176. In extending this system one hundred or two hundred feet, we see at once that the pieces A _c_, B _c_, would become very long and would need to be made large and heavy. We should always so proportion any beam in a bridge that it is at once able to resist all of the several strains to which it may be exposed, without being unnecessarily large.
As to compression, the above system might be extended to almost any amount; but the braces would yield by flexure.
Instead of producing the braces A _c_, A′ _c′_, fig. 64, to their intersection, we stop at _c_ and _c′_, insert _c c′_; to prevent the approach of these points, suspend the points B and B′ from _c_ and _c′_, and commence again with the braces B D, B′ D; and so on as far as necessary.
To prevent the backward motion of the points B, and B′, either the chord A A′, or the counter-braces _m_, _m_, are necessary.
The pieces A _c_, A′_c′_ must support all of the load, including the weight of the bridge, lying within the rectangle B _c_, B′ _c′_. The next set of braces must sustain that part of the load only which comes over the centre of the bridge. Thus the braces should decrease in size as the centre is approached. The rods _c_ B, _c′_ B′, must resist a tension equal in amount to the pressure on the braces, only being vertical they do not need the increase given to the braces on account of their inclination.
177. There is another method of stiffening a beam, as shown in figs. 65 and 66, by trussing rods, and a post. The dimensions being the same, the forces in both cases will be equal. The second, fig. 66, leaves the passage beneath the bridge clear.
The tension on the rods A _c_, B _c_, fig. 66, tends to draw the points A and B together, an effort which is resisted by the top chord A B.
In extending this system, as in art. 176, the rods become either very long, or very large, from the small angle of inclination; evils which remedied as before, by supporting the post _c_ B, fig. 64, from the foot of the first rod, fig. 64, and commencing again from _c_.
To prevent the motion of the triangle _c_ B G, fig. 64, about the angle B, we must introduce either the upper chord _c c′_, or the counter rod _c_ A. If the lower chord is omitted the rod D B must be of the same size as E B. In this truss, either the top or the lower chord simply may theoretically be omitted, due allowance being made in the size of the rods. In practice it is never advisable to omit either, as both are required for lateral bracing, and for support of the road-way.