ned 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 that this state of equilibrium is
produced proves conclusively