Then, making x=diameter of pin, its resisting power= Ax4,500 (see [XCVIII])= .785x x x x 4,500+1′′= 3,532.5x3; and putting this equal to 45×5,000 (the stress above found), we obtain x=4" (very nearly),=required diameter of pin.

242.

=

At the next pin we take the moments of one link 15x14" 210, and one diagonal, 7x8"=56, making 266 in one direction, against that of one link, 22x11"= Hence the resultant moment 24, and 24 × 5,000=3,532.53, gives the required diameter of pin in the centre, x=31', nearly. But this is the general stress in the portion of pin between diagonals, and may be greater or less than at certain points where forces are applied. For instance, if the aggregate moments of forces in opposite directions be equal, the resultant moment is nothing, and the middle portion of the pin, between diagonals has no stress, and might be cut out and removed, as far as strength of chord is concerned. In the case in hand, the moment of link b, with respect to link c, equals 15"x3= 45-stress of pin at centre of c. Hence the required diameter at this point is found by the equation 45×5,000=3,532.5 ×3, whence x=4", the same as pin No. 1.

At the next pin, if we add another link, making 2 links sustaining 34W, at an average of 14′′ from centre, giving a moment of 476, against one link, 22×14, + one diagonal 12x8 = 404, we obtain a resultant moment of 72; whence, 72x5,000 = 3,532.5x3, and x = 4.67 inches, required central diameter of pin, and as will be readily seen on trial, the greatest required at any point.

Again, assuming at the 4th pin 2 links and 1 dia gonal against two links, we have for the former, 34x17"+10x8 658, and for the latter, 44x14

=

=

616, whence the resultant moment is 42. Therefore the equation 42×5,000 = 3,532.5x3, gives x = 3.9 inches. required diameter in centre, while for the outside link on this pin, the stress, 17, multiplied by 3 shows a moment of 51. Hence, x= (51X 5,000) 4.16 inches

=

3,532.5

required diameter at that point.

At the 5th pin, there are 3 links, against 2 links and one diagonal, giving moments for the latter, 44×17 + 8x8 812, and for the former, 52x17 884; whence the resultant moment = 72, and x = ✔ inches.

=

=

72× 5,000
3,532.5

= 4.67

The moments at pin No. 6, are, for 3 links, 52×20, + (for diagonal) 6x8 = 1088, in one direction, and for 3 links, 58×17 = 986, giving a resultant of 102; whence, x=102×5,000) ➡5.24.

3,532.5

Lastly, adding another link at the 7th pin, the moments are 58x20 + (for diagonal) 4×8, = 1,192, against 62×20' 1240, whence the resultant is 48, and x= (48X 5,000) = 4.08.

=

3,532.5

In this case the eyes, or link-ends are supposed to be bored in the direction of the pin, a little obliquely to the direction of the link, so as to bear through the whole thickness, as long as the pins remain perfectly straight. But the pins having a degree of elasticity, and considerable length, must yield to the action of links, springing more or less in the direction of the greater sum of moments. It will be seen, moreover, that in each case, the consecutive ends entering the outside link, as 3 and 4, 5 and 6, &c., are always sprung toward one another; the inevitable result of which must be, a relief or relaxation of the outside link, whence it must sustain a less degree of strain than its fellows located farther from the ends of the pins.

Now, as a 12 foot link, under a stress of 10,000lbs. to the inch is extended less than of a foot, a slight

5

1,000

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 x20= 1,040, showing a difference of 228; whence x= 228×5,000) 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) 5.03 inches required diameter of pin.

=

=

3,532.5

3,532.5

=

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 actual 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 trusses 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