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Now, as a 12 foot link, under a stress of 10,000lbs. to the inch is extended less than 100 of a foot, a slight springing of connecting pins would relax the outside links materially, especially when the pins tend to spring toward one another.
Again, if the links run parallel with the centre of chord, and at right angles with the connecting pins, as indicated by the double black lines (Fig. 43), the moments of forces upon — pin No. 5, for instance, will be — for 3 links acting toward the right hand, 44 x 17 + (for diagonal) 8 x 8 = 812, against 3 links acting toward the left, with moments equal to 52 x 20 = 1,040, showing a difference of 228 ; whence x=3 (228X5,000) =
3,532.5 6.85 inches = required diameter of pin at the centre.
At pin No. 6, are 3 links with a combined moment of 52 x 20, + (for diagonal), 6 x 8, = 1076, against 3 links with a combined moment of 58 x 17 = 986, showing a difference of 90 ; consequently, x = (90x 5,000) =
3,532.5 5.03 inches = required diameter of pin.
Such would be the result as to stress and required diameter of pin, provided the pin remain perfectly straight. It is true that the spring of the pin in the direction of the greater moment, or sum of moments, will, in practice, produce an obliquity in its direction through the eyes, which will throw the centres of bearing upon the pin, nigher to the adjacent sides of the eyes, and thus reduce the difference of opposite moments, and consequently, the stress upon the pin. But such relief to the pin must be attended with a disturbance of the central and uniform strain of the chord bar: the strain being brought near one side of the bar. Moreover, as this can only result from aetual springing of the pin, there must inevitably be a degree of relaxa
tion of the outside link, whenever the pins at its two ends are deflected toward one another. On the contrary, an outside link or bar connecting with two pins springing from one another, is necessarily subjected to greater strain than those nigher the centres of pins, in the same panel.
In this case, the forces tend to spring the pins toward one another at the ends, whence the outside link must suffer more or less relaxation.
It seems unnecessary to carry these examples further. The above results show a decided advantage in the oblique position of links, diverging toward the centre of the span, so as to have the inside link opposed to the diagonal.
The arrangement of links, or eye bars, here assumed, and the amount of stress assigned to them, are no exaggeration upon what has been put in practice. But the preceding calculations must be sufficient to demonstrate the exceptionable character of such practice. Two links upon a side (4 to the panel), after two or three panels next the end, so thin as not to occupy an unnecessary length of pin — each taking hold of the pin outside of the succeeding one toward the centre of the truss, may be admissible. But a greater number, in the opinion of the author, for reasons already given, is not to be recommended.
DOUBLE CHORD. CXXV. To obviate the difficulty attending the use of the multiplex chord, consisting of many links in a panel, we may make use of what may be distinguished as a Double Chord.
We have seen (LvI], that in double cancelated trusser with vertical members, there are two independent seta of diagonals and verticals, which have no interchange of action between one another. Now, each of these sets may have its own lower chord, also acting independently, each of the other, but uniting at the same point at the foot of the king brace, which is common to both sets of web members.
In such case, the two chords (which we may call subchords), may be one above the other, and composed of links or eye-bars, extending horizontally across two panels; the links or bars of one sub-chord connecting opposite the centre of those in the other, and the uprights in one set, being as much longer than those in the other, as the distance, vertically, between the upper and lower sub-chords.
By this means, about one-half of the extra material in chord connections would be saved; and a more uniform stress upon the chord bars secured, than would be practicable, even with 4 links acting upon one connecting pin.
DETACHED, AND CONCRETE PLANS OF CONSTRUCTION.
CXXVI. In the plan of Trapezoidal truss had under consideration in the last few preceding sections, the several members are formed in separate pieces, to be erected in place, and connected by screws, bolts, connecting pins, &c., as the parts of wooden bridges and building frames are erected, after being framed and prepared, each for its particular place.
There is another mode of construction, in which members and parts of members are permanently riveted together in place; or, in case of small bridges, the whole structure is permanently put together at the manufactory, and transported by water or rail to the place of erection and use. The former of these may
be called the detached, and the latter, the concrete mode of construction.
The detached plan is probably the best adapted to wrought and cast iron bridges, and also, at least, equally adapted to bridges entirely, or essentially constructed of wrought iron, when vertical thrust uprights are employed.
But it can hardly be regarded as advisable to con. struct iron bridges with independent members, without thrust verticals. For, although as we have seen, (XLVI,] the latter plan shows a trifle less action upon the material than the plan with verticals, the oblique thrust members in the web, are 40 or 50 per cent longer (according to inclination), as well as being in greater number, and sustaining less average action to the piece.
The 7 panel truss, Fig. 12, has 4 compression verti. cals, liable to an average action of 8w"'; while truss Fig. 13, has not less than 6 diagonals, liable to an average compression of 4w" ✓2 (when the inclination is 45°), equal to 5.65w". In the mean time, these members being over 40 per cent longer, and sustain. ing only about the same aggregate amount of action, can not be so economically proportioned to perform their required labor, when acting independently, as the fewer and shorter uprights.
Still, the Trapezoid with individual members is practicable, probably with about the same economy of material without verticals as with them; and, if it be deemed expedient to adopt the former, the modes of forming and connecting the various parts may be so nearly like those already described for the latter, that particular specifications will not be given in this place.
The essential conditions to be observed, are, besides proportioning the parts to the kind and degree of strain to which they may be exposed, to see that the forms of diagonals liable to compressive action, be made capable of withstanding such action, according to the table of negative resistances (XCIII]; and, that those liable to a change of action from tension to compression, and the contrary, be formed and connected in such manner as to enable them to act in both directions.
CXXVII. In the concrete, or rivet work plan of construction, the Trapezoid without verticals may, it is thought, be generally adopted with advantage. Upon this branch of the subject, however, but little of detail will be attempted at this time, the author having had very little direct practical experience ir. the premises.
The first point to be attended to, of course, as in all cases of bridge construction, is, to arrange the general outline and proportions of the truss; that is, the number of panels, and depth of truss suitable for the particular case in hand. This being done, the amount and kind of force, whether thrust or tension, to which each part is liable, should be determined; for which purpose, the value of w, and of w' (the variable and constant panel load for the truss), must be assumed, or estimated according to the best data at command ; when the stresses of the several parts are readily ob tained by process already explained; [xliv, &c.].
We are then prepared to assigo the requisite crosssection to each part, and to adopt a suitable form of bar, or combination of bars and plates, for each member. Thrust members will usually (if long), be formed of several parts, mostly flat plates, angle iron, T iron, and channel iron, united by riveting in such form of cross-section as may give the largest diameter practi.