MECHANICS 



115 



The bending moment at W l is 11,000X10 = 110,000 ft.-lb., 

 and that at W 2 is (11,000 X 25) - (10.000X 15) = 125,000 ft.-lb. 



Lay off the line cc\ to any convenient scale to represent 

 the bending moment at W lt and at dd} to represent that at 

 Wy. Connect points a, cj, d\ t and b, as shown, and the dia- 

 gram is complete. 



As another illustration, assume that it is desired to plot 

 the bending-moment diagram of the beam shown in Fig. 18. 

 This beam is 50 ft. long and has a uniform load of 1,000 Ib. 

 per running ft. 



First, divide the beam into any number of smaller parts, 

 each, for instance, 10 ft. long, and then find the bending 



-soft. 



10 ft.~* JOft.- 



10 ft. 



moment for each of these parts. In this instance, the 

 reactions R\ and RI are each equal to one-half the total load, 

 or 50,000 -J- 2 = 25,000 Ib. The bending moment at c is 

 (25,000X10) -(1,000X10X5) =200,000 ft.-lb.; at d it is 

 (25,000 X 20) - (1,000 X 20 X 10) =300,000 ft.-lb. In a similar 

 manner, it will be found that the bending moments at points e 

 and / are 300,000 and 200,000 ft.-lb., respectively. 



On laying off these bending moments at c,c 2 , d^, etc. and 

 connecting points a, c\ . . . b, the diagram is complete. The 



