MECHANICS 



103 



This is the sum of the moments of all the loads about R\, 

 as a center. The leverage of the reaction R 2 is 30 ft. Hence, 

 the reaction at R 2 is 586,000 -*- 30 = 19.533$ lb. 



36ft. 



33ft. 



27ft. 



>/< 



3ft. 



FIG. 8 



lb. per running ft. 



Com- 



EXAMPLE 2. A beam is loaded as shown in Fig. 8. 

 pute the reactions R\ and R 2 . 



SOLUTION. Consider, say R 2 , as the center of moments. 

 Then, the negative moments of the loads about R 2 , in foot- 

 pounds, are 



20,000X27 = 540000 



2,000X12= 24000 



3.000X 8= 24000 



Total, 588000 



Now, the positive moments of the loads about R 2 , in foot- 

 pounds, are 



1,000X6X3 = 18000 



5.000X6 =30000 



Total, 48000 



The resultant moment of the loads about R 2 is negative 

 and is -588,000 + 48,000= -540.000 ft.-lb.; 540,000-5-30 

 = 18.000 lb., which is the value of R lm 

 The sum of the loads is 



20000 

 2000 

 3000 



6X1,000= 6000 

 5000 

 36000 

 R 2 = 36,000 - 18,000 = 18,000 lb. 



