HOMOGENEOUS BEAMS 171 



Since, in some cases, it has been decided that the weight 

 of the beam itself must be taken into account, the methods 

 of attaining these results will be considered. As the weight 

 of the beam cannot be obtained until its size is known, and 

 as the size of the beam cannot be found until the total bend- 

 ing moment is known, this problem can be solved only by 

 trial. The following example will serve to illustrate the 

 method to be pursued: 



EXAMPLE. Calculate the size of I beam required to carry, 

 besides its own load, a uniformly distributed load of 960 Ib. 

 per ft. over a span of 20 ft. 



SOLUTION. The total load on the beam, exclusive of its 

 own weight, is 960X20=19,200 Ib. The maximum bend- 



Wl 19,200 X 20 X 12 



ing moment is = = 576,000 in.-lb. 



8 8 



Wl 



M = Ss = = 576,000. Giving 5 a value of 16,000 and 

 8 



neglecting the weight of the beam, 16,000X5 = 576,000, or 

 5 = 576.000 -M 6,000 = 36. On consulting the table on 

 page 148, it will be seen that the value of 5 here found corre- 

 sponds to that of a 12-in. 31.5-lb. I beam. This beam would 

 satisfy the requirements if the weight of the beam itself were 

 left out of consideration, but as it is necessary to provide for 

 this additional load, the next larger size may be chosen and a 

 trial calculation made to see whether it will support the com- 

 bined load. This beam is a 12-in. one, weighing 35 Ib. per ft. ; 

 hence, the weight of the beam is 35 X 20 = 700 Ib. From the 



Wl 



preceding formula , the maximum bending moment due 

 8 



700X20X12 

 to the weight of the beam alone is = 21,000 in.-lb. 



8 



The sum of this moment and that of the external load is 

 576,000 + 21,000 = 597,000 in.-lb. = M. M = Ss, or 597,000 

 = 16,000X5; therefore, 5 = 597,000-^-16,000 = 37.31. As the 

 value given for 5 in the table is greater than this, the beam 

 selected is of ample strength. 



As was stated, it is usually considered safe to neglect 

 the weight of the beam itself in calculations of beam design. 



