There are 6 rivets in single shear and 4 in double shear.

Total rivet section = 14 x 446.16 sq. inches.

265. Joints in a Girder Flange consisting of a Number of Plates. -When the flange of a girder consists of a number of plates of the same width and thickness, the most economical method of arranging the joints is to place them close together in steps, as shown in elevation in fig. 217. The distance apart of the joints should be such that the shearing

area of the rivets between each be not less than the net section of each plate.

If distance apart of joints,

=

Fig. 217.

then, in the case of three plates, the length of the cover-plate = 47.

If the joints be placed far apart, each one must be covered with a separate plate, and in such case the length of each cover 21, so that for the three joints the total length of cover-plates = 6 l.

=

Another advantage of placing the joints close together in large girders is the facility with which they may be disjointed, if it be necessary to transport them to their destination in several lengths; and the ease with which they can be afterwards jointed and rivetted together in situ.

II. PROPORTIONS OF EYES.

266. Method of Connecting Bars Together.-Bars of wrought iron or steel, when not joined by rivets, are usually connected together by bolts, pins, or cotters; and in order to do this the ends of the bars are frequently swelled out in the form of an eye. As the strength of the connection should at least be as great as that of the bar itself, it is important to know what are the best proportions to give to the eye and to the connecting pin; the latter usually being in double shear.

Examples of bars joined together in this manner are very numerous, such as the links in the chains of suspension bridges; the diagonal braces of trussed

girders; the tension members of

roof trusses, &c.

Fig. 218 represents the eye formed at the end of a flat bar, the thickness of the eye and that of the bar being the same.

Fig. 218.

d = diameter of the pin,

c = width of eye at each side of pin-hole.

If a stress be applied in the direction of the arrow, the lines of stress in the shank will run longitudinally, but towards the pin-hole they become diverted, so that the fibres immediately to the left of the pin are exposed to little or no stress. The fibres to the right of the pin-hole undergo various kinds of complex stresses, principally of a compressive and shearing nature.

267. Proportions of Eyes.-The best proportions to give to the eye cannot be determined by considerations of a merely theoretical nature, and we must look to the results of actual experiments for aid to guide us in fixing them. Fortunately, we have plenty of materials of this kind to guide us; the experiments made by Sir C. Fox, Brunel, Berkley, Shaler Smith, and others being very complete.

A flat eye, when exposed to stress, may fail in many ways; the following being the principal :

1. By tearing across the eye through c, c;

2. By tearing through the shoulders at r, r;

3. By the end of the link being torn through at a;

4. By the metal of the link being upset or crushed immediately behind the pin at e;

5. By the pin being bent or shorn.

These different modes of failure may be considered in detail:(1) On theoretical grounds, if the section of the eye across the pin-hole be equal to that of the bar, or if c+c=b, the eye in this direction ought to be as strong as the bar itself. Experiments made prove this to be incorrect, and in practice it is advisable to make this section at least 25 per cent. greater. From this it would appear that the stress on the fibres, at the sides of the link, are not uniform; probably the outside fibres are strained more than those near the pin, which would cause them to fail first. This difference of stress in the fibres will be greater the sharper the curve at the shoulders.

(2) The failure from the second cause is likely to occur when the curvature at the shoulder is so small as to prevent the lines of stress bending gradually round the eye. Mr. Berkley recommends that the radius of curvature of the shoulder r should not be less than b, and that the radius of curvature r1 of the neck should not be less than 1.5 b.

(3) The metal at the back of the pin may be exposed both to bending and shearing stresses; it, in fact, resembles a short

beam whose points of support are at c, c. It may fail by being shorn through, or by the tearing of the fibres on the outside. In order to resist the shearing action, theoretically, the section at a should be rather more than one-half that of the bar. In practice, however, the end of the link does not fail by shearing, but by the tearing of the fibres at the outer circumference. Mr. Brunel considers that the section through a should be about two-thirds that of the bar. This, however, is not sufficient in all cases. Mr. Berkley recommends that the section at a should be at least equal to that of the bar, and this is the safest rule to adopt.

(4) Failure by this means takes place when the diameter of the pin is so small that the bearing surface immediately behind it is too little to transmit the stress without crushing the fibres, and thus elongating the hole. Failure by this method rarely takes place directly, but the elongation of the hole causes the attenuation of the metal at the sides of the pin and brings about failure by the first method. Mr. Berkley recommends a diameter for the pin equal to three-fourths the width of the bar, and in practice this will be found safe.

(5) The pin may fail by shearing or bending when its diameter is too small. Even when the diameter is sufficiently large to resist shearing, the pin may fail by bending; this, however, may be provided against by keeping the links close together. The minimum diameter of the pin depends on the material used; if both link and pin be of wrought iron and the latter be in double shear, its sectional area, as determined from experiments, should be at least equal to two-thirds the area of the bar. If they are both made of mild steel the area of the pin should be greater.

It will be found, however, that in links of the usual proportions the diameter of the pin will be fixed by the rule given in No. 4; its diameter, as fixed by this rule, will generally be found quite sufficient to resist the shearing stress.

Mr. Berkley recommends the following minimum proportions for wrought-iron flat eye-bars :

268. Rules of American Engineers. The practice of American engineers is somewhat different to that adopted by the English

authorities already mentioned. Mr. Shaler Smith, an American authority, finds from his experiments that the best proportions for eye-bars depend to a certain extent on their method of manufacture.

The following table gives some of the results of Mr. Smith's experiments:

TABLE LXXXVIII.-PROPORTIONS OF AMERICAN EYE-BARS, AS DETERMINED BY MR. SHALER SMITH.

269. Gibs and Cotters.-Gibs and cotters are frequently used instead of bolts or pins for connecting the ends of tie rods. Their principal recommendation is that they afford means of slackening or tightening the rods, which is often an advantage, as in the case of the ties of roof trusses, &c. A cotter itself is merely a tapered bar, rectangular in cross-section, and usually made of wrought iron or steel. Fig. 219 shows the method of

connecting a bar to two plates by a simple cotter. The end of the bar is swelled out, and a slot cut in it; slots are also cut in the junction plates. When the stress on the bar acts in the direction of the arrow, the cotter bears against the plates at the surfaces a a, and against the bar at the surface b.

Fig. 219.

By the arrangement shown, it will be seen that the bar can be drawn towards the connecting plates as the cotter is driven in.

The sectional area taken through the slot in the bar should be at least 25 per cent. greater than the sectional area of the bar itself. In actual practice it is usual to make this excess of area somewhat more. The cotter being in double shear, the united area of both sections should never be less than 25 per cent. greater than the bar, and it is advisable to have the excess of area 50 per cent. The cotter should not be made too thin or it will crush the surfaces against which it bears.

270. Proportions of Cotters, &c. Suppose the bar C (fig. 219) has to transmit a safe working stress = P, it is required to determine a suitable diameter for the bar, and the best proportions for the eye, cotter, and connecting plates.

Let f safe tensile working stress on the material,

f safe shearing

fe safe compressive

d= diameter of the bar,

b= mean width of the cotter,

t = thickness of the cotter,

a= thickness of the side plates,

d side of the square into which the end of C is forged.

=

From this equation we can determine the diameter of the bar. In order to determine the size of the head, we get, by taking a section through the cotter hole

from which d1 may be found when t is fixed. This gives the theoretic size of the head; but, as already explained, the actual sectional area through the slot should be from 25 to 50 per cent. greater than that given by this rule.

For the cotter, we get

From this equation b and t may be found having fixed one of them.

As previously explained, 50 per cent. should be added to the theoretic dimension, as found by this rule.