Structural Steel Design / Crane-supporting structures
Fatigue: the limit state that sizes the girder
A crane girder is one of the few building structures where fatigue governs — and where the cheapest fix is a change of weld rather than a change of section.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Corrections checked in this pass
- Worked example now explicitly supplied fatigue action; m3/m5 knee and cut-off branches implemented. No fabricated grinding category upgrade or section mass saving. Independent example damage checks recorded.
- Rebuilt the plotted S-N curve from the same piecewise model as the readout, including the knee and cut-off. Removed the automatic detail-category upgrade and fabrication recommendation.
Checks needed for project use
- A steel-design reviewer must check the first-generation calculation profiles, second-order analysis assumptions, connection rules and execution references against the applicable standards and amendments.
- Establish the actual stress spectrum, fatigue dynamic factors, classified detail geometry, stress definition, thickness effects, partial factor and inspection requirements. A supplied stress block is an educational comparison, not a fabrication-detail specification.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesWhy this matters
The trial girder in the last lesson was at 54% on bending and was nowhere near adequate. The reason is that a crane girder is loaded and unloaded several million times in its life, and steel that is nowhere near its yield strength will still crack if it is cycled often enough. Fatigue is a genuinely different limit state — driven by a different quantity, with a different remedy — and it is the one that sizes the member.
By the end of this lesson you should be able to
- Explain why fatigue depends on stress RANGE, not peak stress
- Apply the cube law and say what doubling the life requires
- Compare improving a detail with increasing a section
- Say why steel grade is irrelevant to fatigue
What you should already know
- Moving loads and the crane girder's moment (previous lesson)
- Weld details and their geometry (Module 12)
- The elastic section modulus (Module 6)
Stress range and fatigue life
For the nominal-stress assessment of the assumed as-welded detail, compare the stress range with the appropriate S–N curve. Equal ranges of 60 N/mm² give the same calculated contribution in this model even when their mean stresses differ. That statement is not universal for every material, detail or stress treatment.
On the m = 3 branch, halving the range multiplies calculated life by eight and reducing it by 20.6% doubles it, provided both points remain on that branch. A nominal normal-stress spectrum spanning the fatigue limit uses the specified m = 5 continuation below the knee, with its cut-off. Do not extend m = 3 to every range.
Yield strength alone does not improve the adopted welded-detail category. Any change of category requires a detail satisfying the relevant geometry, fabrication and inspection conditions.
Try it
Stress range and fatigue damage
Explore a variable-amplitude nominal normal-stress S–N curve with γMf = 1.35. The curve changes from m = 3 to m = 5 at five million cycles and ends at the cut-off at one hundred million. Each result is one supplied stress-range block, not a complete fatigue assessment.
The dot marks the supplied stress-range block on the curve.
- Stress range
- 58 N/mm²
- Assumed category
- 71 N/mm²
- S–N curve life at range
- 1.49 M
- Cycles in supplied block
- 5.0 M
- Block damage D
- 3.353
- Range at D = 1 for block
- 38.8 N/mm²
- Knee range
- 38.8 N/mm²
- Cut-off range
- 21.3 N/mm²
The supplied stress-range block gives D = 3.353 using the variable-amplitude nominal normal-stress curve (m = 3 / m = 5 and cut-off). This is one block contribution; verify the detail category, action factors and complete spectrum. No complete fatigue adequacy is established.
Explore the assumptions
- Compare stress pairs 160/100 and 60/0. They give the same range in this nominal-stress model. Other assessment methods can require different mean-stress treatment.
- Change the category to compare hypothetical classified details. This slider does not show that an existing weld can be upgraded, or prescribe grinding or another treatment.
- Life scales with the inverse cube of range only while both points remain on the m = 3 branch. On the m = 5 branch the exponent is five; crossing a knee or cut-off needs the piecewise calculation.
- Increasing the block count increases its damage. A real spectrum requires the contributions of all applicable blocks, with the correct fatigue actions and detail classification.
- Below the cut-off this model assigns zero block damage. The omitted point must not be read as a guarantee of infinite service life.
Worked example
Comparing section moduli under a supplied fatigue action
Given
- The 12 m gantry girder from the last lesson
- Assume a supplied fatigue-action block of 125 kN per wheel, inclusive of the fatigue dynamic/action treatment selected for this exercise. This value is not derived by omitting dynamic factors from the crane design.
- Two equal wheels at 3.5 m spacing on a 12 m span give a moment-range block of 547.2005 kNm, assuming zero contribution before the crane passage.
- 5 million cycles over the design life; γMf = 1.35
- Compare assumed nominal normal-stress detail categories 71 and 125. No particular weld geometry or treatment is assigned a category without checking the relevant detail table.
Find
Calculate this block’s Miner damage contribution for three supplied elastic section moduli. Do not infer a complete girder size or mass saving.
Assumptions
- The S–N curve and the detail categories are code-calibrated and unverified here
- Treat the block as part of a variable-amplitude nominal-stress history: m = 3 to ND = 5 million, m = 5 to NL = 100 million, then the stated cut-off. The complete spectrum is not supplied.
- The supplied fatigue wheel action already represents this block. A real assessment needs the crane duty spectrum, applicable fatigue dynamic factors, cycle counting and all damage contributions.
Practice
A detail cycles between 160 and 100 N/mm². What is the stress range, in N/mm²?
Practice
The stress range at a detail is halved. By what factor does the fatigue life increase? Take m = 3.
Practice
By what percentage must a stress range fall to DOUBLE the fatigue life? Take m = 3.
Practice
A category 71 detail with γMf = 1.35 is checked for 5 million cycles. What is the permissible stress range, in N/mm²? Take Δσ = (Δσc/γMf)(2/N)^(1/3) with N in millions.
Check yourself
Before crediting an improvement from category 71 to category 125, what must be established?
Summary
- The adopted as-welded fatigue model gives the same damage for equal stress ranges; this is not universal for every material and detail
- Mean stress does not appear in the calculation at all
- On the m=3 branch, life varies as1/(stress range)³: halve the range for eight times the life
- A 26% reduction gives ×2.5, not ×2 — 2^(1/3) = 1.26 divides, it does not subtract
- Permissible range at category 71 over 5M cycles was only 38.8 N/mm²
- Candidate A’s supplied modulus gives a damage contribution of 88.81 for the stated block.
- Candidate C gives D = 0.640 on the m = 5 continuation, before other blocks are added.
- Candidate B with an assumed qualified category 125 detail gives D = 0.458; no mass saving is inferred.