40 PRACTICAL STRUCTURAL DESIGN 



Fig. 36 illustrates an example given in Volume 1 of " Building 

 Construction," edited by F. M. Simpson, in which the weight of 

 the beam is considered. The total length of the beam is 28 ft. and 

 the weight is 100 Ibs. per lineal foot. 



R t -665j/bs. P 2 -2/4J/bs. 



Fig. 35 Beam Carrying Several Concentrated Loads ' 

 Short Overhang at One End 



23 X 1000 + 14 X 1200 + 9 X 2800 - 5 x 500 



= 3125 IDS. 



R 2 = 5500 - 3125 = 1875 Ibs. 



For all the overhanging beam cases the amount and location 

 of bending moment and shear at any point on the beam may be 

 found by the rules previously given for cantilever beams and 

 beams resting on two supports. Notice that the distance from 

 either reaction to the center of gravity of the weight of the beam 

 is equal to the distance from the other reaction to the center of 

 gravity of the weight of the beam for uniformly distributed loads 

 covering the whole beam. This applies as well to the beam alone, 

 for the weight of a beam is uniformly distributed. 



In Fig. 37 the beam weighs 20 Ibs. per lineal foot = 21 x 20 = 420 

 Ibs. Half is carried on each support, for the overhang is equal at 



\ 

 ^ 



L.j'.-4 ~20'~ - 



Ri'3l25lbs. R 2 -2375lbs. 



Fig. 36 Beam Carrying Several Concentrated Loads, with 

 Both Ends Overhanging 



either end. Each support also carries the concentrated load near- 

 est to it in this particular example. 



R l = R 2 = 210 + 250 = 460 Ibs. 



On the moment diagram the upper curved line (parabola with 

 vertex at the support) under the overhanging end shows moment 



