FIRST AND SECOND MOMENTS 



33 



57. In problem 56 find the moment of inertia of the net section with respect 

 to the gravity axis 22. 



58. The section shown in Fig. 33 has the dimensions 6 = 10 in., d = 4 in., t = 1 in. 



Locate the gravity axis 1 1. 

 59. In problem 58 find 

 the moment of inertia of the 





- -->_. __ 



I 2 



FIG. 



I 



i 



-1- 



section with respect to the 

 gravity axis 2 2. 



60. The section shown in 

 Fig. 34 has the dimensions 

 J .8 = 10 in., 6 = 6 in. ,d = 8 in., 

 t x = t z = t s = 1 in. Locate the 

 gravity axis 1 1. 



61. The section shown in 

 Fig. 32 is composed of two 12-in. 

 channels, 20.5 Ib./f t., and two 

 -in. plates. How wide must 

 the plates be in order that the 

 moments of inertia of the section shall be the same about both gravity axes ? 



62. The section shown in Fig. 35 



has the dimensions 6 = 8 in., h = 10 in., $ 



6' = 5 in., h' = 6 in. Find its moments 

 of inertia about both gravity axes. 



63. Two6-in. channels 10.51b./ft. are 

 connected by latticing. How far apart 

 should they be placed, back to back, in ~i 

 order that the moments of inertia may 



be the same about both gravity axes ? 



64. A hollow cast-iron column is 6 in. 

 external diameter and 1 in. thick. Find 

 the moment of inertia of its cross section 

 with respect to a diameter. 



65. The section shown in Fig. 31 is made 

 up of a web plate 9 x | in. and four angles 

 3 x 3 x f in. Find its moment of inertia 

 with respect to both gravity axes. 



66. The top chord of a bridge truss 



has a section like that shown in Fig. 36, with top plate 20 x f ", two web plates 



each 18 x f ", and four angles 3 x 3 x f ". Find 

 the eccentricity of the section ; that is, the dis- 

 tance from center of figure to gravity axis 11. 

 j 67. In problem 66 find the moment of iner- 



^ tia of the net section with respect to the axis 



11, deducting for four |-in. rivets. 



68. A circular table rests on three legs placed 

 j at the edge and forming an equilateral triangle. 



J Find the least weight which will upset the table 



when hung from its edge. 



t 



FIG. 34 



. 35 



