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Introduction to Nominal Stress Approach to Fatigue Design

Introduction to Nominal Stress Approach to Fatigue Design. CE671 – Lecture 21b. What is nominal stress approach?. Different details separated into categories of similar fatigue resistance Resistance is based on test data from full-scale specimens Plotted in terms of nominal stress

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Introduction to Nominal Stress Approach to Fatigue Design

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  1. Introduction to Nominal Stress Approach to Fatigue Design CE671 – Lecture 21b

  2. What is nominal stress approach? • Different details separated into categories of similar fatigue resistance • Resistance is based on test data from full-scale specimens • Plotted in terms of nominal stress • e.g., Mc/I or P/A

  3. Fatigue Life Based on S-N Curves

  4. Fatigue Life Based on S-N Curves • Detail categories account for variables which are difficult to quantify • Weld discontinuities • Local stress concentrations due to geometry of the detail • Residual stresses • Others

  5. Fatigue Life Based on S-N Curves • Usually a link between cracking mode and stress concentration of the various details in a category • Transverse connection plates and transverse butt welds are Cat C • Both have similar cracking modes • Weld toe cracking • Not always similar • H.S. bolted splice and web/flange weld Cat B

  6. Fatigue Life Based on S-N Curves • Design curves are “lower bound” • These are 95% confidence • 97.5% chance fatigue life will be greater than provided by curve • 2.5% chance of failure

  7. Fatigue Life Based on S-N Curves • Equation of all S-N curves has the following form: • N = ASr-3 • N = # cycles to failure • A = Constant dependent on detail category • Sr = Applied nominal constant amplitude stress range • Slope is set at -3.0 on log-log plot • Set at -3 by NCHRP Report 286

  8. Damage Calculation Requires a Knowledge of: • Stress range (Sr) • (constant amplitude) • Number of cycles (N) Using the above information with a knowledge of the detail category, an estimate of fatigue damage and remaining life can be made

  9. Damage Calculations Fall into Three Cases: • Case I • Sreff > CAFL & Srmax > CAFL • Case II • Sreff < CAFL & Srmax > CAFL • Case III • Sreff < CAFL & Srmax < CAFL

  10. Sreff Srmax What is an “Effective Stress Range” % Occurrence Stress or (GVW )

  11. What is an “Effective Stress Range” • Converted stress-range histogram of variable amplitude into equivalent damage of single stress range (Sreff) of N cycles • Conversion made using Miner’s rule

  12. Sreff = 5.9 ksi N = 4 Calculate Sreff Sreff = ( fi x(Sri3))1/3  fi x(Sri3) = 202.25

  13. Sre Relationship Between Stress-Range Spectrum - Fatigue Resistance - % Exceedence CAFL

  14. Example: Case I • Given: • Category E detail (CAFL 4.5 ksi) • Sreff = 5.0 ksi • Srmax = 14.5 ksi • N = 1,755 cycles/day • What is estimated fatigue life in years?

  15. Example: Case I • Sreff > CAFL & Srmax > CAFL • All cycles greater than CAFL • Finite fatigue life • Calculate life using equations for S-N curve (N = A/Sreff3) • For Category E • A = 11.0 x 108 Calculation of ‘N’ yields: • N = 8,800,000 Cycles

  16. Example: Case I • N = 8,800,000 Cycles • Life calculation in years: • Recall 1,755 cycles/day are applied • 8,800,000 ÷ 1,755 cycles/day = 5,014 days • 5,014 days ÷ 365 days/yr = 13.75 yrs

  17. Cat E CAFL = 4.5 ksi Srmax = 14.5 ksi Sreff = 5.0 ksi N = 8,800,000 Example: Case I

  18. Example: Case III • Given: • Category C detail (CAFL 10 ksi) • Sreff = 4.9 ksi • Srmax = 8.5 ksi • N = 5,760 cycles/day • What is estimated fatigue life in years?

  19. Example: Case III • Sreff < CAFL & Srmax < CAFL • Hence: • All cycles less than CAFL • No further action required • Infinite fatigue life

  20. Srmax = 8.5 ksi Cat C CAFL = 10 ksi Sreff = 4.9 ksi Example: Case III

  21. Example: Case II • Given: • Category D detail (CAFL 7.0 ksi) • Sreff = 4.7 ksi • Srmax = 13.5 ksi (> CAFL!) • N = 2,637 cycles/day • What is estimated fatigue life in years?

  22. Example: Case II • Although Srmax is > CAFL we also need to know % exceedence of CAFL • If % exceedence is > 0.01% (1:10,000) than all cycles contribute to damage • If % exceedence is < 0.01% (1:10,000) than infinite life can be assumed • Information pertaining to stress-range histogram is required to calculate % exceedence of CAFL

  23. Stress-Range Histogram • From the histogram: • Sreff = 4.7 ksi • Srmax = 13.5 ksi • NTotal = 18,462 (weekly) • Number cycles > CAFL • Cat D – CAFL = 7.0 ksi • N>CAFL = 1,596 • % Exceedence = 8.6 % • 8.6 % >>> 0.01% Stress-Range Histogram

  24. Example: Case II • Since Srmax > CAFL - And - • CAFL is exceeded more than > 0.01% • Fatigue damage is expected (i.e., Finite life regime) • Calculate life using straight line extension of SN curve • Proceed with calculations just like Case I

  25. Cat D CAFL = 7.0 ksi Straight line extension of S-N curve Illustration of Straight-line Extension of S-N Curve

  26. Example: Case II • Calculate safe life (N) • For Category D: • A = 22.0 x 108 • N = A/Sreff3 • Calculation of ‘N’ yields: • N = 21,189,910 Cycles

  27. Example: Case II • N = 21,189,910 Cycles • Calculation of life in years: • Recall 2,637 cycles/day are applied • 21,189,910 ÷ 2,637 cycles/day = 8,036 days • 8,036 days ÷ 365 days/yr = 22.0 yrs

  28. Cat D CAFL = 7.0 ksi Sreff = 4.7 ksi Srmax = 13.5 ksi N = 21,189,910 Example: Case II

  29. Questions ?

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