ratios of live to dead load stresses. Valuable measurements of the
deformations of girders and tension members due to moving trains have been
made by S.W. Robinson (_Trans. Am. Soc. C.E._ xvi.) and by F.E. Turneaure
(_Trans. Am. Soc. C.E._ xli.). The latter used a recording deflectometer
and two recording extensometers. The observations are difficult, and the
inertia of the instrument is liable to cause error, but much care was
taken. The most striking conclusions from the results are that the
locomotive balance weights have a large effect in causing vibration, and
next, that in certain cases the vibrations are cumulative, reaching a value
greater than that due to any single impact action. Generally: (1) At speeds
less than 25 m. an hour there is not much vibration. (2) The increase of
deflection due to impact at 40 or 50 m. an hour is likely to reach 40 to
50% for girder spans of less than 50 ft. (3) This percentage decreases
rapidly for longer spans, becoming about 25% for 75-ft. spans. (4) The
increase per cent of boom stresses due to impact is about the same as that
of deflection; that in web bracing bars is rather greater. (5) Speed of
train produces no effect on the mean deflection, but only on the magnitude
of the vibrations.

A purely empirical allowance for impact stresses has been proposed,
amounting to 20% of the live load stresses for floor stringers; 15% for
floor cross girders; and for main girders, 10% for 40-ft. spans, and 5% for
100-ft. spans. These percentages are added to the live load stresses.

iii. _Dead Load._--The dead load consists of the weight of main girders,
flooring and wind-bracing. It is generally reckoned to be uniformly
distributed, but in large spans the distribution of weight in the main
girders should be calculated and taken into account. The weight of the
bridge flooring depends on the type adopted. Road bridges vary so much in
the character of the flooring that no general rule can be given. In railway
bridges the weight of sleepers, rails, &c., is 0.2 to 0.25 tons per ft. run
for each line of way, while the rail girders, cross girders, &c., weigh
0.15 to 0.2 tons. If a footway is added about 0.4 ton per ft. run may be
allowed for this. The weight of main girders increases with the span, and
there is for any type of bridge a limiting span beyond which the dead load
stresses exceed the assigned limit of working stress.

Let W_l be the total live load, W_f the total flooring load on