18 LIVE-LOAD STRESSES 



In the -peeial ra>e \\linv the loading has not advanced 

 beyond the left end of tin -pan. W and II ", equal zero and 

 x becomes 



x = | (13a) 



Problems relating to a girder bridge without panels will 

 now be given to illustrate the application of the above 

 formulas and the use of some of the tables following the 

 text. 



Problem. Given a 40-foot deck-girder bridge consisting 

 of one girder per rail. Use Cooper's #50 loading. I-'ind 

 the maximum shear at the end, quarter point, and centre. 

 Determine also the maximum bending moment at the 

 quarter point and at the cent re. and t he absolute maximum 

 bending moment. All values are to be given per rail. 



Solution. Table 5 following the text gives the position 

 of Cooper's loadings for maximum end shear. This table 

 is the result of the solution of end shears for a large num- 

 ber of spans. As a general rule, however, it is safe to as- 

 sume that w z of Cooper's and similar loadings will always 

 give the maximum end or intermediate shear when placed 

 immediately to the right of the given section, the live load 

 being headed toward the left. The exceptions in Table 5 

 to this general rule are not of prime importance, for the 

 actual value of the shear when w 2 is used is sufficiently close 

 to the maximum even in the exceptional cases. There is 

 no satisfactory criterion for determining the position of load- 

 ing for maximum shear in girder bridges without panels, for 

 it is as easy to calculate the actual values of the shears for 

 the successive positions of loading as it is to apply any 

 criterion. In the case of bending moment, however, time 

 is saved by using the criterion. 



Maximum End Shear. 

 Use formula (9), tf, = U ; Ul - W,. Place wheel 2 



