Eurocode 3

Version: December 2010 Edition

List of Classification Parameters

Evaluation Distance
Reference distance to find the evaluation location from the weld element at which the stress values are extracted.
Weld Width
Width of the weld material from the web wall. This parameter is ignored if specifying the evaluation distance is done manually.
Note: Refer to - Find Evaluation Positions.
Safety Factor (Gmf)
Used in calculation of the corrected weld detail category.
Fatigue Limit Slope - Normal Stress (Md)
Slope of the curve at the fatigue limit for normal stress components of tensor. Refer to location 2 in the graph.
Fatigue Limit Slope - Shear Stress (Md)
Slope of the curve at the fatigue limit for shear stress components of tensor. Refer to location 2 in the graph.
Cutoff Limit Slope - Normal Stress (Ml)
Slope of the curve at the cutoff limit for normal stress components of tensor. Refer to location 3 in the graph.
Cutoff Limit Slope - Shear Stress (Ml)
Slope of the curve at the cutoff limit for shear stress components of tensor. Refer to location 3 in the graph.
Number of Cycles at Fatigue Limit (Nd)
Number of cycles in the S-N curve at the fatigue limit.
Number of Cycles at Cutoff Limit (Nd)
Number of cycles in the S-N curve at the cutoff limit.
Desired Cycles Detail From
Parameter that will show where HL-WC is reading the desired number of cycles from.

Location Wise Parameters

Note: Where ‘X’ in the below parameters can be any evaluation location from 1-10.
Weld Detail Category - Transverse Location_X
Weld detail category from the image below that will be considered for the calculation of fatigue and cutoff limits of the normal stress component in the transverse direction (perpendicular to the axis of the weld) at ‘X’.
Weld Detail Category - Longitudinal Location_X
Weld detail category from the image below that will be considered for the calculation of fatigue and cutoff limits of the normal stress component in the longitudinal direction (parallel to the axis of the weld) at ‘X’.
Weld Detail Category - Shear Location_X
Weld detail category from the image below that will be considered for the calculation of fatigue and cutoff limits of the shear stress component at ‘X’.
Material Yield - Location_X
Material yield value used for the static evaluation.


Figure 1.

Symbols

  • Weld detail category (Normal) - Δ σ c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadogaaeqaaaaa@3A30@
  • Weld detail category (Shear) - Δ τ c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqeeaa aaaaaaa8qacqaHepaDpaWaaSbaaSqaaiaadogaaeqaaaaa@3A61@
  • Safety factor for strength - γ M f MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qacqaHZoWzpaWaaSbaaSqaaiaad2eacaWGMbaabeaaaaa@39B2@

Static Assessment

The following process is followed for Static assessment:
  1. Retrieve the six components of stress from the element at the evaluation location.
  2. Calculate the von Mises stress value using these stress components.
  3. Retrieve the material yield value from the Points context.
  4. Determine the static strength ratio: element von Mises stress / material yield value.

Formulation

Stress Component Considered for Evaluation
Δ σ T MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadsfaaeqaaaaa@3A21@ - Transverse component (perpendicular to the axis of the weld)
Δ σ L MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadYeaaeqaaaaa@3A19@ - Longitudinal component (parallel to the axis of the weld)
Δτ MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqeeaa aaaaaaa8qacqaHepaDaaa@393E@ - Shear component
Corrected Weld Detail Category
Δ σ c (Corrected)= Δ σ c,Basic γ Mf MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadogaaeqaaOGaaiikaiaadoeacaWGVbGaamOC aiaadkhacaWGLbGaam4yaiaadshacaWGLbGaamizaiaacMcacqGH9a qpdaWcaaqaaiabfs5aejabeo8aZnaaBaaaleaacaWGJbGaaiilaiaa dkeacaWGHbGaam4CaiaadMgacaWGJbaabeaaaOqaaiabeo7aNnaaBa aaleaacaWGnbGaamOzaaqabaaaaaaa@51F6@
Where:
  • Δ σ c , B a s i c MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadogacaGGSaGaamOqaiaadggacaWGZbGaamyA aiaadogaaeqaaaaa@3F5E@ - Weld detail category before correction.
Note: The above formulas are for the normal component. Similar formulas are applicable to other shear components as well.
Calculation of the Assessment Stress
In the case of Eurocode, stress range is used as assessment stress.
Δσ(StressRange)=( σ max σ min ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4WdmNaaiikaiaadofacaWG0bGaamOCaiaadwgacaWGZbGaam4Caiaa ysW7caWGsbGaamyyaiaad6gacaWGNbGaamyzaiaacMcacqGH9aqpca GGOaGaeq4Wdm3aaSbaaSqaaiGac2gacaGGHbGaaiiEaaqabaGccqGH sislcqaHdpWCdaWgaaWcbaGaciyBaiaacMgacaGGUbaabeaakiaacM caaaa@5311@
If effective stress range is enabled in evaluation to account for mean stress influence on fatigue strength for non-welded and stress-relieved welds, then stress range is calculated as shown below:
Δσ(EffectiveStressRange)=| σ max |+0.6| σ min | MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4WdmNaaiikaiaadweacaWGMbGaamOzaiaadwgacaWGJbGaamiDaiaa dMgacaWG2bGaamyzaiaaysW7caWGtbGaamiDaiaadkhacaWGLbGaam 4CaiaadohacaaMe8UaamOuaiaadggacaWGUbGaam4zaiaadwgacaGG PaGaeyypa0JaaGjbVlaacYhacaaMe8Uaeq4Wdm3aaSbaaSqaaiGac2 gacaGGHbGaaiiEaaqabaGccaaMe8UaaiiFaiabgUcaRiaaysW7caaI WaGaaiOlaiaaiAdacaaMe8UaaiiFaiaaysW7cqaHdpWCdaWgaaWcba GaciyBaiaacMgacaGGUbaabeaakiaaysW7caGG8baaaa@6C7C@


Figure 2.
Fatigue Limit Calculation ( Δ σ D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadseaaeqaaaaa@3A11@ )
For Normal Component: Δ σ D =Δ σ c · ( 2,0e+6 N D ) (1/ m D ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadseaaeqaaOGaeyypa0JaeuiLdqKaeq4Wdm3a aSbaaSqaaiaadogaaeqaaOGaeS4JPF2aaeWaaeaadaWcaaqaaiaaik dacaGGSaGaaGimaiaadwgacqGHRaWkcaaI2aaabaGaamOtamaaBaaa leaacaWGebaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaacI cacaaIXaGaai4laiaad2gadaWgaaadbaGaamiraaqabaWccaGGPaaa aaaa@4EDF@
For Shear Component: Δ σ D = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadseaaeqaaOGaeyypa0JaeyOhIukaaa@3C95@
Where:
  • Δ σ c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadogaaeqaaaaa@3A30@ - Corrected stress range value
  • N D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGebaabeaaaaa@37BB@ - Number of cycles at fatigue limit
  • m D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBamaaBa aaleaacaWGebaabeaaaaa@37DA@ - Slope at fatigue limit
Cutoff Limit Calculation ( Δ σ L MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadYeaaeqaaaaa@3A19@ )
For Normal Component: Δ σ L =Δ σ D · ( N D N L ) (1/ m L ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadYeaaeqaaOGaeyypa0JaeuiLdqKaeq4Wdm3a aSbaaSqaaiaadseaaeqaaOGaeS4JPF2aaeWaaeaadaWcaaqaaiaad6 eadaWgaaWcbaGaamiraaqabaaakeaacaWGobWaaSbaaSqaaiaadYea aeqaaaaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaiikaiaaigdaca GGVaGaamyBamaaBaaameaacaWGmbaabeaaliaacMcaaaaaaa@4BF8@
For Shear Component: Δ σ L =Δ σ c · ( 2,0e+6 N L ) (1/ m L ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadYeaaeqaaOGaeyypa0JaeuiLdqKaeq4Wdm3a aSbaaSqaaiaadogaaeqaaOGaeS4JPF2aaeWaaeaadaWcaaqaaiaaik dacaGGSaGaaGimaiaadwgacqGHRaWkcaaI2aaabaGaamOtamaaBaaa leaacaWGmbaabeaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaacI cacaaIXaGaai4laiaad2gadaWgaaadbaGaamitaaqabaWccaGGPaaa aaaa@4EF7@
Where:
  • Δ σ c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadogaaeqaaaaa@3A30@ - Corrected stress range value
  • Δ σ D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeuiLdqKaeq 4Wdm3aaSbaaSqaaiaadseaaeqaaaaa@3A11@ - Fatigue limit stress value
  • N D MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGebaabeaaaaa@37BB@ - Number of cycles at fatigue limit
  • N L MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGmbaabeaaaaa@37C3@ - Number of cycles at cutoff limit
  • m L MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyBamaaBa aaleaacaWGmbaabeaaaaa@37E2@ - Slope at cutoff limit
Permissible Number of Cycles ( N perm MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtamaaBa aaleaacaWGWbGaamyzaiaadkhacaWGTbaabeaaaaa@3ABA@ )
If ΔσΔ σ D N perm = N D · ( Δσ Δ σ D ) ( m D ) If Δ σ D >ΔσΔ σ L N perm = N L · ( Δσ Δ σ L ) ( m L ) If Δσ<Δ σ L N perm = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGjb GaaeOzaiaabccacqqHuoarcqaHdpWCcqGHLjYScqqHuoarcqaHdpWC daWgaaWcbaGaamiraaqabaaakeaacaaMe8UaaGjbVlaaysW7caaMe8 UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7 caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVl aaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Ua aGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7ca aMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaa ysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaG jbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaM e8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlaad6eadaWgaaWcbaGaamiCaiaadwgacaWGYbGa amyBaaqabaGccqGH9aqpcaWGobWaaSbaaSqaaiaadseaaeqaaOGaeS 4JPF2aaeWaaeaadaWcaaqaaiabfs5aejabeo8aZbqaaiabfs5aejab eo8aZnaaBaaaleaacaWGebaabeaaaaaakiaawIcacaGLPaaadaahaa WcbeqaamaabmaabaGaeyOeI0IaamyBamaaBaaameaacaWGebaabeaa aSGaayjkaiaawMcaaaaaaOqaaiaabMeacaqGMbGaaeiiaiabfs5aej abeo8aZnaaBaaaleaacaWGebaabeaakiabg6da+iabfs5aejabeo8a ZjabgwMiZkabfs5aejabeo8aZnaaBaaaleaacaWGmbaabeaaaOqaai aaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Ua aGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7ca aMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaa ysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaG jbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaM e8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjb VlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8 UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaamOtamaaBaaa leaacaWGWbGaamyzaiaadkhacaWGTbaabeaakiabg2da9iaad6eada WgaaWcbaGaamitaaqabaGccqWIpM+zdaqadaqaamaalaaabaGaeuiL dqKaeq4WdmhabaGaeuiLdqKaeq4Wdm3aaSbaaSqaaiaadYeaaeqaaa aaaOGaayjkaiaawMcaamaaCaaaleqabaWaaeWaaeaacqGHsislcaWG TbWaaSbaaWqaaiaadYeaaeqaaaWccaGLOaGaayzkaaaaaaGcbaGaae ysaiaabAgacaqGGaGaeuiLdqKaeq4WdmNaeyipaWJaeuiLdqKaeq4W dm3aaSbaaSqaaiaadYeaaeqaaaGcbaGaaGjbVlaaysW7caaMe8UaaG jbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaM e8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaays W7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjb VlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8 UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7 caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVl aaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8Ua aGjbVlaaysW7caaMe8UaaGjbVlaaysW7caaMe8UaaGjbVlaaysW7ca aMe8UaaGjbVlaaysW7caWGobWaaSbaaSqaaiaadchacaWGLbGaamOC aiaad2gaaeqaaOGaeyypa0JaeyOhIukaaaa@DDC3@
Damage Calculation
D = N N p e r m MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiraiabg2 da9maalaaabaGaamOtaaqaaiaad6eadaWgaaWcbaGaamiCaiaadwga caWGYbGaamyBaaqabaaaaaaa@3D6F@
Where:
  • N MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOtaaaa@36C6@ - Desired number of cycles per load case combination, derived either from the range data file or the classification area.
Resultant Damage Calculation (D)
D = D δ , y + D δ , x y MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiraiabg2da9iaadseapaWaa0baaSqaa8qacqaH0oazcaGGSaGa amyEaaWdaeaapeGaaG4maaaakiabgUcaRiaadseapaWaa0baaSqaa8 qacqaH0oazcaGGSaGaamiEaiaadMhaa8aabaWdbiaaiwdaaaaaaa@444B@
Where:
  • D δ , y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacqaH0oazcaGGSaGaamyEaaqabaaaaa@3A3E@ - Damage in transverse direction (perpendicular to the axis of the weld)
  • D τ , x y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiramaaBa aaleaacqaHepaDcaGGSaGaamiEaiaadMhaaeqaaaaa@3B5B@ - Damage in the shear direction
Calculation of Accumulated Damage
For the corresponding damage components:

D δ,x,acc = D x,i D δ,y,acc = D y,i D τ,xy,acc = D xy,i MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGeb WaaSbaaSqaaiabes7aKjaacYcacaWG4bGaaiilaiaadggacaWGJbGa am4yaaqabaGccqGH9aqpdaaeabqaaiaadseadaWgaaWcbaGaamiEai aacYcacaWGPbaabeaaaeqabeqdcqGHris5aaGcbaGaamiramaaBaaa leaacqaH0oazcaGGSaGaamyEaiaacYcacaWGHbGaam4yaiaadogaae qaaOGaeyypa0ZaaabqaeaacaWGebWaaSbaaSqaaiaadMhacaGGSaGa amyAaaqabaaabeqab0GaeyyeIuoaaOqaaiaadseadaWgaaWcbaGaeq iXdqNaaiilaiaadIhacaWG5bGaaiilaiaadggacaWGJbGaam4yaaqa baGccqGH9aqpdaaeabqaaiaadseadaWgaaWcbaGaamiEaiaadMhaca GGSaGaamyAaaqabaaabeqab0GaeyyeIuoaaaaa@6332@

For resultant accumulated damage calculation:

D= D δ,y,acc + D δ,xy,acc MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamiraiabg2da9iaadseapaWaa0baaSqaa8qacqaH0oazcaGGSaGa amyEaiaacYcacaWGHbGaam4yaiaadogaa8aabaWdbiaaiodaaaGccq GHRaWkcaWGebWdamaaDaaaleaapeGaeqiTdqMaaiilaiaadIhacaWG 5bGaaiilaiaadggacaWGJbGaam4yaaWdaeaapeGaaGynaaaaaaa@4B17@

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