COMPLEX STRESS DISTRIBUTIONS IN ENGINEERING MATERIALS. 373 
strains against a time base is made, as with the Fereday-Palmer instrument. 
The value of the ratio obviously depends on a large number of factors relating to the 
locomotive and train as well as the bridge itself, such as : 
The moving load and its distribution among the axles. 
Speed. 
The unbalanced revolving and reciprocating parts. 
Stiffness of springs. 
Longitudinal and lateral oscillations of the loads. 
Weight and various characteristics of stiffness, period of vibration, etc., of the 
whole bridge as well as of any particular part under investigation. 
The analysis of the experimental records is difficult, owing to the large number of 
variable factors which affect the results. In some cases, to assist in the analysis of 
the strain-time records, the positions along the girders at which the effects of un- 
balanced weights would take effect have been recorded. These positions can be 
controlled within limits, but equally powerful influences, such as those of the pitching 
and rolling and side-lurching of a locomotive travelling at speed are so far 
uncontrollable. 
A very large number of measurements are available, 362 made by the Ministry 
of Transport, and about 3000 by the Indian Railway Bridge Committee, in addition 
to a large number of American records. Deflections and strains can be measured 
accurately enough under stationary and slowly moving loads; but when the movement 
is rapid, vibrations of the bridge and its parts combined with the inertia of the instru- 
ment have resulted in many of the records being considered of doubtful accuracy. 
The measurements made by the Ministry of Transport, and 1500 of those made by 
the Indian Bridge Committee, were taken with the Fereday-Palmer photo-recording 
instrument, a carefully designed and accurately made apparatus, the records of 
which are considered accurate. All the most accurately measured ratios of the Indian 
experiments are plotted in fig. 8,2 in which the graphs of the various impact formule 
are also drawn. ‘The points marked * are considered unreliable by the investigating 
officer because the ‘ measured static stress on which they are based are extremely 
low.’ It will be seen that for each particular loaded length up to 200 feet the 
numerous ratios are distributed comparatively evenly over a range of from 0 to 
45 per cent. The same ratios plotted against speed fall into no recognisable order, as 
the following figures show. For instance, the ratio for 18 miles per hour is higher 
than that for 45-4 miles per hour, and all that can be deduced is that generally they 
rise with increase of speed. 
Impact Impact Impact 
4 Ratio. Speed . Ratio. gp et ; Ratio. 
1 Per cent. De Per cent. oh Per cent. 
7:8 7:5 30-2 36-0 39-7 28-0 
12-0 3:5 31-7 22-5 40-8 36-5 
16°5 10-2 32°3 32-0 43-8 20-0 
18-0 36-0 34-3 25-0 44-3 56-0 
18-5 32-0 36-7 22-0 45-4 33-5 
24-7 43-5 37-0 45-0 46-3 46-0 
25-7 17-5 37°8 20-0 49-6 56-5 
27-2 16:0 39-0 31-0 55-6 46-0 | 
1 An instance is given by Baker in Long Span Bridges of the destructive effect 
of these influences. The platform and shallow cross girders of a bridge were com- 
pletely destroyed in four years by locomotives of short wheel-base and long overhang, 
although the calculated stresses in the ironwork did not exceed 4 tons per sq. in, 
Also the single very high impact ratio of 159 per cent. obtained by the Ministry 
of Transport in their experiments was measured on one side of a shallow-trough rail- 
bearer, a case where lateral movement and the exact lateral position of the application 
of the load would have a marked effect on the stress. 
2 From the Fifth Report, Indian Railway Bridge Committee. 
