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MIL L. X. G. FILOX OX THP: ELASTIC EQUILIBRIUM OF 
§ 12. The Second Prohlem: Case of ci Cylinder under Pressure udiose Pads arc 
not allowed to expand. {First Method of Constraint.) 
Consider a cylinder (dg. 3) subjected to the following system of load :— 
(l.) There is no shear r: along the curved surface r — a. Over two rings of 
iaeadth e at tlie ends a radial pressure P is made to act, this pressure being so 
adjusted that there is ]io radial shift at the points A, B, C’, D ; the breadth e being- 
in the limit t(j be made indetinitely small. 
Fig. 3 
(2.) The plane ends AB, CD, are constrained to remain plane, and are subject to a 
total normal pressure TreUt^. 
I'he above would tit the case of a cylinder compressed between two rigid planes, 
into whicii shallow circular de})ressions had been cut, to fit the ends of the compressed 
cylinder and prevent them from expanding. 
If we return to tlie expressions for the stresses in the general case, (24), (25), (2G), 
and also to those for the di.splacements, we find that if w is to be constant for z = c 
he = riTT . 
= c, = c 
K, = E, = E = u 
(iV I — A.i) yh -|- 2C = 0.. . . . (5t)). 
Also this gives r: = 0 o\er the plane ends, so that we may suj)pose our rigid con¬ 
straining plane to be idso sinootli. 
