170 HOMOGENEOUS BEAMS 



SOLUTION. The maximum external bending moment is 

 Wl 2,000X137 



=68,500 in.-lb. The modulus of rupture 



4 4 



for white oak is 7,000, and a factor of safety of 6 will be used. 

 Therefore, 5 = 7,000-4-6 = 1,167 Ib. per sq. in. Substituting 

 these values in the formula, 68,500 = 5X1,167, and 



bd 2 



5 = 68,500-5-1,167 = 58.71. 5 = ; therefore, either the 

 6 



breadth or the depth of the beam may be assumed and the 

 other dimensions found. It will also be noted that in the 

 value of 5 the breadth is involved only as a first power, 

 while the depth is squared. Therefore, to design an econom- 

 ical beam, the better plan is to make the beam narrow and 

 as deep as possible. Of course, there are practical considera- 

 tions that govern this matter, such as obtaining commercial 

 sizes of material and the like. 



In the problem at hand, let is be assumed that the beam 



will be 10 in. deep. Then, d = 10 in., 5 = 58.71 = = 



6 6 



6X58.71 



.and b = = 3.523 in. The next larger size of com- 

 mercial timber is 4 in. X 10 in., and is therefore the size to be 

 used. 



The modulus of rupture of metals and timbers will be 

 found in the two tables on pages 126 and 128. 



WEIGHT OF BEAMS 



Every beam, whether it is made of wood, steel, or stone, 

 has a certain weight, and the question is whether it should 

 be considered or not. Neglecting the weight of the beam 

 itself in beam design does not make so much difference on 

 a short span with heavy loads as it does on a long span with 

 comparatively light loads. Just when the weight of the 

 beam itself should be considered and just when it should 

 not, is a matter of experience, and no set rule can be laid 

 down. Usually, however, if the weight of the beam is less 

 than 5% of the load it is intended to carry, its weight may 

 be neglected. 



