332 REPORTS ON THE STATE OF SCIENCE, ETC. 
difficult, and the figures found for the error, viz. between 10 and 20 per cent., must be 
regarded only as an estimate. ; 
Alternating Bending.—The specimen rotating (Wéhler). Any one point of the 
section has a cycle of stress and strain exactly the same as any other point at the same 
distance from the axis of the specimen. The calculation is founded on the data 
obtained by measuring the deflexion (under two-point loading) in the plane of the 
bending couple and also in a plane perpendicular thereto. The latter measurement 
gives the work done per cycle on the specimen, and this work is equated to the work 
done on the fibres which have a measured maximum amount of strain at theskin. The 
error entailed by the use of the usual formula for bending is not less, for the fatigue 
range of stress, than 8 per cent., and is probably more. Further experimental work 
on hollow specimens should determine the error within fairly narrow limits. A 
reduction of 8 per cent. on the ‘ calculated ’ stress brings the stress for the fatigue range 
nearly equal to the proportional elastic limit as observed on the rotating Wohler 
specimen. It is possible that the margin of error may depend on the diameter of the 
specimen ; such scale effect, if any, has not yet been investigated. 
REFERENCES, 
1 See 1923 Report, page 23, Professor B. P. Haigh on ‘ Thermodynamic Theory 
of Mechanical Fatigue.’ Also page 62. 
2 * Distribution of Stress in round bars under alternating torsion or bending,’ 
pp. 42-43. Report of Complex Stress Committee, British Association, 1923. 
3 Loc. cit. p. 54. 
VI. The Effects of Inaccuracy of Axial Loading. 
By Professor ANDREW RoseErtson, D.Sc. 
In any experimental work on the behaviour of a material under a particular type 
of stress, it is always necessary to take precautions to ensure that the desired stress 
distribution does exist in the portion of the material under investigation. The ordinary 
methods of gripping specimens even in such a relatively simple case as a tension test 
do not always secure that the stress across the sectionis uniform. If to this uncertainty 
is added a defective method of measuring the strain, it is not surprising that there is 
oftentimes some uncertainty about the principal elastic properties of materials. It 
is on record that in one series of tests the value of E for a particular steel was given as 
varying from 9-5 x 10® to 65-5 x 108 Ibs. per sq. in. It is the object of this note to 
consider briefly the effects of the inaccuracy of loading produced by the usual gripping 
methods, and to indicate devices which materially diminish the errors and so permit of 
a more accurate determination of the physical properties of the material. The analysis 
of the variation of stress produced by an eccentric load is of course well known and 
does not need to be stated here. It is sufficient to remark that with a round specimen 
of radius r if the eccentricity of the resultant load at any section is ar, the average 
stress p, required to produce a stress of f, is ae , 1.e. if the eccentricity is 1 per 
cent. of the radius, the load p will be 3-9 per cent. less than would be the case with no 
eccentricity. 
Several investigations have been made upon the variation of the strain in a specimen 
when loaded in tension through the usual wedge or screw grips. Perhaps the most 
extensive is that of Dr. Scoble (Complex Stress Committee, B.A., 1919), who measured 
the strain at four places round the specimen. The observations were all very irregular, 
indicating a very unequal stress distribution, but on taking the mean strain the loads 
and corresponding strains gave a straight line and thus enabled a value for E to be 
determined. Using wedge grips the ratio of maximum to mean strain varied from 
1-62 to 1°016, whilst with specimens having screwed ends the ratio varied from 1°39 to 
1-062. These observations indicate very considerable differences in the stress 
distribution, and hence one would expect to get values of the elastic limit smaller than 
the real limit of the material. 
In order to diminish this inaccuracy of loading, the author, in conjunction with 
Mr. Gilbert Cook (now Professor Cook), constructed the axial loading shackles described 
in ‘Engineering,’ December 15th, 1911. The construction will be made quite clear by 
the drawing given in fig. 13, which represents a set. which were used to a considerable 
