Fatigue Life Analyses of Crane Runway Girders

Raymond S. Milman, Chief Structural Engineer, Middough Associates Inc., Cleveland, Ohio

FATIGUE is the process of cumulative damage caused by repeated loadings. Fatigue damage of structures subjected to elastic stress fluctuations occurs at places of stress raisers, where the localized stress (due to the stress concentration effect) exceeds the yield stress of the mate rial. After a certain number of load cycles, the accumulated plastic damage will cause the initiation and subsequent propagation of a crack or cracks. In general, the more severe the stress concentration, the shorter the time required to initiate a fatigue crack.

Fatigue damage was recognized in Europe early in the 19th century. However, implementation of fatigue design criteria in structural engineering did not start until the late 1950's.

The fatigue life of a structure is defined as the number of cycles required to initiate and propagate a fatigue crack to a critical size, which could result in the fractural failure of the structure.

A fatigue-related failure attracted attention of engineers in the mid-1960's, when the failure of relatively young welded crane runway girders occurred significantly more often than the failure of old riveted girders. These failures were mostly represented in the form of cracking of fillet-welded top flange to web, stiffener to web and flange connections. The crack usually started in the welded joint and then propagated to the web or flange. Other cases included the failure of girder to column rigid connections, which restrained the girder support from free rotation, and stitch or plug welded connections of the runway components (eg, walkway plates, girder cap channels, etc).

A significant amount of research was performed and many technical articles have been published regarding premature fatigue failures of welded crane runway girders, some of which were only 2 to 15 years old. The com-mon conclusions and recommendations made in those articles were:

Fillet welded top flange to web connections per form poorly in the presence of loadings resulting from crane operations. These connections can be loaded in vertical and horizontal shear from crane wheel vertical loads, and in torsion from the crane rail eccentricity over the centerline of the web and crane transverse horizontal loads. In addition, high residual stresses in the vicinity of the top flange web stiffener welded intersection help to create conditions for fatigue crack initiation.
New crane girders be designed with complete penetration welded top flange to web connections and provide a deep cope (3 to 4 in.) for the stiffener to minimize interference between welds.
Girder to column connections be revised to provide a free girder support rotation in the vertical plane.
Replace stitch fillet and plug welds with continuous welds or bolted connections.

On the other hand, n limited amount of research information exists on the fatigue of riveted construction. The majority of research, which has been performed in Europe and North America, has concentrated on riveted bridge members (beams, posts, truss diagonals, etc) and riveted connections. Riveted crane girders comprise a high percentage of the total crane runways, especially in the steel industry. However, no information is available about fatigue-related research performed on riveted crane runway girders. This, most likely, can be explained by a significantly less amount of fatigue failures of the old riveted crane girders vs the failures of relatively young welded girders.

Most fatigue failures of riveted crane girders occur in the girder to column connection region, where the typi cal fatigue-sensitive details are located. These fatigue sensitive details originate from discrepancies between analytical models and design practices. Crane girders were originally analyzed as simple span beams. However, design practices at the time the runways were constructed featured restraining girder support rotations, such as:

A web splice over the full height of the girder web between adjacent girders at supports.
A common vertical diaphragm over the full height of the girder web between adjacent girders and the column.
Knee braces between crane girders and columns.

Modification of the riveted girder support details and a proper repair of detected cracks usually helps to prevent reoccurrence of cracking.

In general, most of the fatigue related crane runway research was concentrated on developing recommendations for repair of existing failures and the proper design of new crane runway girders. The words, proper design, of crane runway girders in terms of fracture mechanics mean the design of girders (or any related structures) to prevent brittle fracture due to cracking. This includes providing an appropriate stress level at the locations where crack growth can occur and elimination (as much as possible) of those details that act as stress raisers.

Another subject of fatigue-relate d design of crane runway girders is an evaluation of the expected fatigue life of crane runway girders. This subject is especially important when the expected remaining fatigue life of the existing runway girders is the main concern in crane runway upgrade projects.

By the nature of a crane operation, most runway girders are subjected to variable amplitude loadings. However, the American and Canadian structural codes do not specify this effect, making design engineers use the maximum stresses in the fatigue analyses, which is an overly conservative approach.

On the other hand, the allowable stress ranges recommended by the design codes for fatigue analyses are based on S-N figure design curves, which were developed by testing specimens subjected to a single mode constant amplitude load. It is understood that the S-N curves cannot directly cope with a variable amplitude load spectrum.

Many methods to predict the fatigue life of a specimen subjected to variable amplitude loadings have been proposed. The most popular and widely used method is the Miner's linear damage accumulation hypothesis. The linear damage accumulation hypothesis assumes if cycles of a stress range Sri are applied, where ni is less than Ni (Ni is the fatigue life for stress range Sri), the fatigue dam age occurring during this application is the ratio n/Ni. Failure after m stress cycles will occur when (see image to the right).

An application of Miner's Rule for evaluation of the expected fatigue life of crane runway girders is proposed in this article together with a review of the most important parameters that affect the fatigue life of the crane girder subjected to variable amplitude loadings. These parameters include: joint classification; allowable fatigue stress range; and stress range history.

Joint Classification and Fatigue Stress Range

The joint classification presented tin most governing structural codes (AISC, AASHTO, AWS, etc)1·3 proposes several joint categories (from A to F) based on the sensitivity to fatigue damage. There is no exact agreement on the fatigue category classification and magnitudes of the allowable fatigue stress ranges between different structural codes.

AASHTO specifications (reference 2) and ANSI/AWS Dl.1Code (reference 3) divide structures subjected to cyclic loadings into two types: redundant and non-redundant load path structures, and provide different magnitudes of fatigue stress ranges for each type. The AISC specification (reference 1) does not provide such a division, but the AISC recommended allowable stress ranges closely match AASHTO values for redundant load path structures. Based on the AASHTO definition of redundant load path structures as "structure types with multi-load paths, where a single fracture in a member cannot lead to the collapse crane runway girders should belong to non-redundant load path structures.

By realizing that fatigue life analyses, using the avail able techniques and limited information regarding the real multi-mode stress fluctuation, are approximate, the minor differences in recommended design stress ranges between design codes are acceptable.

While definition of fatigue stress categories for welded structures is well developed for the designers use, limited sources of information are available for definition of the fatigue stress categories for the riveted construction.

Recommendations obtained from available sources are:

Fatigue strength of riveted steel members is best characterized by the category C fatigue strength curve. This strength exists under all service conditions.
- Base metal at the net section of riveted connections should be considered as category D.5,6
- Fatigue strength of rivets in shear may deter mine the fatigue strength of connections. A shear stress range of 14 ksi (100 MPa) may be taken as an approximate constant-amplitude fatigue limit.5
- The fatigue studies used to develop design stress range values as a function of the joint stress category and number of load cycles, have shown that the fatigue life, N;, is related to the applied stress range, Sr, as follows (see image above and to the left).

where:

A = constant of fatigue behavior of a joint

m = approximately 3.0 for all stress categories with an accuracy acceptable in fatigue analyses, except for category F where m = 5.8.

T-N curves and allowable fatigue stress range tables presented in design codes represent the approximate lower limits (lower 95% confidence limit) for test data and provide conservative minimum number of cycles to failure of specimens subjected to constant-amplitude cyclic loads. Having the same slope m on a log-log plot of S-N diagrams, the allowable design stress ranges are represented on S-N diagrams by nearly parallel stress-life lines, except for stress category F (Fig. 1).

Fig. 1 - Design stress range curves for categories A through F. (Source: Redundant Structures ANSI/AWS D 1.1-94, Fig. 9.2)

Each stress category curve has a horizontal line, which indicates the endurance limit. If the stress range in the critical joint never exceeds value, then the structure should have a life. However, to design the structure having such a low stress range would be extremely conservative.

AISE Technical Report No. 13, Guide for Design and Construction of Mill Buildings¹ refers the designer to the AISC Specification1 for the allowable fatigue stress range data (Table A-K 4.3).

The constant A and endurance limit SrL values for stress categories A to F determined by using data of Table A-K4.31 is shown in Table I.

Knowing A, the designer can quickly make a number of valuable calculations, such as an effect of the stress increase on the structure fatigue life or the allowable fatigue stress range, if the number of cycles is known. Two examples follow that illustrate the utility of these calculations.

Example No. 1 - Crane girder bottom flange stress range is increased from 16 to 20 ksi. Assume stress cate gory B. Determine the change in expected girder fatigue life.

An increase of the stress range by 25% reduces the fatigue life by 50%.

Example No. 2 – The expected service life of the crane runway is 30 years. What will be allowable fatigue stress range if the critical joint is defined as category E and the runway is subjected to 100 load cycles/day, 300 days/years.

Stress Range History and Effective Constant Amplitude Stress

Crane runway girders during the operation of a crane are subjected to a wide spectrum of loads, which are delivered to the runway girders through the crane wheel to rail con tact: vertical static (crane bridge, trolley and lifted load weights); vertical dynamic (impact); horizontal dynamic transverse (crane side thrust); and longitudinal (bridge traction).

The vertical static loads are cyclic loads, because they are represented in each crane passage through a critical point of the girder. These loads could fluctuate from minimum loads produced by an unloaded crane to a maximum load from a fully loaded crane. Dynamic vertical and horizontal loads are random occurrence loads, unless specific load conditions are warranted at the specific point of the runway.

The dynamic fatigue loading of each girder in the runway is unrealistic. It is not reasonable to expect that the crane is lifting its maximum load with vertical impact and at the same moment the trolley is reaching the extreme end of its runway with a rated speed, producing a horizontal impact on the stop, and this occurs at the particular
critical point of the girder during each crane passage.

The occurrence described is more likely a once in a lifetime situation which obviously is for an elastic strength check and not for a cyclic loading case. This discussion leads to the conclusion that only crane wheel vertical static loads, presented in each crane passage over the crane runway girder, could create the fluctuating cyclic stresses at the girder critical points at each load cycle (passage). The vertical wheel loads fluctuating from the minimum to the maximum magnitude are variable functions of trolley position on the crane bridge and the weight of the lifted load, which in most cases does not represent the crane maximum lifting capacity. It can be assumed, with an accuracy acceptable in fatigue analyses, that vertical loads on one side of the crane are equal. Thus, it follows that the stress es, produced by the vertical loads in the crane girder, are linear functions of the wheel loads. This means that the wheel load history can be used in developing the design stress history for the complex load cycle or for a series of cycles.

The complex load cycle usually consists of a primary cycle and one or more secondary cycles, which cause additional fatigue damage. Even if secondary cycles pro duce stress ranges below the endurance limit, they should be considered in cumulative damage analyses because they could propagate the crack, which may have already started due to the higher stress of the primary cycle.

Fatigue studies, mostly performed on steel highway bridges,4 8 show that a variable-amplitude stress-range spectrum can be represented by an effective constant amplitude stress range:

Using the effective constant amplitude stress range, the designer is able to utilize S-N curves or equation (2) to determine the number of cycles which represent the fatigue life for the stress range Se.

It often happens in crane runway upgrade projects that the engineer should know how much of the crane runway girder fatigue life remains after the crane capacity is increased. Knowledge of the previous load history and number of load cycles is necessary to solve the task.

The application of the effective constant amplitude stress range and the damage accumulation method in the runway girder fatigue analysis is demonstrated in the following crane runway upgrade case study review.

Case Study

A ladle crane's capacity was increased in 1993 from 300 to 400 tons. The riveted crane runway girders (span 36 ft-8 in.) were in service since 1940. Two cranes operating in the teeming aisle provide the necessary service for 50 heats/day from two steelmaking vessels.

The increase of the crane's lifting capacity from 300 to 400 tons resulted in an increase of the maximum crane wheel load from 133 to 154 kips. Crane girders passed checking for the 400-ton crane vertical with impact and horizontal loadings in accordance with the AISE Technical Report No. 13 (1991 Edition) recommendations.

The report recommends the use of a maximum crane wheel load with full impact factor (1.25) and 50% of the full crane side thrust in fatigue analyses. Following this recommendation, the design fatigue stress range for the girder bottom flange from the 300-ton loads was 13x

1.25 = 16.25 ksi. According to research performed on riveted steel bridge girders, stress category C was recommended for the fatigue analyses of the riveted beam type members. The fatigue life of the riveted girder for the stress range 16.25 ksi was determined by using equation (2):

Fig. 2 - Bending stress diagram for various crane loadings.

If only the fully loaded crane passage cycles (50/day) during 350 working days/year, were accounted, the fatigue life of the girder would be 58.5 years. That indicates the girder fatigue life is close to expiration in 1998 even with out the load increase or accounting for other load cycles such as passages with an empty ladle and unloaded pas sages.

A detailed inspection performed on these girders did not reveal any fatigue associated damage, except for random rivet shear of the web splice at girder supports. It was proposed to perform the fatigue analysis of the crane girder using the damage accumulation method and an effective constant-amplitude stress range approach. The following is a brief review of the results of the analysis.

Design criteria – The design criteria are:

Each heat consists of three cycles: unloaded crane passage; crane loaded with an empty ladle pas sage; and fully loaded crane passage.
No vertical impact and crane side thrust included in the fatigue stress range magnitude.
For conservative analysis, the crane travels along the runway with trolley in the extreme approach to the crane girder, creating the maximum wheel load for a particular passage.

300-ton crane loadings (1940-1993) - Maximum wheel loads for the three load cycles are:

Unloaded crane with trolley in the extreme position, 70 kips/wheel.
Crane loaded with empty ladle, 91 kips/wheel.
Fully loaded crane, 133kips/wheel.

Fluctuating bending stresses in the girder bottom flange, as a function of the moving crane position, were determined using a moving load computer program for each load cycle included in the heat(Fig. 2). Each cload cycle has one primary and one secondary stress range (Fig. 2). The effective constant-amplitude stress range for six cycles composing one heat(Table II) was determined using equation (3).

The secondary cycle effect in this particular case is insignificant. It is presented in the analyses only to follow a proper analytical procedure.

The total number of fatigue life cycles for the effective constant-amplitude stress range produced by the 300-ton crane from equation (2) (see image to the left).

Therefore, number of heats= 7,962,014/6 = 1,327 ,000 Therefore, number of years = 1,327,000/(50x 350) = 75.8

400-ton crane loadings, since 1993- Maximum wheel loads for three load cycles are:

Unloaded crane with trolley in extreme position (same as for 300-ton crane), 70 kips/wheel.
Crane loaded with empty ladle (same as for 300- ton crane), 91 kips/wheel.
Fully loaded crane, 154 kips/wheel.

The effective constant-amplitude stress range calculation for six cycle composing one heat (Table III) follows:

From equation (3): Se= 9.05 ksi

The total number of fatigue life cycles for the effective constant-amplitude stress range produced by the 400-ton crane from equation (2) (see image to the right).

Therefore, number of heats = 5,922,687/6 = 987,115 Therefore, number of years= 987,115/(50 x 350) = 56.4

To determine the remaining fatigue life of the girder under the upgraded 400-ton crane loads, equation (1) can be rewritten as (see image below).

Based on these analyses, the expected remaining fatigue life of the existing riveted crane runway girders was determined to be approximately 17 years from 1993, under 400-ton loadings.

Detailed analyses performed subsequently, which included a more accurate account for the trolley position during the crane travel and the lifted load history based on statistical data for 10 months of 1993, permitted an increase of the expected remaining fatigue life of these crane girders to 24 years. [Ladle weight:fluctuated from 309 to 408 tons (Fig. 3).]

Summary

During crane operation, crane runway girders are subjected to variable amplitude of loadings ranging from empty to fully loaded crane loads. An application of the maximum design stress, produced by the crane, as a constant upper limit for a fatigue range in the fatigue analysis represents an inaccurate approach, which leads to overly conservative results of the fatigue analysis.

Utilization of the damage accumulation principle and the effective-constant amplitude stress range approach in the fatigue life analysis of the crane runway girders subjected to variable amplitude loadings permits a more accurate prediction of the expected girder fatigue life.

An application of the above method in the crane runway upgrade projects in combination with the crane past load history could define an extended remained fatigue life of the existing crane runway.

References and Bibliography

AISC Specification for Structural Steel Buildings (ASD), 1989.
AASHTO Standard Specifications for Highway Bridges (1992 Edition).
AWS/ANSI AWS D.1-1 Structural Welding Code, 1994.
Fisher, J. W., and Wang, D., "Fatigue Strength of Riveted· Bridge Members," ASCE, Journal of The Structural Div., Vol. 110, 1984.
Bruhwiler, F., Smith, F. C., and Hirt, M. A., "Fatigue and Fracture of Riveted Bridge Members," ASCE, Journal of the Structural Div., Vol. 116 , 1990.
Baker, K A., and Kulak, G. L., "Fatigue Strength of Two Steel Details," University of Alberta, 1982.
AISE Technical Report No. 13, "Guide for Design and Construction of Mill Buildings," 1991 Edition.
Shilling, C. G., and Klippstein, K H., "New Method for Fatigue Design of Bridges,• ASCE, Journal of the Structural Div., Vol. 104, 1978.
Barsom, J. M., and Rolfe, S. T., Fracture and Fatigue Control in Structures, Princeton-Hall, 1987.
Bent, R. M., "Fatigue Calculations Are Never Exact,” Conference on Fatigue of Structures, Toronto, 1994