52 



NATURE 



[September io, 1914 



number of cases have been examined, since even the j 

 simplest problems have proved somewhat difficult, 

 and much time and labour have been spent in per- 

 fecting optical and mechanical appliances to suit the 

 special conditions required for investigations on trans- 

 parent models. A simple example of a case easily 

 examined and of practical importance is that of a 

 tension member subjected to an eccentric load. The 

 optical effects here show a linear distribution of 

 stress due to the combination of direct pull and bend- 

 ing, while the neutral axis moves towards the tension 

 side as the stress increases. Not only can these effects 

 be measured, but if the specimen begins to fail 

 some indication is obtained of the way in which the 

 stress distribution is changed to meet the new con- 

 ditions, and there is found a tendency to an equalisa- 

 tion of the maximum stress at the boundary, although 

 at present the form of the curve of distribution beyond 

 the elastic limit is largely conjectural. 



A case like that of a very short member subjected 

 to direct compression is also not without interest, 

 partly because it reveals unexpected difficulties. In 

 the first place it is not easy to apply a pure compres- 

 sion stress, and if the surfaces in contact are not of 

 the same materials it appears to be practically impos- 

 sible, since the lateral changes are unlike, and shear 

 stress is therefore produced at the plane of the sur- 

 faces in contact. In a short member this shear has 

 a very important influence, and by interposing a thin 

 lajer of a material, such as india-rubber, between 

 the pressure plates and the short transparent block, 

 the artificial shear effect produced by the india-rubber 

 is easily shown to influence the distribution through- 

 out, and to increase the stress in a very marked way. 

 Experiments on transparent materials show that the 

 increase of stress may be twenty per cent, or even 

 more. Such an effect is known to take place when 

 cubes of stone are crushed between lead plates, and 

 optical investigations on models have enabled a 

 quantitative measure of the effect to be ascertained 

 in this and other cases, thereby confirming the 

 theoretical investigations of Filon on the distribution 

 of stress in such members under various practical 

 systems of loading. 



The local effects produced near the points of applica- 

 tion of a load are usually of considerable importance, 

 and their influence on the stress distribution in beams 

 has been examined by Carus- Wilson. 



The stress effects produced by discontinuities in 

 materials is also of considerable interest, and the 

 cases arising from the necessities of construction are 

 infinite in their variety. 



The practical importance of an accurate knowledge 

 of the change in stress distribution produced by 

 changes of section in a member is so thoroughly ap- 

 preciated that it needs no insistence, and it has re- 

 ceived much attention from a mathematical point of 

 view. Thus the local effect of a spherical cavity 

 in a member subjected to uniform tension or com- 

 pression load has been shown by Love to double the 

 intensity very nearlv, while Kirsch has shown that a 

 small cylindrical hole in a tension member trebles the 

 stress intensity. If the hole is elliptical the increase 

 of stress may be still greater, and Inglis has shown, 

 among other interesting cases, thai if the minor axis 

 of the ellipse is parallel to the direction of the applied 

 load in a tension member, the stress intensity is in- 

 creased bv an amount measured by twice the ratio 

 of the axis of the ellipse. 



A crack, considered as the limiting case of an 

 elliptical hole, is thus seen to give extremely great 

 stresses at the ends, tending towards infinite values 

 for an extremely fine crack. 



Optical experiments afford an independent means 



NO. 2341, VOL. 94] 



of examining the alterations of stress intensity pro- 

 duced by discontinuities, and the results are found 

 to agree remarkably well with those obtained from 

 the theory of elasticity. The stress at the boundary 

 of a small cylindrical hole in a plate has been found 

 to be almost exactly three times the stress in the full 

 plate, and the effects of holes comparable with the 

 width of the tension member have also been examined 

 in some detail. 



In the case of a rivet just filling the hole and exert- 

 ing no tangential effect at the boundary there is a 

 lessened tension stress across the minimum section at 

 the boundary hole, accompanied by a marked radial 

 tension. Ihese effects have been recently confirmed 

 in a mathematical discussion by Suyehiro. Other 

 cases give satisfactory agreement with calculation, 

 and we may therefore feel some confidence that ex- 

 perimental investigation will prove useful in some of 

 the very complicated cases arising out of engineering , 

 practice where analysis is difficult, if not impossible. 



The effects of overstress in materials may also be 

 examined by optical means, and although the laws 

 relating to stress distribution in overstressed trans- 

 parent material are not known, the general effects 

 observed in simple cases are fairly evident. If, for 

 example, a tension member of glass is stressed, there 

 is no ductile yielding of the material, and the stress 

 will therefore rise very rapidly at the boundary of a 

 small hole, and fracture will therefore occur with a 

 fnoderate load. If, however, a ductile transparent 

 material is employed, and the material shows signs 

 of failure at the hole, the breakdown of the structure 

 spreads outwards as the load is increased, until we 

 may have a condition in which within the elastic 

 limit the curve of stress intensitj' at the minimum 

 section accords with calculation, but at the over- 

 stressed part the stress tends to equalise, and the curve 

 of intensity tends to become horizontal near the hole. 

 The mean value of this part of the stress distribution 

 may be inferred from the difference between the total 

 load and the measured values below the region of 

 failure ; but the true distribution of the overstress has 

 not been accurately determined, so that the shape of 

 this peak is largely conjectural. 



The effects of groups of rivets such as occur in 

 bridges, boilers, and structural members of all kinds, 

 afford ample scope for further inquiry; but before 

 more exact knowledge can be gained of the condition 

 of stress in a complicated riveted joint it appears 

 necessary to examine thoroughly the very simple 

 cases. 



Mr. Scoble and I have examined the case of the 

 load applied by one rivet to a plate with various 

 amounts of overlap, and the stresses around the rivet 

 holes had been measured with fair accuracy. 



Other interesting cases of discontinuity in structure 

 are afforded by the engine hatchways, gun-turrets, 

 funnel openings, and the like, in ships' decks, and 

 some progress in this direction has been made by 

 experiments on model decks, subjected to loads like 

 those produced when a vessel meets the waves due 

 to a head sea. 



Even if the utility of transparent models is left out 

 of account, it is generally acknowledged that many 

 engineering problems are often simplified by the use 

 of models of machines and structures on a small 

 scale, W'hen circumstances forbid experimental ex- 

 amination of the actual work. No defence of their 

 use is, I think, necessary, since the employment of 

 models is a characteristic feature of British methods, 

 not limited to engineers. Kelvin did not disdain 

 their use, and his successors, who have done so much 

 to advance knowledge of the aether and the atomic 

 dust, have freely employed their great ingenuity in 



