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COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 379 
If these stress concentrations due to perforations seriously increased the liability 
to fatigue, only very moderate stresses could be used in practice. For instance, 
assuming that the steel used in a perforated member were of 30 tons per sq. in. ulti- 
mate tensile strength, and that its fatigue limit for pulsating unidirectional stress 
were 40 per cent. of this, say 12 tons per sq. in., then if the stress-concentration ratio 
were as great as 3:1, fatigue would be inevitable if the mean stress pulsated from 
zero to 4 tons per sq. in. This supposition is not supported by the results of the 
experiments. 
The experiments were carried out by the authors on model plates 14 in. wide 
and ,}, in. thickness, 6in. in length. These dimensions were adopted to suit the test- 
ing facilities available, and to reproduce the proportions found in a typical full-size 
plate in a bridge member, 9 in. x 3 in., with +3-in. holes to suit {-in. rivets. To 
simplify the preparation of the test-pieces the holes were not plugged. 
To test the stress-concentration effect under conditions more comparable with 
theory, a test-piece shaped as in experiment A and ? in. wide at mid-length was 
drilled with a very small hole in its centre line. The test-piece thus approximately 
fulfilled the conditions for giving a 3 to 1 magnification of stress at the margin of 
the hole on a transverse section. 
The results of all these experiments are in agreement with what would be expected 
from practical experience with steel structures, for the stress concentrations appear 
to have little effect. The results are given in the following table. Test-pieces E 
had five holes side by side transversely, and the others had rows of three and two holes 
at various pitches giving a staggered arrangement. The stresses are calculated on the 
gross sections, for with staggered holes the net sectional areas cannot be given 
definitely ; but if the net area ratios given in the table be assumed correct, it will be 
seen that these test-pieces withstood maximum stresses approximating to the yield 
stress, applied for from 0-45 to 1-2 million times before fracture. These numbers 
are high enough to indicate that a slight reduction of stress would enable the tests 
to stand an indefinite number of repetitions. 
Experiment E E G F F 
Holes in rows 5 5 2 and 3 2and3 | 2 and3 
Pitch between rows _— — # in. } in. 2 in. 
Endurance millions. -908 1-224 0-538 0-534 0-456 
§ tons per sq. in. 4-01 3-24 4-18 4-89 5-13 
A tons per sq. in. : 2-76 2-78 2-87 3°50 3-67 
(S-+-A) tons per sq. in. 6-77 6-02 7-05 8-39 8-80 
(Net section) 
(Gross section) 0-48 0-47 (?) 0-69 0-69 
Holes deducted . 5 5 (2) 3 3 
Experiment D on the specimen drilled with the fine hole gave the following record : 
Maximum stress 9-5, minimum 0-5 tons per sq. in. (S = 5, A = 4-5). Unbroken 
after 5-69 million. 
Maximum stress 10-5, minimum 0-5 tons per sq. in. (S = 5:5, A = 5-0). 
Unbroken after 2-976 million additional repetitions. 
Maximum stress 11-5, minimum 0-5 tons per sq. in. (S = 6:0, A = 5-5), 
Unbroken after 2-768 million additional repetitions. 
Maximum stress 12:5, minimum 0-5 tons per sq. in. (S = 6:5, A = 6-0). 
Fractured after a further 0-998 million repetitions. 
These stresses are calculated on the gross sectional area. 
The test proves that, in spite of stress concentration, a stress closely approaching 
the yield stress (about 13 tons per sq. in. for the material) was necessary to fracture 
by fatigue. 
In each of the tests failure occurred by cracks starting at the holes. They always 
developed at the ends of the transverse diameters of holes and extended along the 
transverse section. Adjacent holes, placed comparatively closely but not on the 
same transverse centre line, do not appear to affect the development of the crack or 
cause it to deviate from the transverse path, 
