The stresses produced on each bar by the various loads, considered separately, are tabulated as shown. The stresses on bar 1 for the loads W3, Wr, and W11 which affect it are added together and the result written in the first column, as it is compressive. In a similar manner, the stresses on the other bars are added, and written in the first or second column, according as the stress is compressive or tensile.

The stresses in the third and fourth columns due to dead load are found, as in the foregoing examples, by affixing the proper coefficient to the bar and multiplying it by W1 sec (Fig. 171).

1

The total maximum stresses are found by adding the stresses of like kind in the first four columns due to live load and dead load. It should be noted that bars from 3 to 9 are subjected to both tensile and compressive stresses.

The stresses in the remaining 13 bars may be written down by numbering them from the right-hand support.

The stresses in the top and bottom horizontal members are found as before, by adding the coefficients written in the lattice bars, Fig. 171, and multiplying by (W+W1) tan for the increment of flange stress (2 + 5) tan 07 tan 0.

=

Thus the stresses in the top member may be written down

The stresses in both top and bottom members are written down in Fig. 171.

The stresses in the top and bottom members may be plotted to scale as ordinates on the length of the girder as a base, and the extremities joined, forming two polygons, which are the

M

designing a lattice girder or of ascertaining the stresses in a The following example is given to illustrate the method of

used for designing the top and bottom flanges as explained diagrams of direct stresses due to bending, and may be

in Chapter IV.

girder already built. Figs. 172 and 173 show the stresses in the web and flanges of a lattice girder in a bridge on the New South Wales Government Railways. The bridge consists of two lattice main girders, forming a clear span of 150 feet. The girders are 161 feet 9 inches long over all, and placed 14 feet apart in the clear. Between them transverse or roadway girders are placed at a distance of 3 feet from centre to centre.

The bridge carries a single line of way. The lattice girders rest at each pier on cast-iron bed-plates fixed on the piers, with steel expansion rollers at one pier. Each lattice girder is 12 feet deep between the intersection of the lattice bars. The booms are trough-shaped, and connected with double-lattice webs. The web is formed of a double set of lattice bars riveted to the vertical plates of the booms, and inclined at an angle of 43° 25'. Each set of lattice bars consists of seven systems of triangulation, the flat tension bars varying from 6" x 3" to 4" x 1", and

'Railway Bridges Inquiry Commission, New South Wales, 1887.

the channel irons forming struts from 6" x 21" x 1" to 3" x 13" x 1".

The data for calculations are as follows:

Effective span = 156′ 0′′

Weight at each apex due to dead load = 0.6 × 3 = 1.8 tons

The following table gives the bending moments, stresses, and areas required in the bridge. By comparison of this table with the diagram of areas, Fig. 173, we have—

Maximum stress in compression = 3.72 tons per square inch

CHAPTER IX.

BOWSTRING AND POLYGONAL GIRDERS.

THE stresses in girders or trusses with curved or polygonal flanges or chords may be most conveniently ascertained by the method of moments explained in Chapter III.

Let Fig. 174 denote an inverted bowstring girder or truss, in which the bottom chord is a polygon inscribed in a parabolic

curve. Let the span be 48 feet, the central depth 6 feet, the number of panels 8, the length of each panel 6 feet, the live load equivalent to 5 tons at each panel-point, the dead load 1 ton at each panel-point.

The reaction at the left support due to all the panel-points being fully loaded is—

The stress in AO, denoted by AO, is found by taking moments about the point 2, the lever arm or the length 3.2 being 2.62 feet.

AO(2·62)+R(6) = 0

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