In connection with the live-load, it is necessary to make proper allowance for "impact," "centrifugal force," and "traction." The general method of investigating any part of a bridge and of making a classification is as follows;

1. The maximum allowable stress is determined, which, in the simpler cases, is the cross-sectional area of the member multiplied by the limiting unit stress allowed.

2. Deduct from this the total amount of stress in the part due to both "Dead Load" and "Wind Load." The remainder gives the allowable stress for the "Live Load" effect.

3. Dividing this by the stress for unit "Live Load" (Class E-1) gives the classification for allowed "Live Load," if at rest.

4. Divide this classification by the term which takes into account the extra effects of the "Live Load," due to Impact and Centrifugal Force, and the result will be the classification of the allowed "Live Load" at full speed.

Classification of Loadings

The "Class E" loading above described is an assumed typical loading. Actual engine and car loadings vary a great deal as to spacing of the wheels and the distribution of the weight on the various axles. The effects of different loadings on bridges are not in direct proportion to the weight of the engine or cars, but depend on the number of wheels, spacing of wheels, distribution of weight, etc. Actual engine loadings can, however, be reduced to equivalents in the standard train loadings, corresponding to the different span lengths.

This is done by computing the maximum bending moments and end shears for the given train loadings for each different span length. These are divided by the maximum bending moments and end shears for the Unit Class "E-1" loading, for the corresponding span, the result being the "Classification" of the loading.

As an illustration of classification of various engine loadings, Fig. 41a is given. This shows the classification of several types of the new standard locomotives which have been purchased by the Government and are now being assigned to the various railroads. Fig. 41b shows similar classifications for typical car loadings.

In placing restrictions on the use of car loadings over bridges, it is not practicable to take into account all of the variations in car lengths which occur. An equivalent for the various car loadings can be arrived at by considering typical hopper cars about 33 ft. long, as shown in Fig. 41b, for which the wheel spacing given is a fair average. For bridges under 50-ft. span, the trucks of two adjacent cars produce the maximum effects, and, for like axle loads, are independent of the lengths of the cars.

The approximately parallel curves on the diagram represent the classification of these typical car loadings for different weights of cars, where the total weight represents the weight of the car and contents. The said diagram shows by dotted line the classification of a typical ore-car loading, which, on account of the extremely short length of the car, produces a high classification on the long spans; and it records also the classification of a heavy wrecking crane of 120 tons capacity.

Speed Restrictions

In the foregoing the classification has been determined with an allowance for the effect of the maximum speed over bridges.

Where speed is reduced, the effects of the live load are much less; and the allowance for impact and centrifugal force, if any, may be correspondingly reduced. This will, of course, permit heavier loadings to be operated at reduced speed as compared with those permissible for full speed.