frictional resistance of the plates, supposing them to be well flattened so as to bear evenly upon each other, would be 1.5 tons per inch of rivet area.

In Fig. 63 are shown examples of joints used in different parts of iron roofs. A is the connection of a tee iron strut with a rafter by means

A

of two joint plates laid

K

one on each side of

the web of the strut, and having the vertical limb of the rafter between them. B shows another joint of this sort, but with the addition of the upper forked end of a sus

pension-rod, e, which embraces the joint plates, and one bolt fastens all together. fhg is the joint at the top of the roof where the two principal rafters meet. Two plates are put one on each side of the vertical limbs of the rafters, and riveted

through as shown, and also carry between them the eye of a suspension-rod, i, where such a rod occurs in the construction, this rod hanging on a bolt as shown.

N is one of the lower joints, being that at the centre; r is the central suspension or king rod; o and p are two tee iron struts, of which the ends of the tables are turned up to a horizontal position, and drilled to admit the screwed

end of the rod r, which also passes through a hole in the main tie q of the roof, all these elements being fastened and held together by the nuts s and t.

K illustrates the general form of an eye at the end of a rod, and M the screw at the other end, which is to be cut on a part of greater diameter than the rest of the bar, so that the diameter at the base of the thread shall not be less than that of the body of the rod.

Between a nut and the surface upon which it presses should be interposed a metal ring or washer on which the nut will bear, and which will prevent the nut from cutting into the element beneath when it is being tightened up.

It may here be observed that where punching without subsequent drilling out of the holes is the mode of manufacture adopted, spiral punches should be used, as it is found that from their comparatively gradual action the general injury done to the metal is comparatively trivial : they have far more of a cutting action than the ordinary flat punches, and indeed it is as unreasonable to make the cutting edge of a punch horizontal as it is that of a shear, and no practical man would think of bringing the whole length of a shearing edge into action at once. The violent commotion caused amongst the particles of the iron by the flat punch is evident from its texture in the neighbourhood of the punched hole being frequently changed from fibrous to semi-crystalline.

In the connections made with cast iron by means of bolts passing through lugs very great care is called for in the execution of the castings, in order that the lugs may be perfectly sound and not cracked in the re-entering angle, which is apt to occur if the moulds are opened too soon. In all elements of this description the holes should be very carefully drilled to template (or pattern), for cast iron is too rigid to be wrenched into place as is occasionally, though improperly, done with wrought iron; hence, if the

bolt holes do not fit, one of them will be enlarged to let the bolt in, with the result generally of rendering that bolt useless.

In cast-iron piers braced with bars pockets may be formed to receive the ends of the bars, but in these cases the pockets should be made without a bottom; there should be a clear passage through for the escape of any water that might otherwise accumulate, for if not, the water may accumulate and freeze, and by its expansion in so doing cause the rupture of the pocket; this has been known to occur, and is of course attended by great trouble and expense.

The student must be cautioned against putting in joint plates where they are not required, for in such localities harm may result from their presence. For instance, if there be a number of single spans succeeding each other, each span being designed as a single girder; if then by a joint plate it is connected with those at each end, it becomes more or less a girder fixed at the ends instead of freely supported there, and thus the distribution of the stresses throughout the structure will be altered, and therefore will not be such as have been provided for in the design.

It is, as far as manufacture is concerned, very important for the supervising engineer to see that all the connections made during the erection of a structure are properly disposed and adjusted, for it sometimes happens that by ignorance or want of thought on the part of a workman a properly designed work is very unduly strained, either from mode of lifting during erection, or from the condition in which it is left when that process is complete.

CHAPTER XI.

COMBINATIONS OF GIRDERS.

ALL structures of magnitude carried by girders will consist of an aggregation of these elementary parts, but the term "combination" is here applied to indicate such an arrangement of the girders that they assist each other, or by their connection relieve or modify the strains upon each other. An ordinary bridge consisting of main and cross girders will be a simple aggregation of girders; the cross girders. carry the roadway, and are in turn carried bodily by the main girders; the latter form the supports for the former, but in no way reduce or modify the strains upon them.

If a load is equally distributed over a number of girders identical in construction, they will all deflect by the same amount, and under other distribution the deflections will be as the loads. Now although it has been shown that the modulus of elasticity for wrought iron is a very variable quantity, yet it may be assumed that if all the girders in a given structure are made of the same kind of iron, and are under the same strain per sectional square inch, that in this structure the modulus of elasticity may be considered constant for all its parts, and the relative deflections will then follow the general laws, which we have found in the chapter on Deflection to be as follows:

The deflection varies directly as the load, and as the cube of the span of the girder or length of the cantilever,

3 &c.

and inversely, as m, where m = b d3 — b' d' bn dns. If a girder carrying a uniformly distributed load is partly supported at the centre, the deflection at the centre will be the total deflection due to the uniformly distributed load, less the deflection (upwards) due to the sustaining force at the centre. This has been proved by experiment. If, for instance, there is a girder 30 feet span loaded with 20 tons, the value of m being 44,000, the deflection under W 13 20 × 303 this load will be D=44.8 m 44.8 x 44,000

inches.

=

= 0.274

If there is a supporting force in the centre of the beam equal to 6 tons, the deflection equivalent to this will be W 13 20 × 303 28 m 28 x 44,000

D=

=0.131 inch; hence the actual central deflection of the beam will be 0.274 — 0·131 = 0.143 inch. The point of maximum strain will not be at the centre, but there will be two points of maximum strain, one on each side of the centre of the span, the curve of strain being as it were caught up at the centre.

Let / span of the girder, w = load per lineal foot, R = reaction at one end point of support, P= upward sustaining force at the centre of the girder, M = moment of strain at any point distant x from the nearest end support. each end support one-half the total load, less one-half the

central force P, will act; therefore R =

On

Р.

; M =

2

2

w x2 2

The points of maximum

moment of strain must now be determined. When the moment of maximum strain is reached, and that moment is about to be diminished, we may imagine an indefinitely small increase of x during which the moment remains constant; here, then, the increase of the positive quantity must equal that of the negative quantity. Let, then, x become x+a,