=89. Simple Trusses.=—The simplest forms of trussing used for bridge purposes are those shown in Figs. 19, 20, and 21. There are many other forms which are exhibited in complete treatises on bridge structures, but these three are as simple as any, and they have been far more used than any other types. The horizontal members _af_ and _AB_ are called the “chords,” the former being the upper chord and the latter the lower chord. The vertical and inclined members connecting the two chords are called the web members or braces. When a bridge is loaded, either by its own weight only, or by its own weight added to that of a moving train of cars, the upper chord will evidently be in compression, while the lower chord is in tension. A portion, which may be called a half, of the web members will be in tension and the other portion, or half, will be in compression. The function of the upper and lower chords is to take up or resist the horizontal tension and compression which correspond to the direct stresses of tension and compression existing in the longitudinal fibres of a loaded solid or flanged beam. The metal designed to take these so-called direct stresses is concentrated in the chords of trusses, whereas it is distributed throughout the entire section of a beam, whether that beam be solid or flanged. The function of the web members of a truss is to resist the transverse or vertical shear which is represented by the algebraic sum of the reactions and loads. The total section of a solid beam resists these vertical shears, while the web only of a flanged beam is estimated to perform that duty. The horizontal shears, which have already been recognized as existing along the horizontal planes in a bent beam, are resisted by the inclined web members of a truss, the horizontal stress components being the horizontal shears, whereas the vertical shears are resisted by the vertical web members of a truss. If the web members are all inclined, as shown in Fig. 21, each web member resists both horizontal and vertical shear. It is thus seen that the members of a truss perform precisely the same duties as the various portions of either solid or flanged beams. Inasmuch as the chords of bridge-trusses resist the direct or horizontal stresses of tension and compression produced by the bending in the truss, it is obvious that the greatest chord stresses will be found at the centre of the span, and that they will be the smallest at the ends of the span. In the web members, on the contrary, since the vertical shear is the greatest at the ends of the span and equal to the reactions at those points, decreasing towards the centre precisely as in solid beams, the greatest web stresses will be found at the ends of the span and the least near the centre. It is obvious that the areas of cross-sections of either chords or web members must be proportioned to the stresses which they carry. Hence the distribution of stresses just described tends to a uniform