16 LIVE-LOAD STRESSES 



Or 



- -W, . (12) 



There is one more thing to be borne in mind in calcula- 

 tinp maximum bending moments in a girder bridge without 

 panels: it is the rule for finding the section where the 

 absolute maximum bending moment occurs. The rule is often 

 spoken of as the "centre of gravity rule" and may be stated 

 as follows: 



The bending moment under any given wheel becomes maxi- 

 mum when the centre of the span bisects the distance from the 

 wheel in question to the centre of gravity of the loading on the 



In the practical application of this rule, the procedure 

 i- first to find the wheel which gives maximum bending 

 moment at the centre of the span and then to shift tin- 

 wheel so that the bending moment beneath it becomes an 

 absolute maximum according to the centre of gravity rule. 

 For the usual standard loadings the maximum centre mo- 

 ment closely approximates the absolute maximum bending 

 moment for the spans greater than 70 feet. 



The proof of the centre of gravity rule follows. Refer 

 to Fig. 5. Assume that it has been found by trial that 

 the wheel w n gives the maximum centre moment. The 

 general case where load has advanced beyond the span is 

 taken. In order to get an absolute maximum bending 

 moment under w n , this wheel must be shifted a certain 

 distance from the centre. Let such position be distance y 

 from Ri. The sum of the loads on the span is called P 2 

 and equals (JF,_-- Wi). The centre of gravity of the load- 

 P, is distance x from R 2 . The sum of the loads on the 

 span to the left of w n is called Pi, and their centre of gravity 

 is at the fixed distance 6 from w n . 



Taking moments about 7? 2 , 



