portion of the thread plus the clearance, so that d2 may equal

Examples of union screws, such as are generally used in bridge-work, are given on Plate II.

Jib-and-Cotter Joints.-The tie-rod of an iron roof is frequently attached to the principal, and to the shoe at the abutments, by means of a gib-and-cotter joint. Figs. 257 and 258 show this kind of joint. The outside of the gib is made parallel to the outside of the cotter, and the taper of the cotter is made from

FIG. 257.

cotter y

11/4-3/4 y

FIG. 258.

1 in 24 to 1 in 48. The heads of the gib prevent any spread of the side plates. The shearing strength of the gib and cotter at its central section must equal the tensile strength of the main tie-rod, and the pressure on the bearing area must not be excessive. Let t1 = the thickness of the side plates, and t the thickness of the rectangular end of the rod, taken as equal to the diameter of the rod; let c = the breadth of the rectangular end of the rod, a the length of the gib and cotter at the central section, ta the thickness.

tз =

=

Hence, if t2t1, the tensile and bearing strengths of the side plates will equal those of the rectangular end of the rod, and if we take 5 tons as the intensity of working stress in the

tie-rod, 4 tons as the safe shearing stress of the gib and cotter, and 8 tons as the safe intensity of pressure on the bearing area, then, since the gib and cotter are in double shear and must therefore shear at two sections at the same time

If t is known, a can be found from the above equation. Let

d 2 inches, then the safe stress on the tie-rod is

=

Hence if the gib and cotter are made 1 inch thick, the pressure will not be excessive.

To find the breadth c, so that the sectional area shall be the same as the tie-rod after deducting for the hole

It is desirable to have a margin here for possible inaccuracy

in forging, hence c should be made 3 inches.

The depth e in Fig. 257 must be sufficient to avoid shearing a piece out the width of the cotter.

Drilled and Punched Holes (Riveting).—Although punching is largely used for rivet-holes, it is objectionable for the following

reasons:

The spacing of the holes is not done so accurately as with drilling, and when two or more plates are used, as in the flanges of a girder, the holes frequently overlap, and require to be rhymered before the rivets can be inserted. This inequality in the spacing is partly due to the stretching of the plate in the process of punching, and it increases with the length of the bar or plate, also with the ductility of the material; it is most decided in curved girders. As a consequence of the unequal spacing, it is practically impossible to ensure closely butted joints with punched work. Another objection to punching is that the material round the hole is injured by the plastic flow of the metal under the pressure of the punch; in general the harder the material the greater the injury from this cause, but steel is injured by punching more than iron, and should only be used in thin plates. This injury may be removed by drilling or rhymering out the hole generally to about of an inch in diameter, and to some extent by annealing. The method of driving in a conical pin, known as drifting, should never be allowed, as it causes considerable damage to the material. For ordinary wrought-iron girder-work with not more than two flange plates, punching is good enough if the work is done properly, but when several plates are used in bridge-work the holes should be drilled, as it is almost impossible to ensure accurate work of this class with punching. Drilling the rivetholes by means of multiple drilling-machines ensures accurate spacing and avoids the injury to the material round the hole as in punching; the sharp edge, however, left by the drill should be rounded off, as it facilitates the shearing of the rivet.

Machine-riveting, such as by means of hydraulic pressure, is much superior to hand-riveting, as the plates are brought in closer contact and the rivets are made to fill the holes more completely; moreover, the pressure exerted upon the rivets is under control, and may be regulated to any extent. Steel rivets require greater care in closing by hand than iron rivets, as they are more liable to be injured if hammered at a dull red heat. With machine-riveting the plates should be well bolted together,

or the metal will be squeezed out between the plates, forming collars, and it is generally very difficult to cut out a rivet closed by hydraulic machinery.

In both hand and machine riveting the contraction of the rivet longitudinally in cooling causes it to exert a pressure on the plates like a clamp, and with accurately drilled holes and hydraulic riveting the shearing resistance of the rivets may never be developed under the ordinary working stress in the structure; but the amount of frictional resistance due to this cause is uncertain, and may be reduced by vibrations. Again, if the elastic limit of the material of the rivet is exceeded, the grip upon the plates must gradually diminish; it is, therefore, in general neglected in designing riveted joints. Machineriveting is used more in the bridge yard than in the jointing of the various pieces during erection, where it would be of the greatest service, but it has not generally been found convenient to use portable riveting-machines for this purpose, although they will probably be used more extensively in the future. When a bridge or girder is finished, there will generally be a certain proportion of loose rivets, which, if decidedly loose, should be cut out and replaced with well-fitting rivets. Loose rivets may be easily detected by tapping the rivet on one side with a small hammer and holding the finger on the other, but apparently tight rivets may be rendered loose by too frequent tapping, and absolute tightness cannot be expected from the nature of the process.

In designing riveted joints it is generally assumed that the size of the finished rivet is the same as that figured on the drawings. Sometimes, however, the nominal size of the rivet is 32 of an inch smaller than the actual size before it is closed, and if the holes are drilled, they are usually made the correct size; so that there is no practical difference in the figured from the actual sizes, excepting that no rivet can completely fill the hole if put in hot, in consequence of the lateral contraction in cooling. In punched work the holes are generally from 10 to 20 per cent. larger than the nominal sizes of the rivets, and the shearing resistance of the rivets in the joint is consequently always in excess of that calculated, but, since the stresses are not likely to be so well distributed in punched as in drilled work, this excess may be neglected.

Some engineers specify that the rivets shall be the actual

sizes figured on the drawings before being inserted in the work, in which case the finished size is of an inch larger, giving an excess in both drilled and punched work. It will be assumed in the following calculations that the rivets are of the actual sizes figured, which appears to be the general practice.

Joints in Flange Plates and Webs of Girders.-Figs. 259 and 260 represent the methods commonly adopted for covering the joints in the flanges and webs of girders. In each case the total

shearing resistance of the rivets on one side of the joint should be at least equal to the tensile resistance of the net section of the plate through the rivet-holes; or, in other words, the total shearing resistance of the rivets on one side of the joint should not be less than the stress developed at the joint. It is a good rule to make the strength of the rivets about 10 per cent. greater than that of the net section of the plate, as, from the nature of the process of riveting, the stress is not often uniformly distributed over the rivets, some being more severely stressed than others. In Fig. 259 there is a cover-plate on each side of the joint, and the rivets are in double shear, as they must shear at two sections at the same time. In Fig. 260 the cover-plate is on one side only, and the rivets can shear at only one section, consequently the rivets in double shear ought to be twice as strong as those in single shear. Again, in single shear the material is

P