CIKCULAR CYLINDERS UNDER CERTAIN 
PRACTICAL SYSTEMS OF LOAD. 
149 
ends. It is in equilibrium under the stresses, radial and tangential, between the 
inner core and the hollow cylinder produced by the revolution of ABDC. 
Fig. 1. 
But what are these radial and tangential stresses ? If we consider tlje etjuililirium 
of the outer holloAv cylinder only, we see that th.e resultant of the stresses across 
AB, A'B' must exactly lialance the }mll S, however applied. The radial stress will 
probably he small, as it has no external traction to balance, ami the longitudinal 
shears are therefore ec^uivalent to 8. Thus tlie thin cylinder inside is really 
stretched, not liy normal traction over the flat ends, hut liy longitudinal shears over 
tlie curved surface, and a careful investigation will show that, in every practical case, 
extension is obtained by the application of an axial shear to the curved surface of the 
cylinder, never of tractions to the flat ends. The general eftects of such a distribution 
appear, therefore, of great })ractical interest. 
* 
The second problem discussed is that ot a cylinder of moderate length, which is 
com|)ressed l)etween two i-ough rigid planes in such a way tliat the terminal cross- 
sections are constrained to remain plane, hut are not allowed to expand, their 
perimeter being kept tixed. By adding a suitable uniforni distribution of pressure to 
a load system of this type, we can olflain the solution for a cylinder constrained in 
such a way that its ends expand by a definite amount. These two problems are of 
inqjortance witli reference to the behaviour of a block of stone or masonry when 
tested between millboard or metal planes, which practically liinder the block from 
expanding, and when tested between sheets of lead, wliich, on the other hand, favour 
the expansion of the block. The widely divergent results obtained for tlie strength 
of the same material when tested by these two methods liave troubled many 
elastlcians. Unwix (‘Testing of Materials of Comstruction’) is of opinion that the 
results obtained wlieii sheet lead is used are unreliable; whereas Professor Perry, in 
his ‘ Applied Mechanics,’ states that the true strength of the material is the one 
given h}" the lead experiments, and should he usually taken as lialf the published 
streiiP'th. 
O 
Finally, the third problem treated is that of a cylinder sulijected to transverse 
shears over tlie parts of the curved surface near the ends, these shears being 
equivalent to a torsion couple. This is i'eally the analogue, for torsion, of the first 
