32 



RESISTANCE OF MATERIALS 



From the table, the moment of inertia of each channel with respect to an axis 

 perpendicular to the web at center is 103.2 in. 4 , and the distance from this axis to 



) 



i 



I 

 I 

 I 



1 ' 



i 



r 



2 



FIG. 30 



FIG. 31 



the gravity axis of the entire section is 6.07 5 = 1.07 in. Also, the moment of 



bh? 9 x ( 1 ) 8 3 

 inertia of the top plate with respect to its gravity axis is = LilL in. 4 , 



12 12 32 



12 and the distance of this axis from the 



gravity axis of the entire section is 4.18 in. 

 Therefore 



f Ii_i= 2 [103.2 + 8.82 x (1.07) 2 ] + [ 5 \ 



+ 4.5x(4.18) 2 ]=305in. 4 



For the net section the rivet holes must 

 be deducted from this value. Assuming 

 two I -in. rivets, the amount to be deducted 

 - is approximately 24 in. 4 , giving for the net 

 section J 1 _ 1 = 281in. 4 



54. In problem 53 determine the mo- 

 ment of inertia of the net section with 



f respect to the gravity axis 22. 



55. The section shown in Fig. 31 is 

 made up of four angles 4 x 3 x ^ in., 

 with the longer leg horizontal, and a web 

 plate 12 x f in., with f-in. rivets. Find 

 the moment of inertia for its net section 

 with respect to the gravity axis 1 1. 



56. The section shown in Fig. 32 is built up of two 8-in. channels 18.751b./ft. 

 and two plates 9 x in. Find the moment of inertia of its net section about the 

 gravity axis 1 1, deducting the area of four j-in. rivet holes. 



i 3 



FIG. 32 



