Figure 13.3 shows some of the common trusses used for bridges. Pratt trusses have diagonals sloping downward toward the center and parallel chords (Fig. 13.3a). Warren trusses, with parallel chords and alternating diagonals, are generally, but not always, constructed with verticals (Fig. 13.3c) to reduce panel size. When rigid joints are used, such trusses are favored because they provide an  efficient web system. Most modern bridges are of some type of Warren configuration.
Parker trusses (Fig. 13.3d) resemble Pratt trusses but have variable depth. As in other types of trusses, the chords provide a couple that resists bending moment. With long spans, economy is improved by creating the required couple with less force by spacing the chords farther apart. The Parker truss, when simply supported, is designed to have its greatest depth at midspan, where moment is a maximum. For greatest chord economy, the top-chord profile should approximate a parabola. Such a curve, however, provides  too great a change in slope of diagonals, with some loss of economy in weights of diagonals.
In practice, therefore, the top-chord profile should be set for the greatest change in truss depth commensurate with reasonable diagonal slopes; for example, between 40 and 60  with the horizontal.
K trusses (Fig. 13.3e) permit deep trusses with short panels to have diagonals with acceptable slopes. Two diagonals generally are placed in each panel to intersect at midheight of a vertical. Thus, for each diagonal, the slope is half as large as it would be if a single diagonal were used in the panel. The short panels keep down the cost of the floor system. This cost would rise rapidly if panel width were to increase considerably with increase in span. Thus, K trusses may be economical for long spans, for which deep trusses and narrow panels are desirable. These trusses may have constant or variable depth.
Bridges also are classified as highway or railroad, depending on the type of loading the bridge is to carry. Because highway loading is much lighter than railroad, highway trusses generally are built of much lighter sections. Usually, highways are wider than railways, thus requiring wider spacing of trusses.
Trusses are also classified as to location of deck: deck, through, or half-through trusses.
Deck trusses locate the deck near the top chord so that vehicles are carried above the chord.
Through trusses place the deck near the bottom chord so that vehicles pass between the trusses. Half-through trusses carry the deck so high above the bottom chord that lateral and sway bracing cannot be placed between the top chords. The choice of deck or through construction normally is dictated by the economics of approach construction.
The absence of top bracing in half-through trusses calls for special provisions to resist lateral forces. AASHTO Specifications require that truss verticals, floorbeams, and their end connections be proportioned to resist a lateral force of at least 0.30 kip per lin ft, applied at the top chord panel points of each truss. The top chord of a half-through truss should be designed as a column with elastic lateral supports at panel points. The critical buckling force of the column, so determined, should be at least 50% larger than the maximum force induced in any panel of the top chord by dead and live loads plus impact. Thus, the verticals have to be designed as cantilevers, with a concentrated load at top-chord level and rigid connection to a floorbeam. This system offers elastic restraint to buckling of the top chord. The analysis of elastically restrained compression members is covered in T. V. Galambos, Guide to Stability Design Criteria for Metal Structures, Structural Stability Research Council.


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