162 STEEL RAILWAY BRIDGES. CHAP. IV. 



where 5 is the static live load stress and D is the dead load stress. This method is used by the 

 Illinois Central R. R. 



(2) Launhardt-Weyrauch Formulas. Formula (2) is used for determining the allowable 

 stress for stresses of one kind and formula (3) is used for determining the allowable stress for 

 stresses of different kinds. This method is used in Thatcher's Specifications, in Common Standard 

 Specifications (Harriman Lines), and specifications of Pennsylvania Lines West of Pittsburgh. 



(3) Cooper's Method. Cooper uses formula (2) and calculates the area for the dead load 

 and the area for the live load stress separately. For dead loads from formula (2) we have P 28, 

 while for live loads the range of stress is from zero to the maximum, and P = S. 



For a reversal of stress Cooper designs the member to take both kinds of stress, but to each 

 stress he adds eight-tenths of the lesser of the two stresses, 



IMPACT TESTS. The American Railway Engineering Association has made an exhaustive 

 series of tests to determine the effect of impact on railway bridges. The following summary is 

 taken from the Proceedings of Am. Ry. Eng. Assoc., Vol. 12, Part 3. 



(1) With track in good condition the chief cause of impact was found to be the unbalanced 

 drivers of the locomotive. Such inequalities of track as existed on the structures tested were of 

 little influence on impact on girder flanges and main truss members of spans exceeding 60 to 75 

 ft. in length. 



(2) When the rate of rotation of the locomotive drivers corresponds to the rate of vibration 

 of the loaded structure, cumulative vibration is caused, which is the principal factor in pro- 

 ducing impact in long spans. The speed of the train which produces this cumulative vibration is 

 called the "critical speed." A speed in excess of the critical speed, as well as a speed below the 

 critical speed, will cause vibrations of less amplitude than those caused at or near the critical speed. 



(3) The longer the span length the slower is the critical speed and therefore the maximum 

 impact on long spans will occur at slower speeds than on short spans. 



(4) For short spans, such that the critical speed is not reached by the moving train, the 

 impact percentage tends to be constant so far as the effect of counterbalance is concerned, but 

 the effect of rough track and wheels becomes of greater importance for such spans. 



(5) The impact as determined by extensometer measurements on flanges and chord members 

 of trusses is somewhat greater than the percentages determined from measurements of deflection, 

 but both values follow the same general law. 



(6) The maximum impact on web members (excepting hip verticals) occurs under the same 

 conditions which cause maximum impact on chord members, and the percentages of impact for 

 the two classes of members are practically the same. 



(7) The impact on stringers is about the same as on plate girder spans of the same length 

 and the impact on floorbeams and hip verticals is about the same as on plate girders of a span 

 equal to two panels. 



(8) The maximum impact percentage as determined by these tests is closely given by the 

 formula 



T _ IO 



(7) 



i + 



20,600 



in which I = impact percentage and / = span length in feet. 



(9) The effect of differences of design was most noticeable with respect to differences in the 

 bridge floors. An elastic floor, such as furnished by long ties supported on widely spaced stringers, 

 or a ballasted floor, gave smoother curves than were obtained with more rigid floors. The results 

 clearly indicated a cushioning effect with respect to impact due to open joints, rough wheels and 

 similar causes. This cushioning effect was noticed on stringers, hip verticals and short span 

 girders. 



(10) The effect of design upon impact percentage for main truss members was not sufficiently 

 marked to enable conclusions to be drawn. The impact percentage here considered refers to 

 variations in the axial stresses in the members, and does not relate to vibrations of members 

 themselves. 



(n) The impact due to the rapid application of a load, assuming smooth track and balanced 

 loads, is found to be from both theoretical and experimental grounds, of no practical importance. 



(12) The impact caused by balanced compound and electric locomotives was very small and 

 the vibrations caused under the loads were not cumulative. 



(13) The effect of rough and flat wheels was distinctly noticeable on floorbeams, but not 

 on truss members. Large impact was, however, caused in several cases by heavily loaded freight 

 cars moving at high speeds. 





