Steel rivets, which have a tensile strength of 30 tons, have a shearing strength of about 20 tons. The safe working stress to allow for these rivets should not exceed 5 tons to the inch.

259. Strength of Lap-Joints.-A lap-joint, as shown in fig. 211, may fail in at least four different ways, when exposed to a direct pull :

(1) The rivet may be shorn, in which case the strength of the joint is measured by the shearing strength of the rivet.

Let d= diameter of the rivet in inches,

fits shearing strength per square inch of section.

Then if the rivet be the weak portion of the joint, the force necessary to tear the joint

asunder will be

P=7854 f,d2. (1).

(2) The joint may fail by the rivet crushing one or both of the plates by forcing itself into them.

Let t thickness of the

==

The force necessary to cause failure in this

P=td fe

From experiments made, the value of fe in this formula is very much greater than the ordinary crushing strength of the material; for wrought iron of ordinary quality f=40 tons, or about double the crushing strength of the material. This discrepancy is explained by the fact that in the rivetted plate the metal crushed is not an isolated piece, but is supported by the surrounding portion of the plate, and also by the head of the rivet.

(3) The joint may fail by the splitting of the end of the plate along the line EF. According to Mr. Browne,* the strength of the joint in this case will vary directly as the square of EF and the thickness of the plate, and inversely as the diameter of the rivet.

*Min. Inst. M. E., 1872.

Let EF-a, then the strength of the joint along EF

where Q is a constant.

From experiments made by Mr. Fairbairn he found for wrought

4. The joint may fail by one or both of the plates tearing across the line A C D B.

Let A CBD=b,

f= tensile strength of plate,

then strength of joint across A CDB=2bt f

(4).

A fifth way in which the joint may fail is mentioned by Mr. Browne. This occurs by the rivet forcing a piece out of the end of the plate, in which case the resistance against failure

=(CM+DN) xtxf.

where f, ultimate shearing strength of the material. Failure by this method very rarely happens.

(5),

Example 1.-Two flat bars of wrought iron each 3 inches wide by inch thick are lap-jointed by a single rivet 1 inch in diameter. If the centre of the rivet be 11⁄2 inches from the end of each bar, determine the tensile force necessary to break the joint in each of the five different ways above enumerated.

t = }, d = 1, ƒ,= 19 tons, f=40 tons, f, 18 tons.

P = required tensile force in tons.

1. From equation (1)—

P=·7854 × 19 × (1)2 = 15 tons,

which is the force necessary to shear the rivet.

2. From equation (2)—

P× 1 × 40 = 20 tons,

which is the force necessary to cripple the bars.

which is the force necessary to split the end of the bar.

4. From equation (4)—

P=2x1×× 18 18 tons,

which is the force necessary to tear the bar across the eye.

The tensile strength of the iron is supposed to be equal to 22 tons, but in this case 18 tons is sufficient to allow, as the fibres at one side of the hole may be strained to a greater extent than those at the other, whereby there is a tendency for the bar to be broken in detail.

5. From equation (5)—

P = (1+1) × 19 = 28.5 tons,

which is the force necessary to push out the iron at the end of the bar in the manner explained.

From the above it will be seen that the joint is fairly well proportioned, the rivet itself being, however, the weak part. It will also be seen that failure by the fifth method is not likely to occur. Indeed, in joints of this class this method of failure need not be taken into consideration.

260. Proportions of Joints. In order to determine the relative proportions of the various parts of a lap-joint connected by a single rivet, it will be necessary to compare the equations (1) to (5).

To arrive at the relative proportions of the diameter of the rivet and the thickness of the plate compare equations (1) and (2).

When the joint fails simultaneously from the shearing of the rivet and the crushing of the plate, we get

·7854 f,d2=tdfe

Putting 19 and f=40, we get

d
= 2·7,
t

which shows that with wrought-iron plates, connected by wrought-iron rivets, the diameter of the rivet should be between two and three times the thickness of the plates. The ordinary rule in boiler work is to make the diameter of the rivet twice the thickness of the plates.

M. Antoine gives the following empirical formula for the diameter of rivets as used in shipbuilding :

In order to determine the distance of the rivet from the end plate (a), or in other words to find the requisite amount of lap, we must equate (1) and (3), or—

that is, the distance of the edge of the rivet from the end of the plate should be rather less than the diameter of the rivet.

The ordinary rule in practice is to make this distance equal to the diameter of the rivet; the lap of the joint will then be three times the diameter of the rivet--that is, when the latter is double the thickness of the plate.

In order to determine the distance of the edge of the plate from the rivet, or when more than one rivet is used to determine the pitch of the rivets, we must compare equations (1) and (4). Equating these we get

For a lap-joint, therefore, with a single rivet, the width on each side of the rivet should be equal to the diameter of the rivet, and also when more than one rivet occurs transversely, the distance between their edges should be twice the diameter, or their pitch-i.e., their distance apart from centre to centreshould be equal to three times the diameter of the rivet.

261. Double-Rivetted Lap-Joints. In boiler work the following proportions for double-rivetted lap-joints with punched holes

The following are the proportions between the strength of the plate and single- and double-rivetted lap-joints :

Lap-joints are principally employed in boiler-making and shipbuilding; they are cheaper than butt-joints as only half the amount of punching or drilling is required, and they possess many advantages which will always render them desirable for this class of work.

In bridges, and structural work generally, lap-joints are not much used, and are not desirable; butt-joints with single or double cover-plates being almost invariably employed. When two plates are joined together by a lap-joint and exposed to a tensile stress, the direction of the stress in one plate is not exactly in a line with that in the other, but forms with it a couple which has a tendency to bend the joint. This tendency to bend does not exist, or only to a very small extent, when buttjoints are used.

a a1 e

When it becomes necessary to use a lap-joint to connect two plates in a structure, a very good form is that shown in fig. 212. In this arrangement each plate is practically weakened only to the extent of one hole. The full stress on each plate comes at the sections a b and c d respectively, and here the plates are only weakened to the extent of one hole. At the sections a1 b1 and c1 d1, where there are two holes, the stress on the plates is less than the total stress by the amount taken up by the end rivet in each case. At the section ef, where there are three holes, the stress on each plate is less than the total stress by the amount taken up by the three end rivets. In order to illustrate this, suppose each of the plates to be 8 inches wide and

Fig. 212.

=

3.625

inch thick, and to be joined together by nine 4-inch rivets, and suppose the tensile strength of the plates and the shearing strength of the rivets, each equal to 20 tons per square inch. The net section of each plate at ab or c d = 7·25 × 5 square inches. The plates will be on the point of yielding when the total pull 3.625 × 20: 72.5 tons. When this force is applied, the stress at the sections a1 b1 and c1 d1 of the back and

=

=