# Allowable fatigue stress

For cranes as for most other dynamically loaded structures very important.

The allowable fatigue stress depends on the following:

• The material (or the elasticity limit) of the construction.
• The sign of the stress (tension or compression).
• The k-factor (the ratio between the maximum and the minimum stress).
• The number of load cycles (taken into account with the crane group).
• The notch factor.

For pure dynamic load (the maximum stress=- the minimum stress or k -factor = -1) the allowable fatigue stress for different notch factors (W0, W1, W2, K0, K1, K2, K3, K4) is shown in the table below:

Basic values of the allowable stresses for fatigue ‾σ (v(-1)) in N/mm² for x=-1.

Material type Fe 360 (Fe 37) Fe360 (Fe37)
notch group W0 W1 W2 K0 K1 K2 K3 K4
1 180 180 180 180 180 180 180 (152.7)
2 (168) (180) 108
3 (161.4) 141.3 (178.2) 127.3 76.1
4 (169.7) 135.8 118.8 (168) (150) 126 90 54
5 142.7 114.2 99.9 118.8 106.1 89.1 63.6 38.2
6 120 96 84 84 75 63 45 27

Material type Fe 510 (Fe 52) Fe 510 (Fe52)
notch group W0 W1 W2 K0 K1 K2 K3 K4
1 270 270 (247.2) 270 270 270 (254) (152.7)
2 (249) 199.2 (252) 180 108
3 (152.2) 200.6 160.5 (237.6) (212.1) 178.2 127.3 76.1
4 203.2 161.7 129.3 168 150 126 90 54
5 163.8 130.3 104.2 118.8 106.1 89.1 63.6 38.2
6 132 105 84 84 75 63 45 27

The ratio between the stresses of two crane (element) groups with equal notching for notch group W0 – W2 for Fe 360: 1.1892 and for Fe 510: 1.2409; for notch group K0-K4 for Fe 360 and Fe 510: 1.4142.

[NEN 2019, p. 21]

The table above shows the influence of the material type, the crane group, and the notch group (for determination of the notch group see next paragraph). For non-pure dynamic loads, the allowable stress is a mixture of the allowable stress for pure dynamic or fatigue and the static allowable stress. In the figure and table on the next page, this is further explained.

Equations for the allowable stresses (normal stress), depending on x and (see the previous table) and Figure 1 respectively.

 Alternating stress -1 < x < 0 Tension Compression Variable stress 0 < x < +1 Tension Compression

X=0: jumping stress

Figure 1—relation between and

 Symbol Description Allowable fatigue stress depending on the χ-factor Allowable pure dynamic stress (is determined by both the notch and crane group see  the previous page Elasticity limit of material (Rekgrens) Ultimate stress of material (Treksterkte)

Mean (or static) stress is on the horizontal axis and the allowable fatigue stress on the vertical axis. The thick lines represent the allowable combined stress for the tension (positive stress) or compression (negative stress). The table gives the formula for the different situation tension or compression and for varying stress (no change in the sign of the stress) and the alternating stress situation (-1 < χ-factor < 0).

Because of the complex determination of the applicable allowable stress, an excel file with the allowable stress for this course can be found on the blackboard pages of this course. An example of the lay-out of the excel file is shown in the next pages:

Input part of excel file:

Only the blue parts fields in the upper part of the excel file can be changed. The blue fields in the material library table can be used as example material input. Crane or element group can vary from 1-6 (see previous paragraphs).

Material type Ultimate Strength Real Elasticity limit Allowable Elasticity limit Allowable equivalent stress
Fe 360 360 240 240 160 180

Crane or element group: 5

Fatigue criteria:

Material: Fe 360 Notch group
Crane or element group K0 K1 K2 K3 K4 W0 W1 W2
1 160.0 160.0 160.0 160.0 152.7 160.0 160.0 160.0
2 160.0 160.0 160.0 160.0 108.0 160.0 160.0 160.0
3 160.0 160.0 160.0 127.3 76.4 160.0 160.0 160.0
4 160.0 150.0 126.0 90.0 54.0 160.0 160.0 160.0
5 118.8 106.1 89.1 63.6 38.2 160.0 135.8 118.8
6 84.0 75.0 63.0 45.0 27.0 120.0 96.0 84.0

Ratio between maximum stresses of crane groups 1.4142

Material library

Material type Ultimate Strength Real Elasticity limit Allowable Elasticity limit Allowable equivalent stress
Fe 360 360 240 240 160 180
Fe 510 510 360 360 240 271
Type A 660-880 550 460 307 346
Type B 800-950 700 560 373 421
St60-2K 690 490 483 322 363

Example output allowable tension stress with crane group 5 and material Fe 360 for the whole < χ-factor range.

Material: Fe 360 Notch group
Crane or element group 5
ξ values
K0 K1 K2 K3 K4
-1.0 118.8 106.1 89.1 63.6 38.2
-0.9 123.7 110.5 92.8 66.3 39.8
-0.8 129.1 115.3 96.8 69.2 41.5
-0.7 135.0 120.5 101.2 72.3 43.4
-0.6 141.4 126.3 106.1 75.8 45.5
-0.5 148.5 132.6 111.4 79.5 47.7
-0.4 156.3 139.6 117.2 83.7 50.2
-0.3 160.0 147.3 123.7 88.4 53.0
-0.2 160.0 156.0 131.0 93.6 56.2
-0.1 160.0 160.0 139.2 99.4 59.7
0.0 160.0 160.0 148.5 106.1 63.6
0.1 160.0 160.0 155.5 112.9 68.9
0.2 160.0 160.0 160.0 120.7 75.1
0.3 160.0 160.0 160.0 129.7 82.6
0.4 160.0 160.0 160.0 140.1 91.7
0.5 160.0 160.0 160.0 152.3 103.0
0.6 160.0 160.0 160.0 160.0 117.5
0.7 160.0 160.0 160.0 160.0 136.9
0.8 160.0 160.0 160.0 160.0 160.0
0.9 160.0 160.0 160.0 160.0 160.0
1.0 160.0 160.0 160.0 160.0 160.0

Allowable tension stress at values of ξ

## Notch factor or weld atlas

The notch factor library tries to combine information of:

• the weld quality*
• the stress concentration factor

The influence of the weld quality can be best seen by the perpendicular stressed weld type. For a non-welded plate notch-group, W0 is used will for decreasing weld qualities K0 to K4 are applicable. The weld is classified by a 3 digit number, the first digit represents the weld group 0-4 for K0 till K4, the second the stress orientation and the third a geometric type number.

Non-weld group W0

N0. Description Symbol
W01 Part without a hole and joint, with a normal state of the surface, without notch behavior.

Slight notch behavior group K0

N0. Description Symbol
011 Parts, joined by a butt weld of special quantity, perpendicular to the direction of force.

Moderate notch behavior group K1

N0. Description Symbol
111 Parts, joined by a butt weld of ordinary quantity, perpendicular to the direction of force.

Medium notch behavior group K2

N0. Description Symbol
211 Parts, joined by a butt weld of special quantity, perpendicular to the direction of force.

Great notch behavior group K3

N0. Description Symbol
311 Parts, joined by a butt weld with a backing strap, without sealing run and perpendicular to the direction of force. Backing strap fixed by track welding.

and a different connection type 351

N0. Description Symbol
351 Double bevel weld of ordinary quantity, perpendicular to the direction of force, between crossing parts.

Very great notch behavior group K4

N0. Description Symbol
412 Parts of different thickness, joined by a butt weld of ordinary quantity, perpendicular to the direction of force. Asymmetrical joint without slope.

and a different connection type 451

N0. Description Symbol
451 Fillet welds of normal quantity or single bevel weld (included fillet weld) with backing, perpendicular to the direction of force, between crossing parts.

The influence of stress concentrations can be seen in the following perpendicular loaded weld in the plate-plate connection types:

Slight notch behavior group K0

N0. Description Symbol
013 Gusset, jointed by out welds of special quantity, perpendicular to the direction of force.

Moderate notch behavior group K1

N0. Description Symbol
113 Gusset, jointed by butt welds of ordinary quantity, perpendicular to the direction of force.

Medium notch behavior group K2

N0. Description Symbol
213 Butt weld of special quantity and continuous part, both perpendicular to the direction of force, at a crossing of flanges with in-weld corner plates. The ends of the welds are ground to prevent them from notch behavior.

Great notch behavior group K3

N0. Description Symbol
313 Butt weld of ordinary quantity and continuous part, both perpendicular to the direction of force, at a crossing of flanges with in-weld corner plates. The ends of the welds have been ground to prevent them from notch behavior.

Very great notch behavior group K4

N0. Description Symbol
413 Butt weld of ordinary quantity, perpendicular to the direction of force, at a crossing of flanges without corner plates.