HOMOGENEOUS BEAMS 135 



particular case of a rectangle whose base b and altitude d 



are equal. The value of the area A is given in the second 



column. The distance c, given 



in the third column, is the dis- 



tance of the most remote part 



of the figure from the neutral 



axis. The section modulus and 



radius of gyration, the character 



of which will be explained later, 



are given in the last two columns. 



EXAMPLE. What is the area, 

 the distance from the neutral axis ^ IG - 1 



to the extremities of the section, and the moment of inertia 

 about the neutral axis of the section illustrated in Fig. 1 ? 



SOLUTION. Referring to the table, it will be seen that bi 

 = 4 in., 6 = 10^ in., and d = 7 in. Therefore, the area is 



10.5 + 4X7 



Xd= - = 50.75 sq. in. 

 2 2 



Likewise, the distance from the neutral axis to the longer 

 parallel side is 



The distance c, which is the distance of the neutral axis 

 from the shorter parallel side, is 



&I + 2& d 4 + 2X10.5 7 



X-= -- X-=4.023in. 



3 10.5 + 4 3 



As a check, c t +c should equal d, or 7 in. ; thus 2.977 + 4.023 

 = 7.000 in., which indicates that the preceding solution is 

 correct. 



The moment of inertia is found by the formula 





Substituting values for the letters in this formula, 



10.52 + 4X10.5X4 + 42 

 / = - X 73 = 193.348 



36 X (10.5 + 4) 



In general, it one of the values of c and c\ is found by means 

 of the formula, the other may be found by subtracting the 



