Page:Encyclopædia Britannica, Ninth Edition, v. 13.djvu/766

 732 JOINTS Wrought iron and mild steel are above all other metals suitable for tension joints where there is not continuous rapid motion. Where such motion occurs, a layer, or, as it is technically termed, a &quot;bush,&quot; of brass is inserted underneath the iron. The joint then possesses the high strength of a wrought iron one and at the same time the good frictional qualities of a brass surface. Where the running speed is high and the intensity of pressure can be made small by adopting large bearing surfaces, cast iron is now increasingly preferred for pressure joints. But when, owing to want of space or for other reasons, the bearing surface cannot be made large in proportion to the thrust to be transmitted, gun-metal, i.e., the toughest quality of brass, should be used if the speed be high, and steel if the speed be small. Leakage past moving metal joints can be prevented by cutting the surfaces very accurately to fit each other. Steam-engine slide-valves and their seats, and piston &quot; packing-rings &quot; and the cylinders they work to and fro in, may be cited as examples. A subsidiary compressible &quot;packing&quot; is in other situations employed, an instance of which may be seen in the &quot; stuffing boxes &quot; which prevent the escape of steam from steam-engine cylinders through the piston-rod hole in the cylinder cover. Fixed metal joints are made fluid tight (a) by caulking a rivetted joint, i.e., by hammering in the edge of the metal with a square-edged chisel (the tighter the joint requires to be against leakage the closer must be the spacing of the rivets compare the rivet-spacing in bridge, ship, and boiler-plate joints) ; (6) by the insertion between the surfaces of a layer of one or other of various kinds of cement, the layer being thick or thin according to circum stances ; (c) by the insertion of a layer of soft solid substance called &quot;packing&quot; or &quot;insertion.&quot; A special kind of indiarubber and canvas sheet is prepared for this purpose. A very effective species of &quot; insertion &quot; is thin copper gauze. Sometimes a single round of thick copper wire laid in opposite grooves cut on joint-surfaces serves the purpose. The Principles of the Strength of Joints. The conditions of strength of cemented and glued joints are too obvious to require description. It may, however, be mentioned that in most cases the joint is stronger the thinner the layer of cementing material interposed between the surfaces. Nearly all other joints are formed by cutting one or more holes in the ends of the pieces to be joined, and inserting in these holes a corresponding number of pins. The word &quot; pin &quot; is technically restricted to mean a cylindrical pin in a movable joint. The word &quot;bolt&quot; is used when the cylindrical pin is screwed up tight with a nut so as to be immovable. When the pin is not screwed, but is fastened by being beaten down on either end, it is called a &quot; rivet.&quot; The pin is sometimes rectangular in section, and tapered or parallel lengthwise. &quot; Gibs &quot; and &quot; cottars &quot; are examples of the latter. It is very rarely the case that fixed joints have their pins subject to simple compression in the direc tion of their length. They are, however, frequently subject to simple tension in that direction. A good example is the joint between a steam cylinder and its cover. Here the bolts have to resist the whole thrust of the steam, and at the same time to keep the joint steam-tight. If D be the cylinder diameter, t the thickness of the flange of the cover, and n the number of bolts used, it can be shown that the amount the ilange rises between the bolts by bending is proportional to, where p is the steam pressure per unit area. If the same n*t s degree of tightness be desired for all sizes of cylinders, this deflexion should be the same for all. The spacing of the bolts is proportiona to, and, therefore, we should have the spacing ex flp~l. I then the total bolt area is made proportional to the total stean pressure, it would follow that the diameter of bolt oc p$$D*. Again, if t were reckoned in accordance with the shearing force of of the cylinder, i.e., txpD, we would have spacing oc p^D*, and bolt diam. oc ^D^. For reasons connected with technical difficulties in the foundry, is made larger in proportion to D than this rule indicates for the mailer sizes of cylinders ; and, therefore, the spacing and the bolt diameter are not made to increase quite so rapidly as the | and powers of D. No moving joints have their pins exposed to simple tress on sections transverse to the pins axes. The pins of such joints have these transverse sections subjected to shearing and bending stresses, and the sections parallel to the pin axes to compressive stress. The simplest case by which the subject can be illustrated is that in which a cylindrical pin passes through the ends of two links one forked, and the other simple and lying between the branches of the fork of the other, Let the accompanying diagram represent the end of the unforked link. The width of the link parallel to CC is taken as unity, and the letters on the figure indicate the ratios of the respective dimen sions to this width. Let b represent the ratio of the thickness, perpendicular to the paper, of the &quot; eye &quot; to the thickness in the same direction of the main body of the link at D. Let also /be the in tensity of uniform tensive stress on the section at D. Evidently no pres sure comes on the under side of the pin below CC. The whole pull at D is passed round half C- on each side of the pin, and is delivered to the upper side of the pin, on which it produces com pression. Since the side sections t, through which the pull passes, lie out of the direct line of that pull, the stress is much higher on the parts of these sections towards the centre line DD than on those further off. The lines of force crowd as close as possible together near the surface of the pin, i.e., towards the main line DD of the pull. In other words, the inequality of_ stress is occasioned by the bending moments due to the centre of force not passing through the centres of gravity of area of the sections. The inequality begins at the root of the widening out of the link to form the eye, and reaches its maximum at CC 7. The bending moment at CC and the stress caused by it at the edge of the section can be found by the help of the ordinary theory of elasticity. The best method of doing so is to calculate the amount by which the portion of the eye below CC is bent by the forces applied to it. In the equations the bending moment at CC is inserted as an unknown quantity. The section on DD remaining unmoved, each element of the linear deflexion is resolved parallel to CC, and the integral from DD up to CC of all these components parallel to CC is equated to zero, the resultant deflexion at C in the direction of CC being evidently nil. This equation gives value of the bending moment at CC, and from it the correspond stress is obtained. If the section at D be rectangular, as also that at CC, then the average tensive stress on t is and the extra stress caused at the edge of the section by the bend ing moment is 1 The total maximum stress is, therefore, This gives the ratio of the maximum tension at the side of the eye
 * he steam on the circular section of the cover at the circumference