340 REPORTS ON THE STATE OF SCIENCE, ETC. 
therefore clear that with I beams of ordinary section the maximum stress that can be 
applied is the yield stress. 
This point is also of great importance in timber used for aeronautical work. All 
timbers in the air-dry condition show a marked drop of stress at the ultimate. Spruce, 
for instance, when tested in compression has a drop of 20 percent. If therefore these 
timbers are used in the form of I beams, the maximum moment which they can sustain 
is determined by the compression yield stress despite the high value of the tensile 
strength of timber. It isfor this reason that the use of the term ‘ modulus of rupture ’ 
in timber tests gives a misleading idea of the strength when used as I beams. The 
results of some uniform bending tests on spruce are givenin Table V. Four specimens, 
3 in. x 14 in., from the same plane were taken, and two (Nos. 1 and 2) were tested as 
solid beams. Specimen No. 3 was made I section with flanges 0:8 in. thick for about 
3 in. in the centre, the rest being solid, and No. 4 was also made I section but with 
flange 0-4in. The elastic limits, modulus of rupture, and the results of a compression 
test on a sample from the end of the actual specimen are given. It will be seen that 
whereas the ratio of the modulus of rupture to the compression ultimate stress is 
about 1-56 for a solid specimen, it is only about 1:1 for a section with flanges 0-4 in. 
thick. The use of the modulus of rupture as calculated from the solid section would 
therefore be misleading. It may be also noted that the results of a large number of 
tests on actual aeroplane spars all showed that no spar would stand a load appreciably 
greater than that which produced the faint white line which characterises compression 
failure in spruce. 
Complex Stress Distributions and Fatigue. 
In ordinary structural work, involving the use of rivets, the stress distribution in 
the material round the rivet holes is very complicated, and the maximum stress is 
often much greater than the mean stress, provided the material is elastic. Using a 
material which has a drop of stress at yield, however, we have for some types of stress 
cycles a kind of safety valve, for the material will simply flow at any place where the 
stress exceeds the yield, and transfer some of the load on to the under-stressed material. 
For a single application of a load there is no doubt that this does occur, for the ultimate 
tensile strength of a bar of mild steel with a hole in it is always greater than the area 
of the section multiplied by the ultimate strength of the material. This is due to the 
yield phenomena, and also to the effect of the surrounding material in diminishing 
the lateral contraction. With a hard steel, however, this does not occur, and the stress 
concentrations reduce the strength. 
In the case of simple pulsations of stress (i.e. variations between two values both 
of which are tension) on a specimen without stress concentrations, the upper limit for 
a material which has a drop of stress at yield is probably always above the yield. One 
would therefore expect that the stress concentrations due to the presence, say, of a 
hole would have little effect on the fatiguelimits ; certainly nothing like the variation 
suggested by the mathematical analysis (i.e. about 3 to 1). This appears to be sub- 
stantiated by Professor Haigh * and Mr. Wilson’s experiments. They state that, for 
the mild steel they used, the stress concentration due to the presence of holes appeared 
to have little effect on the limit for pulsating stress. The test proved that for the 
particular material tested, ‘ in spite of stress concentration, a stress closely approaching 
the yield stress was necessary to fracture by fatigue.’ 
For materials, however, which have no drop of stress at yield, say hard drawn steel, 
the upper fatigue limit for pulsating stress may be less than the yield, and it is probable 
that stress concentrations may have a very marked effect. In another part of this 
report Professor Haigh describes experiments which show that for a sample of hard 
drawn steel the effect is very marked, though not quite to the extent suggested by the 
mathematical analysis. It is hoped that they will continue this work and test other 
steels, particularly those with high yield points. 
The use of a material with a drop of stress at yield appears to be essential for struc- 
tural work, and any methods of fairing holes which destroy this property, say by 
seriously overstraining the material near the hole, are to be strongly condemned. In 
the abstracts from current periodicals prepared by the Institution of Civil Engineers 
(January 1924) there is given an account by Fiichsel of the failure of a gusset plate due 
to the serious overstraining of the metal round the hole, presumably through excessive 
drawing by means of a drift. 
In the case of complete reversals of stress the upper fatigue limit will be below 
the yield of the material, and there is reason to suppose that the stress concen- 
