Fatigue Failure of C-hook　　　　　　　　HOME　技術資料室　技術用語
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　Strength of C-hook decreases gradually by “metal fatigue” for several years over several decades depending on the frequency of loading. When the strength of C-hook falls below the stress by loading, it has the risk of breakage to cause a disaster. To avoid this risk, it is essential to design C-hook to have enough strength even after “metal fatigue”.
　However, there are not a few C-hooks that seem to be designed and manufactured without considering the stress distribution or fatigue. An example of diagnosis of C-hook is shown below.

１．Metal fatigue
　Strength of steel material decreases gradually by repeated loading (metal fatigue), until it stops at the repetition of about 10⁷ times of loading. After this, the steel material has the constant strength, which is called “Fatigue Limit”. Fatigue Limit varies from 1/2 to 1/10 of the initial Strength, depending on the following factors.
　　①Segregation of chemical elements or inner defects of the steel material
　　②Thermal strain by welding
　　③Notches or rough surface at the corner
　　
　As the decreasing strength of the actual C-hook by every loading cannot be measured, it must be presumed from those data of the initial strength and the fatigue limit of the steel tested at laboratory.

２．Principle of safety design
　If C-hook is designed at the stress level of "X" in the right graph, this C-hook has a risk of fatigue fracture around the loading frequency of “Y”.
　Photos below show the results of such fatigue fracture.

　To avoid the fracture, it is indispensable to design the C-hock so as the generated maximum stress is below the fatigue limit.

３．Method of Diagnosis
　The stress distribution, generated in the C-hook by loading a coil, is analyzed by "Finite Element Method" (FEM), where the C-hook is divided into small elements, as shown in the right figure, and these elements are related each other by formulas and analyzed by computer to obtain the stress distibution.

　FEM was invented and developed by Boeing Co. in USA for designing of airplane.
　Nowadays, it is widely used for designing of various machinery as well as building.

４．Necessary strength of steel material
　The fatigue property of the steel material can be measured only by test pieces in laboratory, not by the actual C-hook. Accordingly, it is necessary to take “safety factor” into account to absorb the various differences between the actual C-hook and its theoretical design.

　The “safety factor” includes
　1) dispersion of the tensile strength of the material,
　2) dimensional deviation in production,
　3) the heat treatment conditions and
　4) the deflection of the fatigue property.

　The average fatigue limit is around forty percent (40%=1/2.5) of its original tensile strength. Other factors shall be taken into account as the safety factor of around two (2).

　So the total safety factor against the original tensile strength of the material shall be
　　　　　　　　2.5 x 2 = 5,
which means the maximum designed stress in the C-hook should be below one fifth (1/5) of the initial tensile strength of the material.

５．Example of analysis
　Flat plate type C-hook as shown below, is taken up, which is used comparatively widely in the world.

1) Size of the C-hook
　The thickness of the main body is 90mm and 12 mm thick plates are welded on both sides for rainforcement.
　　　　　　　
2) Loading capacity：maximum 20 tons

3) Material steel grade
　SS400 (initial tensile strength ≧400 MPa)

4) Analysis of generated stress by loading
　The right figures show the diagram and the elements of this C-hook input to the computer for the FEM analysis.
The stress distribution generated in the C-hook by loading 20 ton (196,000 N) coil, is as in the figure below. The maximum stress is 195.55 MPa at the upper and lower inner corners.

　　　　　　
　There is a possibility that crack originates from these parts when strength of the steel material decreases by fatigue below this stress.

5) Strength of steel material
　Initial tensile strength of SS400 is over 400 MPa (41 kgf/mm²).

6) Calculation of safety factor

Maximum stress a		Initial tensile strength b	Safety factor b/a	Assessment of safety
195.55 MPa		400 MPa	b/a=2.0	This C-hook has a risk of breakage as fatigue progresses.

　As mentioned in item 4, safety factor of b/a in the above table must be more than "5".

６．Consideration
1) Process of fatigue
　In case, this C-hook handles 10,000 tons monthly, where coil weight is 10 tons on average, this C-hook loads 10,000/10=1,000 times monthly, which means 12,000 times annually and 6×10⁴times in 5 years.
　Rough image of the relations among the fatigue properties of the C-hook, the maximum stress added by loading and the effect by manufacturing dispersion is shown in the following figure.
　After aound five years of operation, this C-hook will enter into the colored risky zone.
　　

2) Effects of structure
　The cross-sectional configuration should be based on the stress distribution generated in the C-hook, as shown in the figures below, to decrease the deflection of the stress.
　　　　　　
The figure below shows the safety factor of C-hooks with various cross sections, based on the results of diagnosis of the maximum stress at maximum loading weight. Flat type C-Hook (●) is difficult to secure the safety factor of five (5) comparered to H type (■) .
　
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