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Downloaded from MARCH 1921. CONTACT PRESSURES AND STRESSES. 367The stress function x = c . r 6 sin 6 is a solution of the general This is substantially found to be the case. equation ' = o (1) for plane stress, and from it we obtain : rl 6 . (a) at The University of Auckland Library on June 5, 2016 pme.sagepub.com Downloaded from bfARCH 1091. CONTACT PRESSURE8 AND STRE8SES. 369 rr = a p 1. = a constant = c,. r Ro Downloaded from P m = o , S r 8 = o and 388 = -2 c x = a constant of value sayp.Also, as can be easily verified, there is no stress over the rest Hence the stress function of the boundary, while at infinity all stress vanishes. (7)corresponds to the case of a normal pressure uniformly applied to a limited portion of the plane boundary of a semi-infinite plate.The stress at any point C having co-ordinates T~, el, r,, O, , with reference to the origins A, B, is obtainable by integrating the effect 'of all the elemental loads on the boundary A B. At any point D the load intensityp on an element dz of the boundary gives a radial stress at C of where r,e are the co-ordinates of C with reference to D as origin.As will appear immediately, it is convenient to reckon the stress produced at C with reference to an origin D (r, +) having a vector C D bisecting the angle A C B.The normal, tangential, and shear stresses at C, due t o the distributed load pax, are then

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