IMPACT STRESSES. 161 



KINDS OF STRESS. Bridges must be designed for the stresses due to (i) dead load; 

 (2) live or moving load; (3) wind load; (4) snow load; (5) impact stresses; (6) temperature stresses; 

 (7) rentrifugal stresses, and (8) secondary stresses not taken into account in the calculations. 

 In addition t<> the above it is necessary in determining the allowable stress in any member to take 

 into account imperfections in materials and workmanship, possible increase in live loads, fatigue 

 of metals, the frequency of the application of the stress, corrosion and deterioration of materials, 

 etc. The structure should be so designed that no part will be ever stressed beyond the elastic 

 limit. The allowable stresses for dead load are usually taken at about 60 to 70 per cent of the 

 clastic limit; for an elastic limit of 30,000 lb., the allowable working stresses for dead loads alone 

 would then vary from 18,000 to 21,000 lb. per sq. in. 



IMPACT STRESSES. As a load moves over the bridge it causes shocks and vibrations 

 whereby the actual stresses are increased over those due to the static load alone. It is shown 

 in mechanics of materials that a load suddenly applied to a bar or beam will produce stresses 

 twice the stresses produced by the same load gradually applied. A bridge is a complex structure 

 and it is not possible to determine the exact effect of the moving loads. It has been found by 

 experiment that the ultimate strength for repeated loads is much less than for dead loads. In a 

 bridge it will be seen that the dead load is a fixed load and that the live load is a varying load. 



For stresses of one kind Professor Launhardt has proposed the following formula: 



/ Min^tressN 

 \ Max. stress / 



vhere P is the allowable working stress required, and S is the allowable working stress for live 

 ids, varying from zero to the maximum stress. For stresses of opposite kinds Professor Wey- 

 luch has proposed the following formula: 



p _ o / Min. stress \ 



\ 2 Max. stress / 



irhere P and 5 are the same as for the Launhardt formula, the maximum and minimum stresses 

 eing taken without sign. For columns and struts the allowable stresses as given by formulas 

 i) and (3) are to be reduced by a suitable column formula. 



There are three methods in common use for taking account of impact and fatigue: (l) Impact 

 armulas; (2) Launhardt- Weyrauch formulas, and (3) Cooper's Method. 



(i) Impact Formulas. The formula in most common use is given in the form 



^here 7 = impact stress to be added to the static live load stress, S = the static live load stress, 

 = the length in feet of the portion of the bridge that is loaded to produce the maximum stress 

 the member, and a and b are constants expressed in feet. The American Railway Engineering 

 ciation specifies for railway bridges, a = b = 300 ft. Mr. J. A. L. Waddell specifies a = 400 

 and 6 = 500 ft. for railway bridges; and a = 100 ft., and b = 150 ft. for highway bridges. 

 7 or the names of several roads using A. R. E. A. impact formula, see Table XVI. 



For highway bridges the American Bridge Company specifies that the maximum live load 

 ess shall be increased 25 per cent to cover impact and vibration. 

 Mr. C. C. Schneider, M. Am. Soc. C. E., specifies that for electric railway bridges 



7 = 5- i 5 o/(L + 300) (5) 



In the Osborn Engineering Company's 1901 specifications for railway and for highway 

 bridges the impact is calculated by the formula 



7 = 5- 5/(S + D) (6) 



12 



