EXTERNAL FORCES 39 



The bending moment at Ri is 



M - -750 x 5 - -3750 ft. Ibs., 



indicating a negative bending moment, tending to make the 



beam convex at this support, showing tension to exist in the 



upper part and compression in the lower part of the beam. At 

 section x-x\ 



M = -ft* X 10 = -187.5 x 10 = -1875 ft. Ibs. 



also negative because Rs is negative. 

 Check the moment at R\ as follows, using R 2 : 

 M - -187.5 x 20 = -3750 ft. Ibs. 



This beam has a negative bending moment at all points, which 

 indicates tension above, and compression below, the neutral axis. 



R 2 '- 600 As 



..... 



20f- 



R,-75Olbs. 



Fig. 34 Concentrated Load on Long Overhanging Beam with Supports 

 Close Together 



A positive bending moment indicates tension below, and compres- 

 sion above, the neutral axis. 

 In Fig. 34 the reactions are 



#1 = - = 750 Ibs. 



o 



Ri = 150 - 750 = -600 Ibs. 



Note that the divisor is, in all cases, the distance between sup- 

 ports. Both reactions are large compared with the load, showing 

 the absurdity of considering a beam to be fastened at supports 

 when it runs only a short distance into a wall. No beam should 

 be considered as tied unless it runs into a wall a couple of feet at 

 least and actually carries enough load to counteract the amount 

 of negative reaction. 



Several loads are shown in Fig. 35 on a beam resting on two 

 supports and overhanging one of the supports. 



100x18+200x16+150x13+300x11+50x8+80 



10 



Ri - 880 - 665.625 - 214.375 Ibs. 



V^MIU^ 

 - 665.625 Ibs. 



