making h=v=1, we have as expressions for amount of thrust and tension action upon material in oblique members, 25м for thrust and 17м for tension.

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One half of the lower chord obviously sustains a stress of 28w", equal to horizontal thrust of the end braces, and the other half, 60w", horizontal action of aq, qe and co (under full uniform load), at one end, and of corresponding diagonals at the other end, giving required material for chord equal to 44м.

The compression of the upper chord, equals the horizontal thrust and pull of aq and qc,= 48w", for of its length, with the addition of 12w" for horizontal thrust of co, and 4w" for pull of oe, making 64w" for the two middle panels. Hence expression for material is 40м. The verticals obviously require tension material equal to 4м, and the aggregate for the truss, is,

A corresponding truss with 2 diagonals in each panel, on the plan of Fig. 13, shows the same expressions for materials, or amount of action of both kinds, item for item, and any advantage possessed by either plan, must depend essentially upon the more advantageous action of compression material.

Truss Fig. 15, has fewer intermediate thrust diagonals, and greater concentration of weight upon them; which is favorable; while in the other, the diagonals crossing one another, are enabled to afford mutual support laterally, in certain modes of construction.

The upper chord in Fig. 15, acts at a decided disadvantage, in having no vertical support for a length of 2 panel widths, unless it be especially provided at additional expense. As a deck bridge, with struts, or posts at p, n, l, and lateral tying and bracing, the truss may answer an excellent purpose. But even in that case, it can scarcely be considered as preferable to the truss with a double system of diagonals.

The Ohio river bridge at Louisville, Ky., has its long spans (about 400 ft.), constructed upon the plan of Fig. 15, and no plan which we have considered, shows a less amount of action upon material. These are believed to be the longest spans of Truss Bridging in the country. An eight-panel truss upon the plan of Fig. 12, gives the following expressions for amount of material.

This indicates a difference of nearly 4 per cent, as to amount of action upon material, in favor of the truss without vertical members, generally speaking; i. e. in which there is no regular transfer of action from one to another, between diagonal and vertical members, as in truss Fig. 12.

This advantage is made still larger in certain modes of construction, by the circumstance that the same. members, in trusses 13 and 15, may sometimes act by tension and thrust, on different occasions, without any more material than would be required to act in one direction only.

LI. It may be proper in this place, to refer to still another form of trussing, which has enjoyed a degree of popular favor, and which differs somewhat from any we have hitherto considered. The plan is seen in outline, in Fig. 16. Each weight is sustained primarily by a pair of equally inclined tension members, and thereby transferred either to the king posts standing upon the abutments, or, to posts sustained by other pairs of equally inclined suspension rods of greater horizontal reach; which in turn, transfer a part to king posts, and another part to a post sustained by obliques of still greater reach, until finally, the whole remaining weight is brought to bear upon the abutments by a single pair of obliques, reaching from the centre to each abutment.

FIG. 16.

THE FINCK TRUSS.

In Fig. 16, are represented three different lengths of obliques, in number, inversely as the respective horizontal reaches. The first set contains 8 pieces reaching horizontally across one panel, and sustaining each w. The next longer set, of four pieces, reach across two panels, and sustain each 1w; one-half applied directly, and the other, through posts and short diagonals. The third and longest set, contains but two pieces, reach across four panels, and sustain together 4w; of which 1w is applied directly, 1w through two short diagonals, and 2w through two intermediates.

Now, as each set sustains the same aggregate weight, namely 4w, the material in each set, will

be represented by this weight multiplied by the square of the lengths respectively, and divided by v: and, making kv=1, the squares of respective lengths are 2, 5 and 17, which added together and multiplied by 4w, and w changed to м, gives 96м=amount of material in tension obliques, the only tension members in the truss.

=

The upper chord sustains compression equal to the horizontal pull of one oblique member of each class, obviously equal to 10w, with length 8. Hence, required material equals 84м. End posts sustain together, 7w, centre post 3w, and the two at the quarters, one w each, in all 12w, and the representative for material is 12m; whence the total for thrust material is 96м, making a grand total of thrust and tension material= 192M.

The 8 panels trapezoid with verticals, requires,... 135м Do without verticals,......... 130м

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This comparison exhibits an amount of action in case of the first (Fig. 16), which, considering that it possesses no apparent advantage as to the efficient working of compression material, would seem to exclude it, practically, from the list of available plans of construction.

DISTINCTIVE CHARACTERISTICS OF THE ARCH.

LII. We have seen that all heavy bodies near the earth's surface (except when falling by gravity or ascending by previous impulse), exert a pressure upon the earth equal to their respective weights. We have also seen that the object of a bridge, in general, is, to sustain bodies over void spaces, by transferring the pressure exerted by them upon the earth, from the

points immediately beneath them, to points at greater or less horizontal distances therefrom.

We have, moreover, seen that this horizontal transfer of pressure can only be effected by oblique forces (neither exactly horizontal nor exactly vertical), and have discussed and compared, in a general way, various combinations of members, capable of effecting this horizontal transfer of pressure.

But, without going into unnecessary recapitulation, we find two or three styles of trussing, possessing more or less distinctive features, which promise decidedly more economical and satisfactory results than any others; and, to make the properties and principles of action of the best and most promising plans as thoroughly understood as may be within the proposed limits of this work, will form a prominent object in the discussions of succeeding pages.

The distinctive feature of the arch, as a sustaining structure, consists in the fact that all the oblique action required to sustain a uniformly distributed load, is exerted by a single member of constantly varying obliquity from centre to ends; each section sustaining all the weight between itself and the centre, or crown of the arch, and none of the weight from the section to the end; so that the weight sustained at any point, is as the horizontal distance of that point from the centre. Consequently (the arch being supposed in equilibrio under a uniform horizontal load), the horizontal thrust at all points must be the same, and the inclination of the tangent at any point should be such that the square of the sine, divided by the cosine of inclination (from the vertical), may give a constant quotient. For, regarding each indefinitely short section of the arch as a brace coinciding with the tangent at

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