per C., making, for the pieces together, 24.4 per C., restored. This is diminished by 1-3d of 1, or 8.3 per C. (on account of increased compression upon dp), leaving a balance of 16.1 per C. only, of deflection from contraction of uprights, which is restored in spite of counter-diagonals, in the case under discussion.

Moreover, the main and counter diagonals, producing more or less effect of contraction upon the chords, according to the degree of inclination of the former, and the cross-sections of the latter, it may, perhaps, be reasonably assumed, that the contraction thus effected in the horizontal, is a full offset to the 16 per C. of expansion in the vertical sides of panels, as above shown; so that we may regard the whole deflection from uprights, as being retained by counter-diagonals.

To state the full result of the foregoing investigation then, we find in case of Fig. 52, which is a fair representative of the average of trusses; that counter-bracing, obviates all the deflection due to compression of uprights, together with of that resulting from extension of diagonals; and, making H = 1, in the formula for deflection (p. 267), we have deflection saved by counter-diagonals, (3 × 8 +4)+28, = a little less than 24 per C. of the whole deflection. If H= 0.75 (truss 52), the result would be about 31 per C. saved.

=

But even these results are based upon conditions never occurring in practice. It has been assumed that all parts of the truss undergo equal degrees of change under a full load; which may be nearly true with respect to chords, but not to other parts. The maximum action upon od and dp (Fig. 52), requires those parts to be 2 times as great, as they need be under full load; while pe and cg require more, and, qb and br, 1-20th more

cross-section at the maximum, than under a full load of the truss.

Now the deflection resulting from elasticity in these parts, being less in proportion as the parts are greater, the saving by counter-bracing, must be less in the same degree, as far as it relates to such parts. This at once reduces the above computations for deflection retained, from 313 and 24, to 25 and 19 per C., for the two cases respectively; and, considering the increase of section required for uprights (in iron trusses), on account of great length and small diameter, as heretofore alluded to, it is deemed to have been fully demonstrated, that the effects of counter-diagonals, of half the size of the mains, are, to retain in the truss when unloaded, from one-sixth or less, to one-fourth of the deflection produced by a full movable load.

But it has been seen in the progress of our investigations as to the action of load upon the different parts of the truss, that counter-diagonals are required in one or two panels on either side of the centre, and there, they can not be safely omitted. But, beyond the point where the weight of structure acting on the mains, begins to overbalance the effects of unequal and variable load upon the counters, I do not consider the advantages of counter diagonals to be sufficient to warrant their use.

In the case of rail road trains, gliding smoothly over bridges of ordinary spans, a quarter or a half of an inch more or less of deflection, is of slight importance, while, in bridges for ordinary carriage travel, the only objection to it is, that it slightly increases the degree of vibration produced by successive impulses, as of the trotting of animals, in time with the natural vibrations. Now, counter-bracing tends to shorten the intervals of

the natural vibrations by diminishing their extent; but can not destroy the liability to vibration; and the alteration of interval produced, may as often bring the vibrations nigher in tone with the gait of a trotting horse, as otherwise. In certain cases the effect would be one way, and in others, the opposite; and in general, the only result would be, to diminish the extent of motion; by one quarter, or less.

Such is the result of the best reasoning and science that I have been able to bring to bear upon the subject of counter-bracing.

To find the actual maximum deflection of a truss it is only necessary to know the value of P and H, and to assign to E a value determined by the character of material, and the stress upon the several parts under full load.

In Fig. 52, if H=1=121ft., and the tension of wrought iron equal 15,000lbs. per square inch, the value of E for that material, will be about 0.0075 ft.; and this will apply to the lower chord, and the obliques, ar and li. But the average value of E for diagonals of wrought iron, would be about 0.006ft.

For cast iron, 11,000lbs. to the square inch, requires about the same value for E, as 15,000 upon wrought I.; and, as that is a fair working rate of compression. for cast iron in the upper chord, .0075ft. may be taken as the value of E for chords, in general. Uprights, for reasons heretofore explained, require a value for E", not greater than .005ft.

The above values of E and H, substituted in the formula (PH2, + {P + } PH2, + ¿P,) × E, it becomes ¿PaH2E+ (}P + }PH3)E' + }PE", equal to 1 × 64 × .0075, + (4 + 4).006, + 4 x .005,, 0.188ft. = about 2 inches. Hence, a well proportioned wrought and

×

cast iron truss, one hundred feet long, by 12 feet deep, may be depressed 21" in the centre by a distributed load (including structure), with tension not exceeding 15, and thrust, not exceeding 11 thousand pounds to the square inch in cross-section of iron.

WOODEN BRIDGES.

STRENGTH OF TIMBER, &C.

CXL. The qualities of wood as a building material, have been extensively treated of by authors whose works have long been before the public, with a degree of ability and research to which the present writer can make no pretensions. He will therefore at this time, simply state the conclusions arrived at from reading and observation (coupled with some experimental research) with respect to the average absolute strength, positive, negative, transverse, and to resist splitting, in certain cases; of the timbers principally in use for building purposes; as also, the forces they will bear with safety under various circumstances; leaving it, of course, for others to adopt his views for their own practice, or to modify and correct them, according as their greater experience or better judgment may dictate.

At the same time, the author may be allowed to express his firm belief, that the views about to be presented, if fairly observed, will lead to the adoption or continuance of a safe and economical practice as to the >proportioning of timber work in bridge construction.

Pine timber in this country is perhaps to be ranked as among the most valuable timber in use for building purposes; especially in bridge building. White oak,

and some other varieties, are preferred for certain purposes, as being harder, stiffer, and especially better calculated to sustain a transverse action, whether tending to bend or crush it. But in what follows, reference will principally be had to the ordinary white pine of this country; and the deductions here made, may readily be modified so as to apply to other materials of known strength, when so required.

The absolute positive, or tensile strength of pine, may be stated at about 10,000lbs. to the square inch of cross-section. It might therefore seem to be safely reliable in practice, at 15 or 16 hundred pounds to the inch, upon that part of the section of which the fibres are not separated in forming connections with other parts of the structure. And so it probably would be, when new, sound, and straight grained. But timber in bridges, is usually more or less exposed to wetting and drying, and deterioration in strength,- especially as it regards tension. Moreover, in forming connections of parts and pieces in a structure, it is difficult to secure a uniform strain upon all the uncut fibres;— one side of the piece being often exposed to much greater stress than the other. In view of such facts, it is deemed advisable to seldom allow less than one square inch section of unbroken fibre to each 1,000lbs. of tensile strain.

NEGATIVE STRENGTH OF TIMBER.

CXLI. The ability of pine to resist compression in the direction of the length of piece, is from 4 to 5 thousand pounds to the square inch of section, and this varies but little, whether the pieces be of length equal to once, or five or six times the diameter. It moreover