Failure & performance adds Miner damage, S–N cycles, and floor acceleration calculators—illustrative fatigue and serviceability.

Scope

Fatigue, fracture, progressive collapse, vibration serviceability, and other performance limits beyond ultimate strength.

Handbook alignment. Fatigue, fracture, and progressive collapse appear in the handbook’s later sections (e.g. fatigue and special topics in Section VI); serviceability and reliability link to Ch. 12. This page does not reproduce those chapters. Use project detail categories, code S–N curves, and approved analysis for production design.

Reference check (S–N → Miner → vibration)

  1. Stress range — Classify structural detail and read allowable cycles from the code S–N curve (or a log–log model like the on-page toy).
  2. Damage — Combine cycles at different ranges with Miner’s rule—project spectra and partial factors still govern.
  3. Serviceability — Screen floor acceleration from harmonic motion; full walking crowd or machinery models need specialist dynamic analysis.

Structural Engineering — Failure & Performance Topics

Fatigue, Palmgren–Miner damage, and floor acceleration checks—beyond ULS strength.

How this page relates to the handbook

The handbook treats fatigue, fracture, progressive collapse, and vibration serviceability in dedicated chapters with detail categories, S–N data, and system-level strategies. Below is a topic map of what those treatments involve; the calculators are minimal teaching aids (Miner, log–log S–N line, harmonic acceleration).

Illustrations (fatigue mechanics)

Crack propagation curve and Paris law regions
Crack growth regimes and Paris law (schematic). CC BY-SA 4.0, Wikimedia Commons
S-N Wohler curve log log
Wöhler (S–N) curve—stress range vs cycles to failure. CC BY 3.0, Wikimedia Commons

What failure and performance work produces

  • Fatigue design — Detail category, stress ranges, cumulative damage, and inspection planning.
  • Fracture / robustness — Special assessments for thick tension members or disproportionate collapse strategies where required.
  • Serviceability — Vibration acceptance criteria for floors and footbridges; damping and human comfort checks.

Code basis

Fatigue provisions in steel codes (e.g. SANS 10162 context) reference detail categories and S–N curves. Bridge and machinery projects may use additional standards; performance-based reliability ties to Ch. 12 framing on the Advanced Design Theory page.

Notation (on-page calculators)

  • Miner — n applied cycles; N allowable cycles at one stress range; D damage indicator.
  • Log–log S–N — S stress range (MPa); C, m line parameters; N cycles.
  • Acceleration — f frequency (Hz); x displacement amplitude (mm); a peak acceleration.

Introduction

Bridges, cranes, and slender floors often govern on fatigue or acceleration rather than on ULS bending. Real fatigue design requires stress ranges, detail categories, spectrum loading, and sometimes fracture mechanics. The calculators below are illustrative; hot-spot stress and code S–N data must follow the governing standard.

Fatigue and fracture (handbook themes)

  • S–N approach — Stress-life curves for categories of structural detail; variable amplitude and Miner’s rule.
  • Fracture mechanics — Crack growth for thick tension members and special assessments.
  • Welded details — Toe geometry, residual stress, post-weld treatment; inspection intervals.

Vibration and performance limit states (handbook themes)

  • Human response — Acceleration and frequency acceptance criteria for floors and footbridges.
  • Harmonic vs random — Walking, machinery, wind; damping assumptions.
  • Link to reliability — Serviceability as a limit state with its own target reliability (Ch. 12 context).

Calculators (illustrative)

Miner damage, S–N estimate from a log–log line, and harmonic acceleration from displacement amplitude.

Calculator — Palmgren–Miner damage (single stress range)

D = n / N

Cycles applied vs allowable

Palmgren–Miner damage ratio D = n/N for a single stress range.

Calculator — S–N cycles (log–log line)

log10 N = C − m log10 S

Allowable cycles at stress range S

Cycles to failure N from a log–log S–N line (log10N = C − m log10S).

Calculator — floor peak acceleration (simplified)

Walking / rhythmic excitation screening

a ≈ 4π² f² xpeak   (harmonic; x in m, f in Hz)

Order-of-magnitude acceleration

Peak acceleration from harmonic motion a ≈ 4π²f²x for frequency f and displacement amplitude x.

Software and fatigue / dynamics

Fatigue life prediction, fracture mechanics, and crowd-induced vibration often use specialist software. Examples (official vendor sites):

No endorsement—fatigue and fracture assessments must follow the governing code detail categories and agreed stress analysis basis.

Diagram sources

Educational schematics. Files in Images/failure-performance-topics/ from Wikimedia Commons.