140 HOMOGENEOUS BEAMS 



known one from d. Thus, after having calculated c\ in this 

 example, c would be equal to dc\ = 7 2.977 = 4.023 in., 

 which value corresponds to the one found by means of the 

 formula. 



Many of the beams used in building construction are made 

 of steel. These steel beams are rolled with various cross- 

 sectional shapes, from which they derive their names. 

 These shapes are standard; that is, they are rolled to con- 

 form to certain sizes that have been adopted by many of the 

 large steel companies. In the first column of the accom- 

 panying table, entitled Values for Standard Rolled Sections, 

 are shown the cross-sections of the various structural shapes. 

 The first section shown is known as an angle with equal legs; 

 the second, as an angle with unequal legs; the third, as a 

 channel; the fourth, as a bulb beam; while the fifth, sixth, 

 and seventh sections are known, respectively, as an I beam, 

 a T bar, and a Z bar. 



In this table is given the moment of inertia for each sec- 

 tion about at least two axes, both of which pass through 

 the center of gravity of the section; that is, the moments of 

 inertia are given always with respect to neutral axes. The 

 moments of inertia with respect to different neutral axes are, 

 in general, different, and as a rule there is one neutral axis 

 about which the moment of inertia is less than it is about 

 any other. With the channel, bulb beam, I beam, and T bar, 

 the smallest moment of inertia is about the axis y'-y', or the 

 vertical axis. However, with both styles of angles and with 

 the Z bar, there is another moment of inertia about a neu- 

 tral axis, not horizontal nor vertical, that is smaller than the 

 moment of inertia about any other neutral axis; that is, in 

 certain work, more particularly in the design of columns, it 

 is necessary to know about what neutral axis the moment of 

 inertia will be smallest. It is also necessary to know what 

 this moment of inertia will be. Therefore, in the section 

 of the angle with equal legs, the section of the angle with 

 unequal legs, and the Z-bar section, the moment of inertia is 

 also given for the oblique axis giving the smallest moment 

 of inertia. The position of this neutral axis is found by 

 higher mathematics. With the angle with equal legs, this 



