fireless system--and assist a little
in the development of an invention, in the success of which they have a
tangible interest which is much greater than that of any railway on the
Continent, but there is no sign yet of their having done anything.--_E.,
in The Engineer_.

* * * * *

SIMPLE METHODS OF CALCULATING STRESSES IN GIRDERS.

By CHARLES LEAN, M. Inst. C.E.

_Bowstring Girders._--Having had occasion to get out the stresses in
girders of the bowstring form, the author was not satisfied with the
common formulae for the diagonal braces, which, owing to the difficulty of
apportioning the stresses amongst five members meeting in one point, were
to a large extent based on an assumption as to the course taken by the
stresses. As far as he could ascertain it, the ordinary method was to
assume that one set of diagonals, or those inclined, say, to the
right-hand, acted at one time, and those inclined in the opposite
direction at another time, and, in making the calculations, the
apportionment of the stresses was effected by omitting one set.
Calculations made in this way give results which would justify the common
method adopted in the construction of bowstring girders, viz., of bracing
the verticals and leaving the diagonal unbraced; but an inspection of
many existing examples of these bridges during the passing of the live
load showed that there was something defective in them. The long unbraced
ties vibrated considerably, and evidently got slack during a part of the
time that the live load was passing over the bridge. In order to get some
definite formulae for these girders free from any assumed conditions as to
the course taken by the stresses, or their apportionment amongst the
several members meeting at each joint, the author adopted the following
method, which, he believes, has not hitherto been used by engineers:

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
incli