168 HOMOGENEOUS BEAMS 



pounds; 7, the moment of inertia of the section referred to 

 the inch; c, the distance, in inches, from the neutral axis to 

 the most remote fiber; and s, the maximum stress, in pounds 

 per square inch. This stress, of course, occurs in the most 

 remote fiber. 



This is the general equation for beams. It expresses the 

 bending moment about any section, caused by the loads 

 and reactions, in terms of the maximum unit stress at the 

 section and the dimensions of the beam at that section 



( that is, - I . The stress 5 may be either tension or compres- 

 sion, but it is always the maximum stress in the section. 



It is evident that if a beam is going to break, the break 

 will occur at that section about which the external bending 

 moment is maximum. If this section holds, every other 

 part of the beam will be strong enough. Therefore, it is 

 the section of a beam about which the external bending 

 moment is maximum that is always investigated. 



The quantity is equal to the section modulus ; therefore, 

 the formula is often written 



in which S is the section modulus. 



In the preceding tables the moments of inertia, etc. are 

 given with the inch as a base, and s is usually measured in 

 pounds per square inch. Therefore, in the preceding for- 

 mulas M must be given in inch-pounds and not in foot- 

 pounds. 



EXAMPLE. What is the maximum stress in a simple beam 

 12 ft. long and uniformly loaded with 1,000 Ib. per ft. of 

 length? The beam is rectangular in section, 10 in. broad 

 and 14 in. deep. 



SOLUTION. The total load on the beam is 1,000X12 

 = 12,000 Ib. The maximum bending moment, in foot- 



Wl 

 pounds, is . In this case, W = 12,000 Ib. and / = 12 ft. 



Therefore, the maximum moment, which shall be called M, 



