composite(Wd2= 1.23 t/m) • MomentMd2= -349.8 t • m • Shear forceSd1= 36.9 t • m 4. Moment by DL-24(2lane loading, impaction consideration) • Maximum momentMMAX = 90.7 t • m • Minimum momentMMIN = -817.7 t • m • Maximum Shear forceSMAX = 91.2 t • Minimum Shear forceSMIN= -7.5 t 3. Stress resultant by dead load after composite • Maximum momentMMAX = 79.9 t • m • Minimum momentMMIN= -366.7 t • m • Maximum Shear forceSMAX = 66.5 t • Minimum Shear forceSMIN= -6.0 t

  14. 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 • section1, Is calculation(before composition) • section1, Iv calculation(after composition) n=8, effective width of slab: 327.5cm, Thickness of slab: 27cm, haunch height: 8.5cm.

  15. 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.)

  16. 2. Calculation of fatigue design stress range (In case of negative bending moment , composite effect of floor slab is not considered.) STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 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

  17. 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,

  18. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, calculation

  19. 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 ,

  20. 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,

  21. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  22. 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,

  23. 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,

  24. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  25. 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 ,

  26. 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,

  27. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  28. 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,

  29. 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 DB -24 load,

  30. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  31. 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 ,

  32. 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,

  33. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  34. 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 ,

  35. 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,

  36. STEP 3 Calculation of fatigue design stress range STEP 3.3 Calculation of fatigue design stress range 5) Fatigue design stress range, , calculation

  37. STEP 4 Design propriety judgment Section 1

  38. STEP 4 Design propriety judgment Section 2

  39. STEP 4 Design propriety judgment • Fatigue examination on shear of Section 2 fatigue investigation position① • 1.Calculation of Allowable shear flow range • 1) multi load path structure, stress categoryF • 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) is13mm, • Welding deptha= = = 0.919 cm • 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

  40. 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 (120+7.2/2) = 40046cm2 2) DL load shear force range, Sr = 91200kg –(-7500kg) = 98700kg design shear flow range, Sd calculation Sd= = =326.9kg/cm

  41. STEP 4 Design propriety judgment • 3. Design propriety judgment • DB load: 57.9kg/cm > 240.1kg/cm OK • DL load : 1543.9kg/cm > 326.9kg/cm OK

  42. 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.

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

  44. STEP 5 Design change - Calculation of fatigue design stress range (DB load) ∴ fatigue design stress range : - Design propriety judgment:

  45. 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 than10cm or 12times of thickness and thickness of plate of stiffener is less than 2.5cm (category E), is more than (categoryE’). • After change : length of gusset plate is 70cm, thickness is 1cm, width is 35cm. • radius is 15cm and grinding at groove welding part.(categoryC) ※ 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)

  46. STEP 5 Design change( Fatigue investigation ) 복부판 Before change After change

  47. Thank you

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