Page:Encyclopædia Britannica, Ninth Edition, v. 13.djvu/767

J I J O I 733 to the uniform tension (/) on the main body of the link at D. If the section at D be circular while t remains rectangular, the corre sponding ratio is a little more than ^ TT, or about of the above. If it is desired that this maximum should not exceed/, we obtain a relation between the ratios d, t, and b by putting/" +f f. The following table exhibits the results of this calculation for rectan gular section at D : t = i ft 1 I 1 d=i and 6 = 3-1 2-5 2 1-7 1-5 d=% b = 4 3 24 2 1-7 cl=l ,, b = 4 9 3-, 2-8 2-3 1:9 For circular section at D, b is about f of these values. Although the values of t and d that are commonly used all fall considerably within the limits of the above tables, the values of b usually found in practice are much less than those shown above. This means that the eyes of links as commonly proportioned are much more severely stressed than is the main body of the link. In working joints the frictional resistance to rotation throws more than half the main pull on one side of the eye, and this side is therefore still more severely stressed than is indicated by the above equations. The stresses on the portion of the eye lying above CC are com plicated by the combination with the direct pull already mentioned of the pressure of the upper surface of the pin. This latter is normal at each point if the surface be smooth and the joint a motionless one. It increases from zero at CC to a maximum at the line DD . At this point the intensity of the surface pressure is, according to an approximate theoretic estimate, about , or 1J 7T times greater than if the whole pull were evenly distributed over the projection on CC of the upper half surface of the pin. It has often been fallaciously imagined that the central section t l is exposed to severe shearing stress. From the symmetry of the case, however, it is evident that on this section the shear is zero. The maximum shear occurs on a section nearly parallel to DD , and somewhat less than d distant from DD . The exact position of this section of maximum shear depends upon the dimension-ratio t lt which is usually made considerably greater than t. The pin surface pressure has transverse components parallel to CC , which produce tension and a bending moment on the section ^. A theoretical approximation to this bursting pressure is , or about 7T ^, of the whole pull exerted by the link, and the line of the resultant (parallel to CC ) is situated %d distant from the centre of the pin. A small portion of this is borne by the central section on DD of the main part of the link below CC , but by far the larger part is borne by the section marked t 1 . If it were wholly borne by that section, the average tension on ^ would, for a circular section at D, be -J , and the extra stress produced by this bending moment 4^6 would be -J ( 3 H -- ) . Other bending moments, however, are . thrown on this section due to first, the resultant of the pin-surface- 2 pressure-components parallel to DD , which lies at t d , or about O7T %d, from the line DD ; and, second, the stress at the section CG . Adding all these together, there is obtained an approximation to the actual tension parallel to CC on the lower edge of the section t 1} namely, The shearing and bending stresses upon the pin itself depend upon whether one of the links is forked or both are simple ; and also greatly upon the exactitude with which the pin fits the holes. When the link exerts a thrust instead of a pull through the joint, a similar investigation of the state of stress may be made. A couple of plates joined together by a single row of rivets may, so far as concerns the sections lying between the rivets, be looked upon as a number of flat links laid side by side with their eyes of equal width with the body of the link. We may therefore apply the first of the above equations forf +f" to find the stress close to the rivets on the section coinciding with the line of the rivets. To adapt the formula to this case, it is only necessary to put 6 = 1 and t = |(1 -d). The formula thus derived, however, gives results probably considerably higher than those actually occurring, because of the strips into which the plate has been supposed to be divided, acting on each other in such a way as to produce bending moments partly neutralizing the above increase of stress, The strip of metal between the rivets and the edge of the plate i.s iu the condition of a continuous beam supported oy the rivets. The maximum moment occurs just over the rivets, and is nearly the same as if the load were uniformly distributed over the length of the beam. If t be the ratio to the rivet-spacing of the distance of the edge of the plate to the rivet hole, the supposition of uniformity of distribution of load gives the equation / =/_!_ for 2t-^ the maximum stress on a section perpendicular to the plate edge. To make/ =/, it is necessary to make ^= A,/0 5 = 07. The edge of the plate will then be amply strong enough to resist the greatest shear to which it is anywhere exposed. When there are two or more rows of rivets the investigation of the stress is quite similar to the above. In joints where the movement is rapid and continuous, the size of the pin is determined by considerations of durability against wear. The metal wears rapidly if the bearing surfaces are not well lubricated. The lubricant is pressed out from between these surfaces if the intensity of pressure exceeds a limit determined by the character of the lubricant. The size of the pin must be sufficient to prevent this limiting pressure being reached. Even before the oil is wholly squeezed out the friction becomes so great Us to heat the metal surfaces to a high temperature, which hastens the evaporation of the remaining oil. In order to ensure that the temperature may be kept low by the con tinuous dissipation of the heat generated, some engineers design the bearing surface in proportion to the product of the pressure and the speed, so as to allow a certain area of " conducting surface" for each unit of heat generated per second /T? TT ^ "^ JOINT STOCK COMPANIES. See COMPANY, vol. vi. p. 221. JOINVILLE, JEAN DE (1224-1319), was the second great writer of history in Old French, and in a manner occupies the interval between Villehardouin and Froissart. From the point of view of literary history there are numerous minor chroniclers who fill up the gaps, but no one of them has the idiosyncrasy which distinguishes these three writers, and for general purposes it may be said that they complete the series of historians illustrating, as no series in any other country or language illustrates, the three periods of the Middle Ages adolescence, complete manhood, and decadence. Joinville was born in 1224 of a good family of the province of Champagne, allied to many distinguished houses in the east of France and connected by marriage with the emperor Frederick II. The property of the Joinvilles came, curiously enough, like that of Comines, the fourth great historian of old France, into the hands of the Orleans family, and the castle, which overhung the Marne, was sold in 1791 for purposes of demolition. The provincial court of the counts of Champagne had long been a distinguished one, and the action of Thibaut the poet, together with the neighbourhood of the district to Paris, made the province less rebellious than most of the great feudal divisions of France to the royal authority. Joinville s first appearance at the king s court was in 1241, when he performed the functions of carver for his feudal superior on the occasion of the knighting of Louis IX. s younger brother Alphonse. Seven years afterwards, when he was four and twenty, he took the cross, thereby giving St Louis a valuable follower, and supplying himself with the occasion of an eternal memory. His family -had been persistent crusaders for several generations. The crusade, however, in which he distinguished himself equally by wisdom and prowess, taught his practical spirit several lessons. He returned with the king in 1254. But, though his reverence for the personal character of his prince seems to have known no bounds, he had probably gauged accur ately enough the strategic faculties of the saintly king, and he certainly had imbibed the spirit of the dictum that a man s first duties are those to his own house. He was in the intervals of his residence on his own fief a constant attendant on the court, but he declined to accompany the