The live load is the weight of the heaviest train which can come on the bridge. In the earlier girder bridges the live load was taken to be equivalent to a uniform load of 1 ton per foot run for each line of way. At that time locomotives on railways of 4 ft. 8½ in. gauge weighed at most 35 to 45 tons, and their length between buffers was such that the average load did not exceed 1 ton per foot run. Trains of wagons did not weigh more than three-quarters of a ton per foot run when most heavily loaded. The weights of engines and wagons are now greater, and in addition it is recognized that the concentration of the loading at the axles gives rise to greater straining action, especially in short bridges, than the same load uniformly distributed along the span. Hence many of the earlier bridges have had to be strengthened to carry modern traffic. The following examples of some of the heaviest locomotives on English railways is given by W.B. Farr (Proc. Inst. C.E. cxli. p. 12): -

Passenger Engines.

Total weights, tons

84.35

98.90

91.90

85.48

Tons per ft. over all

1.58

1.71

1.62

1.61

Tons per ft. of wheel base

1.92

2.04

1.97

1.95

Maximum axle load, tons

19.00

16.00

18.70

18.50

Goods Engines.

Total weight, tons

77.90

78.80

76.46

75.65

Tons per ft. over all

1.54

1.50

1.54

1.51

Tons per ft. of wheel base

2.02

2.02

2.03

2.00

Maximum axle load, tons

15.90

16.00

13.65

15.50

Tank Engines.

Total weight, tons

53.80

58.61

60.80

47.00

Tons per ft. over all

1.60

1.68

1.70

1.55

Tons per ft. of wheel base

2.45

2.52

2.23

3.03

Maximum axle load, tons

17.54

15.29

17.10

15.77

Farr has drawn diagrams of bending moment for forty different very heavy locomotives on different spans, and has determined for each case a uniform load which at every point would produce as great a bending moment as the actual wheel loads. The following short abstract gives the equivalent uniform load which produces bending moments as great as those of any of the engines calculated: -

Span in Ft.

Load per ft. run equivalent to actual Wheel Loads in Tons, for each Track.

5.0

7.6

10.0

4.85

20.0

3.20

30.0

2.63

50.0

2.24

100.0

1.97

Fig. 36 gives the loads per axle and the distribution of loads in some exceptionally heavy modern British locomotives.

Express Passenger Engine, G.N. Ry. Express Passenger Engine, G.N. Ry. Goods Engine, L. & Y. Ry. Goods Engine, L. & Y. Ry. Passenger Engine, Cal. Ry. Passenger Engine, Cal. Ry.
Fig. 36.

In Austria the official regulations require that railway bridges shall be designed for at least the following live loads per foot run and per track: -

Span.

Live Load in Tons.

Metres.

Ft.

Per metre run.

Per ft. run.

1

3.3

20

6.1

2

6.6

15

4.6

5

16.4

10

3.1

20

65.6

5

1.5

30

98.4

4

1.2

It would be simpler and more convenient in designing short bridges if, instead of assuming an equivalent uniform rolling load, agreement could be come to as to a typical heavy locomotive which would produce stresses as great as any existing locomotive on each class of railway. Bridges would then be designed for these selected loads, and the process would be safer in dealing with flooring girders and shearing forces than the assumption of a uniform load.

Some American locomotives are very heavy. Thus a consolidation engine may weigh 126 tons with a length over buffers of 57 ft., corresponding to an average load of 2.55 tons per ft. run. Also long ore wagons are used which weigh loaded two tons per ft. run. J.A.L. Waddell (De Pontibus, New York, 1898) proposes to arrange railways in seven classes, according to the live loads which may be expected from the character of their traffic, and to construct bridges in accordance with this classification. For the lightest class, he takes a locomotive and tender of 93.5 tons, 52 ft. between buffers (average load 1.8 tons per ft. run), and for the heaviest a locomotive and tender weighing 144.5 tons, 52 ft. between buffers (average load 2.77 tons per ft. run). Wagons he assumes to weigh for the lightest class 1.3 tons per ft. run and for the heaviest 1.9 tons. He takes as the live load for a bridge two such engines, followed by a train of wagons covering the span. Waddell's tons are short tons of 2000 lb.

ii. Impact. - If a vertical load is imposed suddenly, but without velocity, work is done during deflection, and the deformation and stress are momentarily double those due to the same load at rest on the structure. No load of exactly this kind is ever applied to a bridge. But if a load is so applied that the deflection increases with speed, the stress is greater than that due to a very gradually applied load, and vibrations about a mean position are set up. The rails not being absolutely straight and smooth, centrifugal and lurching actions occur which alter the distribution of the loading. Again, rapidly changing forces, due to the moving parts of the engine which are unbalanced vertically, act on the bridge; and, lastly, inequalities of level at the rail ends give rise to shocks. For all these reasons the stresses due to the live load are greater than those due to the same load resting quietly on the bridge. This increment is larger on the flooring girders than on the main ones, and on short main girders than on long ones. The impact stresses depend so much on local conditions that it is difficult to fix what allowance should be made.

E.H. Stone (Trans. Am. Soc. of C.E. xli. p. 467) collated some measurements of deflection taken during official trials of Indian bridges, and found the increment of deflection due to impact to depend on the ratio of dead to live load. By plotting and averaging he obtained the following results: -

Excess of Deflection and straining Action of a moving Load over that due to a resting Load.

Dead load in per cent of total load

10

20

30

40

50

70

90

Live load in per cent of total load

90

80

70

60

50

30

10

Ratio of live to dead load

9

4

2.3

1.5

1.0

0.43

0.10

Excess of deflection and stress due to moving load per cent

23

13

8

5.5

4.0

1.6

0.3

These results are for the centre deflections of main girders, but Stone infers that the augmentation of stress for any member, due to causes included in impact allowance, will be the same percentage for the same 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.