Let Fig. 1 represent a bowstring girder, the stresses in which it is desired to ascertain under the loads shown on it by the circles, the figures in the small circles representing the dead load per bay, and that in the large circle the total of live and dead load per bay of the main girders.  A girder, Fig. 1A, with parallel flanges, verticals, and diagonals, and depth equal to the length of one bay, was drawn with the same loading as the bowstring.  The stresses in the flanges were taken out, as shown in the figure, keeping separate those caused by diagonals inclined to the left from those caused by diagonals inclined to the right.  The vertical component of the stress in the end bay of the top flange of the bowstring girder, Fig. 1, was, of course, equal to the pressure on the abutment, and the stress in the first bay of the bottom flange and the horizontal component of the stress in the first bay of the top flange was obtained by multiplying this pressure by the length of the bay and dividing by the length of the first vertical.  The horizontal component of the stress in any other bay of the top or bottom flange of the bowstring girder—­Fig. 1—­was found by adding together the product of the stress in the parallel flanged girder, caused by diagonals inclining to the right, divided by the depth of the bowstring girder at the left of the bay, and multiplied by the depth of the parallel flanged girder; and the product of the stress caused by diagonals inclining to the left divided by the depth of the bowstring girder at the right of the bay, multiplied by the depth of the parallel flanged girder.  Thus the horizontal component of the stress in D= _ _ | Stress caused by diagonals Length of right Depth of parallel | | leaning to left. vertical. flanged girder. | | | + |_ 15.75 x 1/4.5 x 10 _| _ _ | Stress caused by diagonals Length of ver- Depth of parallel | | leaning to right. tical to left. flanged girder. | | | |_ 24 x 1/8 x 10 _|

= 65; and the vertical component =

   Horizontal component.  Length of bay.

          65 x 1/10 x (8.0 — 4.5) = 22.75.

In the same way the horizontal and vertical components of the stresses in each of the other bays of the flanges of the bowstring were found; and the stresses in the verticals and diagonals were found by addition, subtraction, and reduction.  These calculations are shown on the table, Fig 1B.  The result of this is a complete set of stresses in all the members of the bowstring girder—­see Fig. 2—­which produce a state of equilibrium at each point.  The fact