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Load Spectrum and Design Life: Converting Duty Cycle to Hours and Cycles

A duty class is a compressed load history: ISO 4301-1:2016 classifies cranes and mechanisms mainly by the total number of working cycles over the design life, a load spectrum factor for the relative frequencies of loads handled, and the average displacements. UTEC Industrial designs, engineers, machines, fabricates, and installs custom material handling systems for aerospace and heavy industry from its Spokane Valley, WA facility, integrating Allen-Bradley PLC and motion control with in-house CNC machining, heat treating, and stress relief. This article shows how operating hours, cycles per hour, and the spread of loads are converted into a cycle count, a load spectrum factor, and a class, why the cube of the load ratio appears in that factor, how bearings, gears, and motors use the same duty differently, and how a control system measures the duty actually delivered. The load spectrum sits at the design end of the build chain, design → engineering → parts machining → fabrication → assembly → weld fatigue → stress relief → drives → controls → tuning → monitoring, and comes back at the monitoring end, where the measured spectrum is compared with the one the design assumed.

What is a load spectrum, and why does a duty class need one?​

A load spectrum is the distribution of loads a machine handles over its life: how many cycles at each load level. The ISO crane classification is built on it. ISO 4301-1:2016 establishes a general classification of cranes and mechanisms "based on the service conditions, mainly expressed by" the total number of working cycles to be carried out during the specified design life, "the load spectrum factor which represents the relative frequencies of loads to be handled", and the average displacements.

Katona and co-authors, in a 2026 conference paper comparing crane classification standards, say the service class "defines the intensity and frequency of use, the load spectrum, and the operating conditions", all of which "directly influence the selection and calculation of structural elements, drive mechanisms, as well as fatigue assessment and reliability analysis". In their statement of FEM 1.001, A-class determination for a complete crane uses the number of working cycles and the load spectrum as "two independent parameters" whose combination yields a single overall class.

As engineering reasoning, the two parameters answer different questions. The cycle count says how many times the structure is loaded; the spectrum says how hard each load is relative to the rating. A machine at rated load on every cycle and one at a third of rated load on most cycles can see the same cycle count and very different fatigue damage, and neither parameter alone sets the class (ISO 4301-1:2016, Abstract; Katona et al. 2026, §1 and §3.2).

How is the load spectrum factor calculated?​

In the paper's statement of FEM 1.001, the load spectrum factor is

kp = Σ (nᵢ ÷ nmax) × (mlᵢ ÷ mlmax)³

where mlᵢ is a load, mlmax the safe working load, and nmax the number of hoisting cycles that determines the total duration of use. The paper defines nᵢ as the number of hoisting cycles "in respect of which the hoisted load is greater than or equal to" the load; in its worked example below it enters the number of cycles at each load. FEM's load spectrum classes run from Q1, kp ≤ 0.125, to Q4, 0.500 < kp ≤ 1.000; the paper's table of these classes heads the kp column "Cubic mean value". The paper states that ISO 4301-1:2016 calculates the factor "in the same way as in FEM 1.001" but uses six Qp-classes instead of four, with the former Q1 divided into three classes, Qp0, Qp1 and Qp2.

The paper's printed Qp table has evident misprints: the Qp1 row gives a lower bound of 0.313, above its upper bound of 0.0625, and the Qp1 and Qp2 rows omit the less-than sign. The lower Qp boundaries are therefore not taken from it here. As understood from ISO 4301-1:2016, Qp0 is kp ≤ 0.0313, Qp1 is 0.0313 < kp ≤ 0.0625, and Qp2 is 0.0625 < kp ≤ 0.125, with Qp3 to Qp5 matching the former Q2 to Q4.

As engineering reasoning, kp is 1.0 only if every cycle is at the safe working load, and a machine that runs half its cycles at rated load and half empty scores 0.5, the Q3/Q4 boundary, because an empty cycle adds nothing to the sum (Katona et al. 2026, §3.2–3.3, Eq. 2; ISO 4301-1:2016, Qp-class table).

Why does the cube of the load ratio appear in the calculation?​

In the bridge fatigue work that defines the root-mean-cube form, the cube is not arbitrary: it follows the slope of the fatigue curve. NCHRP Report 299, on steel bridges, gives an effective stress range from a measured histogram as Sr = (Σ fᵢ Srᵢ³)^(1/3) and explains that "the fatigue damage caused by a given number of cycles of the effective stress range is the same as the damage caused by an equal number of the different stress ranges defined by the histogram". It says this "root-mean-cube formula is based on Miner's Law and a slope of 3 for a straight line log S vs. log N fatigue curve".

NCHRP Report 188, the study Report 299 cites as the origin of the concept, generalizes it as Sre = [Σ aᵢ Srᵢ^B]^(1/B): with B = 2 the result is the root mean square, and with B equal to the reciprocal of the S-N slope it is "equivalent to Miner's Law. For most structural details, B is about 3." For its test spectra the two values "are only slightly different (usually less than 10 percent), the value of 3 being more conservative".

Three limits carry over. Both reports are about welded steel bridge details; the formulas apply to stress ranges at a detail, and using them on loads assumes stress proportional to load. Roylance calls Miner's law a useful approximation that might be accurate enough to use in design, but writes that its assumption of linear damage accumulation "should be viewed skeptically" and that the law "often fails to capture the essential physics of the fatigue process". As engineering reasoning, the crane load spectrum factor has the same cubic form, and the parallel holds only under those assumptions; the fatigue mechanism behind it is covered in Fatigue vs. Static Strength: Why Heavy Machines Crack at Low Stress (Moses et al. 1987, p. 12; Schilling et al. 1978, Summary p. 1; Roylance 2001, pp. 5–6).

How do hours, cycles per hour, and years combine into a design-life cycle count?​

The classification counts cycles, but a buyer may know only the operating hours. The conversion is multiplication: cycles per hour × operating hours per day × working days per year × design life in years. The ISO and FEM schemes then use the result directly; the iso.org page for ISO 4301-1:2016 says that edition "uses the cycle - based classification method", and that the time-based method is in the withdrawn 1986 version.

Katona and co-authors show why the time-based and cycle-based schemes do not convert one-to-one. Their statement of FEM 9.521 gives a time-to-cycle conversion through the total duration of use under full load, the load spectrum factors of both schemes, a drive-utilization ratio α, and the average cycle time tav. The paper says changes in lifting height or hoisting speed alter tav, and reports, citing a 2016 trade-press article, that converting class M5 with the lifting height cut from 12 m to 6 m and the hoist speed raised from 4 m/min to 20 m/min changes the classification from A2 to A6.

As engineering reasoning, the same operating hours can therefore mean very different cycle counts: a faster, shorter cycle packs more load cycles into each hour. A duty statement in hours alone is incomplete; it needs the cycle time or cycles per hour, and the class should be set on the cycles (ISO 4301-1:2016, iso.org page; Katona et al. 2026, §3.4, Eqs. 3–4).

What does a worked duty-to-class conversion look like?​

Katona and co-authors classify an existing 3.2 t single-girder workshop crane that carries cast weights of 460 to 470 kg each. It works 5 hours a day at 20 working cycles per hour: per hour, 5 cycles with one weight (468 kg), 10 with four (1,864 kg), 3 with five (2,328 kg), and 2 with six (2,796 kg). The paper's own arithmetic:

  • Cycles. 100 cycles a day × 260 working days × 10 years = nmax = 260,000, class U5 (250,000 < nmax ≤ 500,000).
  • Spectrum. kp = 0.00078 + 0.099 + 0.058 + 0.067 = 0.225, class Q2 under FEM 1.001 and Qp3 under ISO 4301-1:2016.
  • Class. U5 with Q2 gives A5 under FEM 1.001, and U5 with Qp3 gives A5 under ISO 4301-1:2016.

The arithmetic below is UTEC Industrial's own, on the paper's inputs:

QuantityCalculationResult
Operating hours over the design life5 h × 260 days × 10 years13,000 h
Equivalent full-load cycles (cube rule)0.225 × 260,00058,500
Cube-mean equivalent load0.225^(1/3) × 3,200 kgabout 1,950 kg (0.61 of rated)
Root-mean-square load (B = 2)[Σ fᵢ (mᵢ ÷ 3,200)²]^(1/2) × 3,200 kgabout 1,840 kg, about 5 percent below the cube mean
Arithmetic mean load (the paper's Qs)Σ fᵢ mᵢabout 1,678 kg

The paper states kp = 0.225, the sum of its four printed terms. As this article's own arithmetic, not the paper's, recomputing the four terms without rounding gives kp = 0.224, which leaves the class unchanged. The paper states ISO's design number of full-load cycles for class A5 as 125,000, the basis it says classification may use when the U- and Qp-classes are unknown; as this article's own arithmetic, that equals the upper bounds of the U5 and Qp3 ranges multiplied together (500,000 × 0.250). As engineering reasoning, the crane's 58,500 equivalent full-load cycles would fall within the 63,000 the paper states for A4, so the U × Qp method, which places it in A5, carries margin above the crane's own equivalent duty. As engineering reasoning, the table shows why the arithmetic mean understates duty: the cube mean is about 16 percent above it, because the heavier lifts dominate fatigue damage (Katona et al. 2026, §§3.3 and 4.1–4.3, Eqs. 10–14; Schilling et al. 1978, Summary p. 1).

Where do CMAA and ASME BTH-1 set out the same conversion?​

The U.S. standards place it under their own headings. CMAA 70's 2020 table of contents lists §2.8, "Crane Service Class in Terms of Load Class and Load Cycles", and §4.1, "Mean Effective Load"; the CMAA 74 table of contents (2020 printing) lists a "Crane Service Class in Terms of Load Class and Load Cycles" heading under 74-2 for single-girder cranes. ASME BTH-1-2023's table of contents lists Table 2-3-1, Service Class (p. 10), and, in its commentary appendix, Table B-3-1, Service Class Life (p. 59); the values under these headings are not in any public source read for this article (CMAA Specification No. 70-2020, Contents §§2.8 and 4.1; CMAA Specification No. 74-2025, 74-2; ASME BTH-1-2023, Tables 2-3-1 and B-3-1).

What those headings hold in the printed editions:

  • CMAA load class. As understood from CMAA 70-2025 §2.8, the load class is set by a mean effective load factor k, the cube root of the sum of each load level's ratio to rated load, cubed, times the probability of that load level, and the service class comes from the load class with the load-cycle range.
  • CMAA mechanical sizing. As understood from CMAA 70-2025 §4.1, a mean effective load is used for sizing mechanical components with class-dependent factors.
  • BTH-1 service life. As understood from BTH-1-2023, Table B-3-1 expresses each service class as combinations of load cycles per day and years of service.

As engineering reasoning, the CMAA factor k is the cube root of a factor of the same form as FEM's kp: for the worked crane above, k would be about 0.61 (CMAA Specification No. 70-2025, §§2.8 and 4.1; ASME BTH-1-2023, Table B-3-1).

How is a bearing's equivalent load taken from the same duty cycle?​

Bearings use the same idea with a different exponent. Timken's engineering manual says bearing selection "is often made on the basis of maximum load and speed. However, under these conditions, a more meaningful analysis may be made by examining the loading cycle to determine the weighted average load". For variable speed, load, and proportion of time it gives Fwt = [(n₁t₁F₁^(10/3) + … + nₙtₙFₙ^(10/3)) ÷ nₐ]^0.3, and it states two conditions:

  • Extremes still count. "It is still necessary to consider extreme loading conditions to evaluate bearing contact stresses and alignment."
  • Speed changes lubrication. The weighted average load "does not take into account the effects of different speeds on the lubrication factor a3l"; for load cycles with varying speeds it recommends calculating life for each condition and combining them in a weighted average life equation.

The manual's rating-life exponent is 3 for ball bearings and 10/3 for tapered, cylindrical and spherical roller bearings. ISO 281:2007 says its modified rating life takes into account various reliabilities, lubrication condition, contaminated lubricant and fatigue load, and that it "does not cover the influence of wear, corrosion and electrical erosion on bearing life".

As UTEC Industrial's own arithmetic, applying the 10/3 exponent to the worked crane's spectrum at constant speed, with each cycle given equal time, gives an equivalent load of about 0.62 of rated, against 0.61 by the structural cube: close, but computed separately for each component. How continuous service uses up L10 hours is set out in Designing for 24/7 Operation in Abrasive, Hot, and Wet Environments (Timken Order No. 10424, pp. 48 and 55; ISO 281:2007, Abstract).

How are gears and motors rated against the same duty?​

Gears have their own variable-load method. ISO 6336-6:2019 "specifies the information and standardized conditions necessary for the calculation of the service life (or safety factors for a required life) of gears subject to variable loading for only pitting and tooth root bending strength". The method is limited to those two failure modes; that is a scope statement, not a statement that other gear failure modes are negligible. As understood from ISO 6336-6:2019, the method combines a load spectrum with Miner-rule damage summation for pitting and tooth-root bending life. ANSI/AGMA 6013-B16 (R2021), Standard for Industrial Enclosed Gear Drives, is cited here at standard level only; the ANSI webstore lists this 2021 reaffirmation as the most recent version.

Motors are rated on a different basis again. IEC 60034-1:2026 covers the rating and performance of rotating electrical machines, and for machines with integrated EMC-active components such as a variable frequency converter it applies "to the motor component of the power drive system only". As understood from its clause 4, it defines duty types S1 to S10, with a cyclic duration factor for the intermittent types S3, S4 and S5. The DoD guide specification for top-running bridge cranes requires all motors to have "a minimum of a 60 minute duty rating".

As engineering reasoning, the load spectrum that sets the structural class does not by itself set the motor rating: the motor's duty depends on starts per hour, running time, and the thermal effect of current, so the duty cycle has to be given to the drive designer in time terms as well as in cycles (ISO 6336-6:2019, Abstract; ANSI/AGMA 6013-B16; IEC 60034-1:2026, clause 4; UFGS-41 22 13.14, Chg 1 2021, §2.4.1 p. 35).

What goes wrong when the assumed spectrum is wrong?​

Published sources show what follows when the assumed class or spectrum does not match the real duty:

  • Undersized elements. Katona and co-authors write that an incorrect service class "can lead to oversized components, but more importantly, it can result in undersized critical elements".
  • Loads near the rating. Hectors, Chaudhuri and De Waele write, citing earlier work, that compared with other civil structures "most load cycles occur close to the maximum design loads" on crane runway girders, and that continuous heavy cyclic loading in steel plants "makes crane runway girders especially prone to fatigue damage".
  • Repetitive use beyond intent. An MSHA investigation of a crane boom collapse records that the crane had reportedly been used as a dragline, which "would subject a boom to repetitive loading and possible fatigue cracking of the lacings"; investigators determined that the accident occurred because the crane was used beyond the manufacturer's design capacity. Fatigue was possible; the determined cause was overload.
  • Change of use. Katona and co-authors note that used industrial cranes are often sold and refurbished, and that relocation "changes the operating conditions under which it continues service".

As engineering reasoning, each case is a spectrum assumed once and not re-checked: a kp moving from 0.25 to 0.5 doubles the equivalent full-load cycles for the same cycle count (Katona et al. 2026, §2; Hectors et al. 2022, §1; MSHA MAI-2009-05, Investigation and Conclusion).

How can a control system measure the duty actually delivered?​

ISO 12482:2014 is an ISO crane standard for this step. It "specifies a method for monitoring, during long-term operation, the actual duty of the crane, and a means of comparing this to the original design duty which was specified through classification", with ISO 4301-1 as the related design standard. It says monitoring "provides a tool for predicting the approach of the design limits and for focusing special inspections on the critical areas of a crane", and that approaching the design life limit "means an increased probability of hazards". It applies to cranes with a permanent construction throughout their life, not to mobile or tower cranes except permanently installed tower cranes, and "the method it specifies can be adapted to standards or rules other than ISO 4301-1 which specify classifications". As understood from ISO 12482:2014, it defines the design working period and how the remaining period is computed from monitored use.

A load sensor is already one of the overload-protection options in the DoD guide specification, which lists a separate load indicating device, "a load cell and a digital readout that displays weight", among those options. ISO 17359:2018 gives guidelines for setting up a condition monitoring programme for machines; it gives guidelines, not requirements.

As engineering practice built on these sources, not a requirement of them, the PLC can carry the classification forward in service:

  • Count and bin. Count each working cycle and record its peak load, binned by load level.
  • Running factor. Compute the running kp and equivalent full-load cycles, Σ nᵢ (mᵢ ÷ mmax)³, from the bins.
  • Life used. Compare the equivalent full-load cycles with the design basis of the class assigned, and alarm at set fractions.
  • Inspection prompts. Trigger inspection of the critical welds and the bearings at those fractions, rather than on the calendar alone.

UTEC Industrial, a Rockwell Automation Recognized System Integrator, builds duty logging of this kind on Allen-Bradley ControlLogix and CompactLogix controllers with VFD and servo drives (ISO 12482:2014, Abstract; UFGS-41 22 13.14, Chg 1 2021, §2.4.9 note, p. 43; ISO 17359:2018, Abstract).

Where does the load spectrum sit in the design-to-monitoring chain?​

The spectrum is set once and used at every link:

  • Design and engineering. It sets the class, the fatigue design case, and the equivalent loads for each component.
  • Fabrication and weld fatigue. As this article's own arithmetic on the worked example, the 25 percent of cycles with five or six weights (5 of the 20 an hour) carry 0.125 of the paper's 0.225 spectrum factor (its last two printed terms), more than half; as engineering reasoning, weld detail quality matters for the heavy cycles out of proportion to their number.
  • Stress relief. What thermal and vibratory relief do to a welded frame before final machining is covered in Stress Relief for Machine Bases and Frames Before Final Machining.
  • Drives. Bearings use a 10/3 or 3 exponent, gears their own variable-load method, and motors a time-based duty, all from the same duty data.
  • Controls, tuning, and monitoring. As engineering reasoning, tuned acceleration and deceleration reduce the dynamic part of each load, and duty logging shows whether the spectrum assumed at design is the one delivered.

UTEC Industrial machines the heavy frames and components it builds to tolerances as tight as ±0.001 in (Katona et al. 2026, §1 and §4.2, Eq. 14; Timken Order No. 10424, p. 55; ISO 12482:2014, Abstract).

What duty data should a buyer give the designer?​

A designer can only classify the duty the buyer describes. As engineering practice drawn from the sources above, a specification should give:

  • Cycle rate. Cycles per hour, with the cycle time, not only operating hours.
  • Operating pattern. Hours per day, working days per year, and design life in years.
  • Load spectrum. The share of cycles at each load level, as a table or a measured log, so a kp can be calculated, rather than the rated load alone.
  • Peaks and extremes. The largest loads and any shock or offset loading, since Timken says extreme conditions still have to be checked separately.
  • Speed profile. Speeds and dwell times for the drive and motor duty.
  • Change of use. Whether the machine may later move to heavier service or a new site; Katona and co-authors note that relocation changes the operating conditions a crane continues service under.
  • Monitoring. Whether the machine must log its own duty against the design duty.

As engineering reasoning, for a given cycle count the spectrum can move the class a long way: in the FEM matrix the paper states, class U5 runs from A4 at Q1 to A7 at Q4 (Katona et al. 2026, §2 and §3.2; Timken Order No. 10424, p. 55; ISO 4301-1:2016, Abstract).

Related Articles

References​

  • ISO 4301-1:2016: Cranes — Classification — Part 1: General. International Organization for Standardization, 2016.
  • Katona, M., Zelić, A., Živanić, D., Đokić, R., Jojić, T., Ilanković, N. (2026). "Comparative overview of determining service classes of industrial cranes according to relevant standards and guidelines." Proceedings of the XII International Triennial Conference Engineering TODAY (ET 2026), A25-A31.
  • Moses, F., Schilling, C. G., Raju, K. S. Fatigue Evaluation Procedures for Steel Bridges, NCHRP Report 299. Transportation Research Board, National Research Council, 1987.
  • Schilling, C. G., Klippstein, K. H., Barsom, J. M., Blake, G. T. Fatigue of Welded Steel Bridge Members Under Variable-Amplitude Loadings, NCHRP Report 188. Transportation Research Board, National Research Council, 1978.
  • Roylance, D. Fatigue (3.11 Mechanics of Materials module). Massachusetts Institute of Technology, 2001.
  • CMAA Specification No. 70-2020: Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Overhead Traveling Cranes. Crane Manufacturers Association of America, 2020.
  • CMAA Specification No. 70-2025: Specifications for Top Running Bridge and Gantry Type Multiple Girder Electric Overhead Traveling Cranes. CMAA, 2025.
  • CMAA Specification No. 74-2025: Specifications for Top Running and Under Running Single Girder Electric Traveling Cranes Utilizing Under Running Trolley Hoist. Crane Manufacturers Association of America/MHI, 2025.
  • ASME BTH-1-2023: Design of Below-the-Hook Lifting Devices. ASME, 2023.
  • Timken Order No. 10424: Timken Engineering Manual. The Timken Company, 2024.
  • ISO 281:2007: Rolling Bearings — Dynamic Load Ratings and Rating Life. International Organization for Standardization, 2007.
  • ISO 6336-6:2019: Calculation of Load Capacity of Spur and Helical Gears — Part 6: Calculation of Service Life Under Variable Load. International Organization for Standardization, 2019.
  • ANSI/AGMA 6013-B16 (R2021): Standard for Industrial Enclosed Gear Drives. AGMA, 2016.
  • IEC 60034-1:2026: Rotating Electrical Machines — Part 1: Rating and Performance. International Electrotechnical Commission, 2026.
  • UFGS-41 22 13.14: Bridge Cranes, Overhead Electric, Top Running. U.S. Army Corps of Engineers / Naval Facilities Engineering Systems Command / Air Force Civil Engineer Center, November 2019 (Change 1, February 2021).
  • Hectors K, Chaudhuri S, De Waele W (2022). "Fracture mechanics and hot spot stress-based fatigue life calculation: Case study for a crane runway girder." Fatigue & Fracture of Engineering Materials & Structures, 45(9), 2662-2675. DOI 10.1111/ffe.13729
  • MSHA MAI-2009-05: Report of Investigation, Fatal Machinery Accident, February 19, 2009. Mine Safety and Health Administration, 2009.
  • ISO 12482:2014: Cranes — Monitoring for Crane Design Working Period. International Organization for Standardization, 2014.
  • ISO 17359:2018: Condition Monitoring and Diagnostics of Machines — General Guidelines. International Organization for Standardization, 2018.

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